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Developmental Mathematics - MyWorkBook - 8th edition
Summary: Worksheets for Classroom or Lab Practice offer extra practice exercises for every section of the text, with ample space for students to show their work. These lab- and classroom-friendly workbooks also list the learning objectives and key vocabulary terms for every text section, along with vocabulary practice problems.
8th edition. Book is in overall good condition. There is a small light orange stain on the edges of the pages where they meet the spine at the top. Cover shows some edge wear and corners are lightly w...show moreorn. Pages have Some water damage causing pages to stain and lightly ripple. Does not affect the text. Cover shows considerable wear and tear and pages are moderate to highly marked. ...show moreDefinitely not pretty but still usable tear but pages have minimal marks. Some water damage causing pages to stain. Does not affect the text. Definitely not pretty but sti...show morell usable |
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This DVD-ROM for PC and Mac contains hundreds of friendly, step-by-step video tutorials that clearly explain Higher Level GCSE Maths (for the AQA, Edexcel, OCR and WJEC exam boards). It also includes printable exam-style questions, with fully-worked answers on video. There's grading information to show which topics are the most challenging, plus a full search function that makes it easy to find what you're looking for |
According to OER Commons, this is a "manual to support students in using the Microsoft Office XP operating system and the...
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According to OER Commons, this is a "manual to support students in using the Microsoft Office XP operating system and the Microsoft Office 2003 software suite. In many developing countries IS textbooks tend to be expensive despite the best and, I believe, sincere efforts of educational publishers to keep their developing country rates as low as humanly possible. This book (except for the Access section) has been released under the Creative Commons license, i.e. it is freely available for (educational) use to anyone who wants it.״
This site provides online tutorials for specific finite math and calculus concepts. Step by step directions are provided and...
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This site provides online tutorials for specific finite math and calculus concepts. Step by step directions are provided and students are able to complete examples and exercises. Supplemental material is also available. If students obtain incorrect answers, help is provided.Have you ever thought that you would be able to learn algebra if only you had a...
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This is a free textbook offered by BookBoon.'Have you ever thought that you would be able to learn algebra if only you had a tutor on whom you could call whenever you wanted? Well, Quantitative Analysis – Algebra with a Business Perspective is the next best thing. Written by an experienced mathematics teacher, this e-book is presented in tutorial fashion as if a tutor was sitting next to you . . . talking you through the examples. All you need to do is turn to whatever presentation you wish . . . without having to schedule mutual meeting times and without having to pay an hourly rate.This tutorial textbook has been organized into 4 chapters (units) with several individual tutorial lessons within each chapter. As presented in the table of contents, each of the tutorials has been listed separately with its objective and its starting page. For coding purposes: "Tutorial N.M" means that the tutorial is the Mth lesson in chapter N.The purpose of this tutorial textbook is to present mathematical skills (algebraic concepts) and their various applications that may be important to students of management (business) science. The applications included should allow readers to view math in a practical setting relevant to their intended careers.'
With this module one can use the alphanumeric list at the top of the page to choose an idex in the right column. Clicking on...
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With this module one can use the alphanumeric list at the top of the page to choose an idex in the right column. Clicking on a topic in the right column brings up the topic in the current window. Entries in the Statistical Glossary are taken from the Electronic Manual of STATISTICA and may contain elements that refer to specific features of the STATISTICA system.
This is an online text for an Introductory Statistics class. Topics include: Summarizing and Presenting Data, Producing...
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This is an online text for an Introductory Statistics class. Topics include: Summarizing and Presenting Data, Producing Data, Variation and Probability, Statistical Inference, and Control Charts. A "clickable" glossary is provided as well as exercises with solutions.
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Anne Stuart is a Boston-based freelance journalist who has written about business, technology, and the Internet for nearly a decade. Before going solo, she was a senior writer at Inc. , a senior editor at CIO and CIO Web Business , a founding editor of WebMaster , and a reporter for The Associated Press and several daily newspapers. This site includes links to her biweekly columns that have covered tech tips, news, and trends for growing businesses. |
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Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.
The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further study of partial differential equations.
Audience: First and second year undergraduates in mathematics. Also useful for undergraduate physics and engineering |
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Overview
As the study of shape and form, geometry is able to model the space around us and the forms inhabiting this space. For this reason, geometry has always been highly regarded for its practical value, and geometry and its applications have long been a central part of the study of mathematics. Centuries ago, in prescribing geometry to be a part of the standard educational program for youth, Plato recognized that "for the better apprehension of any branch of knowledge, it makes all the difference whether a man has a grasp of geometry or not."
While there are many textbooks presenting a pure or theoretical approach to geometry and many monographs investigating a single aspect of applied geometry, it is difficult to find a wide-angle view of applied geometry. The purpose of this collection is to give as broad a picture as possible of the applications of geometry.
This collection will be a rich resource for the geometry instructor, whether as a supplement to standard textbook material, as reference material for student reports and projects, or as the starting point for a research program. The papers vary in difficulty, but are accessible to anyone having a college-level acquaintance with geometry.
Editorial Reviews
Charles Ashbacher Technologies
"I strongly recommend that you read this book, it will reinforce your faith in the power of mathematics to change the world."
The Mathematics Teacher
"The articles present applications of geometry that are unlikely to be found elsewhere. Anyone who teaches geometry and enjoys the subject should invest in Geometry at Work. The topics will expand your horizons and serve as a nice resource for your students. An additional feature of the book is that it includes the e-mail addresses of most of the authors, so students and teachers alike can communicate with them."
Zentralblatt fur Mathematik
"The reach of the papers [in this book] is from ancient to modern, concrete to abstract, familiar to cutting edge. All of them, however, show geometry to be the lively and exciting discipline that fascinates us all."
Booknews
The 20 papers in this volume illustrate the practical application of geometry in the areas of art and architecture, Vedic civilization, classroom teaching, engineering, decision-making processes, and mathematics and science. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Part 4: Engineering
Making Measurements on Curved Surfaces, James Casey
Mathematics to the Aid of Surgeons, Ramin Shahidi
The Geometry of Frameworks: Rigidity, Mechanisms and CAD, Brigitte Servatius
Geometry and Geographical Information Systems, George Nagy
On the Other Hands: Geometric Ideas in Robotics, Bud Mishra
Introduction
There is no branch of mathematics, however abstract, that will not eventually be applied to the phenomena of the real world.
-N.I. Lobachevsky
Geometry is the study of shape and form, with origins in surveying land, designing buildings, and measuring volumes. More importantly, geometry is a point of view that sees the shapes and forms that are intrinsic to any mathematical concept or relationship. Indeed, almost every area of mathematics incorporates geometric concepts and the geometric viewpoint in a fundamental way. For example, Descartes used analytic geometry to display the lines and curves associated with algebraic equations. A differential equation has inherent within its formulation a geometric phase space. When confronted with a new group, and algebraist might view it in terms of the symmetries of a higher-dimensional polyhedron to better understand its structure. Binary relations can be understood in terms of trees, and even probability has its foundation in the properties of measure spaces.
Today, geometry encompasses many different approaches, techniques, and theories, including Euclidean and non-Euclidean geometries, projective geometry, finite geometries, transformational geometry, computational geometry, differential geometry, discrete geometry, tilings, and knot theory. The papers in this collection show that the geometric point of view, in all its many different varieties, has many diverse applications going far beyond its origins in measuring distances, areas, and volumes.
Euclidean geometry, which has dominated the development of Western geometry, uses compass and straightedge to study the flat plane or three-dimensional space. We see the influence of Euclidean geometry in many of the papers in this collection. It is used in the field of art in papers by Kim Williams and Jay Kappraff and we see it used by the engineer as a vital tool for design and communication in the paper by Marina Pokrovskaya. Both Ramin Shahidi and Paul Calter show that measuring distances with Euclidean geometry continues to find new applications.
Non-Euclidean geometry takes the view that the intrinsic shape of space need not be flat but may be curved. Many of the shapes in our environment are curved, and Jim casey shows how the engineer can make use of Riemannian geometry to understand these curved shapes.
Analytic geometry integrates algebra and geometry, and it has allowed the geometer to make use of the powerful tools of algebra. Papers by Thomas Burger and Peter Gritzmann, Kristin Bennett and Erin Bredensteiner, Ton Boerkoel, Bud Mishra, and Don Saari demonstrate the effectiveness of integrating algebraic formulations with the study of geometric information.
Recent research in geometry has focused on invariants and other properties subtler than those of measurement. This work includes tilings, knot theory discrete geometry, computational geometry, and graph theory. Applications of these approaches can be found in the papers by Lou Kauffman, Charles Radin, George Nagy, Brigitte Servatius, and Tomaz Pisanski and Milan Randic.
Finally, cultures different from our own have seen geometry quite differently. In papers by Marcia Ascher, Jay Kappraff, John Price, and David Henderson we see that our own understanding of geometry can be used to analyze the work of other cultures and to bridge what gaps there may be in time or space between these cultures and ourselves.
That papers in this collection, written by pioneers and leading experts in their fields, are a valuable resource for geometry teacher and student alike. All of the papers are accessible to anyone having a college-level course in geometry and it is hoped that they will provide a broad vision of applied geometry-geometry at work.
1 The nature of Applications of Knowledge
Some have the attitude that knowledge exists for its own sake, that applications need not be of concern to the mathematician, and in fact may not even be possible for some areas of mathematics. G.H. Hardy espoused the view that number theory, which he considered to be the most beautiful and profound area of mathematics had not the "slightest 'practical' importance." The comment by N.I. Lobachevsky, one of the founders of non-Euclidean geometry, given at the beginning of this introduction, takes quite a different stance. History has proved Hardy wrong-today the very mathematics he cited as an example of the unproductive is the heart of the widely used RSA cryptosystem. Lobachevsky, on the other hand, displayed remarkable prescience, since the revolutionary geometry that he discovered, opposed to the contemporary view of space and originally viewed as unnatural and invalid, turned out to be precisely the viewpoint needed by Albert Einstein in his general theory of relativity. Similarly, many new ideas and discoveries in mathematics and science have eventually proven to have more useful application despite unpromising beginnings. For this reason, it is worthwhile to understand how the theoretical knowledge of mathematics can have real-world applications.
Although in all disciplines the general processes of gaining and applying knowledge are similar, there are significant differences between mathematics and the sciences which can serve to highlight the unique role of mathematics in applying knowledge generally and in the types of applications we see here. In the sciences, physical phenomena are the objects of study, while in mathematics, the objects of study are purely intellectual concepts and constructs. The real number line, for example is purely conceptual, having no physical existence itself. In the sciences, observations of physical phenomena are made by conducting experiments and recording measurements. For the mathematician, computations, examples, counterexamples, special cases, and diagrams replace microscopes and telescopes as a way of observing and measuring the structure and behavior of mathematical objects. From observations, principles of knowledge are derived by the scientist or mathematician which describe pattern of behavior common to a significant class of examples. In science, these principles are verified by experimentation and further measurement; in mathematics, principles are verified intellectually by mathematical proof.
Applying knowledge involves extending these general principles to guide progress in some specific area of life. By its very nature, knoeldge will be relevant to that area of life from which it is derived and can serve as the basis for applications in that area. However, it is our experience that mathematics has applications far beyond the boundaries of the area in which it was first developed. Indeed, mathematics is striking in that the concepts, principles, and techniques developed for the understanding of purely non-physical mathematical constructs provide the essential tools that scientists in all areas use to understand their observations and measurements of the physical world. Eugene Wigner, in discussing the success of mathematics in physics, says,
It is important to point out that the mathematical formulation of the physicist's often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class phenomena.
Moreover, once the scientist's observations have been given a mathematical formulation, the methodology and computations of mathematics can extend these formulations to predictions about behavior that has not yet been observed. This is of enormous importance to the scientist because, as Richard Hamming points out,
Constantly what we predict from the manipulations of mathematical symbols is realized in the real world. … For glamour, I can cite transistor research, space flight, and computer design, but almost all of science and engineering has used extensive mathematical manipulations with remarkable success.
The fact that abstract mathematical concepts, which are often only suggested by observations of the physical world and depend mostly on the imagination of applications is indicative of a common source for both mathematics and the physical world.
As a subjective discipline, mathematics depends on the creativity and aesthetic sensibilities, as well as the intelligence, of the mathematician. Mathematical progress is always in the direction of locating deeper and more abstract concepts, structures, and relationships, every further removed from the physical world. Yet when we look at mathematics in general, or at geometry in particular, we see that the deeper and more abstract the concepts, the greater is the range of application in the real world. In other words, the greater the subjective component of a mathematical theory, the more effective is that theory in its objective role of applications. William Thurston sees this as a natural phenomenon:
My experience as a mathematician has convinced me that the aesthetic goals and the utilitarian goals for mathematics turn out, in the end, to be quite close. Our aesthetic instincts draw us to mathematics of a certain depth and connectivity. The very depth and beauty of patterns make them likely to be manifested, in unexpected ways, in other parts of mathematics, science, and the world.
Mathematical formulations of abstract patterns and relationships appear to be in many cases our deepest understanding of principles that exist throughout nature. Indeed, we can make the case that the wide applicability of mathematics suggests the interconnectedness of all spheres of life, from the abstract to the concrete. The beauty, orderliness, and universality that we see in all areas of mathematics are reflected in the beauty and orderliness that scientists find in their physical world.
2 The Role of Applications in the Study of Geometry
The full range of geometry is from the most theoretical and abstract theorems based on axioms and undefined terms to varied applications in science and technology, as well as in other areas of mathematics. In recent years, applications of geometry have taken on a more prominent and exciting role, both within and outside of mathematics. For example, computers have spurred the development of many new areas, including computational geometry, image processing, visualization, robotics, and dynamic geometry.
Today more than ever, the study of applications is an important component in the study of geometry, a subject traditionally valued for its practicality. We gain a broader and richer understanding of geometrical concepts when we see the unexpected applied contexts in which they appear. In applied settings, geometrical concepts can take on new and quite different interpretations; for example, a finite geometry can become a graph or a knot can become a description of a quantum mechanical operator. Finally, there is charm in seeing familiar theorems and principles showing their value in many different roles. Without studying applications, a student will never see the complete character of geometry.
This collection is an abundant resource for those wishing to include applications in their study of geometry.
This collection is an abundant resource for those wishing to include applications in their study of geometry. We see here geometry used to describe and understand the shapes that we see in the world around us and geometry used to design the shapes that we construct to enrich our environment. We also see how geometry is used in other branches of mathematics and in science to give shape and form to mathematical data or concepts that are not inherently or intrinsically geometric.
3 Geometry Used to Understand the Environment
Many papers in this collection show ways of applying the tools of geometry to the analysis of shapes that exist in our environment. An important such use is to transform measurements that one is capable of obtaining into the kind of information that one can really use. An old example of this is, of course, surveying, but there are very modern examples as well.
Ramin Shahidi in "Geometry to the Aid of Surgeons" and Paul Calter in "Façade Measurement by Trigonometry" both use similar geometric techniques. In the first case, measurements of a patient's anatomy made by medical imaging machinery are converted into a potential surgical trajectory. In the second case, measurements made of the façade of a building by surveying instruments are converted into distances between specific points on the façade.
George Nagy has an analogous problem, that of converting the geographical measurements in a Geographical Information System into a useful format. In a GIS, however, there is so much data that the role of geometry is to synthesize the data into a format that can readily be interpreted by the researcher. For example, elevation data can be transformed into visibility graphs that can then be used for the optimal placement of fire towers or radio transmitters.
Of a subtler nature is the question of the arrangement of atoms in a quasicrystal, a kind of material having a new and surprising symmetrical structure as measured by X-ray diffraction. Studying the possible arrangements of atoms in a quasicrystal, Charles Radin has developed the concepts of statistical symmetry, a way of measuring regularities in an arrangement of shapes that is not, strictly speaking, symmetrical.
The traces left behind by other cultures are sometimes difficult to understand and they can easily be misinterpreted according to the learned fashions of the day. When cultural legacies have shape and form, a geometrical analysis can give us a quite reliable basis from which to make an interpretation of what has been left to us. Marcia Ascher and Jay Kappraff demonstrate how to undertake a geometrical analysis of our cultural legacies. They lead us to a broad-minded appreciation of the possible interpretations that can legitimately be given to what we see in other cultures.
In her paper on spirals, Kim Williams explains techniques for constructing spirals, volutes, and rosettes so that we can understand the challenges facing architects who have incorporated these beautiful geometric shapes into their work. With this, we gain insight into the intentions of the architects and deeper appreciation for their work.
David Henderson and John Price both look at writings left by the Vedic civilization and, through close geometric analysis, give insight into the possible reasoning, computations, and motivations behind the geometric constructions given in the Sulba Sutras. As with the examples given by Ascher, Kappraff, and Williams, we see that this expands our view of the achievements of the past.
4 Geometry Used to Build the Environment
Geometry is essential for designing the shapes that we build to mold our environment. Descriptive, or projective, geometry has been the main tool used by the engineer to develop, record, and communicate plans and designs. Marina Pokrovskaya connects fur us the theoretical aspects of descriptive geometry to simple but realistic examples of the practical applications of descriptive geometry. She shows how these examples can be used in the classroom to train those who will be using descriptive geometry in their work.
In her paper on rigidity of frameworks, Brigitte Servatius examines the structure of rectangular grids to determine whether or not they are rigid. She shows how the determination whether or not they are rigid. She shows how determination of the rigidity of a structure begins with the side-side-side theorem of Euclidean geometry, and then goes on to show that many other geometric ideas can be applied to the analysis of frameworks. In particular, graph theory is very effective in this area since a framework can be viewed as a collection of rods (edges) connected at joints (vertices).
In addition to flat surfaces, the designer or engineer needs curves and curved surfaces. Jim Casey develops our understanding of curvature and Riemannian geometry through measurement and experimentation and then introduces us to the analysis of the structural properties of curved surfaces.
A recent engineering creation is the robot. How should a robot hand be designed so that it can securely grasp any shape? Using the properties of convex sets, Bud Mishra is able to determine the exact number of fingers a robot hand must have, and further, he shows how to determine the placement of those fingers to grasp any given object.
Kim Williams and Jay Kappraff have used geometrical analysis to deduce the intentions of artists from geometrical evidence in their work. In Paul Calter's paper "Sun Disk, Moon Disk," the artist himself explains his experience of integrating his aesthetic purposes with his mathematical thinking in the design and construction of a massive sculpture. This paper shows firsthand the nature of the mathematical thinking that can go into creating |
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more |
pre-MBA quantitative skills course examines essential topics of algebra and differential calculus that are applied to quantitative coursework in an MBA program. Among the algebraic topics covered are equalities and inequalities, absolute values, functions and graphs, linear, nonlinear, and multivariate functions. The course also examines systems of equations and breakeven analysis, laws of exponents, quadratic equations, natural logarithms, and exponential functions. The calculus topics covered are limited to differential topics. Students develop the ability to differentiate functions using the power, product, quotient, and chain rules. The differential calculus is applied to determine optimal solutions to case problems. Students in this course use CD-ROMs to investigate many of these topics. Students who benefit most from this course are those who have been away from quantitative courses for a period of time and whose calculus and algebraic skills need to be refreshed. Students with very weak backgrounds are likely to be better served by enrolling in selected undergraduate courses.
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Graphical Approach to Algebra and Trigonometry, A (5th Edition)
9780321644725
ISBN:
0321644727
Edition: 5 Pub Date: 2010 Publisher: Addison Wesley
Summary: Hornsby, John S. is the author of Graphical Approach to Algebra and Trigonometry, A (5th Edition), published 2010 under ISBN 9780321644725 and 0321644727. Two hundred seventy four Graphical Approach to Algebra and Trigonometry, A (5th Edition) textbooks are available for sale on ValoreBooks.com, one hundred four used from the cheapest price of $86.95, or buy new starting at $204A Graphical Approach to Algebra and Trigonometry illustrates how the graph of a function can be used to support the solutions of equations and inequalities involving the func [more]
A Graphical Approach to Algebra and Trigonometry illustrates how the graph of a function can be used to support the solutions of equations and inequalities involving the function. Beginning with linear functions |
self-teaching guide to basic arithmetic, covering whole numbers, fractions, percentages, ratio and proportion, basic algebra, basic geometry, basic statistics and probability. |
Intermediate Algebra With Applications and Visualization-Text Only - 4th edition
Summary: Gary Rockswold and Terry Krieger focus on teaching algebra in context, giving readers realistic and convincing answers to the perennial question, �When will I ever use this?� The authors� consistent use of real data, graphs, and tables throughout the examples and exercise sets gives meaning to the numbers and equations as readers encounter them. This new edition further enhances Rockswold and Krieger�s focus on math in the real world with new features and updated applications...show more to engage today�s readers Intermediate Algebra With Applications and Visualization-Text Only05 +$3.99 s/h
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Intermediate Algebra
Designed for first-year developmental math students who need support in intermediate algebra, the Fourth Edition of Intermediate Algebra owes its ...Show synopsisDesigned for first-year developmental math students who need support in intermediate algebra, the Fourth Edition of Intermediate Algebra owes its success to the hallmark features for which the Larson team is known: learning by example, accessible writing style, emphasis on visualization, and comprehensive exercise sets. These pedagogical features are carefully coordinated to ensure that students are better able to make connections between mathematical concepts and understand the content. The new Student Support Edition continues the Larson tradition of guided learning by incorporating a comprehensive range of student success materials throughout the text. Additionally, instructors and students alike can track progress with HM Assess, a new online diagnostic assessment and remediation tool from Houghton Mifflin.Hide synopsis
Description:As New. No Jacket. Book. 9x11. Instructor's edition which...As New. No Jacket. Book. 9x11. Instructor's edition which includes answers in the text otherwise the same as the student edition with ISBN #0547102177102177 Hardcover. May include moderately worn cover, writing,...Good. Hardcover. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9780547102177 |
introductory courses in College Algebra and Precalculus. Sobel and Lerner provide teachers with a teachable text and students with a readable text that will properly prepare them for future courses, particularly calculus. The text is designed specifically to ease the transition to calculus and directly involve the graphing calculator. |
IMPORTANT: 1. Always check angle units and numeral bases: trigonometric functions, integration and complex number computation work only for RAD!!! 2. Application contains ads! If you want to remove them purchase special option from application settings. Internet access permission is needed only for showing the ads. ADS ARE ONLY SHOWN ON THE SECONDARY SCREENS! If internet is off - there are no ads!
Features: ++ easy to use ++ home screen widget + no need to press equals button any more - the result is calculated automatically + smart cursor positioning + copy/paste in one button + landscape/portrait orientations ++ drag buttons up or down to use special functions, operators etc ++ modern interface with possibility to choose themes + highlighting of expressions + history with all previous calculations and undo/redo buttons ++ variables and constants support (build-in and user defined) ++ complex number computations + support for a huge variety of functions ++ expression simplification: use 'identical to' sign (≡) to simplify current expression (2/3+5/9≡11/9, √(8)≡2√(2)) + support for Android 1.6 and higher + open source
NOTE ABOUT INTERNET ACCESS: Calculator++ (version 1.2.24) contains advertisement which requires internet access. To get rid of it - purchase a version without ads (can be done from application's preferences).
FAQ
How can I get rid of the ads? You can do it by purchasing the special option in the main application preferences.
Why Calculator++ needs INTERNET permission? Currently application needs such permission only for one purpose - to show ads. If you buy the special option C++ will never use your internet connection.
How can I use functions written in the top right and bottom right corners of the button? Push the button and slide lightly up or down. Depending on value showed on the button action will occur.
How can I toggle between radians and degrees?
To toggle between different angle units you can either change appropriate option in application settings or use the toggle switch located on the 6 button (current value is lighted with yellow color). Also you can use deg() and rad() functions and ° operator to convert degrees to radians and vice versa.
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You've found enough answers to odd-numbered questions, and checked them in the back of the book! It's time to learn deeper mathematics, and to think like a mathematician. In this class students will learn what constitutes a mathematical proof, a variety of classical proof techniques, and apply them in numerous mathematical contexts such as set theory, graph theory, number theory, geometry, and others as chosen by the instructor. (Spring semesters) |
Intermediate Algebra : Graphs and Models - 4th edition
Summary: TheBittinger Graphs and Models Serieshelps readers learn algebra by making connections between mathematical concepts and their real-world applications. Abundant applications, many of which use real data, offer students a context for learning the math. The authors use a variety of tools and techniques-including graphing calculators, multiple approaches to problem solving, and interactive features-to engage and motivate all types of228.30 +$3.99 s/h
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Elementary and Intermediate Algebra: A Practical Approach
Elementary and Intermediate Algebra: A Practical Approach provides concise, manageable treatment of the mathematics required for the combined algebra ...Show synopsisElementary and Intermediate Algebra: A Practical Approach provides concise, manageable treatment of the mathematics required for the combined algebra course. While emphasizing problem solving and the real-world applications of algebra, the text provides solid coverage of core mathematical concepts and essential symbol manipulation skills. Furthermore, the text encourages students to use graphing technology while still requiring them to master pencil-and-paper techniques for certain tasks. Authors Craine, McGowan, and Ruben combine their experience and expertise as a math educator and author, a math researcher, and an authority on math anxiety to deliver a balanced, targeted text that enables instructors to cover all the material for the combined course in one text |
I talk to a surprising number of math teachers who are really uncomfortable with logs. There's something about this topic that just makes people squeamish in Algebra, in the same way that "proving a series converges" makes people squeamish in Calculus.
It doesn't have to be hard. It is not intrinsically more complicated than a radical. When you see
x3x3 size 12{ nroot { size 8{3} } {x} } {} you are seeing a mathematical question: "What number, raised to the 3rd power, gives me
xx?" When you see
log3xlog3x you are seeing a question which is quite similar: "3, raised to what power, gives me xx?" I say this about a hundred times a day during this section. My students may forget the rules of logs and they may forget what a common log is and they will almost certainly forget ee, but none of them will forget that log28log28 means the question "2 to what power is 8?" You may want to show them the "Few Quick Examples" at the beginning of the Conceptual Explanations chapter to drive the point home.
It is possible to take any arbitrary logarithm on a standard scientific or graphing calculator. I deliberately never mention this fact to my students, until the entire unit (including the test) is over. Faced with
log28log28 I want them to think it through and realize that the answer is 3 because 23=823=8. The good news is, none of them will figure out how to do that problem on the calculator, if you don't tell them.
Introduction to Logarithms
This is a pretty short, self-explanatory exercise. There isn't anything you need to say before it. But you do need to do some talking after the assignment. Introduce the word "log" and explain it, as I explained it above:
log28log28 means "2 to what power is 8?" Also discuss the fact that the log is always the inverse of the exponential function.
After they have done the assignment, and heard your explanation of the word log, then they are ready for the homework. It wouldn't hurt if that happens in the middle of the class, so they can get started on the homework in class, and finish it up at home. The in-class exercise is short, the homework is long.
"Homework: Logs"
When going over the homework the next day, #20 can be explained two ways. First: 5 to what power is 5454? When asked that way, it's easy, isn't it? You don't have to find what 5454 is, to see that the answer is 4! But there is also another way to explain it, which gets back to the idea of
5x5x and
log5xlog5x being inverse functions. The first function turns 4 into 5454. So the second one has to reverse this process, and turn 5454 back into 4. This way is harder to understand, but it makes it a lot easier to see why #21 also has to be 4.
Then, there is the graph—as always, make sure they get the right general shape. Point out that the most salient feature of this graph is that it grows…incredibly…slowly as you go farther out to the right. (Every time xx doubles, the graph just goes up by 1.) This is a lot of what makes logs useful, as we will see |
Scott A Wilson
I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?
Socrates
I can answer any questions from the standard four semester Calulus sequence. Derivatives, partial derivatives, chain rule, single and multiple integrals, change of variable, sequences and series, vector integration (Green`s Theorem, Stokes, and Gauss) and applications.
Pre-Calculus, Linear Algebra and Finite Math questions are also welcome.
Clyde Oliver
I can answer all questions up to, and including, graduate level mathematics. I am more likely to prefer questions beyond the level of calculus. I can answer any questions, from basic elementary number theory like how to prove the first three digits of powers of 2 repeat (they do, with period 100, starting at 8), all the way to advanced mathematics like proving Egorov's theorem or finding phase transitions in random networks.
Janet Yang
I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems.
I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.
The higher degree a person gets, the better they are able to understand more complicated analysis. I have a Master's Degree in Mathematics, so I offer assistance in Algebra, Geometry, Trigonometry, Calculus
(1) It is known that tanx = 1/ctnx and tanx = sinx/cosx, which makes ctnx = cosx/sinx. That makes the fraction (1+tanx)/(1+cotx) be (1 + sinx/cosx)/(1 + cosx/sinx). If we multiply by (sinx*cosx)/(sinx*cosx) |
The main goal of this project is to improve student understanding of the geometric nature of multivariable calculus concepts,...
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The main goal of this project is to improve student understanding of the geometric nature of multivariable calculus concepts, i.e., to help them develop accurate geometric intuition about multivariable calculus concepts and the various relationships among them.To accomplish this goal, the project includes four parts:· Creating a Multivariable Calculus Visualization applet using Java and publishing it on a website: web.monroecc.edu/calcNSF· Creating a series of focused applets that demonstrate and explore particular 3D calculus concepts in a more dedicated way.· Developing a series of guided exploration/assessments to be used by students to explore calculus concepts visually on their own.· Dissemination of these materials through presentations and poster sessions at math conferences and through other publications.Intellectual Merit: This project provides dynamic visualization tools that enhance the teaching and learning of multivariable calculus. The visualization applets can be used in a number of ways:- Instructors can use them to visually demonstrate concepts and verify results during lectures.- Students can use them to explore the concepts visually outside of class, either using a guided activity or on their own.- Instructors can use the main applet (CalcPlot3D) to create colorful graphs for visual aids (color overheads), worksheets, notes/handouts, or tests. 3D graphs or 2D contour plots can be copied from the applet and pasted into a word processor like Microsoft Word.- Instructors will be able to use CalcPlot3D to create lecture demonstrations containing particular functions they specify and/or guided explorations for their own students using a scripting feature that is being integrated with this applet.The guided activities created for this project will provide a means for instructors to get their students to use these applets to actively explore and "play" with the calculus concepts.Paul Seeburger, the Principal Investigator (PI) for this grant project, has a lot of experience developing applets to bring calculus concepts to life. He has created 100+ Java applets supporting 5 major calculus textbooks (Anton, Thomas, Varberg, Salas, Hughes-Hallett). These applets essentially make textbook figures come to life. See examples of these applets at Impacts: This project will provide reliable visualization tools for educators to use to enhance their teaching in calculus and also in various Physics/Engineering classes. It is designed to promote student exploration and discovery, providing a way to truly "see" how the concepts work in motion and living color. The applets and support materials will be published and widely disseminated through the web and conference presentations.
Free tool that allows Mac and PC users to capture and share screen shots and animated videos with other users. Instructors...
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Free tool that allows Mac and PC users to capture and share screen shots and animated videos with other users. Instructors can use this tool to show students how to use software. Students can use it to help other students or show their instructors how they are trying to complete a computer task.
Liberty, Equality, Fraternity: Exploring the French Revolution provides an accessible and lively introduction to the French...
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Liberty, Equality, Fraternity: Exploring the French Revolution provides an accessible and lively introduction to the French Revolution as well as an extraordinary archive of some of the most important documentary evidence from the Revolution, including 338 texts, 245 images, and a number of maps and songs.You can now view a one hour webinar by the authors as part of the MERLOT Classics Series on Elluminate at the following site: " target=״_blank״
This site provides a large selection of physics and math simulations. There is also fairly comprehensive explanatory...
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This site provides a large selection of physics and math simulations. There is also fairly comprehensive explanatory information about the science and computation behind the applets. The applets are fairly small, and load quickly (even on dial-up), but are very broad in their coverage of topics. These applets are useful for illustrating physical systems and behavior that can not, in general, observed by experiments.
The MERLOT ELIXR project is intended to develop and test new collaborations amongst faculty development centers and online...
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The MERLOT ELIXR project is intended to develop and test new collaborations amongst faculty development centers and online resource repositories. The goal is to create innovative models for the development, sharing and use of discipline-oriented resources which illustrate exemplary teaching practices and which also support faculty with exemplary learning objects to help implement those practices with their students.In September 2006, the Fund for the Improvement of Post-Secondary Education, a program within the U.S. Department of Education, funded a proposal for ELIXR from a team of MERLOT partners and affiliated institutions. The deliverables center around 96 case studies of exemplary teaching, grouped in 6 theme areas for faculty workshops with discipline-specific cases in 16 disciplines. For example, potential themes could include active learning in large lecture sections, or course redesign to enhance student learning while containing costs for instruction. The case studies involve video of both teachers and students to engage other faculty in trying new approaches, and will be accessed in faculty development workshops for the theme areas and also through MERLOT and other online resource repositories.The MERLOT ELIXR project team includes the CSU Center for Distributed Learning and seven campuses of the California State University – where the initial pilot studies were launched in 2006; three MERLOT state system partners: Minnesota, Georgia and Oklahoma; and several leading campuses from a range of institutional types: Coastline Community College, Indiana State University, University of Texas Health Sciences Center at San Antonio and the Ohio State University.
Noteflight® is an online music writing application that lets you create, view, print and hear music notation with...
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Noteflight® is an online music writing application that lets you create, view, print and hear music notation with professional quality, right in your web browser. Work on a score from any computer on the Internet, share it with other users, and embed it in your own pages. Noteflight is free for individual use.
A collection of Java applets with accompanying text designed to help students understand concepts in introductory mechanics. ...
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A collection of Java applets with accompanying text designed to help students understand concepts in introductory mechanics. Topics include Vectors, 1D Kinematics, 2D Kinematics, Dynamics (Forces), and Work and Energy (under construction). The items are interactive, and provide immediate feedback and a running score, making them suitable for student self-study. A means of recording scores for a homework grade is available from the author. |
More About
This Textbook
Overview
Biology students are notoriously reluctant to use mathematics, yet a simple grasp of numbers reveals real insights into a whole range of biological phenomena. In this introductory text Richard Burton fosters a sense of the importance of maths to biology using a wealth of examples while assuming minimal maths ability. Questions and calculations encourage active participation, and the structure shows how the same reasoning aids the understanding of a range of biological problems. Aimed at beginning undergraduates but of great value to all the number-shy, including graduate students.
Editorial Reviews
From the Publisher
"As a gentle introduction to mathematics for the numerically phobic biology undergraduate, Richard Burton's Biology by Numbers could hardly be bettered. Well-chosen examples take the agony out of algorithms and the confusion out of calculus." New Scientist
"...Burton's book is a cornucopia of such succulent biological fruits as the snail albumin gland, grazers on grasslands, sodium in the diets of moose, and the allometries of stag beetles. Taken in a single serving, it makes for a very rich diet. The book is designed to attract two types of readers: the mathematically inclined who seek an introduction to biological problems, and the mathematically timid who sense a need to use quantitative methods to make sense of biology." Fred Adler, Bulletin of Mathematical |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). |
Basic Math Ref
CES-8473
Section Start Dates
Course Description
Never liked math or just wanting to brush up? You are not alone! Improve your skills in fractions, decimals, percents, and learn the basics of algebra, geometry and statistics. Accomplish all this while reducing anxiety and building confidence in a fun and relaxed learning environment.** |
+ subjects
including algebra 2 |
More About
This Textbook
Overview
A clear, concise presentation of the standard topics of college algebra and trigonometry -- covering the mathematics (algebra, functions, analytic geometry, trigonometry combinatorics, and probability) needed before approaching more advanced subjects such as calculus and discrete mathematics. Written with both instructor and student in mind, the text is easy to use, and each section can be covered in one class. Clearly marked subsections make it easy to omit more basic topics when necessary. The material is carefully organized and paced, offering thoughtful explanations through a combination of examples and theory. Contains an excellent review of basic algebra, with coverage of equations and inequalities, graphs and functions, complex numbers and more. This edition contains more exercises requiring the use of a calculator, new and numerous examples, and end-of-section exercises that provide a good test of the student's 27, 2003
Good Reference Book
This book is your basic text covering all College Algebra and Pre-calculus topics. It covers the entire gammet of topics from basic algebra on up inluding trig, matrices, vectors, probabilty, etc. It's a good reference book for the basics, with lots of examples and tons of problems (with answers included). It is easy to understand and problems explanations are clear. I would recommend it as a good book for the youngsters (or oldsters) just learning the topic. It doesn't assume you have a vast background in algebra.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. |
The final unit of eighth grade CMP Algebra capitalizes on the strong connections between algebra and geometry to extend students' understanding and skill in preparation for Geometry and Advanced Algebra. Students will work with equations for lines and curves. They will develop an understanding of how systems of equations and inequalities can help solve problems.
Students extend their earlier work in algebra and geometry by making connections between them. For example, students connect the idea of the Pythagorean Theorem to the coordinate equation for a circle, and connect properties of polygons to slopes of lines.
A student who has successfully completed eighth grade CMP has completed the same material as Algebra I and will be placed in Geometry as his or her next math course.
For an in-depth explanation of unit goals, specific questions to ask your student and examples of core concepts from the unit, go to Shapes of Algebra |
Mathematics for the Nonmathematician
Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the ...Show synopsisErudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and |
History of Mathematics
9780130190741
ISBN:
0130190748
Pub Date: 2001 Publisher: Prentice Hall
Summary: For junior and senior level undergraduate courses, this text attempts to blend relevant mathematics and relevant history of mathematics, giving not only a description of the mathematics, but also explaining how it has been practiced through time.
Suzuki, Jeff is the author of History of Mathematics, published 2001 under ISBN 9780130190741 and 0130190748. Three hundred twenty eight History of Mathematics text...books are available for sale on ValoreBooks.com, one hundred seventeen used from the cheapest price of $48.60, or buy new starting at $99Blending relevant mathematics and history, this book immerses readers in the full, rich detail of mathematics. It provides a description of mathematics and shows how mathemat [more]
Blending relevant mathematics and history, this book immerses readers in the full, rich detail of mathematics. It provides a description of mathematics and shows how mathematics was actually practiced throughout the millennia by |
2014 Welcome Letter
Please note: You must already be registered to at attend.
Workshop Description
This course is designed to delve into the content and activities appropriate for a Pre-AP Mathematics program. Participants will experience classroom activities designed to help prepare students for Advanced Placement Calculus. Both AP Calculus and AP Statistics require a strong foundation and this course will focus on the skills needed to enter those courses. Number and Quantity, Functions, and Mathematical Modeling will be the focus of the course. Multiple representations of mathematics from Linear Functions up to, and including, Trigonometric Functions will be addressed throughout the course. Participants will explore classroom tested activities and will have the opportunity to share some from their rooms.
What to Bring:
Participants may want to bring their laptops, personal graphing calculator, and a flash drive.
Learning Outcomes
Understand the role functions play in higher mathematics
Understand how to model real world applications with functions
Understand how to use multiple representations to illustrate mathematics to different students
Understand which topics are important to emphasize in a Pre-AP Mathematics curriculum to prepare students for AP Calculus and AP Statistics
Consultant Bio
Corey Boby is currently teaching Trigonometry, AP Calculus, and AP Statistics at Lakeside High School and has been in education since 1994. During his career he has worked for the Arkansas School for Mathematics and Science, Benton Public Schools, and Texas Instruments. Corey believes in the appropriate integration of technology. He uses a SMARTBoard, iPads, TI-Nspire CX, and TI-Navigator in his classroom, but believes technology should be used as a tool to support the mathematics not to do it for students. He is married to Tracy Watson, who also teaches math. They live out in the country and have 6 dogs and 3 cats |
Descriptions and Ratings (1)
Date
Contributor
Description
Rating
19 Jun 2009
MATLAB Central Team
Written for undergraduate students in mathematics, engineering, and science programs, this book provides an introduction to basic terminology and concepts found in mathematical studies of wave phenomena. The book is divided into three parts: an introduction to one-dimensional waves and their visualization, traveling and standing waves, and waves arising from conservation laws. MATLAB functions are presented to animate solutions of examples in the book. |
also taught classes in ACT test preparation in the areas of algebra, chemistry, biology, geometry, pre-calculus, and general science. Algebra is the study of Patterns. It is a way of describing patterns using words, symbols and pictures (graphs). Algebra 2 covers quadratic equations, graphing, complex numbers, functions, sequences and series, and exponents and logarithms |
A refresher course for all ages, this 5-volume series is designed by expert teachers to clearly and concisely convey the basics of Algebra. Algebra Tutor - Lesson 2: The Multiplication Property of Equality movie Topics covered in this volume include the inverse property of equality, reciprocals of whole numbers, using fractions, decimals and coefficients, and more key word definitions and word problems. Properties, Water, Painting on other Material, Woodlands, Misty Hills. Frank Clarke has emerged as one of Ireland's most popular artists and is now world famous for his painting techniques. Through his unique approach to watercolor and acrylic painting and his proven method of teaching others his trade, Frank has introduced thousands of people to the joys of leisure painting. The foundation of Frank's series is his HSMF formula: simplifying pictures into parts - Horizon, Sky, Middle, Foreground - to be tackled one at a time. Frank's contagious aspiration to "Have Some More Fun" offers budding artists the inspiration they need.
Source: TMW Media Group
DVD Features:
Full Frame - 1.33
Algebra Tutor - Lesson 2: The Multiplication Property of Equality film Other Ideas |
Mathematics: A Practical Odyssey - 7th edition
Summary: MATHEMATICS: A PRACTICAL ODYSSEY, 7E demonstrates mathematics' usefulness and relevance to students' daily lives through topics such as calculating interest and understanding voting systems. Well known for its clear writing and unique variety of topics, the text emphasizes problem-solving skills, practical applications, and the history of mathematics, and unveils the relevance of mathematics and its human aspect to students5057Used - Very Good Book. Shipped from US within 4 to 14 business days. Established seller since 2000
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Used - Acceptable Hardcover. Water damaged. 7th Edition Not perfect, but still usable for class. Ships same or next day. Expedited shipping takes 2-3 business days; standard shipping takes 4-14 busine...show moress days. ...show less
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You are here
Modeling Students' Mathematical Modeling Competencies
Publisher:
Springer
Number of Pages:
651
Price:
229.00
ISBN:
9789400762701
This book stems from the 13th International Conference on the Teaching of Mathematical Modeling and Applications (ICTMA 13). The first part focuses on research into what it means for students to understand models and modeling processes (6 sections, comprising 23 chapters), while the second part considers what is needed for modeling activities to be productive in classrooms (5 sections, comprising 30 chapters). The authors come from many countries: South Africa, Taiwan, Japan, Mexico, Germany, Israel, Brazil, Argentina, Sweden, Italy, Australia, Canada, Cyprus, U.K., Spain, Switzerland, Denmark, and the U.S. This book is a veritable fount of information about modeling in classrooms at all levels from elementary through university. In addition, it has chapters dealing with how teachers develop models of modeling (Chapters 30–46) and how new technologies influence modeling in classrooms (Chapters 47–51).
If you are not familiar with the difference between mathematical modeling and mathematical problem solving, Section 6 (Chapters 22–30) will help clarify that for you. While they do overlap, they are quite different. Mathematics problems, even open-ended ones, are already formulated mathematically. They are often artificial, puzzle-like tasks that do not encourage students to rely on their common sense or make realistic connections to the problem context. Modeling problems, however, have an undetermined nature, and do often involve using common sense, making decisions about assumptions, and collecting information, before mathematics can be used. In Chapter 28, one finds that models are "more like powerful/shareable/reusable artifacts and tools" than simple answers to traditional questions and word problems. The difference is between "making mathematics practical" and "making practice mathematical".
Then there's mathematization. According to Chapter 4, mathematization is the part of the modeling process that occurs after the situation has been structured. It consists of translating the objects and relations of the structured situation into appropriate mathematical terms. Chapter 22 provides twenty-one sample tasks for Grades 9–12 that distinguish between modeling tasks (of long and short duration) and mathematization tasks (of short duration). Sample modeling tasks include: "Which means of transportation is the best?" (2–4 weeks) and "How many times can one brush one's teeth with a tube of toothpaste?" (one lesson). A sample mathematization task is: A liqueur glass is cone-shaped. What height of liqueur served in the glass makes it half-way full? This, however, seems more like a mathematical problem-solving task to me.
Much more can be learned from this book. In Chapter 6, Noss and Hoyles report their three-year investigation of companies, such as automobile manufacturing and financial services, where the technology in use often hides the underlying mathematical concepts and procedures. While calculation and basic arithmetic are necessary for workers, these are of less importance than a "conceptual grasp of, for example, variables and relationships in the work flow, how graphs and spreadsheets highlight relationships and trends, how systematics data may be used with powerful, predictive tools to control and improve [workplace] processes." (p. 84). The authors introduce the idea of "Techno-mathematical Literacies" (TmL) — new skills needed in technology-rich workplaces — which can seldom be picked up on the job. The authors discuss industry specific interactive software that they have developed for use with employees to promote effective learning of TmL.
Chapter 11 considers how one can turn general ideas into modeling problems. The authors give five principles for doing this, with Principle 1 being that there should be a genuine link with the real world of the students to provide relevance and motivation (p. 135). They provide sample questions that Australian Year 10 and 11 students investigated in a modeling challenge that allowed them to pose questions themselves. (p. 139). Some of these are: "When will the Aral Sea dry up completely?" and "How much water do we really have left in the Hinze Dam? Will it cater for the current and future population of the Gold Coast of Australia?" The authors note that problems having a social context, rather than a scientific context, are often preferable because they allow more critical analyses of the models produced.
In addition, some chapters discuss model-eliciting activities (MEAs), a concept introduced by Lesh and Doerr in their 2003 book. In Chapter 9, Larsen describes a study of modeling, using an MEA called the "Summer Jobs" problem, which she conducted with college students who were given data on employees' performance at summer jobs. The question was: "Whom to rehire for next summer?" The students had to structure the problem and pick out the important quantities and relationships. They divided the data into busy, slow, and steady times; considered hours, dollars, dollars per hour; and compared the money made by employees during those times. As with most such modeling problems, at the end they had to write a report justifying their recommendations.
In Chapter 21, Carmona and Greenstein report what happened when they gave the same modeling problem to both 3rd graders and to post-baccalaureates enrolled in a summer workshop. The modeling problem was to find the best way to rank (1st to 5th) twelve soccer teams based on win-loss data, provided as labeled points plotted in a quadrant determined by two unit-less axes simply labeled "wins" and "losses". While the 3rd graders were given two 1-hour sessions to do this, the post-baccalaureates worked on the problem in one 2-hour session. The somewhat surprising result was that both groups came up with essentially the same ranking and similar reasoning, but the post-baccalaureates used much more sophisticated mathematics.
Several chapters deal with projects and courses for upper level engineering students. Chapter 7 details how a team of industrial engineering undergraduates engaged in a long-term engineering design project for an industry partner. Their assignment was to provide a recommendation on whether the partner should establish a satellite center at a certain location. The students determined that they needed to do detailed cost analyses for several different options. Chapter 15 describes a pilot course offered to ten junior and senior industrial engineering students at the University of Pittsburgh. Part of a four-year six-institution research project funded by NSF, the course consisted of nine model-integrating activities (MIAs) briefly described in the chapter. The authors also provide a "first cut at assessment" in the form of a two-page rubric (pp. 186–187). This chapter might provide a "head start" for others interested in developing, and assessing, engineering modeling courses.
I got the impression that despite the vast amount of information coming out ICTMA 13 and previous conferences, there are many questions about modeling and teaching modeling that could still be investigated. A question that I had that was not answered in the book was: What's the difference between project-based learning and learning through modeling activities? According to one website I found,
In Project Based Learning (PBL), students.(
It would seem that modeling activities are much less structured and more loosely connected to specific curriculum objectives than PBL.
Who might be interested in this book? While not a "how to" book, teachers at all levels can glean information about modeling — its implementation and assessment — as well as find some interesting modeling tasks to adapt. Also, mathematics education researchers can discover the kind of modeling research that has been done and gain insight into what remains to be done.
I have a few quibbles. There are some insignificant typos, such as "close" when "closed" was surely intended (p. 125) and the inclusion of "Simon Fraser" twice — once as part of Stephen Campbell's last name and again to designate his university (p. xi). Also, the index is very skimpy — several times I tried to find topics that I had read about, but not jotted down the page number of, and could not do so using the index. That said, I found the book a worthwhile read. A plus is the fact that one can skip around and read just what interests one, as the chapters are essentially independent.
Annie Selden is Adjunct Professor of Mathematics at New Mexico State University and Professor Emerita of Mathematics from Tennessee Technological University. She regularly teaches graduate courses in mathematics and mathematics education. In 2002, she was recipient of the Association for Women in Mathematics 12th Annual Louise Hay Award for Contributions to Mathematics Education.
Modeling and Design Research and Assessment Methodologies.- Modeling in High School and College.- Modeling in Middle Schools.- Modeling in the Primary Grades.- Modeling and Teacher Development.- Modeling vs. Traditional Problem Solving.- Modeling in Engineering and in Other 21st Century Design Sciences.- Technological Tools and Data Modeling.- Modeling and Socio-Cultural Perspectives.- Directions for the Future. |
Course Description
This course will provide the learner with a better understanding of the underlying concepts of geometry. Through readings, lessons, quizzes and independent explorations, the learner will leave the course with more complete understanding of geometry and begin to be able to think in a geometrical fashion. Websites are also provided to help the learner further explore the topics on his/her own. At the end of this unit, the learner will be able to describe some of the basic premises behind geometric thinking, reasoning and study. They will also be able to demonstrate the following learning objectives:
Objectives (based on the Van Hiele levels of geometric thought):
Students will be able to demonstrate the ability identify the ways geometry is used by people in their daily lives (i.e. professions, synthetic universe, natural universe, in the home, etc...) |
PH ElementaryStatistics, PicturingTheWorld, 3rd edition Chapter 3. Jackson Public School District Office of Curriculum and Instructional Services Statistics Pacing Guide 2008-2009 Bold and underlined item(s) within the objective indicate the focus for that term.
A Matter of Trust (Massachusetts Weddings, Book 2) By Lisa Harris Download Full Version Of this Book Download Full PDF Version of This Book This is the only site that you can get the free pdf version of this book, enjoy!
Required Text: ElementaryStatistics: PicturingtheWorld (5th edition) by Larson and Farber . Prerequisites: C or better in Math 1010, or ACT of 23 or higher . Homework and Tests . Homework will not be graded, but will be marked as done or not done.
Title: ElementaryStatistics: PicturingtheWorld, 3/e Larson & Farber * The 4th edition is also acceptable. But some of the problems on MyMathLab may be from the 4th edition. Prerequisites A grade of C or better in Math 99 or equivalent.
(Taken from: ElementaryStatistics: PicturingtheWorld, by Ron Larson and Betsy Fifth Edition) You are required to print and bring to every lecture the handout available on my course web page:
• ElementaryStatistics – PicturingtheWorld , 4 th edition by Larson and Farber (0-13-242433-9) • Against All Odds: Inside Statistics video series at Media Services in Murray Library 1 1This video series was produced in the late 1980's.
Title: ElementaryStatistics: PicturingtheWorld, 3/e Larson & Farber * The 4th edition is also acceptable and highly recommended. Prerequisites A grade of C or better in Math 99 or equivalent. COMPASS college algebra score of 49 or better. |
can help you in the following areas:
1). Classification of Differential Equations; Initial-Value Problems, Boundary-value Problems, and Existence of Solutions.
2). Exact Differential Equations and Integrating Factors; Separable Equations; Linear and Bernoulli Equations; Orthogonal and Oblique... |
Developmental Math Lab
The Developmental Math Lab: Help Starts Here!
Hours:
The Developmental Math Lab is closed for the summer. It will open again on the first day of classes in the fall semester.
However, if you are looking for help this summer, check out the Student Resources tab for online tutorials for Math 090 and Math 091.
What math classes does the lab support?
The Developmental Math Lab supports Math 090, Math 091, and Math 081.
Do I need an appointment to get help?
No, it is a walk-in lab, so no appointments are needed.
How do I earn extra credit?
Just come into the lab and get help, then ask a staff member to sign your extra credit sheet.
Don't have a sheet? Just ask for one!
What if I need help and the Developmental Math Lab is closed?
Supplementary worksheets and accmpanying recorded explanation sessions, as well as exam reviews and accompanying video recordings are available on this website. Just click on the word, "Resources" on the left hand side of this page.
Also, you can get help in the Math Lab upstairs (room 2813A) or in the Learning Skills Center when they are open. |
4.1 Introduction
4.1.1 The Intent of Content
Markup
As has been noted in the introductory sections of this report,
Mathematics can be distinguished by its use of a (relatively) formal
language, mathematical notation. Mathematics and its notation should
not be viewed as one and the same thing. The intent of content markup
in HTML maths is to support the encoding of underlying mathematical
content of an expression, rather than any particular rendering for the
expression.
For example the construct "H multiplied by e" is
expressed using an explicit operator H<TIMES/>e. In different
presentational contexts, the multiplication operator might be
invisible (e.g. on paper), or rendered as the spoken word "times".
Knowing the underlying mathematical construct, it is often possible to
generate many different presentations according to the context and
style preferences of the author or reader. For common expressions a
default visual presentation is usually clear. "Take care of the
sense and the sounds will take care of themselves" wrote Lewis
Carroll [LC1]. Going in the reverse
direction, that is from a presentation form to the underlying
construct, is not necessarily easy: "He" could be
interpreted as an atomic text string (or a chemical symbol). Context
information may be required to decide between possible
interpretations. Clues as to the interpretation are plainly important
to speech rendering.
Mathematical presentation changes with culture and time: some
expressions in combinatorial mathematics today would have one meaning
to an English mathematician, and quite another to a French
mathematician. Notations may lose currency, for example the use of
musical sharp and flat symbols to denote minima and maxima. [TWC1] A notation in use in 1644 for the
multiplication mentioned above was .[Cajori]
Encoding the underlying mathematical constructs allows us
to better interchange information with systems which are able to
manipulate the mathematics. In the trivial example above, such a system
could substitute values for the variables H and e,
evaluating the result. Further interesting application areas
include CD-based textbooks and other interactive teaching
aids.
4.1.2 The Scope of Content
Markup
It is clear that the semantics of much mathematical notation is not
yet a matter of consensus. In any case it would be an enormous job to
do to codify most of mathematics. Therefore, the MathML proposal
specifies a number of commonplace mathematical constructs which should
be useful to a large number of potential users. The content tags set
out below should be adequate for simple coding of most of the formulas
used from kindergarten to the end of high school in the US, and
probably beyond through the first two years of college, that is up to
A-Level or Baccalaureat level.
The areas covered to some extent in this initial draft
are:
Algebra
Calculus
Set Theory
Series
Trigonometry
Statistics
Matrices
It is not claimed, or even suggested, that the proposed element set
is complete for these areas.
4.1.3 Basic Concepts of Content Markup
The guidelines governing the design of the MathML content
elements are the following principles:
The encoding of simple mathematical expressions should be as natural
as possible.
The encoding of an expression tree should be explicit, and not
dependent on additional processing such as operator precedence
parsing.
In order to accomplish these goals, MathML introduces two kinds of
content tags. The first kind function as containers, and in general
serve to mark the scope of the operators contained in them, or to
define a context for the elements contained in them, such as a matrix.
The second kind are empty elements, such as <SIN/>, and
typically represent operators and functions. Operators and functions
are applied to arguments by using another empty element, the
<APPLY> element.
While MathML content tags do directly encode mathematical
meanings, they do not directly control the notation used to
present the meaning to a reader. However, content tags have
recommended default visual renderings as described in
comments where appropriate. In addition, all content tags
have a "LAYOUT" attribute (see Section sec4.1.4, which can be used to pass
rendering preference information on to a specific renderer
which can make use of it.
The <EXPR> Construct
The basic building block of a mathematical expression in
MathML content markup is the EXPR element. An EXPR corresponds to a
complete mathematical expression. Roughly speaking, this means a
piece of mathematics which could be surrounded by parentheses or
"logical brackets" without changing its meaning.
For example,
might be encoded as
<EXPR> x <PLUS/> y </EXPR>.
Since the bracketing is logical, it need not necessarily be
rendered. By default, an EXPR is rendered using the MROW presentation
schema. Authors can further control how an EXPR is rendered by mixing
presentation and content tags (for example adding parentheses), or by
using the LAYOUT attribute with a specific renderer.
Using EXPR, (as with braces in traditional mathematics notation),
it is possible to specify exactly the scope of any operator or
function. The content model of EXPR is simple and recursive.
Symbolically, the content model can the described as:
EXPR => a op b
where a and b are simple identifiers, or EXPR constructs
themselves, and op is any operator or function.
Note that this allows EXPR constructs to be nested to
arbitrary depth.
An EXPR may also optionally contain more than one operator:
EXPR => a op b [op c ...]
For example,
can be encoded as
<EXPR> x <PLUS/> y <PLUS/> z
</EXPR>.
When an EXPR is used in this way, it is important to keep in mind
the issue of operator precedence. In cases where several operators
are enclosed in a single EXPR, operator association or precedence must
be resolved by an external processing application, if it wishes to
evaluate the EXPR. Therefore, in most situations, it is probably
preferable to fully bracket expressions, particularly when several
different operators are involved. For example, is better encoded as
<EXPR><EXPR>a<TIMES/>x</EXPR>
<PLUS/>b</EXPR>
although it is also valid to encode it as
<EXPR>a<TIMES/>x<PLUS/>b</EXPR>.
In addition to determining the scope of operators and functions,
the <EXPR> container plays an important role in grouping
expressions within other constructs. For example, by default a
<VECTOR> element expects to have its components separated by an
explicit separator, the <SEP/> tag. However, an
expression enclosed by an EXPR is viewed as a single coherent
molecule, so that the <SEP/> tag is not needed to separate it
from its neighbors.
The APPLY construct
One reason for using MathML content markup is to make the
mathematical expressions easily available to external processing
applications such as computer algebra systems, and intelligent
renderers. Therefore, a key requirement of functional representation
in content markup is that it must be possible to perform symbolic
algebra on mathematical functions as first class objects, and the
apply the result to an argument. That is, in addition to
we must be able to encode
.
To understand the MathML approach to applying a function to an
argument, consider f(x). This can be encoded as
<EXPR>f <APPLY/> x </EXPR>
Note that f and x may be simple identifiers, or more
complex constructs built from EXPRs and other function elements.
For example, one can construct 'new' functions which can then be
applied to an argument using the APPLY element. Thus, the expression
(F + G)-1(x) can be encoded as
Most functions supported explicitly in MathML are all
canonically empty elements and can be used as first class
objects. Examples are <PLUS/>, <SIN/> and user
defined functions such as <FN NAME="F"/>. Although,
it is probably best to always use the APPLY element, just as
it is prudent to fully bracket expressions with EXPRs, the
APPLY element is optional and may be omitted in unambiguous
situations. The only such situation which commonly arises
is when a function named in MathML appears alone with an
argument in an EXPR. For example, we can write sin
(x) as
<EXPR><SIN/>x </EXPR>
as there is no other operator within the EXPR.
There is no linguistic difference in MathML between
operators and functions. The separation in the content model
is only to clarify what is going on. Some functions in this
list may not ever be used in symbolic manipulations.
By default, the APPLY element renders as a thin space between
the function and its argument, or as the spoken word "of". Note that
the default rendering of the APPLY element does not determine whether
or not there are parentheses around the function argument. An author
can control this by mixing content and presentation tags, or by using
the LAYOUT attribute with a specific renderer.
The INVERSE construct
The INVERSE construct is problematic from a mathematical point of
view in that it implicitly involves the definition of an inverse for
an arbitrary function F. Even at the K through 12 level the
concept of an inverse F-1 of many common functions
F is not used in a uniform way. For example, inverse
trigonometric functions are inverses in a slightly different way than
the log function is the inverse of the exponential.
In an effort to be as inclusive as possible, MathML adopts the view
that
"If F is a function from a domain D to
D', then the inverse G of F is a function
over D' such that G(F(x)) = x for x in
D."
This definition does not assert that such an
inverse exists for all or indeed any x in D,
or that it is single-valued anywhere. Authors writing pedagogical
material that may be evaluated by other applications may therefore
wish to address the issue of the existence of a particular inverse
function.
Content or semantic tagging goes along with the (frequently
unconscious) premise that, if you know the semantics, you can
always work out a presentation form. When an author's main goal is to
mark up re-usable, evaluatable mathematical expressions, the exact
rendering of the expression probably doesn't matter, provided it is
easily understandable. However, when an author's goal is more along
the lines of providing enough additional semantic information to
make a document more accessible by facilitating better visual
rendering, voice rendering, or specialized processing, controlling the
exact notation used becomes more of an issue.
To help provide authors with more control over layout, every MathML
content tag accepts a "LAYOUT" attribute. The "LAYOUT" attribute is
there for the author to express a preference between
equivalent forms for a particular construct, where the selection of
the presentation has nothing to do with the semantics. Examples might
be
inline or displayed equations
scriptstyle fractions
use of x with a dot for a derivative over dx/dt
The information provided in the "LAYOUT" attribute is intended for
use by specific renderers, and therefore, the valid values are
determined by the renderer being used.
It is legal for a renderer to ignore this information. This might
be intentional, in the case of a publisher imposing a house style, or
simply because the renderer does not understand them, or is unable to
carry them out.
As a proof of concept, Stilo Technologies have developed a
translator which takes as input mathematical formalism encoded
in the SGML semantic maths DTD, and generates print-quality TeX.
The only presentation information is in the layout attribute,
which is used to select the first two options above. This is not
a commercial product, but it does enough to validate the
concept. There will be a need for the construction of
translators for the layout of material tagged with content tags
according to the wishes of those wanting the output.
To assist developers wishing to implement a MathML compliant
renderer, we give a few suggested default layout rules
for rendering MathML content tags via MathML presentation tags. This
list is far from complete, but should give an idea of what is
intended. Of course, developers are free to use any collection of
default rules, provided that they generate an easily understandable
rendering for any valid MathML expression.
Naked arguments which are numerical (i.e. consist of digits, an
optional decimal point, and an optional preceding minus sign) should
be treated as though they are wrapped in <MN> tags
The characters []{}() and | should be treated as though they are
wrapped in <MF> tags when they appear as naked data.
Other naked arguments should be treated as though they are
wrapped in <MI> tags.
<EXPR> pairs are treated as invisible grouping brackets,
like the braces of TeX; for presentation they are mapped into <MROW>
pairs. If you want a group to be displayed within parentheses or
brackets, then you will have to add this explicitly. It is to be
expected that, for instance, a parenthesis pair added for this
purpose, as, say, in <EXPR><SIN/>(x)</EXPR> will be
thrown away as redundant by a semantically oriented further processor.
A <SET> container should just provide braces around
whatever is within it. The <ST/> should be rendered with a
vertical bar.
A <MATRIX> container should provide parentheses around
whatever is within it, and its subexpressions should be mapped onto an
equivalent <MTABLE> construct.
<INT> containers should map onto the
corresponding expressions in the schema:
The reason for using an explicit equation identifier <E> or
equation array identifier <EA> is that it may be used by an
automatic equation numbering device, or for indexing, say. In each
case there is an attribute EQNOTYPE which can determine whether there
is an equation number or not.
ST and SEP
<ST/> is the "such that" between an equation
and its quantifier, as in "x < 2 such that x in
R" coded as
<SEP/> is a more generic separator for array-like
containers, and things like the INTERVAL container. The
default rendering for <ST/> is a vertical bar, while
by default, lt;SEP/> is not rendered, so that explicit
commas may have to be added.
The FN element is used for encoding author defined functions. It
accepts an optional attribute "NAME" which contains the name of the
function. In any situation where an explicitly defined MathML function
can be used, the FN element may also be used.
The INT element uses the auxiliary qualifier elements UPLIMIT,
LOWLIMIT and BVAR the limits of integration, the variable of
integration. These optional elements may appear at any position
inside the SUM or PRODUCT element. By default, the upper and lower
limits are rendered in their usual positions, and the bound variable
is rendered with a small space and the letter "d" in front of it.
BVAR
The BVAR element specifies a "bound variable". In different
contexts, this means different things. In an integral, it specifies
what integral is being integrated. In a derivative, it indicates
which variable is being differentiated. The BVAR element is also used
with sums and products.
LOWLIMIT and UPLIMIT
These elements specify lower and upper limits. In different
contexts, this means different things. In an integral, they specify
the limits of integration. These elements are also used to specify
the limits of an index for sums and products, and also to specify a
limiting value for a variable in a limit.
DEGREE
There are a number basic mathematical constructs which come in
families, such as derivatives, moments, and logarithms to various
bases. Rather than introduce special tags for each of these families,
MathML uses a single general construct, the DEGREE element.
These elements both contain their entries as content. When the
entries are ordinary data (#PCDATA) it is necessary to use a
separator, in order to specify where one entry ends and another
begins. In MathML, the SEP element is used.
When the entries are actually valid MathML expressions,
then no separator is needed.
For example, if a MATRIXROW contains of a sequence of fully delimited
EXPRS, the SEP elements may be omitted.
4.3 Syntax and Semantics
The use of content rather than presentation tagging for
mathematics is sometimes referred to as "semantic tagging"
[BUS1].
The parse-tree of a fully bracketed MathML content tagged
element structure corresponds directly to the
expression-tree of the underlying mathematical expression.
We therefore regard the content tagging itself as encoding
the syntax of the mathematical expression. This is, in
general, sufficient to obtain some rendering and even some
symbolic manipulation (e.g., polynomial factorization).
However, even in such apparently simple expressions as X
+ Y, some additional information may be required for
applications such as computer algebra. Are X and Y
integers,or functions, etc.? What field's addition does the 'plus'
represent? This additional information is referred
to as Semantic Mapping. In MathML, it can be provided by the
SEMANTICS and SEMINFO elements.
The SEMANTICS element expects up to three child elements. The first
is the element (which may itself be a complex element structure) for
which this additional semantic information is being defined. The
second child is an optional separator. The third, optional, child is
the SEMINFO element which contains the detailed semantic
information:
The SEMINFO element is a container for arbitrary data. This data may
be in the form of text, computer algebra encodings, C programs, or
whatever a processing application expects. If the additional semantic
information is contained in a well-formed XML element, as is the case
for OpenMath SGML encoding, than this element can simply replace the
placeholder SEMINFO element. For Example:
where <OM_APP>..</OM_APP> are the elements
defining the additional semantic information.
The SEMANTICS tags also accepts a "SEMTYPE" attribute for use by
external processing applications. One use might be a URL for a
semantic context dictionary, for example. Since the semantic mapping
information might in some cases be provided entirely by the "SEMTYPE"
attribute, the SEMINFO element is optional.
Of course, providing an explicit semantic mapping at all is
optional, and in general would only be provided where there is some
requirement to process or manipulate the underlying mathematics.
4.3.2 Semantic Mappings
Although semantic mappings can easily be provided by
various proprietary, or highly specialized encodings, there
are no widely available, non-proprietary standard semantic
mapping schemes. In part to address this need, the goal of
the OpenMath effort is to provide a platform-independent,
vendor-neutral standard for the exchange of mathematical
objects between applications. Such mathematical objects
include semantic mapping information. The OpenMath group
has defined an SGML syntax for the encoding of this
information [OM]. This element set
could provide the basis of one SEMINFO element set.
Part of the attraction of this mechanism is that the
OpenMath syntax is SGML specified, so that the whole
expression is checkable by a DTD-based parser. |
Mathematics
Mathematics is the abstract science of number, quantity, and space. Mathematics may be studied in its own right (pure mathematics) or may be applied to other disciplines such as physics and engineering (applied mathematics)
It is said that a degree in mathematics provides you with a broad range of skills in problem solving, logical reasoning and flexible thinking which would lead you to careers that are exciting, challenging, and diverse in nature as employers nowadays sought out for professional who have greater analytical and quantitative skills.
Furthermore, it is a proven fact that almost all industries require mathematicians. Mathematics is present in the field of business, finance, science and education. This would mean to say that if you have a degree in Mathematics and has a plan of entering into the Educational Industry, you would have to prepare yourself for the criterions that your licensing state would have to require from you.
Every beginning teacher in the specialization of Mathematics would have to take and pass the Praxis II Mathematics Exam for them to be able to officially teach Mathematics in education institutions. Thus, candidates must be aware that their knowledge, skills and abilities will be put to test as the state would have to ensure the public that all teachers teaching in the schools are of great caliber and will be able to provide quality education to the students of the United States of America.
If you are that driven in becoming a Math Teacher, then, we will surely be able to help you with that. In this website, you will not just find relevant information about the Praxis Exams but as well as study guides about Praxis 2 Mathematics that will help you pass that state certification exam. We have a list of Math exam secrets and flashcards about different topics ranging from the knowledge content of Mathematics to proofs and models. Plus, we would also like to give you a helping hand literally! Just pick up the phone and to hire one of our highly competitive tutors that specailizes Praxis 2 Mathematics in the state! Here is your chance to get that teaching certificate you have always dreamed of! Contact us now and be one of the most successful Math Teachers in your state today!
MATHEMATICS AS THE SUBJECT OF MATTER
As a review, we have figured out that Mathematics is the abstract science of number, quantity, and space. And that having a degree in mathematics provides you with a broad range of skills in problem solving, logical reasoning and flexible thinking which would... |
Geometry: Fundamental Concepts and Applications
9780321473318
ISBN:
0321473310
Edition: 1 Pub Date: 2007 Publisher: Pearson
Summary: This Geometry workbook makes the fundamental concepts of geometry accessible and interesting for college students and incorporates a variety of basic algebra skills in order to show the connection between Geometry and Algebra.
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You are here
A Math Toolkit for Java Developers
The JOMA Developers' Area can provide a real service to the mathematical developer community by
providing a single source that developers can go to in search of code that they can use and
encouraging developers to create code in a way that would be the most useful.
The first step in this process is to generate a discussion about how this should take place. I would like to launch that discussion by sharing some thoughts about what developers can do to make their code most useful to others and by offering my own vision of one direction that this might take. Finally, I will describe a prototype that I have developed. In short, I propose a coordinated effort by developers to construct a Math Toolkit that would provide, in a single download, Java files that could be used to accomplish most of the common tasks required by mathematical Java developers.
The Problem
Almost anyone who attempts to learn Java for the purpose of teaching mathematics encounters a familiar set of challenges. First, there is the chore of learning the language itself. This can be a daunting task, particularly for those who are unfamiliar with the object-oriented paradigm that was embraced so enthusiastically by the creators of Java. The second challenge is becoming familiar with the vast libraries that come with Java. These contain some very powerful and well-documented tools, but it requires a bit of background to be able to use them correctly.
In addition to these challenges, though, mathematicians face some special obstacles. The first one is encountered very early: It is the problem of allowing for numerical input by the user. The fact that all input comes in the form of a String of characters that must be converted into a numerical data type can be a troublesome inconvenience when trying to write even the simplest mathematics program. Java does provide (literally!) methods for doing this when the String represents a number, but that doesn't solve the problem of allowing for numerical expressions such as "3*4" or "Pi^2".
The second obstacle encountered by almost every mathematical developer is the problem of displaying graphs. Again, there are some useful tools built into the language, but it is soon clear that they were not designed with mathematicians in mind. For example, there is a coordinate system, but, as with other programming languages, the coordinates are in pixel units, which means that all coordinates must be integers. As if that weren't enough of an outrage, the y-axis is upside down and the origin is in the upper left hand corner!
When faced with these and other obstacles, some mathematicians relish the challenge and take this as an opportunity to delve deeply into the Java programming language in order to come up with individual solutions. Others search far and wide for Java code that they can copy into their own programs. I fear that there may be still others who give up entirely.
What we need is a library of tools that can be used by both novice and experienced programmers to overcome these and other obstacles. There are plenty of tools out there, but JOMA can provide a real service by organizing them in a centralized location and by helping developers to construct these tools in a manner that will make them easier to use.
Java Component Technology
What are some of the considerations for constructing reusable software? The best example of reusable software is provided by Sun. Consider the components that come with the Java Development Kit, such as the TextField or the Panel (or the Swing versions JTextField and JPanel). Sun has obviously put a lot of thought into their construction. They share a number of different characteristics.
They are versatile.
They are well documented.
It is not necessary to read the source code in order to use them -- all interaction is done with well-documented methods.
To achieve the same goals with mathematical components, it will be necessary to anticipate future uses of them as they are being designed. However, it is important that any single component not try to do too much. For example, in my opinion, a graphing calculator would not be an appropriate component -- it does too much. In the object-oriented spirit, it would be better to split the graphing calculator concept into its separate objects and design components to model each one. There should be something to play the role of the display screen, some way to provide input, and some way to do the computation. Those are all separate tasks and should be performed by separate components. Each of these components could then be used in other applications that didn't require all the power of a graphing calculator.
Finally, there is one other characteristic that many of Sun's components share: They are compatible with all visual development environments. This means, for example, that most of the properties of the components can be adjusted at design time by making entries into a property list. It also means that they can be manipulated with a drag-and-drop interface, and their dimensions can be adjusted with a mouse. Our mathematical components can achieve this by conforming to the JavaBeans standard. Chung and Digiano, in a future article in JOMA, will discuss the JavaBeans standard. In order to be the most useful, I would propose that most -- but not all -- mathematical components be JavaBeans.
Which components should be JavaBeans? Basically, a component should be a JavaBean if it would be useful to manipulate it using the tools of a visual development environment. This would be true for almost any visual component (such as a Panel or a TextArea), but it might also be true for non-visual components which might have properties that could be adjusted using the property list of the development environment. For example, in the MathToolkit discussed below there is a SymbolicFunction class that defines a function according to a formula. While this is an invisible component, it is a JavaBean because it is convenient to enter the formula from the property list. (There is actually another advantage: By making it a JavaBean, it can easily be added as a property to other JavaBeans, such as a table or a graph.) On the other hand, an equation parser, while a useful component, would not make a good JavaBean, because it is not visual and does not have any properties that need to be adjusted using the property list.
A Unified Vision
If we accept that there is a need for reusable mathematical components, what is the best way to achieve this, and how can JOMA help? One possibility is to allow JOMA to serve as a marketplace for a wide variety of components with developers submitting them for review just as they do with Mathlets. This can easily be done and probably should be done. However, I have a proposal for an effort that could take place in parallel with this. My proposal is that we set up an open-source collaborative effort to construct a single Mathematics Toolkit that would contain one or more packages of components and files that would serve the most common needs of mathematical Java Developers. There are a number of advantages to this approach. Before discussing them it may be useful to see an illustration. In a joint project with Chuck Pheatt, funded by an NSF grant (DUE-9950714), I have developed a prototype for such a toolkit. (Almost all the components in the toolkit are based on Swing components so, in order to view the applet, you will need to make sure that your browser is Swing compliant.)
In addition to the components in the demonstration, the MathToolkit contains a number of other components, including a FunctionTable and a ParametricTable, that are similar to the MathTable except that they accept as properties one or more functions or parametric equations and display the values on a table. There are beans that facilitate the creation of parametric curves for display on the MathGrapher and one that creates a random piecewise linear function that is useful for constructing examples. Other beans aid in the construction of secant lines and tangent lines for curves. MathToolkitZip contains the MathToolkit, documentation, source code, and tutorials for using it with JBuilder.
One of the advantages of having such a toolkit is that, in one download, the developer can get tools for accomplishing the most common tasks with an assurance that they will all be compatible with one another. In addition, by putting everything into one jar file it is possible to avoid duplication of efforts. For example, the MathToolkit contains a MathUtility class that contains a number of static methods used by many of the components, and the MathTextField is used in a number of the components.
By coordinating the construction of the components it will be possible to provide a consistent appearance across all components. Finally, if the MathToolkit should achieve the level of a standard, the very fact that many developers use it extensively would give some assurance of reliability.
If the development of the Mathematics Toolkit is done in parallel with the submission of individual components, some of the best of those could be considered for incorporation into the Toolkit.
I'm sure that there are others who have developed similar tools, and I am not suggesting that mine is the best. For example, some might argue that the reliance on Swing components is a drawback for the moment. What I am suggesting is that such an effort is worthwhile, and we should begin a discussion on how to achieve it. |
-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Clear, straightforward presentation of the properties of the apparatus, the representation of numbers by continued fractions, and the measure theory of continued fractions. 1964 edition. Prefaces. |
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Accessible Mathematics is Steven Leinwand?s latest important book for math teachers. He focuses on the crucial issue of classroom instruction. He scours the research and visits highly effective classrooms for practical examples of small adjustments to teaching that lead to deeper student learning in math. Some of his 10 classroom-tested teaching shifts... more...
Advanced numerical simulations that use adaptive mesh refinement (AMR) methods have now become routine in engineering and science. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. The underlying physical models... more...
This volume is designed for the student desiring a greater understanding of the abacus and its calculative functions. The text provides thorough explanations of the advanced operations involving negative numbers, decimals, different units of measurement, and square roots. Diagrams illustrate bead manipulation, and numerous exercises provide ample... more...
Since its introduction in 1984, MATLAB's ever-growing popularity and functionality have secured its position as an industry-standard software package. The user-friendly, interactive environment of MATLAB 6.x, which includes a high-level programming language, versatile graphics capabilities, and abundance of intrinsic functions, helps users focus on... more...
Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete problems.... more...
Algorithms and Theory of Computation Handbook, Second Edition: General Concepts and Techniques provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. Along with updating and revising many... more...
Algorithms and Theory of Computation Handbook, Second Edition: Special Topics and Techniques provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems.
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From the reviews: "Volumes III and IV complete L. Hormander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades...It is a superb book, which must be present in every mathematical... more... |
The author's...
More About
This Book
The author's aim is to introduce the concepts of higher mathematics while bringing the reader to a more thorough understanding of elementary mathematics. His lucid explanations cover these major areas:
OUR NUMBER SYSTEM: Sets, Cardinal Numbers, Order Relations, Real Numbers, Fields and Number Systems, more.
THEORY OF NUMBERS: Divisibility, Prime Numbers, Bases, Division Algorithm, Decimal Notations, Linear Congruences, more.
THEORY OF POLYNOMIALS: Rational Functions, Irreducible Polynomials, Functions, Limits, Continuity, Derivatives, more.
THEORY OF EQUATIONS: Zeros of a Polynomial, Change of a Variable, Number of Roots, Quartic Equations, more.
DETERMINANTS AND MATRICES: Historical Development, Permutations, Inversions, Transpositions, Cramer's Rule, more.
CONSTRUCTIONS: The Algebraic Viewpoint, Classical Constructions, Mechanical Angle Trisectors, Linkages, more.
GRAPHICAL REPRESENTATIONS: Euclidean and Complex Spaces, Conic Sections, Quadric Surfaces, Curve Tracing, more.
While intended for students who have previously studied college mathematics through calculus, this book has also been successfully used where calculus was not a prerequisite. It provides a very easily followed presentation and may also be used as an introductory or supplementary textbook. For prospective teachers of secondary mathematics, for students preparing for specialized advanced undergraduate courses in mathematics, and for the general reader in search of a firmer grasp of the essentials of algebra, there is no better, more helpful guide than Mes |
am an actuary and one of the topics covered in our syllabus was Finite Difference, which is basically the same as Discrete Math. Discrete math can cover many different topics and is a fairly advanced topic. I have assisted students at a high school on Discrete Math as it is taught there. |
State: Virginia
Grades: Secondary
Content: Mathematics
Standard Correlation Date: 9/03
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX09-02 Solve Linear Algebra I The student will solve multistep linear equations and
Equations With inequalities in one variable, solve literal equations (formulas)
One Unknown for a given variable, and apply these skills to solve practical
problems. Graphing calculators will be used to confirm
algebraic solutions.
MX11-04 Solve Linear Algebra I The student will solve multistep linear equations and
Inequalities in inequalities in one variable, solve literal equations (formulas)
One Unknown for a given variable, and apply these skills to solve practical
problems. Graphing calculators will be used to confirm
algebraic solutions.
PX37-02 Use Your Algebra I The student will solve multistep linear equations and
Calculator inequalities in one variable, solve literal equations (formulas)
Sparingly for a given variable, and apply these skills to solve practical
problems. Graphing calculators will be used to confirm
algebraic solutions.
PX17-01 Add or Subtract Algebra I The student will represent verbal quantitative situations
to Cancel Out algebraically and evaluate these expressions for given
Numbers replacement values of the variables. Students will choose an
appropriate computational technique, such as mental
mathematics, calculator, or paper and pencil.
PX17-02 Multiply or Algebra I The student will represent verbal quantitative situations
Divide to algebraically and evaluate these expressions for given
Cancel Out replacement values of the variables. Students will choose an
Numbers appropriate computational technique, such as mental
mathematics, calculator, or paper and pencil.
PX17-03 Plug In Algebra I The student will represent verbal quantitative situations
Numbers algebraically and evaluate these expressions for given
replacement values of the variables. Students will choose an
appropriate computational technique, such as mental
mathematics, calculator, or paper and pencil.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
PX17-04 Make the Algebra I The student will represent verbal quantitative situations
Center Look algebraically and evaluate these expressions for given
Like the replacement values of the variables. Students will choose an
Columns appropriate computational technique, such as mental
mathematics, calculator, or paper and pencil.
PX17-05 Eliminate Algebra I The student will represent verbal quantitative situations
Choices algebraically and evaluate these expressions for given
replacement values of the variables. Students will choose an
appropriate computational technique, such as mental
mathematics, calculator, or paper and pencil.
PX37-02 Use Your Algebra I The student will represent verbal quantitative situations
Calculator algebraically and evaluate these expressions for given
Sparingly replacement values of the variables. Students will choose an
appropriate computational technique, such as mental
mathematics, calculator, or paper and pencil.
MX09-01 Solve Equations Algebra I The student will justify steps used in simplifying expressions
by Substitution and solving equations and inequalities. Justifications will
include the use of concrete objects; pictorial representations;
and the properties of real numbers, equality, and inequality.
MX09-02 Solve Linear Algebra I The student will justify steps used in simplifying expressions
Equations With and solving equations and inequalities. Justifications will
One Unknown include the use of concrete objects; pictorial representations;
and the properties of real numbers, equality, and inequality.
MX09-03 Solve Quadratic Algebra I The student will justify steps used in simplifying expressions
Equations and solving equations and inequalities. Justifications will
include the use of concrete objects; pictorial representations;
and the properties of real numbers, equality, and inequality.
MX09-04 Solve Equations Algebra I The student will justify steps used in simplifying expressions
With More Than and solving equations and inequalities. Justifications will
One Unknown include the use of concrete objects; pictorial representations;
and the properties of real numbers, equality, and inequality.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX09-05 Use a Solution Algebra I The student will justify steps used in simplifying expressions
of One Equation and solving equations and inequalities. Justifications will
to Solve include the use of concrete objects; pictorial representations;
Another and the properties of real numbers, equality, and inequality.
MX09-06 General Algebra I The student will justify steps used in simplifying expressions
Quadratic and solving equations and inequalities. Justifications will
Equations include the use of concrete objects; pictorial representations;
Using a and the properties of real numbers, equality, and inequality.
Formula
MX11-01 Add or Subtract Algebra I The student will justify steps used in simplifying expressions
Quantities to and solving equations and inequalities. Justifications will
Inequalities include the use of concrete objects; pictorial representations;
and the properties of real numbers, equality, and inequality.
MX11-02 Multiply or Algebra I The student will justify steps used in simplifying expressions
Divide an and solving equations and inequalities. Justifications will
Inequality include the use of concrete objects; pictorial representations;
and the properties of real numbers, equality, and inequality.
MX11-03 Find the Algebra I The student will justify steps used in simplifying expressions
Product of Two and solving equations and inequalities. Justifications will
Numbers or include the use of concrete objects; pictorial representations;
Expressions in and the properties of real numbers, equality, and inequality.
Inequalities
MX11-04 Solve Linear Algebra I The student will justify steps used in simplifying expressions
Inequalities in and solving equations and inequalities. Justifications will
One Unknown include the use of concrete objects; pictorial representations;
and the properties of real numbers, equality, and inequality.
MX11-05 Solve Higher Algebra I The student will justify steps used in simplifying expressions
Order and solving equations and inequalities. Justifications will
Inequalities in include the use of concrete objects; pictorial representations;
One Unknown and the properties of real numbers, equality, and inequality.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX11-06 Use Inequalities Algebra I The student will justify steps used in simplifying expressions
to Compare and solving equations and inequalities. Justifications will
Fractions include the use of concrete objects; pictorial representations;
and the properties of real numbers, equality, and inequality.
MX66-01 Addition and Algebra I The student will use matrices to organize and manipulate data,
Subtraction including matrix addition, subtraction, and scalar multiplication.
Data will arise from business, industrial, and consumer
situations.
MX66-02 Scalar Algebra I The student will use matrices to organize and manipulate data,
Multiplication including matrix addition, subtraction, and scalar multiplication.
Data will arise from business, industrial, and consumer
situations.
MX109-02 Form and Algebra I The student will create and use tabular, symbolic, graphical,
Function verbal, and physical representations to analyze a given set of
data for the existence of a pattern, determine the domain and
range of relations, and identify the relations that are functions.
MX09-01 Solve Equations Algebra I The student will select, justify, and apply an appropriate
by Substitution technique to graph linear functions and linear inequalities in
two variables. Techniques will include slope-intercept, x- and y-
intercepts, graphing by transformation, and the use of the
graphing calculator.
MX09-02 Solve Linear Algebra I The student will select, justify, and apply an appropriate
Equations With technique to graph linear functions and linear inequalities in
One Unknown two variables. Techniques will include slope-intercept, x- and y-
intercepts, graphing by transformation, and the use of the
graphing calculator.
MX09-03 Solve Quadratic Algebra I The student will select, justify, and apply an appropriate
Equations technique to graph linear functions and linear inequalities in
two09-04 Solve Equations Algebra I The student will select, justify, and apply an appropriate
With More ThanMX09-05 Use a Solution Algebra I The student will select, justify, and apply an appropriate
of One Equation technique to graph linear functions and linear inequalities in
to Solve two variables. Techniques will include slope-intercept, x- and y-
Another intercepts, graphing by transformation, and the use of the
graphing calculator.
MX09-06 General Algebra I The student will select, justify, and apply an appropriate
Quadratic technique to graph linear functions and linear inequalities in
Equations two variables. Techniques will include slope-intercept, x- and y-
Using a intercepts, graphing by transformation, and the use of the
Formula graphing calculator.
MX11-01 Add or Subtract Algebra I The student will select, justify, and apply an appropriate
Quantities to technique to graph linear functions and linear inequalities in
Inequalities two variables. Techniques will include slope-intercept, x- and y-
intercepts, graphing by transformation, and the use of the
graphing calculator.
MX11-02 Multiply or Algebra I The student will select, justify, and apply an appropriate
Divide an technique to graph linear functions and linear inequalities in
Inequality two variables. Techniques will include slope-intercept, x- and y-
intercepts, graphing by transformation, and the use of the
graphing calculator.
MX11-03 Find the Algebra I The student will select, justify, and apply an appropriate
Product of Two technique to graph linear functions and linear inequalities in
Numbers or two variables. Techniques will include slope-intercept, x- and y-
Expressions in intercepts, graphing by transformation, and the use of the
Inequalities graphing calculator.
MX11-04 Solve Linear Algebra I The student will select, justify, and apply an appropriate
Inequalities in11-05 Solve Higher Algebra I The student will select, justify, and apply an appropriate
Order technique to graph linear functions and linear inequalities in
Inequalities in two variables. Techniques will include slope-intercept, x- and y-
One Unknown intercepts, graphing by transformation, and the use of the
graphing calculator.
MX11-06 Use Inequalities Algebra I The student will select, justify, and apply an appropriate
to Compare technique to graph linear functions and linear inequalities in
Fractions two variables. Techniques will include slope-intercept, x- and y-
intercepts, graphing by transformation, and the use of the
graphing calculator.
MX13-01 Number Lines Algebra I The student will select, justify, and apply an appropriate
technique to graph linear functions and linear inequalities in
two variables. Techniques will include slope-intercept, x- and y-
intercepts, graphing by transformation, and the use of the
graphing calculator.
PX37-02 Colons and Algebra I The student will select, justify, and apply an appropriate
Semicolons technique to graph linear functions and linear inequalities in
two variables. Techniques will include slope-intercept, x- and y-
intercepts, graphing by transformation, and the use of the
graphing calculator.
MX13-08 Find the Slope Algebra I The student will determine the slope of a line when given an
equation55-02 Solve Systems Algebra I The student will determine the slope of a line when given an
of Linear equation of the line, the graph of the line, or two points on the
EquationsSkill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX56-02 Solve a Line- Algebra I The student will determine the slope of a line when given an
Parabola equation of the line, the graph of the line, or two points on the
SystemMX13-03 Distance Algebra I The student will determine the slope of a line when given an
Between Two equation of the line, the graph of the line, or two points on the
Points109-01 Time for a Algebra I The student will determine the slope of a line when given an
Change equationPX37-02 Use Your Algebra I The student will determine the slope of a line when given an
Calculator equation of the line, the graph of the line, or two points on the
Sparingly13-01 Number Lines Algebra I The student will write an equation of a line when given the
graph of the line, two points on the line, or the slope and a
point on the line.
MX13-05 Plot the Graph Algebra I The student will write an equation of a line when given the
of a Line graph of the line, two points on the line, or the slope and a
point on the line.
MX09-04 Solve Equations Algebra I The student will solve systems of two linear equations in two
With More Than variables both algebraically and graphically and apply these
One Unknown techniques to solve practical problems. Graphing calculators
will be used both as a primary tool for solution and to confirm
an algebraic solution.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
PX37-02 Use Your Algebra I The student will solve systems of two linear equations in two
Calculator variables both algebraically and graphically and apply these
Sparingly techniques to solve practical problems. Graphing calculators
will be used both as a primary tool for solution and to confirm
an algebraic solution.
MX12-01 Exponents Algebra I The student will apply the laws of exponents to perform
operations on expressions with integral exponents, using
scientific notation when appropriate.
MX08-01 Find Common Algebra I The student will factor completely first- and second-degree
Factors binomials and trinomials in one or two variables. The graphing
calculator will be used as a tool for factoring and for confirming
algebraic factorizations.
MX08-03 Factor Algebra I The student will factor completely first- and second-degree
Trinomials into binomials and trinomials in one or two variables. The graphing
Binomials calculator will be used as a tool for factoring and for confirming
algebraic factorizations.
PX37-02 Use Your Algebra I The student will factor completely first- and second-degree
Calculator binomials and trinomials in one or two variables. The graphing
Sparingly calculator will be used as a tool for factoring and for confirming
algebraic factorizations.
MX21-04 Approximate Algebra I The student will express the square root of a whole number in
Square Roots simplest radical form and approximate square roots to the
nearest tenth.
MX09-03 Solve Quadratic Algebra I The student will solve quadratic equations in one variable both
Equations algebraically and graphically. Graphing calculators will be used
both as a primary tool in solving problems and to verify
algebraic solutions.
MX109-02 Form and Algebra I The student will, given a rule, find the values of a function for
Function elements in its domain and locate the zeros of the function
both algebraically and with a graphing calculator. The value of
f(x) will be related to the ordinate on the graph.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
PX37-02 Use Your Algebra I The student will, given a rule, find the values of a function for
Calculator elements in its domain and locate the zeros of the function
Sparingly both algebraically and with a graphing calculator. The value of
f(x) will be related to the ordinate on the graph.
MX111-01 Understand Algebra I The student will, given a set of data points, write an equation
Scatter plot for a line of best fit and use the equation to make predictions.
Data
MX49-01 Box-and- Algebra I The student will compare and contrast multiple one-variable
Whisker and data sets, using statistical techniques that include measures of
Stem-and-Leaf central tendency, range, and box-and-whisker graphs.
Plots
PX02-01 Translate The student will construct and judge the Geometry translating a short verbal argument into symbolic form;
Words into validity of a logical argument consisting
Math of a set of premises and a conclusion.
This will include
MX25-04 Venn Diagrams The student will construct and judge the Geometry using Venn diagrams to represent set relationships; and
validity of a logical argument consisting
of a set of premises and a conclusion.
This will include
MX13-01 Number Lines The student will use pictorial Geometry investigating and using formulas for finding distance, midpoint,
representations, including computer and slope;
software, constructions, and coordinate
methods, to solve problems involving
symmetry and transformation. This will
include
MX50-01 Translation and The student will use pictorial Geometry determining whether a figure has been translated, reflected, or
Reflection representations, including computer rotated.
software, constructions, and coordinate
methods, to solve problems involving
symmetry and transformation. This will
include
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX50-02 Dilation and The student will use pictorial Geometry determining whether a figure has been translated, reflected, or
Rotation representations, including computer rotated.
software, constructions, and coordinate
methods, to solve problems involving
symmetry and transformation. This will
include
MX54-01 The Language The student will use pictorial Geometry The student will solve practical problems involving
of Geometry54-02 Congruence The student will use pictorial Geometry The student will solve practical problems involving
and Similarity16-06 Regular and The student will use pictorial Geometry The student will solve practical problems involving
Irregular representations, including computer complementary, supplementary, and congruent angles that
Polygons and software, constructions, and coordinate include vertical angles, angles formed when parallel lines are
Other Shapes methods, to solve problems involving cut by a transversal, and angles in polygons.
symmetry and transformation. This will
include
MX54-01 The Language The student will Geometry investigate and identify congruence and similarity relationships
of Geometry between triangles; and
MX54-02 Congruence The student will Geometry investigate and identify congruence and similarity relationships
and Similarity between triangles; and
MX54-01 The Language The student will Geometry prove two triangles are congruent or similar, given information
of Geometry in the form of a figure or statement, using algebraic and
coordinate as well as deductive proofs.
MX54-02 Congruence The student will Geometry prove two triangles are congruent or similar, given information
and Similarity in the form of a figure or statement, using algebraic and
coordinate as well as deductive proofs.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX15-01 Triangle Basics The student will Geometry prove two triangles are congruent or similar, given information
in the form of a figure or statement, using algebraic and
coordinate as well as deductive proofs.
MX15-02 Perpendicular The student will Geometry prove two triangles are congruent or similar, given information
Bisectors in the form of a figure or statement, using algebraic and
coordinate as well as deductive proofs.
MX15-03 Equilateral The student will Geometry prove two triangles are congruent or similar, given information
Triangles in the form of a figure or statement, using algebraic and
coordinate as well as deductive proofs.
MX15-04 Altitude The student will Geometry prove two triangles are congruent or similar, given information
in the form of a figure or statement, using algebraic and
coordinate as well as deductive proofs.
MX15-05 Area and The student will Geometry prove two triangles are congruent or similar, given information
Perimeter of in the form of a figure or statement, using algebraic and
Triangles coordinate as well as deductive proofs.
MX15-06 Area and The student will Geometry prove two triangles are congruent or similar, given information
Perimeter of in the form of a figure or statement, using algebraic and
Right Triangles coordinate as well as deductive proofs.
MX15-07 Area and The student will Geometry prove two triangles are congruent or similar, given information
Perimeter of in the form of a figure or statement, using algebraic and
Equilateral coordinate as well as deductive proofs.
Triangles
MX15-01 Triangle Basics02 Perpendicular The student will Geometry The student, given information concerning the lengths of sides
Bisectors and/or measures of angles, will apply the triangle inequality
properties to determine whether a triangle exists and to order
sides and angles. These concepts will be considered in the
context of practical situations.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX15-03 Equilateral The student will Geometry The student, given information concerning the lengths of sides
Triangles and/or measures of angles, will apply the triangle inequality
properties to determine whether a triangle exists and to order
sides and angles. These concepts will be considered in the
context of practical situations.
MX15-04 Altitude05 Area and The student will Geometry The student, given information concerning the lengths of sides
Perimeter of and/or measures of angles, will apply the triangle inequality
Triangles properties to determine whether a triangle exists and to order
sides and angles. These concepts will be considered in the
context of practical situations.
MX15-06 Area and The student will Geometry The student, given information concerning the lengths of sides
Perimeter of and/or measures of angles, will apply the triangle inequality
Right Triangles properties to determine whether a triangle exists and to order
sides and angles. These concepts will be considered in the
context of practical situations.
MX15-07 Area and The student will Geometry The student, given information concerning the lengths of sides
Perimeter of and/or measures of angles, will apply the triangle inequality
Equilateral properties to determine whether a triangle exists and to order
Triangles sides and angles. These concepts will be considered in the
context of practical situations.
MX15-02 Perpendicular The student will Geometry The student will solve practical problems involving right
Bisectors triangles by using the Pythagorean Theorem, properties of
special right triangles, and right triangle trigonometry.
Solutions will be expressed in radical form or as decimal
approximations.
MX16-02 Rectangles16-04 Squares04-01 Multiply and The student will Geometry The student will solve practical problems involving right
Divide by triangles by using the Pythagorean Theorem, properties of
Powers of 10 special right triangles, and right triangle trigonometry.
Solutions will be expressed in radical form or as decimal
approximations.
MX04-02 Convert The student will Geometry The student will solve practical problems involving right
Between triangles by using the Pythagorean Theorem, properties of
Decimals and special right triangles, and right triangle trigonometry.
Fractions Solutions will be expressed in radical form or as decimal
approximations.
MX04-03 Perform The student will Geometry The student will solve practical problems involving right
Arithmetic with triangles by using the Pythagorean Theorem, properties of
Decimals special right triangles, and right triangle trigonometry.
Solutions will be expressed in radical form or as decimal
approximations.
MX04-04 Scientific The student will Geometry The student will solve practical problems involving right
Notation triangles by using the Pythagorean Theorem, properties of
special right triangles, and right triangle trigonometry.
Solutions will be expressed in radical form or as decimal
approximations.
MX21-01 Round Off21-02 Approximate The student will Geometry The student will solve practical problems involving right
Sums triangles21-03 Approximate The student will Geometry The student will solve practical problems involving right
Products triangles by using the Pythagorean Theorem, properties of
special right triangles, and right triangle trigonometry.
Solutions will be expressed in radical form or as decimal
approximations.
MX21-04 Approximate The student will Geometry The student will solve practical problems involving right
Square Roots triangles by using the Pythagorean Theorem, properties of
special right triangles, and right triangle trigonometry.
Solutions will be expressed in radical form or as decimal
approximations.
MX40-01 Angles and The student will Geometry investigate and identify properties of quadrilaterals involving
Trigonometric opposite sides and angles, consecutive sides and angles, and
Functions diagonals;
MX14-02 Angles The student will Geometry investigate and identify properties of quadrilaterals involving
opposite sides and angles, consecutive sides and angles, and
diagonals;
MX14-03 Complimentary The student will Geometry investigate and identify properties of quadrilaterals involving
and opposite sides and angles, consecutive sides and angles, and
Supplementary diagonals;
Angles
MX14-04 Vertical Angles The student will Geometry investigate and identify properties of quadrilaterals involving
opposite sides and angles, consecutive sides and angles, and
diagonals;
MX16-01 Parallelograms The student will Geometry prove these properties of quadrilaterals, using algebraic and
coordinate methods as well as deductive reasoning; and
MX16-01 Parallelograms The student will Geometry use properties of quadrilaterals to solve practical problems.
MX16-06 Regular and The student will Geometry The student will use measures of interior and exterior angles
Irregular of polygons to solve problems. Tessellations and tiling
Polygons and problems will be used to make connections to art,
Other Shapes construction, and nature.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX18-01 Tangents to a The student will Geometry The student will investigate and solve practical problems
Circle02 Central Angles The student will Geometry The student will investigate and solve practical problems
involving03 Inscribed The student will Geometry The student will investigate and solve practical problems
Angles04 Two Tangents The student will Geometry The student will investigate and solve practical problems
to a Circle05 Area and The student will Geometry The student will investigate and solve practical problems
Circumference involving circles, using properties of angles, arcs, chords,
of a Circle tangents, and secants. Problems will include finding arc length
and the area of a sector, and may be drawn from applications
of architecture, art, and construction.
MX15-02 Perpendicular The student will Geometry The student will construct a line segment congruent to a given
Bisectors line segment, the bisector of a line segment, a perpendicular
to a given line from a point not on the line, a perpendicular to a
given line at a point on the line, the bisector of a given angle,
and an angle congruent to a given angle.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX110-01 Change a The student will Geometry The student will make a model of a three-dimensional figure
Dimension from a two-dimensional drawing and make a two-dimensional
representation of a three-dimensional object. Models and
representations will include scale drawings, perspective
drawings, blueprints, or computer simulations.
MX110-01 Change a The student will Geometry The student will use formulas for surface area and volume of
Dimension three-dimensional objects to solve practical problems.
Calculators will be used to find decimal approximations for
results.
PX37-02 Use Your The student will Geometry The student will use formulas for surface area and volume of
Calculator three-dimensional objects to solve practical problems.
Sparingly Calculators will be used to find decimal approximations for
results.
MX110-01 Change a The student will Geometry determine how changes in one dimension of an object affect
Dimension area and/or volume of the object.
MX01-01 Fractions and The student will Algebra II add, subtract, multiply, divide, and simplify radical expressions
Mixed Numbers containing positive rational numbers and variables and
expressions containing rational exponents; and
MX01-02 Equivalent The student will Algebra II add, subtract, multiply, divide, and simplify radical expressions
Fractions containing positive rational numbers and variables and
expressions containing rational exponents; and
MX01-03 Multiply and The student will Algebra II add, subtract, multiply, divide, and simplify radical expressions
Divide Fractions containing positive rational numbers and variables and
expressions containing rational exponents; and
MX01-04 Add and The student will Algebra II add, subtract, multiply, divide, and simplify radical expressions
Subtract containing positive rational numbers and variables and
Fractions expressions containing rational exponents; and
MX12-01 Exponents The student will Algebra II write radical expressions as expressions containing rational
exponents and vice versa.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX20-04 Absolute Values The student will Algebra II The student will solve absolute value equations and
inequalities graphically and algebraically. Graphing calculators
will be used as a primary method of solution and to verify
algebraic solutions.
MX11-01 Add or Subtract The student will Algebra II The student will solve absolute value equations and
Quantities to The student will solve absolute value equations and
Divide an inequalities graphically and algebraically. Graphing calculators
Inequality will be used as a primary method of solution and to verify
algebraic solutions.
MX11-03 Find the The student will Algebra II The student will solve absolute value equations and
Product of Two inequalities graphically and algebraically. Graphing calculators
Numbers or will be used as a primary method of solution and to verify
Expressions in algebraic solutions.
Inequalities
MX11-04 Solve Linear The student will Algebra II The student will solve absolute value equations and
Inequalities in inequalities graphically and algebraically. Graphing calculators
One Unknown will be used as a primary method of solution and to verify
algebraic solutions.
MX11-05 Solve Higher The student will Algebra II The student will solve absolute value equations and
Order The student will solve absolute value equations and
to Compare inequalities graphically and algebraically. Graphing calculators
Fractions will be used as a primary method of solution and to verify
algebraic solutions.
PX37-02 Use Your The student will Algebra II The student will solve absolute value equations and
Calculator inequalities graphically and algebraically. Graphing calculators
Sparingly will be used as a primary method of solution and to verify
algebraic solutions.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX08-01 Find Common The student will Algebra II The student will identify and factor completely polynomials
Factors representing the difference of squares, perfect square
trinomials, the sum and difference of cubes, and general
trinomials.
MX09-03 Solve Quadratic The student will Algebra II The student will select, justify, and apply a technique to solve a
Equations quadratic equation over the set of complex numbers. Graphing
calculators will be used for solving and for confirming the
algebraic solutions.
PX37-02 Use Your The student will Algebra II The student will select, justify, and apply a technique to solve a
Calculator The student will solve equations containing rational
by Substitution expressions and equations containing radical expressions
algebraically and graphically. Graphing calculators will be used
for solving and for confirming the algebraic solutions.
MX09-02 Solve Linear The student will Algebra II The student will solve equations containing rational
Equations With The student will solve equations containing rational
Equations expressions and equations containing radical expressions
algebraically and graphically. Graphing calculators will be used
for solving and for confirming the algebraic solutions.
MX09-04 Solve Equations The student will Algebra II The student will solve equations containing rational
With More Than expressions and equations containing radical expressions
One Unknown algebraically and graphically. Graphing calculators will be used
for solving and for confirming the algebraic solutions.
MX09-05 Use a Solution The student will Algebra II The student will solve equations containing rational
of One Equation expressions and equations containing radical expressions
to Solve algebraically and graphically. Graphing calculators will be used
Another for solving and for confirming the algebraic solutions.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX09-06 General The student will Algebra II The student will solve equations containing rational
Quadratic The student will solve equations containing rational
Calculator expressions and equations containing radical expressions
Sparingly algebraically and graphically. Graphing calculators will be used
for solving and for confirming the algebraic solutions.
MX55-01 Solve Systems The student will Algebra II The student will recognize multiple representations of
of Linear functions (linear, quadratic, absolute value, step, and
Equations exponential functions) and convert between a graph, a table,
Algebraically and symbolic form. A transformational approach to graphing
will be employed through the use of graphing calculators.
MX55-02 Solve Systems The student will Algebra II The student will recognize multiple representations of
of Linear functions (linear, quadratic, absolute value, step, and
Equations exponential functions) and convert between a graph, a table,
Graphically and symbolic form. A transformational approach to graphing
will be employed through the use of graphing calculators.
MX56-01Algebraically and symbolic form. A transformational approach to graphing
will be employed through the use of graphing calculators.
MX56-02Graphically and symbolic form. A transformational approach to graphing
will be employed through the use of graphing calculators.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX56-03 Solve a Line- The student will Algebra II The student will recognize multiple representations of
Circle System functions (linear, quadratic, absolute value, step, and
Algebraically exponential functions) and convert between a graph, a table,
and symbolic form. A transformational approach to graphing
will be employed through the use of graphing calculators.
MX56-04 Solve a Line- The student will Algebra II The student will recognize multiple representations of
Circle System functions (linear, quadratic, absolute value, step, and
Graphically exponential functions) and convert between a graph, a table,
and symbolic form. A transformational approach to graphing
will be employed through the use of graphing calculators.
MX20-04 Absolute Values The student will Algebra II The student will recognize multiple representations of
functionsMX23-01 Tables and The student will Algebra II The student will recognize multiple representations of
Charts The student will recognize multiple representations of
Calculator The student will find the domain, range, zeros, and inverse of
Change The student will find the domain, range, zeros, and inverse of
Function01 Exponents02 Roots03 Evaluate The student will Algebra II The student will find the domain, range, zeros, and inverse of
Expressions a function; the value of a function for a given element in its
Involving domain; and the composition of multiple functions. Functions
Exponents will include exponential, logarithmic, and those that have
domains and ranges that are limited and/or discontinuous. The
graphing calculator will be used as a tool to assist in
investigation of functions.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX63-01 Bases and The student will Algebra II The student will find the domain, range, zeros, and inverse of
Powers X-Intercept The student will Algebra II The student will investigate and describe through the use of
graphs the relationships between the solution of an equation,
zero of a function, x-intercept of a graph, and factors of a
polynomial expression.
MX66-01 Addition and The student will Algebra II The student will use matrix multiplication to solve practical
Subtraction problems. Graphing calculators or computer programs with
matrix capabilities will be used to find the product.
MX66-02 Scalar The student will Algebra II The student will use matrix multiplication to solve practical
Multiplication problems. Graphing calculators or computer programs with
matrix capabilities will be used to find the product.
PX37-02 Use Your The student will Algebra II The student will use matrix multiplication to solve practical
Calculator problems. Graphing calculators or computer programs with
Sparingly matrix capabilities will be used to find the product.
MX55-01 Solve Systems The student will Algebra II The student will represent problem situations with a system of
of Linear The student will represent problem situations with a system of
of Linear linear equations and solve the system, using the inverse
Equations matrix method. Graphing calculators or computer programs
Graphically with matrix capability will be used to perform computations.
PX37-02 Use Your The student will Algebra II The student will represent problem situations with a system of
Calculator linear equations and solve the system, using the inverse
Sparingly matrix method. Graphing calculators or computer programs
with matrix capability will be used to perform computations.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX57-01 Solve Systems The student will Algebra II The student will solve practical problems, using systems of
of Inequalities linear inequalities and linear programming, and describe the
Algebraically results both orally and in writing. A graphing calculator will be
used to facilitate solutions to linear programming problems.
MX57-02 Solve Systems The student will Algebra II The student will solve practical problems, using systems of
of Inequalities linear inequalities and linear programming, and describe the
Graphically results both orally and in writing. A graphing calculator will be
used to facilitate solutions to linear programming problems.
PX37-02 Use Your The student will Algebra II The student will solve practical problems, using systems of
Calculator linear inequalities and linear programming, and describe the
Sparingly results both orally and in writing. A graphing calculator will be
used to facilitate solutions to linear programming problems.
MX56-01Algebraically used as a tool to visualize graphs and predict the number of
solutions.
MX56-02Graphically used as a tool to visualize graphs and predict the number of
solutions.
MX56-03 Solve a Line- The student will Algebra II The student will solve nonlinear systems of equations,
Circle System including linear-quadratic and quadratic-quadratic,
Algebraically algebraically and graphically. The graphing calculator will be
used as a tool to visualize graphs and predict the number of
solutions.
MX56-04 Solve a Line- The student will Algebra II The student will solve nonlinear systems of equations,
Circle System including linear-quadratic and quadratic-quadratic,
Graphically algebraically and graphically. The graphing calculator will be
used as a tool to visualize graphs and predict the number of
solutions.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
PX37-02 Use Your The student will Algebra II The student will solve nonlinear systems of equations,
Calculator56-01Algebraically sections, using transformations.
MX56-02 The student will identify conic sections (circle, ellipse,
Circle System The student will identify conic sections (circle, ellipse,
Circle System The student will identify conic sections (circle, ellipse,
Reflection The student will identify conic sections (circle, ellipse,
Rotation The student will collect and analyze data to make predictions
Scatter plot and solve practical problems. Graphing calculators will be
Data used55-01 Solve Systems The student will Algebra II The student will collect and analyze data to make predictions
of Linear and solve practical problems. Graphing calculators will be
Equations used to investigate scatterplots and to determine the equation
Algebraically for a curve of best fit. Models will include linear, quadratic,
exponential, and logarithmic functions.
MX55-02 Solve Systems The student will Algebra II The student will collect and analyze data to make predictions
of Linear and solve practical problems. Graphing calculators will be
Equations used to investigate scatterplots and to determine the equation
Graphically for a curve of best fit. Models will include linear, quadratic,
exponential, and logarithmic functions.
MX58-03 Use Quadratic The student will Algebra II The student will collect and analyze data to make predictions
Equations01 Exponents02 Roots12-03 Evaluate The student will Algebra II The student will collect and analyze data to make predictions
Expressions and solve practical problems. Graphing calculators will be
Involving used to investigate scatterplots and to determine the equation
Exponents for a curve of best fit. Models will include linear, quadratic,
exponential, and logarithmic functions.
MX63-01 Bases and The student will Algebra II The student will collect and analyze data to make predictions
Powers40-01 Angles and Trigonometry The student will use the definitions of the six trigonometric
Identities and Trigonometry The student, given the value of one trigonometric function, will
Trigonometric find the values of the other trigonometric functions. Properties
Functions of the unit circle and definitions of circular functions will be
applied.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX40-01 Angles and The student will Trigonometry The student will find without the aid of a calculating utility the
Trigonometric values of the trigonometric functions of the special angles and
Functions their related angles as found in the unit circle. This will include
converting radians to degrees and vice versa.
MX40-01 Angles and The student will Trigonometry The student will find with the aid of a calculator the value of
Trigonometric any trigonometric function and inverse trigonometric function.
Functions
MX40-02 Trigonometric The student will Trigonometry The student will verify basic trigonometric identities and make
Identities and substitutions, using the basic identities.
Formulas
MX110-01 Change a The student, given one of the six Trigonometry state the domain and the range of the function;
Dimension trigonometric functions in standard form
will
MX110-02 Change a The student, given one of the six Trigonometry state the domain and the range of the function;
Variable trigonometric functions in standard form
will
MX40-03 Periodicity of The student, given one of the six Trigonometry The student will identify the domain and range of the inverse
Trigonometric trigonometric functions in standard form trigonometric functions and recognize the graphs of these
Functions will functions. Restrictions on the domains of the inverse
trigonometric functions will be included.
MX15-01 Triangle Basics02 Perpendicular The student, given one of the six Trigonometry The student will identify, create, and solve practical problems
Bisectors trigonometric functions in standard form Trigonometry The student will identify, create, and solve practical problems
Triangles trigonometric functions in standard form04 Altitude Trigonometry The student will identify, create, and solve practical problems
Perimeter of trigonometric functions in standard form Trigonometry The student will identify, create, and solve practical problems
Perimeter of trigonometric functions in standard form Trigonometry The student will identify, create, and solve practical problems
Perimeter of trigonometric functions in standard form involving triangles. Techniques will include using the
Equilateral will trigonometric functions, the Pythagorean Theorem, the Law of
Triangles Sines, and the Law of Cosines.
MX20-04 Absolute Values The student will Algebra II and The student will solve absolute value equations and
Trigonometry inequalities graphically and algebraically. Graphing calculators
will be used as a primary method of solution and to verify
algebraic solutions.
MX11-01 Add or Subtract The student will Algebra II and The student will solve absolute value equations and
Quantities to Trigonometry and The student will solve absolute value equations and
Divide an Trigonometry inequalities graphically and algebraically. Graphing calculators
Inequality will be used as a primary method of solution and to verify
algebraic solutions.
MX11-03 Find the The student will Algebra II and The student will solve absolute value equations and
Product of Two Trigonometry inequalities graphically and algebraically. Graphing calculators
Numbers or will be used as a primary method of solution and to verify
Expressions in algebraic solutions.
Inequalities
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX11-04 Solve Linear The student will Algebra II and The student will solve absolute value equations and
Inequalities in Trigonometry inequalities graphically and algebraically. Graphing calculators
One Unknown will be used as a primary method of solution and to verify
algebraic solutions.
MX11-05 Solve Higher The student will Algebra II and The student will solve absolute value equations and
Order Trigonometry and The student will solve absolute value equations and
to Compare Trigonometry inequalities graphically and algebraically. Graphing calculators
Fractions will be used as a primary method of solution and to verify
algebraic solutions.
MX09-03 Solve Quadratic The student will Algebra II and The student will select, justify, and apply a technique to solve a
Equations Trigonometry quadratic equation over the set of complex numbers. Graphing
calculators will be used for solving and for confirming the
algebraic solutions.
PX37-02 Use Your The student will Algebra II and The student will select, justify, and apply a technique to solve a
Calculator Trigonometry and The student will solve equations containing rational
by Substitution Trigonometry expressions and equations containing radical expressions
algebraically and graphically. Graphing calculators will be used
for solving and for confirming the algebraic solutions.
MX09-02 Solve Linear The student will Algebra II and The student will solve equations containing rational
Equations With Trigonometry and The student will solve equations containing rational
Equations Trigonometry expressions and equations containing radical expressions
algebraically and graphically. Graphing calculators will be used
for solving and for confirming the algebraic solutions.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX09-04 Solve Equations The student will Algebra II and The student will solve equations containing rational
With More Than Trigonometry expressions and equations containing radical expressions
One Unknown algebraically and graphically. Graphing calculators will be used
for solving and for confirming the algebraic solutions.
MX09-05 Use a Solution The student will Algebra II and The student will solve equations containing rational
of One Equation Trigonometry expressions and equations containing radical expressions
to Solve algebraically and graphically. Graphing calculators will be used
Another for solving and for confirming the algebraic solutions.
MX09-06 General The student will Algebra II and The student will solve equations containing rational
Quadratic Trigonometry and The student will solve equations containing rational
Calculator Trigonometry expressions and equations containing radical expressions
Sparingly algebraically and graphically. Graphing calculators will be used
for solving and for confirming the algebraic solutions.
MX109-01 Time for a The student will Algebra II and The student will recognize multiple representations of
Change Trigonometry and The student will recognize multiple representations of
Calculator Trigonometry and The student will find the domain, range, zeros, and inverse of
Change and The student will find the domain, range, zeros, and inverse of
FunctionPX37-02 Use Your The student will Algebra II and The student will find the domain, range, zeros, and inverse of
Calculator Trigonometry a function; the value of a function for a given element in its
Sparingly domain student will Algebra II and The student will investigate and describe through the use of
Trigonometry graphs the relationships between the solution of an equation,
The X-Intercept
zero of a function, x-intercept of a graph, and factors of a
polynomial expression.
MX66-01 The student will Algebra II and The student will use matrix multiplication to solve practical
Addition and
Trigonometry problems. Graphing calculators or computer programs with
Subtraction
matrix capabilities will be used to find the product.
MX66-02 The student will Algebra II and The student will use matrix multiplication to solve practical
Scalar
Trigonometry problems. Graphing calculators or computer programs with
Multiplication
matrix capabilities will be used to find the product.
PX37-02 Use Your The student will Algebra II and The student will use matrix multiplication to solve practical
Calculator Trigonometry problems. Graphing calculators or computer programs with
Sparingly matrix capabilities will be used to find the product.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX55-01Graphically with matrix capability will be used to perform computations.
MX53-01 Recognize The student will Algebra II and The student will represent problem situations with a system of
Famous Trigonometry linear equations and solve the system, using the inverse
Patterns matrix method. Graphing calculators or computer programs
with matrix capability will be used to perform computations.
MX53-02 Solve Pattern The student will Algebra II and The student will represent problem situations with a system of
Problems Trigonometry linear equations and solve the system, using the inverse
matrix method. Graphing calculators or computer programs
with matrix capability will be used to perform computations.
PX37-02 Use Your The student will Algebra II and The student will represent problem situations with a system of
Calculator Trigonometry linear equations and solve the system, using the inverse
Sparingly matrix method. Graphing calculators or computer programs
with matrix capability will be used to perform computations.
MX11-04 Solve Linear The student will Algebra II and The student will solve practical problems, using systems of
Inequalities in Trigonometry linear inequalities and linear programming, and describe the
One Unknown results both orally and in writing. A graphing calculator will be
used to facilitate solutions to linear programming problems.
PX02-01 Translate The student will Algebra II and The student will solve practical problems, using systems of
Words into Trigonometry linear inequalities and linear programming, and describe the
Math results both orally and in writing. A graphing calculator will be
used to facilitate solutions to linear programming problems.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
PX37-02 Use Your The student will Algebra II and The student will solve practical problems, using systems of
Calculator Trigonometry linear inequalities and linear programming, and describe the
Sparingly results both orally and in writing. A graphing calculator will be
used to facilitate solutions to linear programming problems06 General The student will Algebra II and The student will solve nonlinear systems of equations,
Quadratic Trigonometry including linear-quadratic and quadratic-quadratic,
Equations algebraically and graphically. The graphing calculator will be
Using a used as a tool to visualize graphs and predict the number of
Formula solutions.
MX58-03 Use predict the number of
solutions.
PX37-02 Use Your The student will Algebra II and The student will solve nonlinear systems of equations,
Calculator Trigonometry12-01 ExponentsSkill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX12-02 RootsMX12-03 Evaluate The student will Algebra II and The student will recognize the general shape of polynomial,
Expressions Trigonometry exponential, and logarithmic functions. The graphing calculator
Involving will be used as a tool to investigate the shape and behavior of
Exponents these functions.
MX63-01 Bases and The student will Algebra II and The student will recognize the general shape of polynomial,
Powers Trigonometry exponential, and logarithmic functions. The graphing calculator
will be used as a tool to investigate the shape and behavior of
these functions.
PX37-02 Use Your The student will Algebra II and The student will recognize the general shape of polynomial,
Calculator Trigonometry exponential, and logarithmic functions. The graphing calculator
Sparingly will be used as a tool to investigate the shape and behavior of
these functions.
MX04-03 Perform The student will Algebra II and The student will investigate and apply the properties of
Arithmetic with Trigonometry arithmetic and geometric sequences and series to solve
Decimals practical problems, including writing the first n terms, finding
the nth term, and evaluating summation formulas. Notation will
n.
MX04-04 Scientific The student will Algebra II and The student will investigate and apply the properties of
Notation Trigonometry arithmetic and geometric sequences and series to solve
practical problems, including writing the first n terms, finding
the nth term, and evaluating summation formulas. Notation will
n.
PX12-01 Simplify to The student will Algebra II and The student will perform operations on complex numbers and
Avoid Tedious Trigonometry express the results in simplest form. Simplifying results will
Calculations involve using patterns of the powers of i.
MX56-01Algebraically sections, using transformations.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX56-02 and The student will identify conic sections (circle, ellipse,
Reflection Trigonometry and The student will identify conic sections (circle, ellipse,
Rotation Trigonometry and The student will collect and analyze data to make predictions
Scatter plot Trigonometry and solve practical problems. Graphing calculators will be
Data used to investigate scatter plots and to determine the equation
for a curve of best fit. Models will include linear, quadratic,
exponential, and logarithmic functions.
MX109-01 Time for a The student will Algebra II and The student will collect and analyze data to make predictions
Change109-02 Form and The student will Algebra II and The student will collect and analyze data to make predictions
FunctionPX37-02 Use Your The student will Algebra II and The student will collect and analyze data to make predictions
Calculator Trigonometry and solve practical problems. Graphing calculators will be
Sparingly used to investigate scatter plots and to determine the equation
for a curve of best fit. Models will include linear, quadratic,
exponential, and logarithmic functions.
MX40-01 Angles and Algebra II and The student will use the definitions of the six trigonometric
Identities and TrigonometrySkill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX40-02 Trigonometric The student will Algebra II and The student, given the value of one trigonometric function, will
Identities and Trigonometry find the values of the other trigonometric functions. Properties
Formulas of the unit circle and definitions of circular functions will be
applied.
MX40-03 Periodicity ofMX40-01 Angles and The student will Algebra II and The student will find without the aid of a calculating utility the
Trigonometric Trigonometry values of the trigonometric functions of the special angles and
Functions their related angles as found in the unit circle. This will include
converting radians to degrees and vice versa.
PX37-02 Use Your The student will Algebra II and The student will find with the aid of a calculator the value of
Calculator Trigonometry any trigonometric function and inverse trigonometric function.
Sparingly
MX40-02 Trigonometric The student will Algebra II and The student will verify basic trigonometric identities and make
Identities and Trigonometry substitutions, using the basic identities.
Formulas
MX109-01 Time for a The student, given one of the six Algebra II and state the domain and the range of the function;
Change trigonometric functions in standard form, Trigonometry
will
MX109-02 Form and The student, given one of the six Algebra II and state the domain and the range of the function;
Function trigonometric functions in standard form, Trigonometry
will
MX40-03 Periodicity of The student, given one of the six Algebra II and sketch the graph of the function by using transformations for at
Trigonometric trigonometric functions in standard form, Trigonometry least a one-period interval. The graphing calculator will be
Functions will used to investigate the effect of changing A, B, C, and D on
the graph of a trigonometric function.
PX37-02 Use Your The student, given one of the six Algebra II and sketch the graph of the function by using transformations for at
Calculator trigonometric functions in standard form, Trigonometry least a one-period interval. The graphing calculator will be
Sparingly will used to investigate the effect of changing A, B, C, and D on
the graph of a trigonometric function.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX40-01 Angles and The student, given one of the six Algebra II and The student will identify the domain and range of the inverse
Trigonometric trigonometric functions in standard form, Trigonometry trigonometric functions and recognize the graphs of these
Functions will functions. Restrictions on the domains of the inverse
trigonometric functions will be included.
MX109-02 Form and The student, given one of the six Algebra II and The student will identify the domain and range of the inverse
Function trigonometric functions in standard form, Trigonometry trigonometric functions and recognize the graphs of these
will functions. Restrictions on the domains of the inverse
trigonometric functions will be included.
MX57-01Algebraically will solve basic trigonometric inequalities. Graphing utilities will be
used to solve equations, check for reasonableness of results,
and verify algebraic solutions.
MX57-02Graphically will solve basic trigonometric inequalities. Graphing utilities will be
used to solve equations, check for reasonableness of results,
and verify algebraic solutions.
MX109-01 Time for a The student, given one of the six Algebra II and The student will solve trigonometric equations that include
Change109-02 Form and The student, given one of the six Algebra II and The student will solve trigonometric equations that include
Function15-01 Triangle Basics02 Perpendicular The student, given one of the six Algebra II and The student will identify, create, and solve practical problems
Bisectors Algebra II and The student will identify, create, and solve practical problems
Triangles04 Altitude Algebra II and The student will identify, create, and solve practical problems
Perimeter of trigonometric functions in standard form, Trigonometry Algebra II and The student will identify, create, and solve practical problems
Perimeter of trigonometric functions in standard form, Trigonometry Algebra II and The student will identify, create, and solve practical problems
Perimeter of trigonometric functions in standard form, Trigonometry involving triangles. Techniques will include using the
Equilateral will trigonometric functions, the Pythagorean Theorem, the Law of
Triangles Sines, and the Law of Cosines.
MX40-01 Angles and The student, given one of the six Algebra II and The student will identify, create, and solve practical problems
Trigonometric trigonometric functions in standard form, Trigonometry involving triangles. Techniques will include using the
Functions will trigonometric functions, the Pythagorean Theorem, the Law of
Sines, and the Law of Cosines.
MX19-01 AveragesSkill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX19-02 Medians03 Modes04 Histograms05 Percentiles, The student, given one of the six Probability and The student will analyze numerical characteristics of univariate
Quartiles, and trigonometric functions in standard form, Statistics data sets to describe patterns and departure from patterns,
Range will using mean, median, mode, variance, standard deviation,
interquartile range, range, and outliers. Appropriate technology
will be used to calculate statistics.
MX19-06 Standard The student, given one of the six Probability and The student will analyze numerical characteristics of univariate
Deviation and trigonometric functions in standard form, Statistics data sets to describe patterns and departure from patterns,
Variance will using mean, median, mode, variance, standard deviation,
interquartile range, range, and outliers. Appropriate technology
will be used to calculate statistics.
MX111-01 Understand The student, given one of the six Probability and The student will analyze scatterplots to identify and describe
Scatter plot trigonometric functions in standard form, Statistics the relationship between two variables, using shape; strength
Data will of relationship; clusters; positive, negative, or no association;
outliers; and influential points. Appropriate technology will be
used to generate scatterplots and identify outliers and
influential points.
MX63-01 Bases and The student, given one of the six Probability and The student will make logarithmic and power transformations
Powers trigonometric functions in standard form, Statistics to achieve linearity. Appropriate technology will be used.
will
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX22-01 Permutations The student, given one of the six Probability and The student will compute and distinguish between
and trigonometric functions in standard form, Statistics permutations and combinations and use technology for
Combinations will applications.
MX52-02 Effect of The student, given one of the six Probability and The student will identify and describe two or more events as
Replacement trigonometric functions in standard form, Statistics complementary, dependent, independent, and/or mutually
will exclusive.
MX52-03 Compound The student, given one of the six Probability and The student will identify and describe two or more events as
Events trigonometric functions in standard form, Statistics complementary, dependent, independent, and/or mutually
will exclusive.
MX52-03 Compound The student, given one of the six Probability and The student will find probabilities (relative frequency and
Events trigonometric functions in standard form, Statistics theoretical), including conditional probabilities for events that
will are either dependent or independent, by applying the "law of
large numbers" concept, the addition rule, and the
multiplication rule.
MX52-02 Effect of The student, given one of the six Probability and The student will identify random variables as independent or
Replacement trigonometric functions in standard form, Statistics dependent and find the mean and standard deviations for
will sums and differences of independent random variables.
MX52-03 Compound The student, given one of the six Probability and The student will identify random variables as independent or
Events trigonometric functions in standard form, Statistics dependent and find the mean and standard deviations for
will sums and differences of independent random variables.
PX37-02 Use Your The student, given one of the six Probability and The student will identify properties of a normal distribution and
Calculator trigonometric functions in standard form, Statistics apply the normal distribution to determine probabilities, using a
Sparingly will table or graphing calculator.
MX03-03 ProportionsMX19-01 AveragesSkill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX67-03 Induction, The student, given one of the six Discrete The student will model problems, using vertex-edge graphs.
Iteration, and trigonometric functions in standard form, Mathematics The concepts of valence, connectedness, paths, planarity, and
Recurrence will directed graphs will be investigated. Adjacency matrices and
matrix operations will be used to solve problems.
MX67-04 Make The student, given one of the six Discrete The student will apply algorithms, such as Kruskal's, Prim's, or
Mathematical trigonometric functions in standard form, Mathematics Dijkstra's, relating to trees, networks, and paths. Appropriate
Models will technology will be used to determine the number of possible
solutions and generate solutions when a feasible number
exists.
MX67-04 Make The student, given one of the six Discrete The student will use algorithms to schedule tasks in order to
Mathematical trigonometric functions in standard form, Mathematics determine a minimum project time. The algorithms will include
Models will critical path analysis, the list-processing algorithm, and student-
created algorithms.
MX67-04 Make The student, given one of the six Discrete The student will analyze and describe the issue of fair division.
Mathematical trigonometric functions in standard form, Mathematics Algorithms for continuous and discrete cases will be applied.
Models will
MX53-01 Recognize The student will use the recursive Discrete the Fibonacci sequence.
Famous process and difference equations with Mathematics
Patterns the aid of appropriate technology to
generate
MX25-01 Statements, The student will describe and apply Discrete The student will select, justify, and apply an appropriate
Negations, and sorting algorithms and coding algorithms Mathematics technique to solve a logic problem. Techniques will include
Compound used in storing, processing, and Venn diagrams, truth tables, and matrices.
Sentences communicating information. These will
include
MX25-02 The Language The student will describe and apply Discrete The student will select, justify, and apply an appropriate
of Logic sorting algorithms and coding algorithms Mathematics technique to solve a logic problem. Techniques will include
used in storing, processing, and Venn diagrams, truth tables, and matrices.
communicating information. These will
include
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX25-03 Truth Values25-04 Venn Diagrams22-01 Permutations The student will apply the formulas of Discrete permutations and combinations; and
and combinatorics in the areas of Mathematics
Combinations
MX61-03 Examine the X- The student will apply the formulas of Mathematical The student will investigate and identify the characteristics of
and Y- combinatorics in the areas of Analysis polynomial and rational functions and use these to sketch the
Intercepts graphs13-06 The Y-Intercept The student will apply the formulas of Mathematical The student will investigate and identify the characteristics of
combinatorics in the areas of Analysis polynomial and rational functions and use these to sketch the
graphs109-01 Time for a The student will apply the formulas of Mathematical The student will find compositions of functions and inverses of
Change combinatorics in the areas of Analysis functions. Analytical methods and graphing utilities will be
used to investigate and verify the domain and range of
resulting functions.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX109-02 Form and The student will apply the formulas of Mathematical The student will find compositions of functions and inverses of
Function combinatorics in the areas of Analysis functions. Analytical methods and graphing utilities will be
used to investigate and verify the domain and range of
resulting functions.
MX109-01 Time for a The student will apply the formulas of Mathematical The student will investigate and describe the continuity of
Change combinatorics in the areas of Analysis functions, using graphs. The functions will include absolute
value, piecewise, and step functions.
MX08-01 Find Common The student will apply the formulas of Mathematical The student will expand binomials having positive integral
Factors combinatorics in the areas of Analysis exponents through the use of the Binomial Theorem, the
formula for combinations, and Pascal's Triangle.
MX67-03 Induction, The student will apply the formulas of Mathematical The student will use mathematical induction to prove
Iteration, and combinatorics in the areas of Analysis formulas/statements.
Recurrence
MX109-01 Time for a The student will apply the formulas of Mathematical The student will find the limit of an algebraic function, if it
Change combinatorics in the areas of Analysis exists, as the variable approaches either a finite number or
infinity. A graphing utility will be used to verify intuitive
reasoning, algebraic methods, and numerical substitution.
MX50-01 Translation and The student will apply the formulas of Mathematical The student will investigate and identify the characteristics of
Reflection combinatorics in the areas of Analysis conic section equations in (h, k) and standard forms. The
techniques of translation and rotation of axes in the coordinate
plane will be used to graph conic sections.
MX50-02 Dilation and The student will apply the formulas of Mathematical The student will investigate and identify the characteristics of
Rotation combinatorics in the areas of Analysis conic section equations in (h, k) and standard forms. The
techniques of translation and rotation of axes in the coordinate
plane will be used to graph conic sections.
MX12-01 ExponentsSkill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX12-02 Roots12-03 Evaluate The student will apply the formulas of Mathematical The student will investigate and identify the characteristics of
Expressions combinatorics in the areas of Analysis exponential and logarithmic functions in order to graph these
Involving functions and solve equations and practical problems. This will
Exponents include63-01 Bases and The student will apply the formulas of Mathematical The student will investigate and identify the characteristics of
Powers combinator15-01 Triangle Basics02 Perpendicular The student will apply the formulas of Mathematical The student will identify, create, and solve practical problems
Bisectors combinatorics in the areas of Analysis involving triangles. Techniques will include using the
trigonometric functions, the Pythagorean Theorem, the Law of
Sines, and the Law of Cosines.
Skill/ Skill/ Strategy Strand Text Standard Text Objective Text
Strategy # Name
MX15-03 Equilateral The student will apply the formulas of Mathematical The student will identify, create, and solve practical problems
Triangles combinatorics in the areas of Analysis involving triangles. Techniques will include using the
trigonometric functions, the Pythagorean Theorem, the Law of
Sines, and the Law of Cosines.
MX15-04 Altitude05 Area and The student will apply the formulas of Mathematical The student will identify, create, and solve practical problems
Perimeter of combinatorics in the areas of Analysis involving triangles. Techniques will include using the
Triangles trigonometric functions, the Pythagorean Theorem, the Law of
Sines, and the Law of Cosines.
MX15-06 Area and The student will apply the formulas of Mathematical The student will identify, create, and solve practical problems
Perimeter of combinatorics in the areas of Analysis involving triangles. Techniques will include using the
Right Triangles trigonometric functions, the Pythagorean Theorem, the Law of
Sines, and the Law of Cosines.
MX15-07 Area and The student will apply the formulas of Mathematical The student will identify, create, and solve practical problems
Perimeter of combinatorics in the areas of Analysis involving triangles. Techniques will include using the
Equilateral trigonometric functions, the Pythagorean Theorem, the Law of
Triangles Sines, and the Law of Cosines.
MX40-01 Angles and The student will apply the formulas of Mathematical The student will identify, create, and solve practical problems
Trigonometric combinatorics in the areas of Analysis involving triangles. Techniques will include using the
Functions trigonometric functions, the Pythagorean Theorem, the Law of
Sines, and the Law of Cosines.
MX06-01 Transitivity02 Add or Subtract The student will apply the formulas of Advanced The student will define and apply the properties of elementary
the Same combinatorics in the areas of Placement functions, including algebraic, trigonometric, exponential, and
Number in Calculus composite functions and their inverses, and graph these
Equ03 Multiply or The student will apply the formulas of Advanced The student will define and apply the properties of elementary
Divide by the combinatorics in the areas of Placement functions, including algebraic, trigonometric, exponential, and
Same Number Calculus composite functions and their inverses, and graph these
in Equ04 Commutativity05 Signed The student will apply the formulas of Advanced The student will define and apply the properties of elementary
Numbers06 Algebraic Sums The student will apply the formulas of Advanced The student will define and apply the properties of elementary
of07 Multiply or The student will apply the formulas of Advanced The student will define and apply the properties of elementary
Divide08 Associative and The student will apply the formulas of Advanced The student will define and apply the properties of elementary
Distributive combinatorics in the areas of Placement functions, including algebraic, trigonometric, exponential, and
Properties09 Order of The student will apply the formulas of Advanced The student will define and apply the properties of elementary
Operations12-01 Exponents02 Roots03 Evaluate The student will apply the formulas of Advanced The student will define and apply the properties of elementary
Expressions combinatorics in the areas of Placement functions, including algebraic, trigonometric, exponential, and
Involving Calculus composite functions and their inverses, and graph these
Exponents functions, using a graphing calculator. Properties of functions
will include domains, ranges, combinations, odd, even,
periodicity, symmetry, asymptotes, zeros, upper and lower
bounds, and intervals where the function is increasing or
decreasing.
MX40-01 Angles and40-02 Trigonometric The student will apply the formulas of Advanced The student will define and apply the properties of elementary
Identities and combinatorics in the areas of Placement functions, including algebraic, trigonometric, exponential, and
Formulas40-03 Periodicity of01 Time for a The student will apply the formulas of Advanced The student will define and apply the properties of elementary
Change02 Form and The student will apply the formulas of Advanced The student will define and apply the properties of elementary
FunctionPX37-02 Use Your The student will apply the formulas of Advanced The student will define and apply the properties of elementary
Calculator combinatorics in the areas of Placement functions, including algebraic, trigonometric, exponential, and
Sparingly18-01 Tangents to a The student will investigate the Advanced using local linear approximation to find the slope of a tangent
Circle derivative at a point on a curve. This will Placement line to a curve at the point;
include Calculus
MX109-01 Time for a The student will investigate the Advanced defining instantaneous rate of change as the limit of average
Change derivative at a point on a curve. This will Placement rate of change; and
include Calculus
MX109-01 Time for a The student will investigate the Advanced approximating rate of change from graphs and tables of
Change derivative at a point on a curve. This will Placement values.
include Calculus
MX109-01 Time for a The student will apply the derivative to Advanced interpretation of the derivative as a rate of change in applied
Change solve problems. This will include Placement contexts, including velocity, speed, and acceleration; and
Calculus
State: Virginia
Grades: Secondary
Content: Science
Standard Correlation Date: 9/03
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX26-01 Measurement The student will plan and conduct investigations in Earth volume, area, mass, elapsed time, direction,
Instruments and which Science temperature, pressure, distance, density, and
Techniques changes in elevation/depth are calculated utilizing the
most appropriate tools;
MX26-02 Measurement The student will plan and conduct investigations in Earth volume, area, mass, elapsed time, direction,
Problems which Science temperature, pressure, distance, density, and
changes in elevation/depth are calculated utilizing the
most appropriate tools;
MX41-01 Graphs The student will plan and conduct investigations in Earth scales, diagrams, maps, charts, graphs, tables, and
which Science profiles are constructed and interpreted;
MX41-02 Diagrams The student will plan and conduct investigations in Earth scales, diagrams, maps, charts, graphs, tables, and
which Science profiles are constructed and interpreted;
MX41-03 Tables The student will plan and conduct investigations in Earth scales, diagrams, maps, charts, graphs, tables, and
which Science profiles are constructed and interpreted;
MX92-01 Formation of the The student will investigate and understand the Earth position of the Earth in the solar system;
Solar System characteristics of the Earth and the solar system. Science
Key concepts include
MX86-03 Earth and Its The student will investigate and understand the Earth sun-Earth-moon relationships (seasons, tides, and
Moon characteristics of the Earth and the solar system. Science eclipses);
Key concepts include
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX86-01 Observing the The student will investigate and understand the Earth characteristics of the sun, planets, their moons,
Sky characteristics of the Earth and the solar system. Science comets, meteors, and asteroids; and
Key concepts include
MX86-02 Stars The student will investigate and understand the Earth characteristics of the sun, planets, their moons,
characteristics of the Earth and the solar system. Science comets, meteors, and asteroids; and
Key concepts include
MX86-03 Earth and Its The student will investigate and understand the Earth characteristics of the sun, planets, their moons,
Moon characteristics of the Earth and the solar system. Science comets, meteors, and asteroids; and
Key concepts include
MX91-01 The Rock Cycle02 Types of Rocks01 The Rock Cycle The student will investigate and understand how to Earth uses of minerals.
identify major rock-forming and ore minerals Science
based on physical and chemical properties. Key
concepts include
MX91-02 Types of Rocks The student will investigate and understand how to Earth igneous (intrusive and extrusive);
identify common rock types based on mineral Science
composition and textures and the rock cycle as it
relates to the origin and transformation of rock
types. Key concepts include
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX91-02 Types of Rocks The student will investigate and understand how to Earth sedimentary (clastic and chemical); and
identify common rock types based on mineral Science
composition and textures and the rock cycle as it
relates to the origin and transformation of rock
types. Key concepts include
MX91-02 Types of Rocks The student will investigate and understand how to Earth metamorphic (foliated and unfoliated) rocks.
identify common rock types based on mineral Science
composition and textures and the rock cycle as it
relates to the origin and transformation of rock
types. Key concepts include
MX80-01 Energy The student will investigate and understand the Earth advantages and disadvantages of various energy
Transformations differences between renewable and nonrenewable Science sources;
resources. Key concepts include
MX80-02 Physical, The student will investigate and understand the Earth advantages and disadvantages of various energy
Chemical, and differences between renewable and nonrenewable Science sources;
Nuclear resources. Key concepts include
Changes
MX80-03 Conservation of The student will investigate and understand the Earth advantages and disadvantages of various energy
Mass-Energy differences between renewable and nonrenewable Science sources;
resources. Key concepts include
MX78-01 Biomagnification The student will investigate and understand the Earth making informed judgments related to resource use
differences between renewable and nonrenewable Science and its effects on Earth systems; and
resources. Key concepts include
MX78-02 Pollution The student will investigate and understand the Earth making informed judgments related to resource use
differences between renewable and nonrenewable Science and its effects on Earth systems; and
resources. Key concepts include
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX78-03 Conservation The student will investigate and understand the Earth making informed judgments related to resource use
differences between renewable and nonrenewable Science and its effects on Earth systems; and
resources. Key concepts include
MX78-01 Biomagnification The student will investigate and understand the Earth environmental costs and benefits.
differences between renewable and nonrenewable Science
resources. Key concepts include
MX78-02 Pollution The student will investigate and understand the Earth environmental costs and benefits.
differences between renewable and nonrenewable Science
resources. Key concepts include
MX78-03 Conservation The student will investigate and understand the Earth environmental costs and benefits.
differences between renewable and nonrenewable Science
resources. Key concepts include
MX84-01 Plate Tectonics02 Glaciation03 Weathering, The student will investigate and understand Earth how geologic processes are evidenced in the
Erosion, and geologic processes including plate tectonics. Key Science physiographic provinces of Virginia including the
Deposition concepts include Coastal Plain, Piedmont, Blue Ridge, Valley and
Ridge, and Appalachian Plateau;
MX84-04 Earthquakes and The student will investigate and understand Earth how geologic processes are evidenced in the
Volcanoes geologic processes including plate tectonics. Key Science physiographic provinces of Virginia including the
concepts include Coastal Plain, Piedmont, Blue Ridge, Valley and
Ridge, and Appalachian Plateau;
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX91-01 The Rock Cycle91-02 Types of Rocks01 Plate Tectonics02 Glaciation03 Weathering, The student will investigate and understand Earth processes (faulting, folding, volcanism,
Erosion, and geologic processes including plate tectonics. Key Science metamorphism, weathering, erosion, deposition, and
Deposition concepts include sedimentation) and their resulting features; and
MX84-04 Earthquakes and The student will investigate and understand Earth processes (faulting, folding, volcanism,
Volcanoes geologic processes including plate tectonics. Key Science metamorphism, weathering, erosion, deposition, and
concepts include sedimentation) and their resulting features; and
MX85-01 Atmosphere and The student will investigate and understand Earth processes (faulting, folding, volcanism,
Weather geologic processes including plate tectonics. Key Science metamorphism, weathering, erosion, deposition, and
concepts include sedimentation) and their resulting features; and
MX85-02 Climate ChangesSkill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX84-01 Plate Tectonics The student will investigate and understand Earth tectonic processes (subduction, rifting and sea floor
geologic processes including plate tectonics. Key Science spreading, and continental collision).
concepts include
MX77-02 Water Cycle The student will investigate and understand how Earth identification of groundwater zones including water
freshwater resources are influenced by geologic Science table, zone of saturation, and zone of aeration;
processes and the activities of humans. Key
concepts include
MX77-02 Water Cycle The student will investigate and understand how Earth identification of other sources of fresh water including
freshwater resources are influenced by geologic Science rivers, springs, and aquifers with reference to the
processes and the activities of humans. Key hydrologic cycle;
concepts include
MX78-01 Biomagnification02 Pollution03 Conservation The student will investigate and understand how Earth dependence on freshwater resources and the effects
freshwater resources are influenced by geologic Science of human usage on water quality; and
processes and the activities of humans. Key
concepts include
MX91-02 Types of Rocks The student will investigate and understand that Earth traces or remains of ancient, often extinct, life are
many aspects of the history and evolution of the Science preserved by various means in many sedimentary
Earth and life can be inferred by studying rocks rocks;
and fossils. Key concepts include
MX85-01 Atmosphere and The student will investigate and understand that Earth systems interactions (density differences, energy
Weather oceans are complex, interactive physical, Science transfer, weather, and climate);
chemical, and biological systems and are subject
to long- and short-term variations. Key concepts
include
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX85-02 Climate Changes The student will investigate and understand that Earth systems interactions (density differences, energy
oceans are complex, interactive physical, Science transfer, weather, and climate);
chemical, and biological systems and are subject
to long- and short-term variations. Key concepts
include
MX80-01 Energy The student will investigate and understand that Earth systems interactions (density differences, energy
Transformations oceans are complex, interactive physical, Science transfer, weather, and climate);
chemical, and biological systems and are subject
to long- and short-term variations. Key concepts
include
MX80-02 Physical, The student will investigate and understand that Earth systems interactions (density differences, energy
Chemical, and oceans are complex, interactive physical, Science transfer, weather, and climate);
Nuclear chemical, and biological systems and are subject
Changes to long- and short-term variations. Key concepts
include
MX80-03 Conservation of The student will investigate and understand that Earth systems interactions (density differences, energy
Mass-Energy oceans are complex, interactive physical, Science transfer, weather, and climate);
chemical, and biological systems and are subject
to long- and short-term variations. Key concepts
include
MX85-01 Atmosphere and The student will investigate and understand the Earth scientific evidence for atmospheric changes over
Weather origin and evolution of the atmosphere and the Science geologic time;
interrelationship of geologic processes, biologic
processes, and human activities on its
composition and dynamics. Key concepts include
MX85-01 Atmosphere and The student will investigate and understand that Earth observation and collection of weather data;
Weather energy transfer between the sun, Earth, and the Science
Earth's atmosphere drives weather and climate on
Earth. Key concepts include
MX85-01 Atmosphere and The student will investigate and understand that Earth prediction of weather patterns;
Weather energy transfer between the sun, Earth, and the Science
Earth's atmosphere drives weather and climate on
Earth. Key concepts include
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX85-01 Atmosphere and The student will investigate and understand that Earth severe weather occurrences such as tornadoes,
Weather energy transfer between the sun, Earth, and the Science hurricanes, and major storms; and
Earth's atmosphere drives weather and climate on
Earth. Key concepts include
MX85-01 Atmosphere and The student will investigate and understand that Earth weather phenomena and the factors that affect
Weather energy transfer between the sun, Earth, and the Science climate including radiation and convection.
Earth's atmosphere drives weather and climate on
Earth. Key concepts include
MX85-02 Climate Changes The student will investigate and understand that Earth weather phenomena and the factors that affect
energy transfer between the sun, Earth, and the Science climate including radiation and convection.
Earth's atmosphere drives weather and climate on
Earth. Key concepts include
MX92-01 Formation of the The student will investigate and understand Earth nebulae;
Solar System scientific concepts related to the origin and Science
evolution of the universe. Key concepts include
MX92-01 Formation of the The student will investigate and understand Earth the origin of stars and star systems;
Solar System scientific concepts related to the origin and Science
evolution of the universe. Key concepts include
MX92-02 The Big Bang The student will investigate and understand Earth the origin of stars and star systems;
scientific concepts related to the origin and Science
evolution of the universe. Key concepts include
MX86-01 Observing the The student will investigate and understand Earth stellar evolution;
Sky scientific concepts related to the origin and Science
evolution of the universe. Key concepts include
MX92-02 The Big Bang The student will investigate and understand Earth galaxies; and
scientific concepts related to the origin and Science
evolution of the universe. Key concepts include
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX92-02 The Big Bang The student will investigate and understand Earth cosmology (the Big Bang).
scientific concepts related to the origin and Science
evolution of the universe. Key concepts include
PX48-01 Steps of the The student will plan and conduct investigations in Biology hypotheses are formulated based on direct
Scientific Method which observations and information from the scientific
literature;
PX48-02 Be Skeptical The student will plan and conduct investigations in Biology hypotheses are formulated based on direct
which observations and information from the scientific
literature;
PX48-03 Be Fair The student will plan and conduct investigations in Biology hypotheses are formulated based on direct
which observations and information from the scientific
literature;
PX48-04 Know What Can The student will plan and conduct investigations in Biology hypotheses are formulated based on direct
Go Wrong which observations and information from the scientific
literature;
PX48-01 Steps of the The student will plan and conduct investigations in Biology variables are defined and investigations are designed
Scientific Method which to test hypotheses;
PX48-02 Be Skeptical The student will plan and conduct investigations in Biology variables are defined and investigations are designed
which to test hypotheses;
PX48-03 Be Fair The student will plan and conduct investigations in Biology variables are defined and investigations are designed
which to test hypotheses;
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
PX48-04 Know What Can The student will plan and conduct investigations in Biology variables are defined and investigations are designed
Go Wrong which to test hypotheses;
PX48-01 Steps of the The student will plan and conduct investigations in Biology differentiation is made between a scientific hypothesis
Scientific Method which and theory;
PX48-02 Be Skeptical The student will plan and conduct investigations in Biology differentiation is made between a scientific hypothesis
which and theory;
PX48-03 Be Fair The student will plan and conduct investigations in Biology differentiation is made between a scientific hypothesis
which and theory;
PX48-04 Know What Can The student will plan and conduct investigations in Biology differentiation is made between a scientific hypothesis
Go Wrong which and theory;
MX71-01 Cells The student will investigate and understand the Biology evidence supporting the cell theory;
history of biological concepts. Key concepts
include
MX76-01 Evidence for The student will investigate and understand the Biology scientific explanations of the development of
Evolution history of biological concepts. Key concepts organisms through time (biological evolution);
include
MX76-02 Natural Selection The student will investigate and understand the Biology scientific explanations of the development of
history of biological concepts. Key concepts organisms through time (biological evolution);
include
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX76-03 Adaptation in The student will investigate and understand the Biology scientific explanations of the development of
Action history of biological concepts. Key concepts organisms through time (biological evolution);
include
MX75-02 Mutation The student will investigate and understand the Biology development of the structural model of DNA; and
history of biological concepts. Key concepts
include
MX72-01 Photosynthesis The student will investigate and understand the Biology the capture, storage, transformation, and flow of
and Respiration chemical and biochemical principles essential for energy through the processes of photosynthesis and
life. Key concepts include respiration.
MX72-02 Food Webs and The student will investigate and understand the Biology the capture, storage, transformation, and flow of
Chains chemical and biochemical principles essential for energy through the processes of photosynthesis and
life. Key concepts include respiration.
MX72-03 Populations in The student will investigate and understand the Biology the capture, storage, transformation, and flow of
Ecosystems chemical and biochemical principles essential for energy through the processes of photosynthesis and
life. Key concepts include respiration.
MX72-04 Succession The student will investigate and understand the Biology the capture, storage, transformation, and flow of
chemical and biochemical principles essential for energy through the processes of photosynthesis and
life. Key concepts include respiration.
MX71-01 Cells The student will investigate and understand Biology characteristics of prokaryotic and eukaryotic cells;
relationships between cell structure and function.
Key concepts include
MX71-01 Cells The student will investigate and understand Biology exploring the diversity and variation of eukaryotes;
relationships between cell structure and function.
Key concepts include
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX71-01 Cells The student will investigate and understand Biology similarities between the activities of a single cell and a
relationships between cell structure and function. whole organism; and
Key concepts include
MX71-04 Coordination and The student will investigate and understand Biology cell membrane model (diffusion, osmosis, and active
Control relationships between cell structure and function. transport).
Key concepts include
MX73-01 The Five The student will investigate and understand life Biology how their structures and functions vary between and
Kingdoms functions of archaebacteria, monerans within the kingdoms;
(eubacteria), protists, fungi, plants, and animals,
including humans. Key concepts include
MX74-01 Characteristics The student will investigate and understand life Biology comparison of their metabolic activities;
of Living Things functions of archaebacteria, monerans
(eubacteria), protists, fungi, plants, and animals,
including humans. Key concepts include
MX74-01 Characteristics The student will investigate and understand life Biology maintenance of homeostasis;
of Living Things functions of archaebacteria, monerans
(eubacteria), protists, fungi, plants, and animals,
including humans. Key concepts include
MX78-02 Pollution The student will investigate and understand Biology prediction of inheritance of traits based on the
common mechanisms of inheritance and protein Mendelian laws of heredity;
synthesis. Key concepts include
MX75-02 Mutation The student will investigate and understand Biology genetic variation (mutation, recombination, deletions,
common mechanisms of inheritance and protein additions to DNA);
synthesis. Key concepts include
MX75-04 Genetic The student will investigate and understand Biology exploration of the impact of DNA technologies.
Engineering common mechanisms of inheritance and protein
synthesis. Key concepts include
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX75-03 Population The student will investigate and understand how Biology how genetic variation, reproductive strategies, and
Genetics populations change through time. Key concepts environmental pressures impact the survival of
include populations;
MX76-02 Natural Selection The student will investigate and understand how Biology how natural selection leads to adaptations;
populations change through time. Key concepts
include
MX76-03 Adaptation in The student will investigate and understand how Biology how natural selection leads to adaptations;
Action populations change through time. Key concepts
include
MX76-01 Evidence for The student will investigate and understand how Biology scientific explanations for biological evolution.
Evolution populations change through time. Key concepts
include
MX76-02 Natural Selection The student will investigate and understand how Biology scientific explanations for biological evolution.
populations change through time. Key concepts
include
MX76-03 Adaptation in The student will investigate and understand how Biology scientific explanations for biological evolution.
Action populations change through time. Key concepts
include
MX72-01 PhotosynthesisThe student will investigate and understand Biology nutrient cycling with energy flow through ecosystems;
dynamic equilibria within populations,
and Respiration
communities, and ecosystems. Key concepts
include
MX72-02 Food Webs and The student will investigate and understand Biology nutrient cycling with energy flow through ecosystems;
Chains dynamic equilibria within populations,
communities, and ecosystems. Key concepts
include
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX72-03 Populations in The student will investigate and understand Biology nutrient cycling with energy flow through ecosystems;
Ecosystems dynamic equilibria within populations,
communities, and ecosystems. Key concepts
include
MX72-04 Succession The student will investigate and understand Biology succession patterns in ecosystems;
dynamic equilibria within populations,
communities, and ecosystems. Key concepts
include
MX78-01 Biomagnification The student will investigate and understand Biology the effects of natural events and human influences on
dynamic equilibria within populations, ecosystems; and
communities, and ecosystems. Key concepts
include
MX78-02 Pollution The student will investigate and understand Biology the effects of natural events and human influences on
dynamic equilibria within populations, ecosystems; and
communities, and ecosystems. Key concepts
include
MX78-03 Conservation The student will investigate and understand Biology the effects of natural events and human influences on
dynamic equilibria within populations, ecosystems; and
communities, and ecosystems. Key concepts
include
MX79-01 Measuring The student will investigate and understand that Chemistry mathematical manipulations (SI units, scientific
Matter experiments in which variables are measured, notation, linear equations, graphing, ratio and
analyzed, and evaluated, produce observations proportion, significant digits, dimensional analysis);
and verifiable data. Key concepts include
MX79-02 Atoms The student will investigate and understand that Chemistry average atomic mass, mass number, and atomic
the placement of elements on the periodic table is number;
a function of their atomic structure. The periodic
table is a tool used for the investigations of
MX79-02 Atoms The student will investigate and understand that Chemistry isotopes, half lives, and radioactive decay;
the placement of elements on the periodic table is
a function of their atomic structure. The periodic
table is a tool used for the investigations of
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX79-02 Atoms The student will investigate and understand that Chemistry trends including atomic radii, electronegativity,
the placement of elements on the periodic table is shielding effect, and ionization energy;
a function of their atomic structure. The periodic
table is a tool used for the investigations of
MX79-02 Atoms The student will investigate and understand that Chemistry electron configurations, valence electrons, and
the placement of elements on the periodic table is oxidation numbers;
a function of their atomic structure. The periodic
table is a tool used for the investigations of
MX79-01 Measuring The student will investigate and understand that Chemistry chemical and physical properties; and
Matter the placement of elements on the periodic table is
a function of their atomic structure. The periodic
table is a tool used for the investigations of
MX87-02 Reaction The student will investigate and understand how Chemistry balancing chemical equations;
Equations conservation of energy and matter is expressed in
chemical formulas and balanced equations. Key
concepts include
MX79-04 Chemical The student will investigate and understand how Chemistry bonding types (ionic, covalent);
Reactions conservation of energy and matter is expressed in
chemical formulas and balanced equations. Key
concepts include
MX80-02 Physical, The student will investigate and understand how Chemistry reaction types (synthesis, decomposition, single and
Chemical, and conservation of energy and matter is expressed in double replacement, oxidation-reduction,
Nuclear chemical formulas and balanced equations. Key neutralization, exothermic and endothermic); and
Changes concepts include
MX87-01 Understanding The student will investigate and understand how Chemistry reaction types (synthesis, decomposition, single and
Chemical conservation of energy and matter is expressed in double replacement, oxidation-reduction,
Reactions chemical formulas and balanced equations. Key neutralization, exothermic and endothermic); and
concepts include
MX87-01 Understanding The student will investigate and understand how Chemistry reaction rates and kinetics (activation energy,
Chemical conservation of energy and matter is expressed in catalysis, degree of randomness).
Reactions chemical formulas and balanced equations. Key
concepts include
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX79-02 Atoms The student will investigate and understand that Chemistry Avogadro's principle and molar volume;
quantities in a chemical reaction are based on
molar relationships. Key concepts include
MX87-03 Solubility The student will investigate and understand that Chemistry solution concentrations;
quantities in a chemical reaction are based on
molar relationships. Key concepts include
MX79-01 Measuring The student will investigate and understand that Chemistry pressure, temperature, and volume;
Matter the phases of matter are explained by kinetic
theory and forces of attraction between particles.
Key concepts include
PX48-01 Steps of the The student will investigate and understand how to Physics instruments are selected and used to extend
Scientific Method plan and conduct investigations in which observations and measurements of mass, volume,
temperature, heat exchange, energy transformations,
motion, fields, and electric charge;
PX48-02 Be Skeptical03 Be Fair04 Know What Can The student will investigate and understand how to Physics instruments are selected and used to extend
Go Wrong plan and conduct investigations in which observations and measurements of mass, volume,
temperature, heat exchange, energy transformations,
motion, fields, and electric charge;
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
PX10-01 Set Up or Verify The student will investigate and understand how to Physics metric units are used in all measurements and
with Units plan and conduct investigations in which calculations;
PX10-01 Set Up or Verify The student will investigate and understand how to Physics data gathered from non-SI instruments are
with Units plan and conduct investigations in which incorporated through appropriate conversions; and
PX48-01 Steps of the The student will investigate and understand how to Physics The student will investigate and understand how to
Scientific Method plan and conduct investigations in which analyze and interpret data. Key concepts include
PX48-02 Be Skeptical The student will investigate and understand how to Physics The student will investigate and understand how to
plan and conduct investigations in which analyze and interpret data. Key concepts include
PX48-03 Be Fair The student will investigate and understand how to Physics The student will investigate and understand how to
plan and conduct investigations in which analyze and interpret data. Key concepts include
PX48-04 Know What Can The student will investigate and understand how to Physics The student will investigate and understand how to
Go Wrong plan and conduct investigations in which analyze and interpret data. Key concepts include
PX02-01 Translate Words The student will investigate and understand how to Physics a description of a physical problem is translated into a
into Math plan and conduct investigations in which mathematical statement in order to find a solution;
MX82-01 Newton's Laws The student will investigate and understand the Physics linear motion;
interrelationships among mass, distance, force,
and time through mathematical and experimental
processes. Key concepts include
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX82-02 Machines The student will investigate and understand the Physics linear motion;
interrelationships among mass, distance, force,
and time through mathematical and experimental
processes. Key concepts include
MX82-01 Newton's Laws The student will investigate and understand the Physics uniform circular motion;
interrelationships among mass, distance, force,
and time through mathematical and experimental
processes. Key concepts include
MX82-02 Machines The student will investigate and understand the Physics uniform circular motion;
interrelationships among mass, distance, force,
and time through mathematical and experimental
processes. Key concepts include
MX82-01 Newton's Laws The student will investigate and understand the Physics projectile motion;
interrelationships among mass, distance, force,
and time through mathematical and experimental
processes. Key concepts include
MX82-02 Machines The student will investigate and understand the Physics projectile motion;
interrelationships among mass, distance, force,
and time through mathematical and experimental
processes. Key concepts include
MX82-01 Newton's Laws The student will investigate and understand the Physics Newton's laws of motion;
interrelationships among mass, distance, force,
and time through mathematical and experimental
processes. Key concepts include
MX82-02 Machines The student will investigate and understand the Physics Newton's laws of motion;
interrelationships among mass, distance, force,
and time through mathematical and experimental
processes. Key concepts include
MX89-01 A Force to Be The student will investigate and understand the Physics gravitation;
Reckoned With interrelationships among mass, distance, force,
and time through mathematical and experimental
processes. Key concepts include
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX80-01 Energy The student will investigate and understand the Physics work, power, and energy.
Transformations interrelationships among mass, distance, force,
and time through mathematical and experimental
processes. Key concepts include
MX80-01 Energy The student will investigate and understand that Physics kinetic and potential energy;
Transformations quantities including mass, energy, momentum,
and charge are conserved. Key concepts include
MX81-01 Electricity The student will investigate and understand that Physics electric power.
quantities including mass, energy, momentum,
and charge are conserved. Key concepts include
MX81-02 Electrical Circuits The student will investigate and understand that Physics electric power.
quantities including mass, energy, momentum,
and charge are conserved. Key concepts include
MX81-03 Magnetism The student will investigate and understand that Physics electric power.
quantities including mass, energy, momentum,
and charge are conserved. Key concepts include
MX80-01 Energy The student will investigate and understand that Physics transformation of energy among forms, including
Transformations energy can be transferred and transformed to mechanical, thermal, electrical, gravitational,
provide usable work. Key concepts include chemical, and nuclear; and
MX80-02 Physical, The student will investigate and understand that Physics transformation of energy among forms, including
Chemical, and energy can be transferred and transformed to mechanical, thermal, electrical, gravitational,
Nuclear provide usable work. Key concepts include chemical, and nuclear; and
Changes
MX83-01 Waves The student will investigate and understand that Physics wave characteristics (period, wavelength, frequency,
energy can be transferred and transformed to amplitude and phase);
provide usable work. Key concepts include
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX83-03 Light The student will investigate and understand how to Physics fundamental wave processes (reflection, refraction,
use models of transverse and longitudinal waves diffraction, interference, polarization, Doppler effect);
to interpret wave phenomena. Key concepts and
include
MX83-02 Sound The student will investigate and understand how to Physics light and sound in terms of wave models
use models of transverse and longitudinal waves
to interpret wave phenomena. Key concepts
include
MX83-03 Light The student will investigate and understand how to Physics light and sound in terms of wave models
use models of transverse and longitudinal waves
to interpret wave phenomena. Key concepts
include
MX83-03 Light The student will investigate and understand that Physics the properties and behaviors of radio, microwaves,
different frequencies and wavelengths in the infrared, visible light, ultraviolet, X-rays, and gamma
electromagnetic spectrum are phenomena ranging rays; and
from radio waves through visible light to gamma
radiation. Key concepts include
MX82-01 Newton's Laws The student will investigate and understand how to Physics inverse square laws (Newton's law of universal
use the field concept to describe the effects of gravitation and Coulomb's law); and
gravitational, electric, and magnetic forces. Key
concepts include
MX89-01 A Force to Be The student will investigate and understand how to Physics inverse square laws (Newton's law of universal
Reckoned With use the field concept to describe the effects of gravitation and Coulomb's law); and
gravitational, electric, and magnetic forces. Key
concepts include
MX81-03 Magnetism The student will investigate and understand how to Physics operating principles of motors, generators,
use the field concept to describe the effects of transformers, and cathode ray tubes.
gravitational, electric, and magnetic forces. Key
concepts include
MX81-01 Electricity The student will investigate and understand how to Physics series, parallel, and combined circuits; and
diagram and construct basic electrical circuits and
explain the function of various circuit components.
Key concepts include
Skill/ Skill/ Strategy Strand Text Standard Objective Text
Strategy # Name Text
MX81-02 Electrical Circuits The student will investigate and understand how to Physics series, parallel, and combined circuits; and
diagram and construct basic electrical circuits and
explain the function of various circuit components.
Key concepts include
MX81-02 Electrical Circuits The student will investigate and understand how to Physics circuit components including resistors, batteries,
diagram and construct basic electrical circuits and generators, fuses, switches, and capacito
explain the function of various circuit components.
Key concepts include
MX80-02 Physical, The student will investigate and understand that Physics nuclear physics;
Chemical, and extremely large and extremely small quantities are
Nuclear not necessarily described by the same laws as
Changes those studied in Newtonian physics. Key concepts
include
MX81-01 Electricity The student will investigate and understand that Physics superconductivity; and
extremely large and extremely small quantities are
not necessarily described by the same laws as
those studied in Newtonian physics. Key concepts
include
MX81-02 Electrical Circuits The student will investigate and understand that Physics superconductivity; and
extremely large and extremely small quantities are
not necessarily described by the same laws as
those studied in Newtonian physics. Key concepts
include
MX81-03 Magnetism The student will investigate and understand that Physics superconductivity; and
extremely large and extremely small quantities are
not necessarily described by the same laws as
those studied in Newtonian physics. Key concepts
include
MX80-02 Physical, The student will investigate and understand that Physics radioactivity.
Chemical, and extremely large and extremely small quantities are
Nuclear not necessarily described by the same laws as
Changes those studied in Newtonian physics. Key concepts
include
State: Virginia
Grades: Secondary
Content: Language Arts
Standard Correlation Date: 9/03
Skill/ Skill/ Strategy Name Grade Strand Text Standard Objective Text
Strategy # Text
MX27-01 Analyze the Setting 9 The student will read and analyze a Reading Identify format, text structure, and main idea.
variety of literature. Analysis
MX27-05 Identify and Compare 9 The student will read and analyze a Reading Identify the characteristics that distinguish literary
Genres variety of literature. Analysis forms.
MX27-01 Analyze the Setting 9 The student will read and analyze a Reading Use literary terms in describing and analyzing
variety of literature. Analysis selections.
MX27-02 Identify and Interpret 9 The student will read and analyze a Reading Explain the relationships between and among
Point of View variety of literature. Analysis elements of literature: characters, plot, setting,
tone, point of view, and theme.
MX29-01 Identify Author's 9 The student will read and analyze a Reading Explain the relationship between author's style
Purpose and Point of variety of literature. Analysis and literary effect.
View
MX28-02 Symbol 9 The student will read and analyze a Reading Describe the use of images and sounds to elicit
variety of literature. Analysis the reader's emotions.
MX27-03 Classify and Evaluate 9 The student will read dramatic Reading Compare and contrast the elements of character,
Character selections. Analysis setting, and plot in one-act plays and full-length
plays.
MX27-04 Determine and 9 The student will read dramatic Reading Describe how stage directions help the reader
Support Theme or selections. Analysis understand a play's setting, mood, characters,
Tone plot, and theme.
MX30-01 The Writing Process 9 The student will develop narrative, Writing Generate, gather, and organize ideas for writing.
expository, and informational
writings to inform, explain, analyze,
or entertain.
MX30-02 Identify Your Audience 9 The student will develop narrative, Writing Plan and organize writing to address a specific
and Purpose expository, and informational audience and purpose.
writings to inform, explain, analyze,
or entertain.
Skill/ Skill/ Strategy Name Grade Strand Text Standard Objective Text
Strategy # Text
MX30-02 Identify Your Audience 9 The student will develop narrative, Writing Communicate clearly the purpose of the writing.
and Purpose expository, and informational
writings to inform, explain, analyze,
or entertain.
MX31-01 Develop the 9 The student will develop narrative, Writing Write clear, varied sentences.
Introduction, Body, expository, and informational
and Conclusion writings to inform, explain, analyze,
or entertain.
MX31-02 Provide Supporting 9 The student will develop narrative, Writing Use specific vocabulary and information.
Details expository, and informational
writings to inform, explain, analyze,
or entertain.
MX30-06 Group Ideas and 9 The student will develop narrative, Writing Arrange paragraphs into a logical progression.
Sequence Information expository, and informational
writings to inform, explain, analyze,
or entertain.
MX32-01 Reread and Revise 9 The student will develop narrative, Writing Revise writing for clarity.
expository, and informational
writings to inform, explain, analyze,
or entertain.
MX32-02 Proofread Carefully 9 The student will develop narrative, Writing Proofread and prepare final product for intended
expository, and informational audience and purpose.
writings to inform, explain, analyze,
or entertain.
MX39-01 Reach an Agreement 9 The student will edit writing for Writing Use and apply rules for the parts of a sentence
correct grammar, capitalization, including: subject/verb, direct/indirect object,
punctuation, spelling, sentence predicate nominative/predicate adjective.
structure, and paragraphing.
MX30-05 Select an 9 The student will edit writing for Writing Use parallel structures across sentences and
Organizational correct grammar, capitalization, paragraphs.
Structure punctuation, spelling, sentence
structure, and paragraphing.
Skill/ Skill/ Strategy Name Grade Strand Text Standard Objective Text
Strategy # Text
MX38-01 Commas 9 The student will edit writing for Writing Use commas and semicolons to distinguish and
correct grammar, capitalization, divide main and subordinate clauses.
punctuation, spelling, sentence
structure, and paragraphing.
MX27-04 Determine and 10 The student will read, comprehend, Reading Identify text organization and structure.
Support Theme or and critique literary works. Analysis
Tone
MX27-04 Determine and 10 The student will read, comprehend, Reading Identify main and supporting ideas.
Support Theme or and critique literary works. Analysis
Tone
MX27-05 Identify and Compare 10 The student will read, comprehend, Reading Explain similarities and differences of techniques
Genres and critique literary works. Analysis and literary forms represented in the literature of
different cultures and eras.
MX27-05 Identify and Compare 10 The student will read and interpret Reading Compare and contrast product information
Genres informational materials. Analysis contained in advertisements with instruction
manuals and warranties.
MX27-05 Identify and Compare 10 The student will read and analyze a Reading Compare and contrast the use of rhyme, rhythm,
Genres variety of poetry. Analysis and sound to convey a message.
MX27-05 Identify and Compare 10 The student will read and analyze a Reading Compare and contrast the ways in which poets
Genres variety of poetry. Analysis use techniques to evoke emotion in the reader.
MX27-03 Classify and Evaluate 10 The student will read and critique Reading Explain the use of asides, soliloquies, and
Character dramatic selections. Analysis monologues in the development of a single
character.
MX69-02 Compare and Contrast 10 The student will read and critique Reading Compare and contrast character development in
dramatic selections. Analysis a play to characterization in other literary forms.
MX30-01 The Writing Process 10 The student will develop a variety of Writing Generate, gather, plan, and organize ideas for
writing with an emphasis on writing.
exposition.
MX30-03 Choose a Topic or 10 The student will develop a variety of Writing Elaborate ideas clearly through word choice and
Controlling Idea writing with an emphasis on vivid description.
exposition.
Skill/ Skill/ Strategy Name Grade Strand Text Standard Objective Text
Strategy # Text
MX30-01 The Writing Process 10 The student will develop a variety of Writing Write clear, varied sentences.
writing with an emphasis on
exposition.
MX30-06 Group Ideas and 10 The student will develop a variety of Writing Organize ideas into a logical sequence.
Sequence Information writing with an emphasis on
exposition.
MX32-01 Reread and Revise 10 The student will develop a variety of Writing Revise writing for clarity and content of
writing with an emphasis on presentation.
exposition.
MX32-02 Proofread Carefully 10 The student will develop a variety of Writing Proofread and prepare final product for intended
writing with an emphasis on audience and purpose.
exposition.
MX38-02 Colons and 10 The student will edit writing for Writing Apply rules governing use of colon.
Semicolons correct grammar, capitalization,
punctuation, spelling, sentence
structure, and paragraphing.
MX68-05 Evaluate the Work of 10 The student will critique professional Writing Analyze the writing of others.
Others and peer writing.
MX29-01 Identify Author's 10 The student will critique professional Writing Describe how the author accomplishes the
Purpose and Point of and peer writing. intended purpose of a writing.
View
MX31-01 Develop the 10 The student will use writing to Writing Explain concepts contained in literature and other
Introduction, Body, interpret, analyze, and evaluate disciplines.
and Conclusion ideas.
MX31-02 Provide Supporting 10 The student will use writing to Writing Translate concepts into simpler or more easily
Details interpret, analyze, and evaluate understood terms.
ideas.
MX68-02 Judge Organization 10 The student will collect, evaluate, Research Organize information from a variety of sources.
and Approach organize, and present information.
MX45-02 Get Organized 10 The student will collect, evaluate, Research Develop the central idea or focus.
organize, and present information.
Skill/ Skill/ Strategy Name Grade Strand Text Standard Objective Text
Strategy # Text
MX69-01 Find the Facts 10 The student will collect, evaluate, Research Verify the accuracy and usefulness of
organize, and present information. information.
MX31-03 Use Quoted Material 10 The student will collect, evaluate, Research Credit sources for both quoted and paraphrased
Appropriately organize, and present information. ideas.
MX30-06 Group Ideas and 10 The student will collect, evaluate, Research Use technology to access information, organize
Sequence Information organize, and present information. ideas, and develop writing.
MX30-05 Select an 11 The student will make informative Oral Gather and organize evidence to support a
Organizational and persuasive presentations. Language position.
Structure
MX30-04 Select an 11 The student will make informative Oral Present evidence clearly and convincingly.
Organizational and persuasive presentations. Language
Structure
MX30-02 Identify Your Audience 11 The student will make informative Oral Use grammatically correct language, including
and Purpose and persuasive presentations. Language vocabulary appropriate to the topic, audience,
and purpose.
MX27-05 Identify and Compare 11 The student will read and analyze Reading Describe contributions of different cultures to the
Genres relationships among American Analysis development of American literature.
literature, history, and culture.
MX27-05 Identify and Compare 11 The student will read and analyze Reading Compare and contrast the development of
Genres relationships among American Analysis American literature in its historical context.
literature, history, and culture.
MX27-05 Identify and Compare 11 The student will read and analyze Reading Discuss American literature as it reflects
Genres relationships among American Analysis traditional and contemporary themes, motifs,
literature, history, and culture. universal characters, and genres.
MX27-02 Identify and Interpret 11 The student will read and analyze a Reading Analyze information from a text to draw
Point of View variety of informational materials. Analysis conclusions.
MX27-02 Identify and Interpret 11 The student will read and critique a Reading Analyze the poetic elements of contemporary and
Point of View variety of poetry. Analysis traditional poems.
Skill/ Skill/ Strategy Name Grade Strand Text Standard Objective Text
Strategy # Text
MX27-03 Classify and Evaluate 11 The student will read and critique a Reading Identify the poetic elements and techniques that
Character variety of poetry. Analysis are most appealing and that make poetry
enjoyable.
MX27-05 Identify and Compare 11 The student will read and critique a Reading Compare and contrast the works of
Genres variety of poetry. Analysis contemporary and past American poets.
MX28-03 Irony 11 The student will read and critique a Reading Explain the use of verbal, situational, and
variety of dramatic selections. Analysis dramatic irony.
MX30-01 The Writing Process 11 The student will write in a variety of Writing Generate, gather, plan, and organize ideas for
forms with an emphasis on writing.
persuasion.
MX30-04 Select an 11 The student will write in a variety of Writing Develop a focus for writing.
Organizational forms with an emphasis on
Structure persuasion.
MX31-02 Provide Supporting 11 The student will write in a variety of Writing Evaluate and cite applicable information.
Details forms with an emphasis on
persuasion.
MX30-06 Group Ideas and 11 The student will write in a variety of Writing Organize ideas in a logical manner.
Sequence Information forms with an emphasis on
persuasion.
MX30-04 Select an 11 The student will write in a variety of Writing Elaborate ideas clearly and accurately.
Organizational forms with an emphasis on
Structure persuasion.
MX30-02 Identify Your Audience 11 The student will write in a variety of Writing Adapt content, vocabulary, voice, and tone to
and Purpose forms with an emphasis on audience, purpose, and situation.
persuasion.
MX32-01 Reread and Revise 11 The student will write in a variety of Writing Revise writing for accuracy and depth of
forms with an emphasis on information.
persuasion.
MX32-02 Proofread Carefully 11 The student will write in a variety of Writing Proofread final copy and prepare document for
forms with an emphasis on intended audience or purpose.
persuasion.
Skill/ Skill/ Strategy Name Grade Strand Text Standard Objective Text
Strategy # Text
MX28-03 Irony 11 The student will edit writing for Writing Use verbals and verbal phrases to achieve
correct grammar, capitalization, sentence conciseness and variety.
punctuation, spelling, sentence
structure, and paragraphing.
MX30-02 Identify Your Audience 11 The student will edit writing for Writing Adjust sentence and paragraph structures for a
and Purpose correct grammar, capitalization, variety of purposes and audiences.
punctuation, spelling, sentence
structure, and paragraphing.
MX32-01 Reread and Revise 11 The student will edit writing for Writing The student will write, revise, and edit personal,
correct grammar, capitalization, professional, and informational correspondence
punctuation, spelling, sentence to a standard acceptable in the workplace and
structure, and paragraphing. higher education.
MX30-05 Select an 11 The student will edit writing for Writing Organize information to support purpose and
Organizational correct grammar, capitalization, form of writing.
Structure punctuation, spelling, sentence
structure, and paragraphing.
MX30-06 Group Ideas and 11 The student will edit writing for Writing Present information in a logical manner.
Sequence Information correct grammar, capitalization,
punctuation, spelling, sentence
structure, and paragraphing.
MX30-01 The Writing Process 11 The student will analyze, evaluate, Research Narrow a topic.
synthesize, and organize information
from a variety of sources to produce
a research product.
MX68-01 Examine Ideas and 11 The student will analyze, evaluate, Research Develop a plan for research.
Support synthesize, and organize information
from a variety of sources to produce
a research product.
MX68-01 Examine Ideas and 11 The student will analyze, evaluate, Research Collect information to support a thesis.
Support synthesize, and organize information
from a variety of sources to produce
a research product.
Skill/ Skill/ Strategy Name Grade Strand Text Standard Objective Text
Strategy # Text
MX30-06 Group Ideas and 11 The student will analyze, evaluate, Research Synthesize information in a logical sequence.
Sequence Information synthesize, and organize information
from a variety of sources to produce
a research product.
MX68-02 Judge Organization 11 The student will analyze, evaluate, Research Edit writing for clarity of content and effect.
and Approach synthesize, and organize information
from a variety of sources to produce
a research product.
MX68-03 The Little Details 11 The student will analyze, evaluate, Research Edit copy for grammatically correct use of
Count synthesize, and organize information language, spelling, punctuation, and
from a variety of sources to produce capitalization.
a research product.
MX32-02 Proofread Carefully 11 The student will analyze, evaluate, Research Proofread final copy and prepare for publication
synthesize, and organize information or submission.
from a variety of sources to produce
a research product.
MX27-05 Identify and Compare 12 The student will read and analyze Reading Recognize major literary forms and their
Genres the development of British literature Analysis elements.
and literature of other cultures.
MX27-04 Determine and 12 The student will read and analyze Reading Recognize the characteristics of major
Support Theme or the development of British literature Analysis chronological eras.
Tone and literature of other cultures.
MX27-04 Determine and 12 The student will read and analyze Reading Relate literary works and authors to major
Support Theme or the development of British literature Analysis themes and issues of their eras.
Tone and literature of other cultures.
Skill/ Skill/ Strategy Name Grade Strand Text Standard Objective Text
Strategy # Text
MX27-05 Identify and Compare 12 The student will read and analyze a Reading Identify formats common to new publications and
Genres variety of informational materials, Analysis information resources.
including electronic resources.
MX27-04 Determine and 12 The student will read and critique a Reading Explain how the choice of words in a poem
Support Theme or variety of poetry. Analysis creates tone and voice.
Tone
MX27-01 Analyze the Setting 12 The student will read and critique Reading Describe the conflict, plot, climax, and setting.
dramatic selections from a variety of Analysis
authors.
MX27-03 Classify and Evaluate 12 The student will read and critique Reading Compare and contrast ways in which character,
Character dramatic selections from a variety of Analysis scene, dialogue, and staging contribute to the
authors. theme and the dramatic effect.
MX30-01 The Writing Process 12 The student will develop expository Writing Generate, gather, and organize ideas for writing.
and informational writings.
MX30-02 Identify Your Audience 12 The student will develop expository Writing Consider audience and purpose when planning
and Purpose and informational writings. for writing.
MX30-04 Select an 12 The student will develop expository Writing Write analytically about literary, informational,
Organizational and informational writings. and visual materials.
Structure
MX30-04 Select an 12 The student will develop expository Writing Elaborate ideas clearly and accurately.
Organizational and informational writings.
Structure
MX32-01 Reread and Revise 12 The student will develop expository Writing Revise writing for depth of information and
and informational writings. technique of presentation.
MX68-03 The Little Details 12 The student will develop expository Writing Apply grammatical conventions to edit writing for
Count and informational writings. correct use of language, spelling, punctuation,
and capitalization.
MX32-02 Proofread Carefully 12 The student will develop expository Writing Proofread final copy, and prepare document for
and informational writings. publication or submission.
Skill/ Skill/ Strategy Name Grade Strand Text Standard Objective Text
Strategy # Text
MX69-01 Find the Facts 12 The student will write documented Writing Identify and understand the ethical issues of
research papers. research and documentation.
MX68-01 Examine Ideas and 12 The student will write documented Writing Evaluate the accuracy and usefulness of
Support research papers. information.
MX68-01 Examine Ideas and 12 The student will write documented Writing Synthesize information to support the thesis.
Support research papers.
MX30-06 Group Ideas and 12 The student will write documented Writing Present information in a logical manner.
Sequence Information research papers.
MX30-05 Select an 12 The student will write documented Writing Cite sources of information using a standard
Organizational research papers. method of documentation, including Modern
Structure Language Association (MLA) or American
Psychological Association (APA).
MX68-03 The Little Details 12 The student will write documented Writing Edit copies for correct use of language, spelling,
Count research papers. punctuation, and capitalization.
MX32-02 Proofread Carefully 12 The student will write documented Writing Proofread final copy, and prepare document for
research papers. publication or submission.
State: Virginia
Grades: Secondary
Content: Social Science
Standard Correlation Date: 9/03
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX96-01 Beginnings World History The student will demonstrate an World History and describing artistic, literary, and intellectual
and Geography: understanding of the political, Geography ideas of the Renaissance;
1500 a.d. to the cultural, and economic conditions
Present in the world about 1500 a.d. by
MX96-01 Beginnings World History The student will demonstrate an World History and analyzing major trade patterns;
and Geography: understanding of the political, Geography
1500 a.d. to the cultural, and economic conditions
Present in the world about 1500 a.d. by
MX96-01 Beginnings Era V: The student will demonstrate World History and describing changing cultural values,
Emergence of a knowledge of the Reformation in Geography traditions, and philosophies, and assessing
Global Age, terms of its impact on Western the role of the printing press.
1500 to 1650 civilization by
a.d.
MX96-01 Beginnings Era V: The student will demonstrate World History and explaining the roles of explorers and
Emergence of a knowledge of the impact of the Geography conquistadors;
Global Age, European Age of Discovery and
1500 to 1650 expansion into the Americas,
a.d. Africa, and Asia by
MX96-01 Beginnings Era V: The student will demonstrate World History and describing the influence of religion;
Emergence of a knowledge of the impact of the Geography
Global Age, European Age of Discovery and
1500 to 1650 expansion into the Americas,
a.d. Africa, and Asia by
MX96-02 Colonization and Era V: The student will demonstrate World History and explaining migration, settlement patterns,
Settlement Emergence of a knowledge of the impact of the Geography cultural diffusion, and social classes in the
Global Age, European Age of Discovery and colonized areas;
1500 to 1650 expansion into the Americas,
a.d. Africa, and Asia by
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX96-02 Colonization and Era V: The student will demonstrate World History and defining the Columbian Exchange;
Settlement explaining the triangular trade;
New Nation describing the impact of precious metal
New Nation Emergence of a knowledge of the impact of the Geography exports from the Americas.
Global Age, European Age of Discovery and
1500 to 1650 expansion into the Americas,
a.d. Africa, and Asia by
MX97-01 Industrialization Era VI: Age of The student will demonstrate World History and citing scientific, technological, and
Revolutions, knowledge of the effects of the Geography industrial developments and explaining
1650 to 1914 Industrial Revolution during the how they brought about urbanization and
a.d. nineteenth century by social and environmental changes;
MX97-02 Emergence of Era VI: Age of The student will demonstrate World History and explaining the emergence of capitalism as
Modern America Revolutions, knowledge of the effects of the Geography a dominant economic pattern, and
1650 to 1914 Industrial Revolution during the subsequent development of socialism and
a.d. nineteenth century by communism;
MX97-02 Emergence of Era VI: Age of The student will demonstrate World History and describing the evolution of the nature of
Modern America Revolutions, knowledge of the effects of the Geography work and the labor force, including its
1650 to 1914 Industrial Revolution during the effects on families, the status of women
a.d. nineteenth century by and children, the slave trade, and the labor
union movement;
MX97-02 Emergence of Era VI: Age of The student will demonstrate World History and explaining the rise of industrial economies
Modern America Revolutions, knowledge of the effects of the Geography and their link to imperialism and
1650 to 1914 Industrial Revolution during the nationalism;
a.d. nineteenth century by
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX97-02 Emergence of Era VI: Age of The student will demonstrate World History and assessing the impact of European
Modern America Revolutions, knowledge of the effects of the Geography economic and military power on Asia and
1650 to 1914 Industrial Revolution during the Africa, with emphasis on the competition
a.d. nineteenth century by for resources and the responses of
colonized peoples
MX97-02 Emergence of Era VII: Era of The student will demonstrate World History and explaining economic and political causes,
Modern America Global Wars, knowledge of the worldwide Geography major events, and identifying major leaders
1914 to 1945 impact of World War I by of the war, with emphasis on Woodrow
Wilson and Kaiser Wilhelm II;
MX97-02 Emergence of Era VII: Era of The student will demonstrate World History and explaining the outcomes and global effect
Modern America Global Wars, knowledge of the worldwide Geography of the war and the Treaty of Versailles;
1914 to 1946 impact of World War I by
MX97-02 Emergence of Era VII: Era of The student will demonstrate World History and citing causes and consequences of the
Modern America Global Wars, knowledge of the worldwide Geography Russian Revolution.
1914 to 1947 impact of World War I by
MX97-02 Emergence of Era VII: Era of The student will demonstrate World History and describing the League of Nations and the
Modern America Global Wars, knowledge of political, economic, Geography mandate system;
1914 to 1948 social, and cultural developments
during the Interwar Period by
MX97-03 Great Depression Era VII: Era of The student will demonstrate World History and citing causes and assessing the impact of
and World War II Global Wars, knowledge of political, economic, Geography worldwide depression in the 1930s;
1914 to 1949 social, and cultural developments
during the Interwar Period by
MX97-03 Great Depression Era VII: Era of The student will demonstrate World History and examining events related to the rise,
and World War II Global Wars, knowledge of political, economic, Geography aggression, and human costs of dictatorial
1914 to 1950 social, and cultural developments regimes in the Soviet Union, Germany,
during the Interwar Period by Italy, and Japan, and identifying their major
leaders, i.e., Joseph Stalin, Adolf Hitler,
Benito Mussolini, Hirohito, and Hideki Tojo.
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX97-03 Great Depression Era VII: Era of The student will demonstrate World History and explaining economic and political causes,
and World War II Global Wars, knowledge of the worldwide Geography major events, and identifying leaders of the
1914 to 1951 impact of World War II by war, with emphasis on Franklin D.
Roosevelt, Harry Truman, Dwight D.
Eisenhower, Douglas MacArthur, George
Marshall, Winston Churchill, Joseph Stalin,
Adolf Hitler, Hideki Tojo, and Hirohito;
MX97-03 Great Depression Era VII: Era of The student will demonstrate World History and examining the Holocaust and other
and World War II Global Wars, knowledge of the worldwide Geography examples of genocide in the twentieth
1914 to 1952 impact of World War II by century;
MX97-03 Great Depression Era VII: Era of The student will demonstrate World History and explaining the terms of the peace, the war
and World War II Global Wars, knowledge of the worldwide Geography crimes trials, the division of Europe, plans
1914 to 1953 impact of World War II by to rebuild Germany and Japan, and the
creation of international cooperative
organizations.
MX97-04 The Post-War Era Era VIII: The The student will demonstrate World History and explaining key events of the Cold War,
Post War knowledge of major events and Geography including the competition between the
Period, 1945 to outcomes of the Cold War by American and Soviet economic and
the Present political systems and the causes of the
collapse of communism in the Soviet
Union and Eastern Europe;
MX97-04 The Post-War Era Era VIII: The The student will demonstrate World History and assessing the impact of nuclear weaponry
Post War knowledge of major events and Geography on patterns of conflict and cooperation
Period, 1945 to outcomes of the Cold War by since 1945;
the Present
MX97-04 The Post-War Era Era VIII: The The student will demonstrate World History and describing conflicts and revolutionary
Post War knowledge of major events and Geography movements in eastern Asia, including
Period, 1945 to outcomes of the Cold War by those in China and Vietnam, and their
the Present major leaders, i.e., Mao Tse-tung
(Zedong), Chiang Kai-shek, and Ho Chi
Minh.
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX103-03 Government Era VIII: The The student will demonstrate World History and describing the struggles for self-rule,
Systems Post War knowledge of political, economic, Geography including Gandhi's leadership in India;
Period, 1945 to social, and cultural aspects of
the Present independence movements and
development efforts by
MX105-01 Interactions Among Era VIII: The The student will demonstrate World History and describing Africa's achievement of
Nations Post War knowledge of political, economic, Geography independence, including Kenyatta's
Period, 1945 to social, and cultural aspects of leadership of Kenya;
the Present independence movements and
development efforts by
MX105-02 American Foreign Era VIII: The The student will demonstrate World History and describing the end of the mandate system
Policy Post War knowledge of political, economic, Geography and the creation of states in the Middle
Period, 1945 to social, and cultural aspects of East.
the Present independence movements and
development efforts by
MX97-04 The Post-War Era Era VIII: The The student will demonstrate World History and assessing the impact of economic
Post War knowledge of cultural, economic, Geography development and global population growth
Period, 1945 to and social conditions in developed on the environment and society, including
the Present and developing nations of the an understanding of the links between
contemporary world by economic and political freedom;
MX97-04 The Post-War Era Era VIII: The The student will demonstrate World History and describing economic interdependence,
Post War knowledge of cultural, economic, Geography including the rise of multinational
Period, 1945 to and social conditions in developed corporations, international organizations,
the Present and developing nations of the and trade agreements.
contemporary world by
MX99-05 Speculate About World The student will use maps, globes, World History and analyze and explain how different cultures
Alternatives Geography photographs, and pictures in order Geography develop different perspectives on the world
to and its problems;
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX99-04 Analyze Impact World The student will analyze how World History and explaining how technology affects one's
Geography selected physical and ecological Geography ability to modify the environment and adapt
processes shape the Earth's to it
surface by
MX98-04 Build the Big Picture World The student will locate and World History and Latin America and the Caribbean, Europe,
Geography analyze physical, economic, and Geography United States and Canada, North Africa
cultural characteristics of world and Southwest Asia, Sub-Saharan Africa,
regions: Russia and Central Asia, South Asia,
Southeast Asia, East Asia, Australia and
the Pacific Islands, and Antarctica.
MX98-02 Compare and World The student will World History and compare and contrast the distribution,
Contrast Geography Geography growth rates, and characteristics of human
population in terms of settlement patterns
and the location of natural and capital
resources.
MX100-03 Examine Influences World The student will World History and analyze past and present trends in human
Geography Geography migration and cultural interaction as they
are influenced by social, economic,
political, and environmental factors.
MX101-01 Back to Basics World The student will identify natural, World History and showing patterns of economic activity and
Geography human, and capital resources and Geography land use;
explain their significance by
MX100-05 Predict World The student will identify natural, World History and evaluating perspectives and consequences
Consequences Geography human, and capital resources and Geography regarding the use of resources.
explain their significance by
MX101-04 Economic Systems World The student will World History and distinguish between developed and
Geography Geography developing countries and relate the level of
economic development to the standard of
living and quality of life.
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX101-02 Economic Policy World The student will analyze the global World History and identifying criteria that influence economic
Geography patterns and networks of Geography activities;
economic interdependence by
MX101-03 Markets and Trade World The student will analyze the global World History and explaining comparative advantage and its
Geography patterns and networks of Geography relationship to international trade;
economic interdependence by
MX101-04 Economic Systems World The student will analyze the global World History and describing ways that economic and social
Geography patterns and networks of Geography interactions have changed over time;
economic interdependence by
MX101-03 Markets and Trade World The student will analyze the global World History and describing and evaluating the formation of
Geography patterns and networks of Geography economic unions.
economic interdependence by
MX101-04 Economic Systems World The student will analyze how the World History and explaining and analyzing reasons for the
Geography forces of conflict and cooperation Geography different spatial divisions at the local and
affect the division and control of regional levels;
the Earth's surface by
MX101-04 Economic Systems World The student will analyze how the World History and explaining and analyzing the different
Geography forces of conflict and cooperation Geography spatial divisions at the national and
affect the division and control of international levels;
the Earth's surface by
MX99-04 Analyze Impact World The student will analyze how the World History and analyzing ways cooperation occurs to solve
Geography forces of conflict and cooperation Geography problems and settle disputes.
affect the division and control of
the Earth's surface by
MX99-04 Analyze Impact World The student will analyze the World History and applying the concepts of site and situation
Geography patterns of urban development by Geography to major cities in each region;
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX99-01 Gather Information Virginia and The student will demonstrate skills World History and identify, analyze, and interpret primary and
United States for historical and geographical Geography secondary source documents, records,
History analysis, including the ability to and data, including artifacts, diaries,
letters, photographs, journals, newspapers,
historical accounts, and art to increase
understanding of events and life in the
United States;
MX99-02 Establish Context Virginia and The student will demonstrate skills World History and evaluate the authenticity, authority, and
United States for historical and geographical Geography credibility of sources;
History analysis, including the ability to
MX99-01 Gather Information Virginia and The student will demonstrate skills World History and formulate historical questions and defend
United States for historical and geographical Geography findings based on inquiry and
History analysis, including the ability to interpretation;
MX99-02 Establish Context Virginia and The student will demonstrate skills World History and develop perspectives of time and place,
United States for historical and geographical Geography including the construction of maps and
History analysis, including the ability to various time lines of events, periods, and
personalities in American history;
MX99-03 Look at Different Virginia and The student will demonstrate skills World History and communicate findings orally and in
Points of View United States for historical and geographical Geography analytical essays and/or comprehensive
History analysis, including the ability to papers;
MX99-04 Analyze Impact Virginia and The student will demonstrate skills World History and develop skills in discussion, debate, and
United States for historical and geographical Geography persuasive writing with respect to enduring
History analysis, including the ability to issues and determine how divergent
viewpoints have been addressed and
reconciled;
MX99-04 Analyze Impact Virginia and The student will demonstrate skills World History and apply geographic skills and reference
United States for historical and geographical Geography sources to understand how relationships
History analysis, including the ability to between humans and their environment
have changed over time;
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX98-01 Identify Context and Virginia and The student will demonstrate skills World History and interpret the significance of excerpts from
Purpose United States for historical and geographical Geography famous speeches and other documents.
History analysis, including the ability to
MX96-02 Colonization and Early America: The student will describe World History and how early European exploration and
Settlement Early Claims, Geography colonization resulted in cultural interactions
Early Conflicts among Europeans, Africans, and American
Indians (First Americans).
MX96-03 Revolution and the Early America: The student will describe World History and how the values and institutions of
New Nation Early Claims, Geography European economic life took root in the
Early Conflicts colonies and how slavery reshaped
European and African life in the Americas.
MX96-03 Revolution and the Revolution and The student will demonstrate World History and analyzing how the political ideas of John
New Nation the New Nation knowledge of events and issues of Geography Locke and those expressed in Common
the Revolutionary Period by Sense helped shape the Declaration of
Independence;
MX96-03 Revolution and the Revolution and The student will demonstrate World History and describing the political differences among
New Nation the New Nation knowledge of events and issues of Geography the colonists concerning separation from
the Revolutionary Period by Britain;
MX96-03 Revolution and the Revolution and The student will demonstrate World History and analyzing reasons for colonial victory in the
New Nation the New Nation knowledge of events and issues of Geography Revolutionary War.
the Revolutionary Period by
MX96-03 Revolution and the Revolution and The student will demonstrate World History and explaining the origins of the Constitution,
New Nation the New Nation knowledge of the issues involved Geography including the Articles of Confederation;
in the creation and ratification of
the United States Constitution and
how the principles of limited
government, consent of the
governed, and the social contract
are embodied in it by
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX96-03 Revolution and the Revolution and The student will demonstrate World History and identifying the major compromises
New Nation the New Nation knowledge of the issues involved Geography necessary to produce the Constitution, and
in the creation and ratification of the roles of James Madison and George
the United States Constitution and Washington;
how the principles of limited
government, consent of the
governed, and the social contract
are embodied in it by
MX96-03 Revolution and the Revolution and The student will demonstrate World History and describing the conflict over ratification,
New Nation the New Nation knowledge of the issues involved Geography including the Bill of Rights and the
in the creation and ratification of arguments of the Federalists and Anti-
the United States Constitution and Federalists;
how the principles of limited
government, consent of the
governed, and the social contract
are embodied in it by
MX96-03 Revolution and the Revolution and The student will demonstrate World History and examining the significance of the Virginia
New Nation the New Nation knowledge of the issues involved Geography Declaration of Rights and the Virginia
in the creation and ratification of Statute for Religious Freedom in the
the United States Constitution and framing of the Bill of Rights.
how the principles of limited
government, consent of the
governed, and the social contract
are embodied in it by
MX96-03 Revolution and the Expansion and The student will demonstrate World History and identifying the economic, political, and
New Nation Reform: 1801 to knowledge of the major events Geography geographic factors that led to territorial
1860 during the first half of the expansion and its impact on the American
nineteenth century by Indians (First Americans);
MX96-03 Revolution and the Expansion and The student will demonstrate World History and describing the key features of the
New Nation Reform: 1801 to knowledge of the major events Geography Jacksonian Era, with emphasis on federal
1861 during the first half of the banking policies;
nineteenth century by
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX96-04 Expansion and Expansion and The student will demonstrate World History and describing the cultural, economic, and
Reform Reform: 1801 to knowledge of the major events Geography political issues that divided the nation,
1862 during the first half of the including slavery, the abolitionist and
nineteenth century by women's suffrage movements, and the
role of the states in the Union.
MX96-05 Civil War and Civil War and The student will demonstrate World History and identifying the major events and the roles
Reconstruction Reconstruction: knowledge of the Civil War and Geography of key leaders of the Civil War Era, with
1860 to 1877 Reconstruction Era and its emphasis on Abraham Lincoln, Ulysses S.
importance as a major turning Grant, Robert E. Lee, and Frederick
point in American history by Douglass;
MX96-05 Civil War and Civil War and The student will demonstrate World History and analyzing the significance of the
Reconstruction Reconstruction: knowledge of the Civil War and Geography Emancipation Proclamation and the
1860 to 1878 Reconstruction Era and its principles outlined in Lincoln's Gettysburg
importance as a major turning Address;
point in American history by
MX96-05 Civil War and Civil War and The student will demonstrate World History and examining the political, economic, and
Reconstruction Reconstruction: knowledge of the Civil War and Geography social impact of the war and
1860 to 1879 Reconstruction Era and its Reconstruction, including the adoption of
importance as a major turning the 13th, 14th, and 15th Amendments to
point in American history by the Constitution of the United States.
MX97-01 Industrialization Reshaping the The student will demonstrate World History and explaining the relationship among territorial
Nation and the knowledge of how the nation grew Geography expansion, westward movement of the
Emergence of and changed from the end of population, new immigration, growth of
Modern Reconstruction through the early cities, and the admission of new states to
America: 1877 twentieth century by the Union;
to 1930s
MX97-01 Industrialization Reshaping the The student will demonstrate World History and describing the transformation of the
Nation and the knowledge of how the nation grew Geography American economy from a primarily
Emergence of and changed from the end of agrarian to a modern industrial economy
Modern Reconstruction through the early and identifying major inventions that
America: 1877 twentieth century by improved life in the United States;
to 1930s
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX97-01 Industrialization Reshaping the The student will demonstrate World History and analyzing prejudice and discrimination
Nation and the knowledge of how the nation grew Geography during this time period, with emphasis on
Emergence of and changed from the end of "Jim Crow" and the responses of Booker T.
Modern Reconstruction through the early Washington and W.E.B. Du Bois;
America: 1877 twentieth century by
to 1930s
MX97-01 Industrialization Reshaping the The student will demonstrate World History and identifying the impact of the Progressive
Nation and the knowledge of how the nation grew Geography Movement, including child labor and
Emergence of and changed from the end of antitrust laws, the rise of labor unions, and
Modern Reconstruction through the early the success of the women's suffrage
America: 1877 twentieth century by movement.
to 1930s
MX97-02 Emergence of Reshaping the The student will demonstrate World History and explaining the changing policies of the
Modern America Nation and the knowledge of the emerging role of Geography United States toward Latin America and
Emergence of the United States in world affairs Asia and the growing influence of the
Modern and key domestic events after United States in foreign markets;
America: 1877 1890 by
to 1930s
MX97-02 Emergence of Reshaping the The student will demonstrate World History and evaluating United States involvement in
Modern America Nation and the knowledge of the emerging role of Geography World War I, including Wilson's Fourteen
Emergence of the United States in world affairs Points, the Treaty of Versailles, and the
Modern and key domestic events after national debate over treaty ratification and
America: 1877 1890 by the League of Nations;
to 1930s
MX97-03 Great Depression Reshaping the The student will demonstrate World History and explaining the causes of the Great
and World War II Nation and the knowledge of the emerging role of Geography Depression, its impact on the American
Emergence of the United States in world affairs people, and the ways the New Deal
Modern and key domestic events after addressed it.
America: 1877 1890 by
to 1930s
MX97-03 Great Depression Conflict: The The student will demonstrate World History and identifying the causes and events that led
and World War II World at War: knowledge of World War II by Geography to American involvement in the war,
1939 to 1945 including military assistance to Britain and
the Japanese attack on Pearl Harbor;
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX97-03 Great Depression Conflict: The The student will demonstrate World History and describing the major battles and turning
and World War II World at War: knowledge of World War II by Geography points of the war in North Africa, Europe,
1939 to 1946 and the Pacific, including Midway,
Stalingrad, the Normandy landing (D-Day),
and Truman's decision to use the atomic
bomb to force the surrender of Japan;
MX97-03 Great Depression Conflict: The The student will demonstrate World History and describing the role of all-minority military
and World War II World at War: knowledge of World War II by Geography units, including the Tuskegee Airmen and
1939 to 1947 Nisei regiments;
MX97-03 Great Depression Conflict: The The student will demonstrate World History and describing the Geneva Convention and the
and World War II World at War: knowledge of World War II by Geography treatment of prisoners of war during World
1939 to 1948 War II;
MX97-03 Great Depression Conflict: The The student will demonstrate World History and analyzing the Holocaust (Hitler's "final
and World War II World at War: knowledge of World War II by Geography solution"), its impact on Jews and other
1939 to 1949 groups, and postwar trials of war criminals.
MX97-03 Great Depression Conflict: The The student will demonstrate World History and explaining how the United States mobilized
and World War II World at War: knowledge of the effects of World Geography its economic, human, and military
1939 to 1950 War II on the home front by resources;
MX97-03 Great Depression Conflict: The The student will demonstrate World History and describing the contributions of women and
and World War II World at War: knowledge of the effects of World Geography minorities to the war effort;
1939 to 1951 War II on the home front by
MX97-03 Great Depression Conflict: The The student will demonstrate World History and explaining the internment of Japanese
and World War II World at War: knowledge of the effects of World Geography Americans during the war;
1939 to 1952 War II on the home front by
MX97-04 The Post-War Era Conflict: The The student will demonstrate World History and describing the role of media and
World at War: knowledge of the effects of World Geography communications in the war effort.
1939 to 1953 War II on the home front by
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX97-04 The Post-War Era The United The student will demonstrate World History and describing outcomes of World War II,
States since knowledge of United States Geography including political boundary changes, the
World War II foreign policy since World War II formation of the United Nations, and the
by Marshall Plan;
MX97-04 The Post-War Era The United The student will demonstrate World History and explaining the origins of the Cold War, and
States since knowledge of United States Geography describing the Truman Doctrine and the
World War II foreign policy since World War II policy of containment of communism, the
by American role in wars in Korea and
Vietnam, and the role of the North Atlantic
Treaty Organization (NATO) in Europe;
MX97-04 The Post-War Era The United The student will demonstrate World History and explaining the role of America's military
States since knowledge of United States Geography and veterans in defending freedom during
World War II foreign policy since World War II the Cold War;
by
MX97-05 Contemporary The United The student will demonstrate World History and explaining the collapse of communism and
America States since knowledge of United States Geography the end of the Cold War, including the role
World War II foreign policy since World War II of Ronald Reagan.
by
MX97-05 Contemporary The United The student will demonstrate World History and identifying the importance of the Brown v.
America States since knowledge of the Civil Rights Geography Board of Education decision, the roles of
World War II movement of the 1950s and Thurgood Marshall and Oliver Hill, and how
1960s by Virginia responded;
MX97-05 Contemporary The United The student will demonstrate World History and describing the importance of the National
America States since knowledge of the Civil Rights Geography Association for the Advancement of
World War II movement of the 1950s and Colored People (NAACP), the 1963 March
1960s by on Washington, the Civil Rights Act of
1964, and the Voting Rights Act of 1965.
MX97-05 Contemporary The United The student will demonstrate World History and analyzing the effects of increased
America States since knowledge of economic, social, Geography participation of women in the labor force;
World War II cultural, and political
developments in the contemporary
United States by
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX97-05 Contemporary The United The student will demonstrate World History and analyzing how changing patterns of
America States since knowledge of economic, social, Geography immigration affect the diversity of the
World War II cultural, and political United States population, the reasons new
developments in the contemporary immigrants choose to come to this country,
United States by and their contributions to contemporary
America;
MX97-05 Contemporary The United The student will demonstrate World History and explaining the media influence on
America States since knowledge of economic, social, Geography contemporary American culture and how
World War II cultural, and political scientific and technological advances
developments in the contemporary affect the workplace, health care, and
United States by education.
MX100-01 Clarify the Issue Virginia and The student will demonstrate World History and analyze primary and secondary source
United States mastery of the social studies skills Geography documents;
Government citizenship requires, including the
ability to
MX100-01 Clarify the Issue Virginia and The student will demonstrate World History and create and interpret maps, diagrams,
United States mastery of the social studies skills Geography tables, charts, graphs, and spreadsheets;
Government citizenship requires, including the
ability to
MX100-03 Examine Influences Virginia and The student will demonstrate World History and analyze political cartoons, political
United States mastery of the social studies skills Geography advertisements, pictures, and other
Government citizenship requires, including the graphic media;
ability to
MX100-02 Find Parallels and Virginia and The student will demonstrate World History and distinguish between relevant and irrelevant
Precedents United States mastery of the social studies skills Geography information;
Government citizenship requires, including the
ability to
MX100-03 Examine Influences Virginia and The student will demonstrate World History and evaluate information for accuracy,
United States mastery of the social studies skills Geography separating fact from opinion;
Government citizenship requires, including the
ability to
MX100-01 Clarify the Issue Virginia and The student will demonstrate World History and identify a problem and prioritize solutions;
United States mastery of the social studies skills Geography
Government citizenship requires, including the
ability to
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX100-06 Present and Justify Virginia and The student will demonstrate World History and select and defend positions in writing,
Results United States mastery of the social studies skills Geography discussion, and debate.
Government citizenship requires, including the
ability to
MX103-03 Government Virginia and The student will demonstrate World History and describing the development of Athenian
Systems United States knowledge of the political Geography democracy and the Roman republic;
Government philosophies that shaped the
development of Virginia and
United States constitutional
government by
MX103-02 Purpose of Virginia and The student will demonstrate World History and explaining the influence of the Magna
Government United States knowledge of the political Geography Carta, the English Petition of Rights, and
Government philosophies that shaped the the English Bill of Rights;
development of Virginia and
United States constitutional
government by
MX103-03 Government Virginia and The student will demonstrate World History and examining the writings of Hobbes, Locke,
Systems United States knowledge of the political Geography and Montesquieu;
Government philosophies that shaped the
development of Virginia and
United States constitutional
government by
MX103-03 Government Virginia and The student will demonstrate World History and explaining the guarantee of the rights of
Systems United States knowledge of the political Geography Englishmen set forth in the charters of the
Government philosophies that shaped the Virginia Company of London;
development of Virginia and
United States constitutional
government by
MX104-01 Read the Rules Virginia and The student will demonstrate World History and analyzing the natural rights philosophies
United States knowledge of the political Geography expressed in the Declaration of
Government philosophies that shaped the Independence.
development of Virginia and
United States constitutional
government by
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX104-03 Making Decisions, Virginia and The student will demonstrate World History and recognizing the fundamental worth and
Seeking Consensus, United States knowledge of the concepts of Geography dignity of the individual;
and Resolving Government democracy by
Conflicts
MX104-03 Making Decisions, Virginia and The student will demonstrate World History and recognizing the equality of all citizens
Seeking Consensus, United States knowledge of the concepts of Geography under the law;
and Resolving Government democracy by
Conflicts
MX104-03 Making Decisions, Virginia and The student will demonstrate World History and recognizing majority rule and minority
Seeking Consensus, United States knowledge of the concepts of Geography rights;
and Resolving Government democracy by
Conflicts
MX104-03 Making Decisions, Virginia and The student will demonstrate World History and recognizing the necessity of compromise;
Seeking Consensus, United States knowledge of the concepts of Geography
and Resolving Government democracy by
Conflicts
MX104-03 Making Decisions, Virginia and The student will demonstrate World History and recognizing the freedom of the individual.
Seeking Consensus, United States knowledge of the concepts of Geography
and Resolving Government democracy by
Conflicts
MX103-01 Structure of Virginia and The student will demonstrate World History and examining the ratification debates and The
Government United States knowledge of the Constitution of Geography Federalist;
Government the United States by
MX103-01 Structure of Virginia and The student will demonstrate World History and identifying the purposes for government
Government United States knowledge of the Constitution of Geography stated in the Preamble;
Government the United States by
MX103-01 Structure of Virginia and The student will demonstrate World History and examining the fundamental principles upon
Government United States knowledge of the Constitution of Geography which the Constitution of the United States
Government the United States by is based, including the rule of law, consent
of the governed, limited government,
separation of powers, and federalism;
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX104-01 Read the Rules Virginia and The student will demonstrate World History and illustrating the structure of the national
United States knowledge of the Constitution of Geography government outlined in Article I, Article II,
Government the United States by and Article III;
MX103-01 Structure of Virginia and The student will demonstrate World History and describing the amendment process.
Government United States knowledge of the Constitution of Geography
Government the United States by
MX103-01 Structure of Virginia and The student will demonstrate World History and explaining the relationship of the state
Government United States knowledge of the federal system Geography governments to the national government;
Government described in the Constitution of the
United States by
MX103-01 Structure of Virginia and The student will demonstrate World History and describing the extent to which power is
Government United States knowledge of the federal system Geography shared;
Government described in the Constitution of the
United States by
MX103-01 Structure of Virginia and The student will demonstrate World History and identifying the powers denied state and
Government United States knowledge of the federal system Geography national governments;
Government described in the Constitution of the
United States by
MX103-01 Structure of Virginia and The student will demonstrate World History and examining the ongoing debate that focuses
Government United States knowledge of the federal system Geography on the balance of power between state and
Government described in the Constitution of the national governments.
United States by
MX104-03 Making Decisions, Virginia and The student will demonstrate World History and describing the organization, role, and
Seeking Consensus, United States knowledge of local, state, and Geography constituencies of political parties;
and Resolving Government national elections by
Conflicts
MX104-03 Making Decisions, Virginia and The student will demonstrate World History and describing the nomination and election
Seeking Consensus, United States knowledge of local, state, and Geography process;
and Resolving Government national elections by
Conflicts
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX104-03 Making Decisions, Virginia and The student will demonstrate World History and examining campaign funding and
Seeking Consensus, United States knowledge of local, state, and Geography spending;
and Resolving Government national elections by
Conflicts
MX104-03 Making Decisions, Virginia and The student will demonstrate World History and analyzing the influence of media coverage,
Seeking Consensus, United States knowledge of local, state, and Geography campaign advertising, and public opinion
and Resolving Government national elections by polls;
Conflicts
MX104-02 Democracy in Action Virginia and The student will demonstrate World History and examining the impact of reapportionment
United States knowledge of local, state, and Geography and redistricting;
Government national elections by
MX104-01 Read the Rules Virginia and The student will demonstrate World History and identifying how amendments extend the
United States knowledge of local, state, and Geography right to vote;
Government national elections by
MX104-03 Making Decisions, Virginia and The student will demonstrate World History and analyzing voter turnout.
Seeking Consensus, United States knowledge of local, state, and Geography
and Resolving Government national elections by
Conflicts
MX103-01 Structure of Virginia and The student will demonstrate World History and examining the legislative, executive, and
Government United States knowledge of the organization and Geography judicial branches;
Government powers of the national government
by
MX103-01 Structure of Virginia and The student will demonstrate World History and analyzing the relationship between the
Government United States knowledge of the organization and Geography three branches in a system of checks and
Government powers of the national government balances.
by
MX103-01 Structure of Virginia and The student will demonstrate World History and examining the legislative, executive, and
Government United States knowledge of the organization and Geography judicial branches;
Government powers of the state and local
governments described in the
Constitution of Virginia by
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX103-01 Structure of Virginia and The student will demonstrate World History and examining the structure and powers of
Government United States knowledge of the organization and Geography local governments: county, city, and town;
Government powers of the state and local
governments described in the
Constitution of Virginia by
MX103-01 Structure of Virginia and The student will demonstrate World History and analyzing the relationship among state and
Government United States knowledge of the organization and Geography local governments.
Government powers of the state and local
governments described in the
Constitution of Virginia by
MX103-01 Structure of Virginia and The student will demonstrate World History and examining different perspectives on the
Government United States knowledge of the process by Geography role of government;
Government which public policy is made by
MX103-01 Structure of Virginia and The student will demonstrate World History and explaining how local, state, and national
Government United States knowledge of the process by Geography governments formulate public policy;
Government which public policy is made by
MX103-01 Structure of Virginia and The student will demonstrate World History and describing the process by which policy is
Government United States knowledge of the process by Geography implemented by the bureaucracy at each
Government which public policy is made by level;
MX104-03 Making Decisions, Virginia and The student will demonstrate World History and analyzing how individuals, interest groups,
Seeking Consensus, United States knowledge of the process by Geography and the media influence public policy.
and Resolving Government which public policy is made by
Conflicts
MX103-01 Structure of Virginia and The student will demonstrate World History and explaining the jurisdiction of the federal
Government United States knowledge of the operation of the Geography courts;
Government federal judiciary by
MX103-01 Structure of Virginia and The student will demonstrate World History and examining how John Marshall established
Government United States knowledge of the operation of the Geography the Supreme Court as an independent, co-
Government federal judiciary by equal branch of government through his
opinions in Marbury v. Madison;
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX103-01 Structure of Virginia and The student will demonstrate World History and describing how the Supreme Court decides
Government United States knowledge of the operation of the Geography cases;
Government federal judiciary by
MX103-01 Structure of Virginia and The student will demonstrate World History and comparing the philosophies of judicial
Government United States knowledge of the operation of the Geography activism and judicial restraint.
Government federal judiciary by
MX104-01 Read the Rules Virginia and The student will demonstrate World History and examining the Bill of Rights, with emphasis
United States knowledge of civil liberties and civil Geography on First Amendment freedoms;
Government rights by
MX104-01 Read the Rules Virginia and The student will demonstrate World History and analyzing due process of law expressed in
United States knowledge of civil liberties and civil Geography the 5th and 14th Amendments;
Government rights by
MX104-01 Read the Rules Virginia and The student will demonstrate World History and explaining selective incorporation of the Bill
United States knowledge of civil liberties and civil Geography of Rights;
Government rights by
MX104-02 Democracy in Action Virginia and The student will demonstrate World History and exploring the balance between individual
United States knowledge of civil liberties and civil Geography liberties and the public interest;
Government rights by
MX104-02 Democracy in Action Virginia and The student will demonstrate World History and explaining every citizen's right to be treated
United States knowledge of civil liberties and civil Geography equally under the law.
Government rights by
MX105-02 American Foreign Virginia and The student will demonstrate World History and describing the responsibilities of the
Policy United States knowledge of the role of the Geography national government for foreign policy and
Government United States in a changing world national security;
by
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX105-02 American Foreign Virginia and The student will demonstrate World History and assessing the role played by national
Policy United States knowledge of the role of the Geography interest in shaping foreign policy and
Government United States in a changing world promoting world peace;
by
MX101-02 Economic Policy Virginia and The student will demonstrate World History and examining the relationship of Virginia and
United States knowledge of the role of the Geography the United States to the global economy;
Government United States in a changing world
by
MX101-02 Economic Policy Virginia and The student will demonstrate World History and examining recent foreign policy and
United States knowledge of the role of the Geography international trade initiatives since 1980.
Government United States in a changing world
by
MX103-01 Structure of Virginia and The student will demonstrate World History and describing the distribution of governmental
Government United States knowledge of how governments in Geography power;
Government Mexico, Great Britain, and the
People's Republic of China
compare with government in the
United States by
MX103-01 Structure of Virginia and The student will demonstrate World History and explaining the relationship between the
Government United States knowledge of how governments in Geography legislative and executive branches;
Government Mexico, Great Britain, and the
People's Republic of China
compare with government in the
United States by
MX103-01 Structure of Virginia and The student will demonstrate World History and comparing the extent of participation in the
Government United States knowledge of how governments in Geography political process.
Government Mexico, Great Britain, and the
People's Republic of China
compare with government in the
United States by
MX101-01 Back to Basics Virginia and The student will demonstrate World History and identifying the basic economic questions
United States knowledge of economic systems Geography encountered by all economic systems;
Government by
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX101-04 Economic Systems Virginia and The student will demonstrate World History and comparing the characteristics of free
United States knowledge of economic systems Geography market, command, and mixed economies,
Government by as described by Adam Smith and Karl
Marx;
MX101-02 Economic Policy Virginia and The student will demonstrate World History and evaluating the impact of the government's
United States knowledge of economic systems Geography role in the economy on individual economic
Government by freedoms;
MX101-04 Economic Systems Virginia and The student will demonstrate World History and explaining the relationship between
United States knowledge of economic systems Geography economic freedom and political freedom;
Government by
MX101-02 Economic Policy Virginia and The student will demonstrate World History and examining productivity and the standard of
United States knowledge of economic systems Geography living as measured by key economic
Government by indicators.
MX102-02 Understand Business Virginia and The student will demonstrate World History and assessing the importance of
Behavior United States knowledge of the United States Geography entrepreneurship, the profit motive, and
Government market economy by economic independence to the promotion
of economic growth;
MX102-02 Understand Business Virginia and The student will demonstrate World History and comparing types of business
Behavior United States knowledge of the United States Geography organizations;
Government market economy by
MX101-01 Back to Basics Virginia and The student will demonstrate World History and describing the factors of production;
United States knowledge of the United States Geography
Government market economy by
MX101-01 Back to Basics Virginia and The student will demonstrate World History and explaining the interaction of supply and
United States knowledge of the United States Geography demand;
Government market economy by
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX101-01 Back to Basics Virginia and The student will demonstrate World History and illustrating the circular flow of economic
United States knowledge of the United States Geography activity;
Government market economy by
MX101-02 Economic Policy Virginia and The student will demonstrate World History and analyzing global economic trends, with
United States knowledge of the United States Geography emphasis on the impact of technological
Government market economy by innovations.
MX101-02 Economic Policy Virginia and The student will demonstrate World History and analyzing the impact of fiscal and monetary
United States knowledge of the role of Geography policies on the economy;
Government government in the Virginia and
United States economies by
MX101-03 Markets and Trade Virginia and The student will demonstrate World History and describing the creation of public goods and
United States knowledge of the role of Geography services;
Government government in the Virginia and
United States economies by
MX101-02 Economic Policy Virginia and The student will demonstrate World History and examining environmental issues, property
United States knowledge of the role of Geography rights, contracts, consumer rights, labor-
Government government in the Virginia and management relations, and competition in
United States economies by the marketplace.
MX104-03 Making Decisions, Virginia and The student will demonstrate World History and practicing trustworthiness and honesty courtesy and respect for the
Seeking Consensus, United States knowledge of personal character Geography rights of others;
and Resolving Government traits that facilitate thoughtful and
Conflicts effective participation in civic life
by
MX104-03 Making Decisions, Virginia and The student will demonstrate World History and practicing responsibility, accountability, and
Seeking Consensus, United States knowledge of personal character Geography self-reliance;
and Resolving Government traits that facilitate thoughtful and
Conflicts effective participation in civic life
by
Skill/ Skill/ Strategy Name Topic Strand Text Standard Text Objective Text
Strategy #
MX104-03 Making Decisions, Virginia and The student will demonstrate World History and practicing respect for the law patriotism.
Seeking Consensus, United States knowledge of personal character Geography
and Resolving Government traits that facilitate thoughtful and
Conflicts effective participation in civic life
by
MX104-03 Making Decisions, Virginia and The student will understand that World History and obeying the law and paying taxes;
Seeking Consensus, United States thoughtful and effective Geography
and Resolving Government participation in civic life is
Conflicts characterized by
MX104-03 Making Decisions, Virginia and The student will understand that World History and serving as a juror;
Seeking Consensus, United States thoughtful and effective Geography
and Resolving Government participation in civic life is
Conflicts characterized by
MX104-03 Making Decisions, Virginia and The student will understand that World History and participating in the political process;
Seeking Consensus, United States thoughtful and effective Geography
and Resolving Government participation in civic life is
Conflicts characterized by
MX104-03 Making Decisions, Virginia and The student will understand that World History and performing public service;
Seeking Consensus, United States thoughtful and effective Geography
and Resolving Government participation in civic life is
Conflicts characterized by
MX104-03 Making Decisions, Virginia and The student will understand that World History and keeping informed about current issues;
Seeking Consensus, United States thoughtful and effective Geography
and Resolving Government participation in civic life is
Conflicts characterized by
MX104-03 Making Decisions, Virginia and The student will understand that World History and respecting differing opinions in a diverse
Seeking Consensus, United States thoughtful and effective Geography society.
and Resolving Government participation in civic life is
Conflicts characterized |
Algebra and Trigonometry-Stud. Solution Manual - 2nd edition
Summary a...show morelso included that provide more detailed annotations using everyday language. This approach gives them the skills to understand and apply algebra and trigonometry |
An engaging, entertaining, and informative introduction to probability and prediction in our everyday lives Although Probably Not deals with probability and statistics, it is not heavily mathematical and is not filled with complex derivations, proofs, and theoretical problem sets. This book unveils the world of statistics through questions such as... more...
A user-friendly presentation of the essential concepts and tools for calculating real costs and profits in personal finance Understanding the Mathematics of Personal Finance explains how mathematics, a simple calculator, and basic computer spreadsheets can be used to break down and understand even the most complex loan structures. In an easy-to-follow... more...
The first of its kind uniquely devoted to the field of computational electrostatics, this book dives headfirst into the actual problems that engineers are expected to solve using method of moment (MoM), finite difference, and finite element techniques. Readers are guided step by step through specific problems and challenges, covering all aspects of... more... |
Study Guide with Solutions for Faires/DeFranza's PrecalculusAuthored by Faires and DeFranza. Besides providing complete solutions to all odd-numbered exercises in the text, this guide includes additional material for students who want a more intensive review of algebra and trigonometry. The Study Guide also includes two copies of an examination - one copy to be taken at the beginning of the course to test their readiness for PreCalculus and a second copy to be used at the end of the course so students can assess their improvement and readiness for calculus. |
Mathematics
Mathematics
The Mathematics Department offers a broad, in-depth curriculum for exploring all aspects of mathematics – including quantities, changes, abstraction, structure and space – through small, engaging classroom settings. Within the department there is a great sense of discovery and collaboration as students and faculty are active in research, journal publication, conference presentations, mathematics competitions and many have received distinguished awards and recognition.
Research
is an integral part of the program and is incorporated into coursework as well as ongoing, unique research solutions outside of the classroom. In addition to collaborative research projects with faculty, students are highly active in the Math Club where they have the opportunity to discuss mathematics, solve problems and participate in social activities. A dedicated tutoring facility, great professor accessibility and the encouragement of open discussions in the classroom all contribute to a nurturing and supportive learning environment that lends a deep exploration of mathematics. Graduates are poised to excel in graduate programs and have become highly successful alumni who are skilled educators, actuaries, engineers, financial mathematicians and more.
Wally Sizer, mathematics, attended the Progress on Difference Equations 2014 conference May 21-24 in Izmir, Turkey, and presented the paper, "The Equation x(n+1) = ([x(n)]^k)/x(n-1)". The conference was attended by about 100 mathematicians from Asia, Europe, Africa, and North America.
Mike Miller, Mathematics, and Elementary Education majors Anna Adrover and Trista Bentler presented "No Borrowing Allowed!" at the Minnesota Council of Teachers of Mathematics Conference in Duluth on Friday, May 2nd. The presentation involved three alternative strategies to the standard subtraction algorithm.
Tim Harms, Mathematics Department, has been awarded tuition assistance for Add+VantageMR® Champion training in Apple Valley, MN, June 23-27, 2014. Dr. Harms was one of three educators selected to receive $3,500 by the US Math Recovery Council for Math Recovery Summer Institute registration. |
Math Instructor Creates Videos for Students
The movie "Argo" was a hit with critics and audiences last year, and now another Argo - Math Instructor Kevin Argo – is a hit on screen at College of The Albemarle.
Last fall, Argo began producing his own instructional videos in math for his students. From his campus office, Argo films himself working out tough algebra problems, showing students how to graph linear equations and add fractions.
"The camera has a flexible arm and I place the paper underneath," Argo said, explaining his production process. He uses Camtasia, a screen recording and video editing software, to create his videos, which he then uploads to the school's website. There, students can view the 30-minute math tutorials until their heart's content.
"I thought it might be helpful for the students to watch it while they're at home, so I started to do these videos," Argo said. "This is a common tool for teaching these days."
His students have become big fans.
When Jennifer Perez started taking her prerequisite math classes several semesters ago, she quickly discovered she was struggling to solve problems involving linear equations and inequalities.
Perez ended up failing DMA 040, one of eight developmental classes offered by College of The Albemarle, and had to repeat the course. She passed it the second time, and fortunately since then, she has had a little extra help learning the concepts taught in the remaining developmental math classes she has had to take. Although the algebra taught in DMA 050 and DMA 060 was no easier to learn – Perez was learning about things like linear modeling and factoring polynomials – she knew she could count on Argo's videos to show her how to work difficult math problems anytime she wanted.
Since he began producing the videos in August, Argo has created 62 math videos, but he gets ideas for new topics every time a student stops by his office looking for help.
Sometimes, Argo said, he features these students who come by his office with questions – the back-and-forth dialog makes the videos more interesting. But most of the videos rely only on Argo as he works to solve tricky math problems from course textbooks, recording the complicated processes involved and explaining the step-by-step procedure.
Perez, 38, said if Argo's videos had been available when she took DMA 040, she doubts she would have failed the class the first time. She credits the online tutorials with helping her pass the remaining developmental math courses she has had to take.
"I used the videos for DMA 050 and DMA 060," Perez said. "In DMA 050, I kept begging for more of them because I was sitting at home trying to figure it out."
Argo has gotten positive feedback from many of his students about the videos, especially from his online students who don't meet in the classroom. And aside from the odd coughing spell, or ill-timed phone call, Argo said his production of the videos has also improved over time.
Not bad, he added, for someone who was 14 when electronic calculators were invented.
"I'm fairly old," Argo said. "So all of this technology is new to me. I try to keep up."
Perez and many of Argo's other math students think he has done much more than keep up. He has helped them wrap their minds around difficult algebraic concepts and more, and pass courses they may have had difficulty with otherwise.
"He just has a way to explain the problems like he would in the classroom if he was teaching," Perez said. "These videos are like a one-on-one with somebody. Without these videos, I would be pretty lost. I probably would not have passed 050 or 060." |
mathematics form 2 final exam paper and answer |
Problem Solving
9780759342644
0759342644
Summary: Problem Solving provides students with a general approach and strategies to solve problems in real life. The text is easy to read and geared mainly for students who dislike math. Problems throughout the book range from easy to difficult, and require minimal mathematical experience. While possessing knowledge is one important requirement to solving problems, there are many others. Problem Solving focuses on providing ...strategies to help students become proactive, successful, and confident problem solvers.
DeFranco, Thomas is the author of Problem Solving, published 2004 under ISBN 9780759342644 and 0759342644. One hundred ninety three Problem Solving textbooks are available for sale on ValoreBooks.com, thirty eight used from the cheapest price of $1.00 |
ClassPad330
Variations
Manual
At A Glance
The ClassPad 330 comes with all the functions of the ClassPad 300 including an impressive collection of applications that support self-study, like 3D Graphing, Geometry, eActivity for creating discovery based lessons and lots more. Additional features of the ClassPad 330 include upgraded CAS Technology and Geometry Application, new AP Statistics functionality, and three new applications: Differential Equation Graph, Financial and Probability.
Special Features
Features of the ClassPad 330 Graphing CAS Calculator include:
Pen Touch operation-Computer-like intuitive operations for menu selection, button operations, etc. Drag & Drop provides a quick way to copy within a window or display in another window
Advanced CAS (Computer Algebra Systems) with Laplace, Fourier and FFT
Natural display input enables input of fractions, differentials, integrals, Sum calculations, lim calculations, and other expressions in the same format as that used in mathematics texts.
Presentation Application-Register application screen screen shots for playback in slide show format that is great for presenting eActivity results and other lessons. Includes Auto Play, Manual Play, and page editing functions |
The Algebra 1: The Complete Course DVD Series will help students build confidence in their ability to understand and solve algebraic problems.
In this episode, students will learn to visualize concepts with the aid of manipulatives. The properties of the reciprocal function and also the general form of a rational function are also taught. Grades 5-9. 30 minutes on DVD. |
0486675491","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":9.03,"ASIN":"0872209547","isPreorder":0}],"shippingId":"0486675491::QCgE03WS2w%2FeAWlNv741Ab%2B%2FcQRf8%2FzDxCetp3dnJLd6Czi1%2BbFgVzvbZxx7FbkLJj02GlJwQXQw7xcaCO6oypALRz5fBoNxwo44SO54N2M%3D,0872209547::goXaE9EMTB0qwIgK9kn97u1ZwpzZkXfL8H1LdpUhah7JLDSmEW%2BxWrlCOBt2670T2Zbx%2F1m1G2%2Bzplxol3hpp8SOjZjKlosyblnG36AG6Freund's text, which is based on a course that the author taught to university students fulfilling their general education requirement, is a clearly written and carefully constructed introduction to basic discrete probability. Each topic is placed in context and is illustrated by copious examples that demonstrate both the relevance and utility of probability. The exercises at the end of each section, which are generally straightforward applications of the material covered in that section, reinforce the reader's understanding of the material. Answers are provided to the odd-numbered exercises, making the text suitable for self-study. This text is a good entry point to the study of probability. However, the scope of the text is limited. The emphasis is on how to solve problems rather than the underlying theory. Freund succeeds in making the text as widely accessible as possible, albeit at the expense of a deeper understanding of the material.
The text begins with a chapter on enumerative combinatorics that covers tree diagrams, the Multiplication Principle, factorials, permutations, combinations, and indistinguishable objects. Freund then introduces the classical, frequentist, and subjective (Bayesian) approaches to probability. He contrasts the different approaches, demonstrates how each is applied, discusses their limitations, and shows that they lead to equivalent results. In the following chapter on the mathematical expectation of an event, Freund illustrates how probability is used in making business decisions. Next, Freund puts probability on a formal footing, discussing events, sample spaces, compound events, mutually exclusive events, and probability measures. Freund then discusses conditional probability and independent events, demonstrating how to calculate the posterior probability that a known effect had a particular cause. The remainder of the text is devoted to probability functions. The binomial, hypergeometric, geometric, and multinomial distributions are introduced, as are the concepts of mean, variance, and standard of deviation. The text culminates with Chebyshev's Theorem about the probability that a random variable will assume a value within k standard deviations of the mean and the Law of Large Numbers, which states that for a binomial distribution that if the number of trials is sufficiently large, then the number of successes will be very close to the probability of success for an individual trial.
The text is carefully sequenced so that the foundation for each new topic is covered in the preceding sections. Preceding examples are often referenced in the discussion; exercises often refer to the preceding examples, exercises, or the results of those exercises. Consequently, while the text does an effective job of teaching you the material, it does not work well as a reference.
Freund includes tables of factorials, binomial coefficients, binomial probabilities, and square roots. The presence of the last table is indicative of how old the book is. It was written before hand-held calculators came into widespread use. Reading the examples in the text will give you some idea of how much society has changed since the book was first published in 1973.
Working through Samuel Goldberg's text Probability: An Introduction after, or instead of, reading Freund's text would enable you to delve deeper into the subject. Goldberg places a greater emphasis on probability theory and proof, provides more robust examples, and challenges the reader to solve non-routine exercises.Read more ›
I've never seen a probability book with such good examples. Most books on probability give you all of the equations, but they don't really tell you how to apply them to real situations. This book has nothing but real examples. It is the book on probability that I have been looking for
As an introduction to probability, this is an excellent book: easy to read, easy to follow, good contents, etc. The title does say introduction, so don't expect to emerge as the master of probability/statistics after reading this book.
This book is very good for those who have little knowledge in Probability but do manage some basic math concepts: polinomials, factorials, limits, etc. I bought it because I was looking for a mathematical course in Probability but this book is not for that, it is very simple. It is not a "definition-theorem-proof" book. |
:: 2014 AP* Summer Institutes at UT Austin
Pre-AP Middle School Math for Experienced Teachers
The goal of the course is that teachers work together to build on their own experiences as pre-AP mathematics teachers as they explore ways to further student understanding and use of the concepts and skills needed for success in pre-AP and AP mathematics courses. A variety of activities, strategies, and methods, including manipulatives, graphing calculators, and other tools, will be used. Emphasis will be on investigation and problem solving algebraically, numerically, graphically, and verbally, since facility changing a problem's representation is often critical in revealing a method of solution. Teachers will share best practices and activities that they have found to be effective in fostering student comprehension in their own classrooms.
Materials to Bring:
A TI-83 of TI-84 graphing calculator, if you have one.
An activity (10-20 minutes) to share. Please bring 30 copies for use with fellow participants.
Lead Consultant: Debbie Preston
Deborah B. Preston attended Rice University and received her BS in mathematics from UTSA, and her Master of Arts degree in mathematics from the University of the Incarnate Word. She has been teaching for 30 years, 26 of which have been in AP and Pre-AP mathematics classes at Keystone School, where she chairs the Upper School Mathematics Department. A member of the National Council of Teachers of Mathematics, she co-authored the Instructor's Guide to accompany Paul A. Foerster's Calculus: Concepts and Applications. For 12 years, she and Mr. Foerster taught mathematics summer institutes for teachers through the University of California at Berkeley. She makes presentations at national conferences on technology use in the mathematics curriculum and is an experienced writer of standardized mathematics tests. A national consultant for the College Board for 18 years, she has presented many AP summer institutes in middle-school pre-AP mathematics and calculus and has spoken at numerous 1- and 2-day conferences regionally and nationally. Ms. Preston has been recognized as a Woodrow Wilson Fellow and a Radio Shack/Tandy Technology Outstanding Teacher, and was a recipient of the state-level Presidential Award for Excellence in Mathematics Teaching. In February 2006, the College Board's Report to the Nation reported that the 2005 Calculus BC AP scores for Ms. Preston's students were the best in the nation for small schools under 300 students.
* Trademark Notice: College Board, AP, Advanced Placement Program, AP Vertical Teams, Pre-AP, and the acorn logo are registered trademarks of the College Board. Used with permission. |
An unread copy that is in excellent condition! Clean crisp pages. Square binding. Minor shelf wear. No dust jacket. Includes sealed Access Code & Interactive Video CD. Get it ...fast! DOMESTIC & INTERNATIONAL EXPEDITED SHIPPING is available for this item. Same or next Postal business day shipping. All orders securely packaged. Domestic orders include USPS TrackingRead moreShow Less
More About
This Textbook
Overview
Make math a snap with ELEMENTARY ALGEBRA. Using everyday language and lots of examples, Kaufman and Schwitters show you how to apply algebra concepts and ace the test. And if tutoring is in your future, with this edition you get 40 hours of free tutoring per week through Personal Tutor with SMARTHINKING, the live online tutoring program that connects with you with an algebra expert who has a copy of your textbook. Plus, you'll get the powerful web-based iLrn Homework program that makes your assignments a breeze. Get the grade you want with ELEMENTARY ALGEBRA.
Related Subjects
Meet the Author |
Elementary Linear Algebra - 4th edition
Summary: The text starts off using vectors and the geometric approach, plus, it features a computational emphasis. The combination helps students grasp the concepts. At the same time, it provides a challenge for mathematics majors45 +$3.99 s/h
LikeNew
BookCellar-NH Nashua, NH
053495190261 +$3.99 s/h
Good
TGChavez La Mesa, CA
Good VERY little pencil notes thru-out-still VERY USABLE-clean cover-We ship out FAST w/FREE tracking on this item-(Gotta have it fast? ) Expedited shipping AVAILABLE-(Personalized Service~Safe Pack...show moreaging~Expedited |
Precalculus, provides a solid foundation of algebraic
and trigonometric skills necessary to achieve a mastery of calculus. The text starts
with an in-depth review of algebraic skills used throughout precalculus and then eases
into exciting new topics necessary to move forward into calculus. This text is
presented in a comprehensive and engaging style. Each topic is presented in a rigorous
and thorough manner, accompanied by several examples worked out in a step-by-step manner.
Detailed work-out notes included in the examples provide further clarification and
understanding. Definitions and theorems are clearly identified in yellow boxes throughout
the text for easy reference, while common errors are highlighted to warn students against
common pitfalls. Each chapter ends with a chapter project which encourages the student to
synthesize the important skills from the chapter and apply them to a real world application.
Technology, including Mathematica® and TI-83 Plus instruction, has been incorporated
throughout the text when appropriate. |
Egghead's Guide to Geometry [NOOK Book]...
More About
This Book knowledge of geometry for standardized tests.
egghead's strategies and advice for improving geometry skills
Foundational geometry for students who need basic and remedial instruction
Dozens of sample exercises and solutions with loads of geometric figures and illustrations
Easy-to-read lessons with fun graphics that provide essential information and skills to help those students who learn visually |
Algebraic Geometry 2 - 99 edition
Summary: Modern algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes was explained in Algebraic Geometry 1: From Algebraic Varieties to Schemes ...show morea The text covers the important topics of sheaf theory, including types of sheaves and the fundamental operations on them, such as * coherent and quasicoherent sheaves. * proper and projective morphisms. * direct and inverse images. * Cech cohomology. For34.9838.00 +$3.99 s/h
New
Sequitur Books Boonsboro, MD
Brand new. We distribute directly for the publisher. Modern algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes was explained in Algebraic Geometry 1:...show more From Algebraic Varieties to Schemes, aThe text covers the important topics of sheaf theory, including types of sheaves and the fundamental operations on them, such as ... * coherent and quasicoherent sheaves. * proper and projective morphisms. * direct and inverse images. * ????ech cohomology.For As a result, he is able to make algebraic geometry very accessible to a wide audience of non-specialists.The book contains numerous problems and exercises with solutions. It would be an excellent text for the second part of a course in algebraic geometry |
9780136007029
ISBN:
0136007023
Edition: 5 Pub Date: 2008 Publisher: Prentice Hall
Summary: Clearly explained concepts, study skills help, and real-life applications will help the reader to succeed in learning algebra.
Martin-Gay, Elayn is the author of Beginning Algebra (The Martin-Gay Developmental Algebra Series) (Hardcover), published 2008 under ISBN 9780136007029 and 0136007023. Ninety two Beginning Algebra (The Martin-Gay Developmental Algebra Series) (Hardcover) textbooks are available for s...ale on ValoreBooks.com, fifty five used from the cheapest price of $0.42, or buy new starting at $11 |
Students work in small groups with a small set of 8 nuts and 5 bolts to assemble into combinations of 1 nut: 1 bolt, and 2 nuts: 1 bolt. They explore the outcome and discuss. Then a student mixes two clear, colorless solutions together and get "thick" yellow stuff.
In this limiting behavior of equations activity, learners use the Klien and Nishima formula to find the limit for large X which is the ratio of energy carried by a photon compared to the rest mass energy of an electron.
In this limit worksheet, students use algebra to compute limits. They find the slope of the secant line and find a formula giving the slope of the secant line. This one-page worksheet contains six multi-step problems, with answers.
In this limit of slopes worksheet, students compute the limit of slopes, find the slope of the secant line, and determine the slope of the tangent line. This one-page worksheet contains five multi-step problems.
In this limits worksheet, students compute the answers to thirteen limits problems. They answer one short answer question. Students follow listed steps to simplify two limits problems. Students answer three short answer questions about a function (finding asymptotes, critical points, and extrema). They graph one function using the graphing calculator.
In this successive approximations worksheet, students use the Babylonian algorithm to determine the roots of given numbers. They identify the limits of a function, and compute the rate of change in a linear function. This two-page worksheet contains explanations, examples, and approximately ten problems.
Chemistry classes learn the importance of a limiting reactant by first considering a cake recipe. Given the recipe and the total amount available for each ingredient, they must calculate how many cakes can be made. Finally, they apply this exercise to the photosynthesis reaction. The presentation offers a brief introduction, but you will definitely want to follow it with other examples of limiting reactants within their reactions.
In this calculus worksheet, students evaluate functions and solve problems using the derivative. They apply the rules of limits to solve functions where the limit of x approaches zero. There are 12 problems to solve.
In this population growth worksheet, students will brainstorm examples of limiting factors in an ecosystem. Then students will write down what effect that factor has on population growth. This worksheet is a graphic organizer.
This pre-calculus worksheet is short, yet challenging. High schoolers calculate the limit of piecewise functions, rational functions, and graphs as x approaches a number from the positive or negative side. There are four questions |
Summary: Mathematics 129A
Fall 2005
Instructor: Professor R. Alperin, Duncan 239, Email: alperin@math.sjsu.edu,
Office hours: Mon 1-2:30, 4-5:30 PM; Wed 12:30-2:30 PM or by appointment, Phone:
924-5066
Text: Elementary Linear Algebra with Applications by R. C. Alperin, available
on-line http : // alperin
Course: Linear Algebra
The main goal of this class is to introduce the students to ideas of linear
algebra and its applications, methods of proof in mathematics, and use of computer
packages.
Final grade based on 400 point total on tests, and (computer) homework
projects. The two mid-terms will count 100 points each. The final will be com-
prehensive and worth 150 points.
The computer projects are to be done in groups with 2-4 students each, three
is the optimal size of a group. You are responsible for finding other students to
work with in your group. Registration in Math 110 is required for a computer
account and admission to the computer labs; register for Math 110 and sign up for
your computer account in the Math office. Each project will count 10 points. The
project will involve using MAPLE, a computer linear algebra system, as an aid in |
With a focus on the needs of educators and students, Making Sense of Data presents the steps and issues that need to be considered in order to successfully complete a data analysis or data mining project. ...
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Written at a readily accessible level, Basic Data Analysis for Time Series with R emphasizes the mathematical importance of collaborative analysis of data used to collect increments of time or space. Balancing...
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From triangles, rotations and power laws, to cones, curves and the dreaded calculus, Alex takes you on a journey of mathematical discovery with his signature wit and limitless enthusiasm. He sifts through over...
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A wealth of research in recent decades has seen the economic approach to human behavior extended over many areas previously considered to belong to sociology, political science, law, and other fields. Research...
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In this Formulary of Mathematical Analysis are presented the most important and useful formulas of analysis. The principal arguments are mathematical analysis and complex analysis. The last chapter is for constants...
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Well-illustrated, practical approach to creating star-faced spherical forms that can serve as basic structures for geodesic domes. Complete instructions for making models from circular bands of paper with just...
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The book aims to provide an introduction to mathematical models that describe the dynamics of tumor growth and the evolution of tumor cells. It can be used as a textbook for advanced undergraduate or graduate 13.99
"…a very useful resource for courses in nonparametric statistics in which the emphasis is on applications rather than on theory. It also deserves a place in libraries of all institutions where introductory... |
Basic Multivariable Calculus fills the need for a student-oriented text devoted exclusively to the third-semester course in multivariable calculus. In this text, the basic algebraic, analytic, and geometric concepts of multivariable and vector calculus are carefully explained, with an emphasis on developing the student's intuitive understanding and computational technique. A wealth of figures supports geometrical interpretation, while exercise sets, review sections, practice exams, and historical notes keep the students active in, and involved with, the mathematical ideas. All necessary linear algebra is developed within the text, and the material can be readily coordinated with computer laboratories. Basic Multivariable Calculus is the product of an extensive writing, revising, and class-testing collaboration by the authors of Calculus III (Springer-Verlag) and Vector Calculus (W.H. Freeman & Co.). Incorporating many features from these highly respected texts, it is both a synthesis of the authors' previous work and a new and original textbook.
Designed
More editions of Hamiltonian Reduction by Stages (Lecture Notes in Mathematics, Vol. 1913):
A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. The book includes numerous specific applications, making it beneficial to physicists and engineers. Specific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering. This second edition has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available.
More editions of Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems (Texts in Applied Mathematics):
A monograph on some of the ways geometry and analysis can be used in mathematical problems of physical interest. The roles of symmetry, bifurcation and Hamiltonian systems in diverse applications are explored.
More editions of Lectures on Geometric Methods in Mathematical Physics (CBMS-NSF Regional Conference Series in Applied Mathematics):
The use of geometric methods in classical mechanics has proven fruitful, with wide applications in physics and engineering. In this book, Professor Marsden concentrates on these geometric aspects, especially on symmetry techniques. The main points he covers are: the stability of relative equilibria, which is analyzed using the block diagonalization technique; geometric phases, studied using the reduction and reconstruction technique; and bifurcation of relative equilibria and chaos in mechanical systems. A unifying theme for these points is provided by reduction theory, the associated mechanical connection and techniques from dynamical systems. These methods can be applied to many control and stabilization situations, and this is illustrated using rigid bodies with internal rotors, and the use of geometric phases in mechanical systems. To illustrate the above ideas and the power of geometric arguments, the author studies a variety of specific systems, including the double spherical pendulum and the classical rotating water moleculeMore editions of Manifolds, Tensor Analysis and Applications (Global analysis, pure and applied): me chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivateThis advanced-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is directed to mathematicians, engineers and physicists who wish to see this classical subject in a modern setting with examples of newer mathematical contributions. Prerequisites include a solid background in advanced calculus and the basics of geometry and functional analysis. The first two chapters cover the background geometry developed as needed and use this discussion to obtain the basic results on kinematics and dynamics of continuous media. Subsequent chapters deal with elastic materials, linearization, variational principles, the use of functional analysis in elasticity, and bifurcation theory. Carefully selected problems are interspersed throughout, while a large bibliography rounds out the text. Jerrold E. Marsden is Professor of Mathematics, University of California, Berkeley. Thomas J. R. Hughes is Professor of Mechanical Engineering, Stanford University.
Vector Calculus helps students foster computational skills and intuitive understanding. This edition offers revised coverage in several areas and a new section looking at applications to Differential Geometry, Physics and Forms of Life as well as a large number of new exercises and expansion of the book's signature Historical Notes. |
Abstract Algebra - 3rd edition
Summary: Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their ...show moreinterplay lead to powerful results and insights in a number of different settings. ...show less
047143334963.70 +$3.99 s/h
VeryGood
Bookbyte-OR Salem, OR
Has minor wear and/or markings. SKU:9780471433347-3-0
$70.44 |
overview of the geometry associated with computer graphics that provides everything a reader needs to understand the topic.
Includes a summary hundreds of formulae used to solve 2D and 3D geometric problems; worked examples; proofs; mathematical strategies for solving geometric problems; a glossary of terms used in geometry. |
9780078682094
ISBN:
0078682096
Publisher: Glencoe/McGraw-Hill
Summary: NoteablesTM: Interactive Study Notebook with FoldablesTM is a complete note-taking system with guided note taking for every lesson - in a workbook format. Plus, vocabulary builder and a chapter test preparation section are included for every chapter.
Zike, Dinah is the author of Glencoe Algebra 2, Noteables Interactive Study Notebook With Foldables, published under ISBN 9780078682094 and 0078682096. Two hund...red forty five Glencoe Algebra 2, Noteables Interactive Study Notebook With Foldables textbooks are available for sale on ValoreBooks.com, one hundred eight used from the cheapest price of $3.42, or buy new starting at $17.51 |
More About
This Textbook
Overview
Enhance your classroom experience with this Student Activities Manual. This manual is designed to accompany Mathematics for Elementary Teachers: A Contemporary Approach, 7th Edition. It will enhance student learning as well as begin to model effective classroom practices. Since many instructors are working with students to create a personalized journal, this edition of the manual is three-hole punched for easy customization.
When students truly understand the mathematical concepts, it's magic. Students who use Mathematics for Elementary Teachers: A Contemporary Approach are motivated to learn mathematics. They become more confident and are better able to appreciate the beauty and excitement of the mathematical world.
That's why the new Seventh
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Meet the Author
Gary L. Musser is currently Professor Emeritus from Oregon State University. He earned both his B.S. in Mathematics Education in 1961 and his M.S. in Mathematics in 1963 at the University of Miami in Florida. He taught at the junior and senior high, junior college, college, and university levels for more than 30 years. He served his last 24 years teaching prospective teachers in the Department of Mathematics at Oregon State University. While at OSU, Dr. Musser developed the mathematics component of the elementary teacher program. Soon after Professor William F. Burger joined the OSU Department of Mathematics in a similar capacity, the two of them began to write the first edition of this book. Professor Burger passed away during the preparation of the second edition, and later Professor Blake E. Peterson was hired at OSU. Professor Peterson joined Professor Musser as a coauthor beginning with the fifth edition. Professor Musser has published 40 papers in many journals, including the Pacific Journal of Mathematics, Canadian Journal of Mathematics, The Mathematics Association of America Monthly, the NCTM's The Mathematics Teacher, the NCTM's The Arithmetic Teacher, School Science and Mathematics, The Oregon Mathematics Teacher, and the Computing Teacher. In addition, he is a coauthor of two other college mathematics Books: College Geometry- A Problem-Solving Approach with Applications and Mathematics in Life, Society, and the World. He also coauthored the K-8 series Mathematics in Action. He has given more than 64 invited lectures/workshops at a variety of conferences, including NCTM and MAA conferences, and was awarded 15 federal, state, and local grants to improve the teaching of mathematics.
While Professor Musser was at OSU, he was awarded the university's prestigious College of Science Carter Award for Teaching. he is currently living in sunny Las Vegas, where he continues to write, ponder the mysteries of the stock market, entertain his faithful yellow lab, Zoey, and enjoy watching his granddaughter blossom into a young lady.
Blake E. Peterson is currently an Associate Professor in the Department of Mathematics Education at Brigham Young University. He was born and raised in Logan, Utah, where he graduated from Logan High School. Before completing his BA in secondary mathematics education at Utah State University, he spent two years in Japan as a missionary for the church of Jesus Christ of Latter Day Saints. After graduation, he took his new wife, Shauna, to southern California, where he taught and coached at Chino High School for two years. In 1988, he began graduate school at Washington State University, where he later completed an M.S. and Ph.D. in pure mathematics.
After completing his Ph.D., Dr. Peterson was hired as a mathematics educator in the Department of Mathematics at Oregon State University in Corvallis, Oregon, where he taught for three years. It was at OSU that he met Gary Musser. He has since moved his wife and four children to Provo, Utah, to assume his position at Brigham Young University. As a professor, his first love is teaching, for which he has received a College Teaching he Award in the College of Science. He has also designed the "Mathematics Teaching with Technology" and "Mathematics Methods" courses at Brigham Young University.
Dr. Peterson has published papers in Rocky Mountain Mathematics Journal, The American Mathematical Monthly, The Mathematical Gazette, and Mathematics magazine, as well as NCTM's mathematics Teacher and Mathematics Teaching in the Middle School. His current research interests are the mathematical dialogue that occurs during teacher collaborations. This research recently took him back to Japan where he studied mathematics student teachers at a Japanese junior high school. In addition to teaching, research, and writing, Dr. Peterson has done consulting for the College Board, founded the Utah Association of mathematics Teacher Educators, is an associate chair of the department of mathematics education at BYU.
Aside from his academic interests, Dr. Peterson enjoys spending time with his family, playing basketball, mountain biking, water skiing, and working in |
Our team of Math Professors has developed easy-to -follow methods to crack the arithmetic problems, which appear in the law entrance examination.
The material has been developed after analyzing the past year papers with respect to type and standard of problems and thorough coverage has been made on the following areas: [1] Ratios and proportions [2] Averages [3] Profit & Loss [4] Simple and compound interest [5] Time and distance [6] Time and work [7] Problems on general arithmetic [8] Sets.
Detailed explanation of the concept, formulae, steps to be followed along with plenty of worked out examples can be found in each of these topics.
More than 500 problems along with solutions and explanations have been provided.
GENERAL KNOWLEDGE
About the Book
To gain mastery over general knowledge, the subject matter has been systematically arranged in alphabetical order. Hence the book is titled "A to Z on GK".
Each chapter has been dealt in a user friendly manner in the form of tables for easy reading. Undoubtedly it would be sheer delight to study GK.
No of pages : 300
LOGICAL REASONING
About the Book
Logical reasoning is an important component of the law school entrance test. Our book on logical reasoning describes the theory of logic and various postulates with illustrations to explain the intricacies.
Critical reasoning, which the students often find unclear and complicated, has been elucidated with a step by step approach for easy understanding.
Over 400 problems on a variety of topics ranging from arguments to syllogism have been fully solved with explanations in the book.
LEGAL REASONING VOLUME I
About the Book
This book has 2 sections, namely Legal GK and Constitution.
Under Section 1, the student is introduced to basics of law, legal terminology and information on a wide range of legal topics.
Section 2 contains an exhaustive coverage of the Indian Constitution, as it is a very significant constituent of the law entrance examination.
The subject matter under Constitution has been presented in a simple and lucid form with plenty of flow charts, tables and notes.
Over 100 case laws have been discussed in a comprehensive manner in this book.
Further, 250 objective type questions have been included in order to test the students' understanding of the subject.
LEGAL REASONING VOLUME II
About the Book
This Book addresses the topics on legal reasoning.
It includes subject matter under law of contracts, law of torts and Indian Penal Code.
To help the students grasp the subject with ease, concepts have been presented in a simple form with plenty of examples and in-depth explanations of case laws.
Past year questions based on the above-mentioned topics have been inserted under appropriate topics with elaborate answers.
This module will no doubt be a boon to crack the legal reasoning segment in CLAT.
PAST YEAR SOLUTION BOOK
About the Book
To help students to work out the past year papers with confidence, SRIRAM LAW ACADEMY provides complete solutions to past year papers of NLSIU and NALSAR with detailed explanations. Besides, this module also contains model test papers on the lines of CLAT with answers.
How to enroll for SRIRAM TARGET COURSE?
Step 1: Click Register. [A registration form will open. Fill all details including your email id and password as chosen by you and click register.]
Step 4: Select SRIRAM TARGET COURSE and fill in the enrolment page with DD number and click apply
Step 5 : Print the form and send it to our office address mentioned on the form together with one passport size photograph and a Multi-city cheque [or] Demand Draft drawn in favour of SRIRAM LAW ACADEMY LLP payable at CHENNAI.
Note: As soon as we receive your admission form and the DD,
We will despatch the books immediately by speed post
We will send you access password to download all the online material, test papers, quizzes, GK updates and newsletters loaded on our website
We will send you a GUIDANCE NOTE to chalk out your preparation
FOREIGN STUDENTS
Students residing in foreign countries may please contact us over phone 044-26162495 or +91 9840097395 to ascertain the cost of despatch/courier charges. The draft should be taken for Rs 7,800 PLUS courier charges in respect of foreign students. |
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About the book:
If you think algebra has to be boring, confusing and unrelated to anything in the real world, think again! Written in a humorous, conversational style, this book gently nudges students toward success in pre-algebra and Algebra I. With its engaging question/answer format and helpful practice problems, glossary and index, it is ideal for homeschoolers, tutors and students striving for classroom excellence. It features funky icons and lively cartoons by award-winning Santa Fe artist Sally BlakemoreThe Algebra Survival Guide is the winner of a Paretns' Choice award, and it meets the Standards 2000 of the National Council of Teachers of Mathematics. Its 12 content chapters tackle all the trickiest topics: Properties, Sets of Numbers, Order of Operations, Absolute Value, Exponents, Radicals, Factoring, Cancelling, Solving Equations, the Coordinate Plane and yes even those dreaded word problems. The Guide is loaded with practice problems and answers, and its pages give students the boost they need in a style they'll enjoy to master the skills of algebra.
Softcover, ISBN 0965911381 Publisher: Singing Turtle IS WORN, PAGES ARE CLEAN
Softcover, ISBN 0965911381 Publisher: Singing Turtle Press, 2000 Used - Good, Usually ships in 1-2 business days, Moderate reading wear to cover and page edges. Your purchase helps put people to work and learn life skills to reach their full potential, Thank you.
Softcover, ISBN 0965911381 Publisher: Singing Turtle Press, 2000 |
Geometry - Hardcover
Author:
Unknown
ISBN-13:
9780395977286
ISBN:
0395977282
Publisher: Holt McDougal
Summary: The theorems and principles of basic geometry are clearly presented in this workbook, along with examples and exercises for practice. All concepts are explained in an easy-to-understand fashion to help students grasp geometry and form a solid foundation for advanced learning in mathematics. Each page introduces a new concept, along with a puzzle or riddle which reveals a fun fact. Thought-provoking exercises encourag...e students to enjoy working the pages while gaining valuable practice in geometry |
1. Not all problems in each homework set will be graded. We will
typically choose a subset of the assigned problems to grade.
2. Your homework solutions must be legible. If your handwriting is not
legible, use a word processor to produce solutions.
3. Each claim you make must follow from the hypothesis or previous
claims.
4. Critique your own proofs carefully before submitting them. We are
focusing not only on writing correct proofs, but learning to recognize
when a proof is, and is not, correct.
5. Pictures should not appear in your proofs. A picture can convey an
idea, but a picture is not a formal proof.
6. After a homework set is handed in, you are expected to be prepared
to present your solution on the board in class.
7. Homework solution sets must be stapled together at the top left
corner. Your solutions should not folded in any way or placed in a
binder or folder. Put your name, EID and discussion section time in the
top right corner. |
Maths and science
Mathematics and science are often a part of university study, so it is important to develop the mathematical skills necessary for study within some disciplines. Particular resources are available for students who have maths anxiety or for students who are studying mathematics off-campus. Assistance is also available with using calculators and maths assessment.
Online readiness testing and study materials are available to assist students to be prepared for the maths in USQ programs such as nursing, economics, statistics and engineering.
A range of downloadable print materials for a range of maths and science topics are available to help you to improve your prerequisite mathematics skills, as well as additional online maths and sciences resources [no content yet]. Activities and fully worked solutions are included for topics from arithmetic through to introductory calculus. |
Buy Used
$7.71 clear introduction to tessellations and other intriguing geometric designs help students explore polygons, regular polygons and combinations of regular polygons, Escher-type tessellations, Islamic art designs, and tessellating letters. Step-by-step directions for creating tessellations support discussions of the symmetries and transformations involved. The companion book of overhead masters contains more than 270 patterns students can use to create and analyze polygonal, regular, demi-regular, and demi-regular tessellations; star polygons, tessellating curves; and polyominoes. Reproducible. Grades 6-12A plane tessellation is where a small number of patterns (sometimes only one) are repeated to completely cover a planar surface. To be a true tessellation, the covering can be extended to infinity in all directions. In many ways, tessellations are a merger of art and mathematics, because it is fairly easy to prove which geometric shapes can be used to tessellate the plane. There are also many practical uses in design, as they appear as the floors, walls and ceilings of many structures. The authors provide many colorful examples of tessellations as well as give instructions on how to create them. Basic geometry and knowledge of angles is all the mathematics you will need to understand them. The range of the types of tessellations surprised me, as a mathematician I am familiar with the concepts of tiling the plane, but the wide variety of shapes, even the face of a witch, a fish and the face of a dog are used to create tessellations. If you have any interest at all in tessellations, particularly if you are an artist, then this is a book you must read. It is also a great resource for elementary and middle schoolteachers.
Dale Seymour's Introduction to Tessellations is the clearest and most thorough explanation of tessellations I have come across. Although the book contains material that is suitable for a college level course, those following the Singapore Mathematics curriculum will find much of it perfectly suitable for use as supplementary material for grades 5 and up. Graph and dot paper suitable for student use is included in the book and separate teaching masters Tessellation Teaching Masters: 07900 are available. |
0132504669 PrenticeHall Mathematics: Algebra2 - Transparency and PowerPoint $479.97 Free upon request, ... Teachers may include trigonometry, statistics or precalculus readiness in the Algebra2 course along with more traditional topics.
Algebra2 Cove High School ... Book: Algebra2PrenticeHall Bellman, Bragg, Handlin Online Version: Teacher: Lisa Murchison ... Online quizzes: will have a quiz for each section. These are to
... Algebra and Trigonometry, ... 2010, PrenticeHall, Pearson. The paper copy of the textbook is recommended, but not required since an electronic version of the textbook is ... Analytic Trigonometry Sections 6.1, 6.2, 6.3, 6.5 Law of Sines and Cosines Sections 7.1, 7.2
Algebra2 Cove High School ... Book: Algebra2PrenticeHall Bellman, Bragg, Handlin Online Version: ... Also, trigonometry is covered in Geometry. Assignments: Assignments will be given almost every day. Each assignment can be done
... and Bittinger, Algebra2withTrigonometry, PrenticeHall, 2001 Prerequisite: Grade of "C" or better in Algebra 2A Student ... Students who master Algebra2 will gain experience with algebraic solutions ... a free online collection of just under 2,000 videos on ...
Precalculus Masters accompany PrenticeHall Mathematics, Algebra 2to help you highlight key skills that will ensure success for all your students who continue their study of mathematics. ... right triangle trigonometry, circles, and transformations.
Algebra & Trigonometry, ... PrenticeHall publishers. A hard copy of this textbook is available in the campus bookstore, and ... economical way to acquire the book (in electronic form) is to purchase it online along with access to the support program called "MyMathLab". If you want to ... |
Intermediate Algebra, Third Edition by Elayn Martin-Gay. Good study skills are essential to your success in mathematics. This text features Study Skill Builders to help make sure you are getting the most from the time you spend doing homework and studying.
Table of Contents
Tools to Help Students Succeed
ix
Additional Resources to Help You Succeed
xi
Preface
xiii
Applications Index
xxiii
Real Numbers and Algebraic Expressions
1
(68)
Tips for Success in Mathematics
2
(5)
Algebraic Expressions and Sets of Numbers
7
(8)
Equations, Inequalities, and Properties of Real Numbers
15
(8)
Operations on Real Numbers
23
(11)
Integrated Review--Real Numbers
32
(2)
Order of Operations and Algebraic Expressions
34
(9)
Exponents and Scientific Notation
43
(9)
More Work with Exponents and Scientific Notation
52
(17)
Group Activity: Geometry Investigations
58
(1)
Vocabulary Check
59
(1)
Highlights
59
(3)
Review
62
(5)
Test
67
(2)
Equations, Inequalities, and Problem Solving
69
(84)
Linear Equations in One Variable
70
(12)
An Introduction to Problem Solving
82
(13)
Formulas and Problem Solving
95
(8)
Linear Inequalities and Problem Solving
103
(15)
Integrated Review--Linear Equations and Inequalities
116
(2)
Sets and Compound Inequalities
118
(9)
Absolute Value Equations and Inequalities
127
(26)
Group Activity: Nutrition Labels
138
(1)
Vocabulary Check
139
(1)
Highlights
139
(5)
Review
144
(5)
Test
149
(2)
Cumulative Review
151
(2)
Graphs and Functions
153
(104)
Graphing Linear Equations
154
(16)
The Slope of a Line
170
(13)
The Slope-Intercept Form
183
(8)
More Equations of Lines
191
(11)
Integrated Review---Linear Equations in Two Variables
200
(2)
Graphing Linear Inequalities
202
(7)
Introduction to Functions
209
(12)
Finding Domains and Ranges from Graphs and Graphing Piecewise-Defined Functions |
Problems Plus In IIT Mathematics (English) (Paperback) Price: Rs.345
Problems Plus In IIT Mathematics is a book written for the IIT-JEE entrance examination preparation by A. Das Gupta. It serves as an excellent guidebook for the brushing up of vital concepts and contains practice questions required for the IIT-JEE aspirants.
Summary Of The Book
This book, Problems Plus In IIT Mathematics, has been compiled mainly to hone the skills of students and help them in their preparation for the IIT-JEE. A lot of exercises have been provided in the book for the necessary revision and practice of the IIT-JEE aspirants.
The book carries with it some salient features which separate it from the rest of its kind. The inception of every chapter occurs with a gist of facts, formulae, and working techniques. Icons are given to mark the tricks and hints. Solved questions are provided for each chapter which include both short and long objective type questionnaires. In addition to that, multiple answer questions have also been included. Practice tests have been given at the end for the benefit of the students along with solutions. Moreover, a separate chapter comprising miscellaneous questions is there in the end. This provision should turn out to be very helpful for the students because they would not know the chapter from which the question is given beforehand.
The contents of the book are widely categorised into various topics. The first topic is Algebra, which consists of sub-topics like Determinants and Cramer's Rule, Progressions, Equations, Inequations and Expressions, Infinite Series, Principle of Mathematical Induction (PMI), and Matrices. The next topics given is Trigonometry. It comes with sub-categories like Identities, Inverse Circular Functions, Logarithm, Solution of Equations, Heights and Distances, Properties of Triangle, Trigonometrical Inequalities and Inequations, and Circular Functions. The next sub heading covered is Coordinate Geometry. It consists of sub-topics like Circles, Parabola, Ellipse and Hyperbola, and Transformation of Axes. Then there is the topic called Calculus. It involves the sub-headings of Differentiation, Function, Indeterminate Form, Limit, Differentiability and Graph of Function, Continuity, Maxima and Minima, Application of dy/dx, Monotonic Function and Lagrange's Theorem, Definite Integration, and Differential Equation of the First Order. The next topic is Vectors. It contains the sub-topics of Application of Vectors, Product of two Vectors, Vectors and Addition of Vector, and Product of three or more Vectors. Next topic is Probability having subtopics such as Total Conditional Probability, Elementary Probability, and Bayes' Theorem. Then comes Coordinate Geometry of Three Dimensions containing sub-headings of Planes, Points, and Direction cosines and Direction ratios. The book concludes with practice tests comprising Miscellaneous Exercises.
In short, the book is comprehensively written and covers its topics well. It is a useful read for students and mathematics buffs.
About A. Das Gupta
Apart from this book, A. Das Gupta is renowned for authoring or co-authoring many other books, some of which include books such as Principles Of Physical Geography.
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HC verma of mathematics(Expand) is very good for revision after your preparation not for beginners.
This book covers all the theory (over and above standard 12th class knowledge) required for cracking the engineering competitive exams. The questions are of really high quality. You first need to have solid grasp of basics before attempting this book, as this book takes up the student from the basics to the advanced knowledge, rigor and practice required for engineering exams. This makes a worthy companion to other high quality books published Bharathi Bhawan (HC Verma's Concept of Pysics book, Physics/Chem/Maths MCQ).
P.s. The book requries the student to have the ability to solve average questions, n then only can one give a. Das a try.
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A great collection of fantastic questions !!(Expand) you. Containing above 3000 problems, this book covers a wide range of problems ranging from easy to challenging. Unlike the MCQ book of ADG, none of the problems are provided with an explanatory solution, merely the answer is given. In a nutshell, if you are an expert...this book is a must but if you are a beginner, this book will be of no help to you !
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Hat's off to Flipkart!!
Hat's off to Flipkart...the book was delivered within 48 hours and that also to a tier-3 city...The book is already a classic...best book for revision if you have completed the portion and have 2 to 3 months for revision....Go for this book and ur lyf will change forever :-)
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a definite buy
really excellent book....complete recap of formulae......lot of solved examples for all tricks to solve questions....lot of unconventional questions...but level of book is quite difficult...buy only after going through a good jee main or aieee book like objective mathematics by r d sharma.... (View complete review)
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Presents a set of good problems and a large number of them too.
The book is a question bank. Covers all the chapters and key areas. The summary of concepts and formulae are good for a quick revision. Problems are really high-quality. Some are higher than JEE adv level. The subjective questions are especially tricky. Objective problems are very low in number.... (View complete review) |
048646296X
9780486462967
Foundations of Analysis:This introduction to basic analysis presents a careful development of the real number system and the theory of calculus on the real line, extending the theory to real and complex planes. Designed as a first encounter with rigorous, formal mathematics for students with one year of calculus, the work features extended discussions of key ideas and detailed proofs of difficult theorems. Authors David F. Belding and Kevin J. Mitchell are Professors of Math at Hobart and William Smith Colleges in Geneva, New York. Their approach emphasizes the connections between ideas, rather than rote, computational aspects of calculus. Their two-part treatment begins with the real number system and covers functions, limits, and continuity, as well as differentiation and integration and aspects of sequences and series. The second part explores calculus in two dimensions in addition to line integrals and Green's theorem. The text concludes with a concise survey of complex analysis.
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Rent Foundations of Analysis 2nd edition today, or search our site for David F. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Dover Publications, Incorporated. |
This course provides a conceptual study of problems involving graphic and algebraic representations of lines. Topics include slope, equations of lines, interpretation of basic graphs, and linear modeling. Upon completion, students should be able to solve contextual application problems and represent real-world situations as linear equations in two variables |
numbers just don't add up… Following in the footsteps of the successful The Humongous Books of Calculus Problems, bestselling author Michael Kelley has taken a typical algebra workbook, and made notes in the margins, adding missing steps and simplifying concepts and solutions. Students will learn how to interpret and solve problems as they are typically presented in algebra courses—and become prepared to solve those problems that were never discussed in class but always seem to find their way onto exams. • Annotations throughout the text clarify each problem and fill in missing steps needed to reach the solution, making this book like no other algebra workbook on the market |
Dr. Cheryl Lentz has compiled the valuable information she gives in her blog regarding how to develop effective study skills in one easy to use handbook. The study tips are designed to help any student improve learning and understanding, and ultimately earn higher grades.
Practice solving linear equations with these fifty basic problems in elementary algebra. The student selects a single variable linear equation, solves for the variable, and checks the answer by viewing the step-by-step solution. Problems start with low difficulty and gradually increase to challenging. Most appropriate for 4th and 5th grade students |
Elementary Technical Mathematics - 10th edition
Summary: Elementary Technical Mathematics Tenth Edition was written to help students with minimal math background...show more system and measurement, algebra, geometry, trigonometry, and statistics, all as they are related to technical and trade fields. The goal of this text is to engage students and provide them with the math background they need to succeed in future courses and |
Synopses & Reviews
Publisher Comments:
The Dugopolski series in developmental mathematics has helped thousands of students succeed in their developmental math courses. Intermediate Algebra, 3e is system between the examples and exercise sets, so no matter where the students start, they will see the connection between the two. Finally, the author finds it important to not only provide quality but also a wide variety and quantity of exercises and |
Topics reflect the latest developments in technology and are relevant to student's needs. The course uses core language common to a range of specialisations. Grammar is regularly practised and there is a comprehensive grammar summary section.
Clear structure, closely mirroring the Student's Book content New listening tasks per unit, with all audio contained on the CD Lots of exam practice throughout the pages and in the Get Ready for your Exam sections Plenty of revision, reviews for each pair of units, and a self-check page (and answers provided) at the end of every unit ... second edition of this highly successful textbook has been completely revised and now includes a new chapter on vectors. Mathematics is the basis of all science and engineering degrees, and a source of difficulty for some students. Jenny Olive helps resolve this problem by presenting the core mathematics needed by students starting science or engineering courses in user-friendly comprehensible terms. |
The Math Forum's mission is to provide resources, materials, activities, person-to-person interactions, and educational products and services that enrich and support teaching and learning in an increasingly technological world.
Fathom does for data-driven mathematics and statistics what The Geometer's Sketchpad did for a geometric approach to mathematical modeling. With Fathom, you can explore data, plot functions, and create animated simulations. Fathom allows you to type in your own data, to use the over 300 data files that come with Fathom, or to import data from text files or directly from the Internet. |
books.google.com - This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies... Through Problems
Problem-solving Through Problems: With 104 Illustrations
This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam. |
Multidimensional Analysis
This web page gives a brief introduction to Multidimensional
Analysis,
a generalization of linear algebra which incorporates ideas from
dimensional
analysis. My book gives the full presentation, with examples,
historical
discussion, and answered exercises, all at a level which assumes a
standard
undergraduate familiarity with linear algebra. You
can purchase this book quickly and easily through Amazon.com.
The central idea is that vectors and matrices as used in science and
engineering can be thought of as having elements which are not just
real
(or complex) numbers, but formally have different types, such as length
or voltage. Quantities with different types do not form an
algebraic
field as they are not closed under addition, e.g., 1 meter + 1 volt
is undefined. Traditional linear algebra assumes that vectors and
matrices
are isomorphic to arrays of elements which are closed under addition,
and
so traditional linear algebra is not formally valid for many
applications
in science and engineering.
Typically, scientists and engineers "drop" the units from
dimensioned
quantities and place just their numeric values as elements in vectors
and
matrices. Doing so allows one to use traditional mathematical and
computational
tools on the resulting numeric arrays. Unfortunately, this is
misleading
as it causes one to miss the real mathematical properties of vectors
and
matrices which contain dimensioned elements. Dimensioned matrices have
very different properties from dimensionless ones. By examining the
examples
below, one can see that traditional linear algebra can not be
isomorphic
to the algebra which scientists and engineers really need to use.
A. Scalars
One must begin with the study of ``dimensioned scalars," such as
1 volt,
and 2 meters. The study of their possible interrelationships
forms
an interesting branch of applied mathematics (or physics or
engineering)
called dimensional analysis. Traditionally this field only
concerns
scalar quantities (not vectors and matrices). You are probably familiar
with it. The essential difference between dimensioned quantities and
traditional
algebraic structures is that it is not closed under addition, e.g., 1
volt
+ 2 meters is undefined, yet they are part of the same algebra
as their product is defined.
A very useful computer program (which I have written and placed in
the
public domain) for manipulating, converting, and calculating with
dimensioned
scalars is available. The program,
DimCalc, runs on PCs with Microsoft
Windows (3.1, 95, 98, or higher) software. The file to get is DimCalc.zip
which is a compressed package of the software and extensive on-line
help
information. It includes the standard vbrun300.dll subroutine
file in case you do not have it on your system already.
B. Vectors and Matrices
The linear algebra which results when one considers vectors and
matrices
which contain dimensioned quantities as their components is
surprisingly
interesting and rich. It is not an algebra over a field because the
elements
are not closed under addition. Although this algebra is implicit in all
branches of modern engineering, it has not been carefully studied
before.
As motivation, consider these 2-by-2 arrays:
where m abbreviates meters, and s seconds. Try now to directly
multiply
out the matrix product X^2 using the standard formalism, and
you
will see that the product X^2 is undefined, as its diagonal
elements
would have to be the undefined sums "1m^2 + 1s^2". Thus the familiar
property
that "any square matrix can be squared" does not hold in this algebra,
as matrix products contain scalar sums, and sums are only sometimes
defined.
If matrix elements are chosen carefully however, products are defined.
The standard method of matrix multiplication shows that:
An important difference between Y and Z is that Z^2
preserves
the dimensions of Z, so that Y^2+Y is undefined,
while Z^2+Z is defined. As a consequence of this
property,
all integer powers of Z have the same dimensional structure as Z.
In
particular, the Taylor series for the matrix exponential (or any other
transcendental function) requires summing these powers, so exp(Z)
is
defined, but exp(X) and exp(Y) are undefined. These
different
properties show that X, Y, and Z come from
three different
classes of dimensioned matrices.
C. Pop Quiz!
If you think that you know linear algebra and that there is nothing new
and interesting about matrices with scientific and engineering
quantities
like 1 meter, then take this simple quiz, and you'll find out a
few things:
Note that X above has no determinant, while Y and Z
do have a determinant: the product of the off-diagonal elements of X
can not be subtracted from the product of the diagonal elements of X,
as
would be necessary in the calculation of a 2-by-2 determinant. One
might
now hypothesize a conjecture along the lines that "a square dimensioned
matrix has a determinant iff it can be squared." That conjecture is too
strong however. The "if" part holds but not the "only if." Find a
2-by-2
counterexample, i.e., a matrix with a determinant but which can not be
squared.
Find a square 2-by-2 matrix P such that P times P
inverse
gives a different result from P inverse times P. Of
course,
in traditional linear algebra, the product of a matrix and its inverse
is the same regardless of order, (assuming an inverse exists,) but
you're
not in Kansas anymore.
D. Some Surprising Theorems
Here a few interesting differences between traditional linear algebra
and
dimensioned linear algebra:
On arbitrary n-by-n arrays of dimensioned quantities, most familiar
algebraic
operations (e.g., products, determinants, eigenvalues, and the
singular-value
decomposition) are not defined. There are certain very special classes
of dimensional structures for which these operations make sense, and
only
these special forms are ever applied in engineering applications.
The traditional concept of a vector as a quantity with direction and
magnitude
is far too narrow for engineering purposes, while the traditional
concept
of a matrix as an array of scalars is far too broad. (Most vectors have
no magnitude. Most arrays are not matrices.)
The well-known restriction that the argument to transcendental
functions
in physical laws be dimensionless is only true for scalars. It is not
true
in the multivariable case. For example, the matrix exponential, for a
certain
class of dimensioned square matrices, including Z above, is not
only well-defined, but essential to a proper treatment of linear
systems
analysis.
There is a natural nesting to many of the dimensional forms for
matrices.
For example, among the square matrices, the dimensionless matrices of
traditional
linear algebra are a proper subset of the set of matrices that can be
the
argument to the exponential, which is a proper subset of the set of
matrices
that have eigenstructure, which is a proper subset of the set of
matrices
that have determinants and inverses, which is a proper subset of the
set
of matrices which can be multiplied with other matrices, which is a
proper
subset of the set of arrays in which the elements carry physical
dimensions.
Many well-known theorems do not hold for dimensioned matrices, e.g.,
the null space of a matrix is the orthogonal complement
of
the image space of its transpose
and
a matrix is positive definite if and only if its
eigenvalues
are positive.
In fact, the set of matrices for which definiteness is defined barely
intersects
the set of matrices for which eigenvalues are defined. By analyzing the
dimensional structures of these classes of matrices, flaws in the
traditional
proofs become obvious, along with the special conditions under which
the
theorems hold.
For a nonsingular square matrix, A with inverse B,
it is
true as expected that AB=I and BA=I, but in general AB
does not equal BA. The explanation lies in the fact that there
are
many different dimensionally distinct identity matrices.
E. Further Information
To learn more about these and other matrix classes, and other phenomena
concerning dimensioned linear algebra and dimensional analysis of
matrix
relationships, be sure to check out my book, written for anyone with an
undergraduate background in linear algebra. You
can purchase this book quickly and easily through Amazon.com. |
Give your Saxon Math 6/5 students support and reinforcement! Comprehensive lesson instructions feature complete solutions to every practice problem, problem set, and test problem with step-by-step explanations and helpful hints. These user-friendly CD-ROMs contain hundreds of hours of instruction, allowing students to see and hear actual textbook problems being worked on a digital whiteboard. A slider button allows students to skip problems they don't need help on, or rewind, pause, or fast-forward to get to the sections they'd like to access. Problem set questions can be watched individually after the being worked by the student; the practice set is one continuous video that allows for easy solution review. For use with the 3rd Edition. Four Lesson CDs and 1 Test Solutions CD included.
System Requirements:
Windows:
98, 2000, ME, XP, Vista with latest updates, Windows 7
450 MHz or faster
128 MB RAM
8x CD-ROM Drive
800 x 600 display
Macintosh:
10.2 or up
G3, 500 MHz or faster
128 MB RAM
8x CD-ROM Drive
800 x 600 display Saxon Teacher for Math 6/5, Third Edition on CD-Rom
Review 1 for Saxon Teacher for Math 6/5, Third Edition on CD-Rom
Overall Rating:
5out of5
Date:November 30, 2013
HSU mom
Age:45-54
Gender:female
Quality:
5out of5
Value:
4out of5
Meets Expectations:
5out of5
This is the best math curriculum I have found in 23 years of Home Schooling.
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Review 2 for Saxon Teacher for Math 6/5, Third Edition on CD-Rom
Overall Rating:
3out of5
Date:September 2, 2009
Cleo Haygood
I was a little disappointed in this product. I did'nt realize it just repeats exactly what is in the book. My son enjoys using it & if he has trouble with a problem he can click on the problem number & get an explanation of how to do the problem. |
Teaching Textbooks
Homeschool Math Books
Founded by two Harvard educated brothers, Greg and Shawn Sabouri, Teaching Textbooks is designed to make learning math in a homeschool setting the best possible experience. Since it was designed specifically for homeschoolers, the text is self-explanatory and the CD-ROM teaching allows students to work through problems with a tutor in the comfort of their own homes! Plain language, friendly fonts, highlighted phrases, constant review and flexibility make Teaching Textbooks a very popular math programs. Having a solution worked out for each problem is invaluable, especially in the upper levels.
The student workbook is 669 pages with 119 lessons, while the four CD-ROMs provide step-by-step audiovisual solutions to every homework and test problem. The CD-ROM's digital gradebook grades answers as soon as they are entered and calculates percentages for each assignment; a softcover answer booklet is also provided. Windows 2000 or Macintosh.
A textbook written directly to the student, answer booklet and CD-ROM collection with step-by-step audiovisual solutions to every one of the thousands of homework and test problems are included to start your students on the right track to upper-level math.
Topics covered include fractions, decimals, percents, simple geometry (e.g. area and perimeter), units of measure, probability, bar and circle graphs, and equation-solving. Math 6 also features a digital gradebook that grades answers as soon as they are entered, providing immediate feedback while the problems are still fresh in the student's minds. This kit includes: a 546-page consumable workbook, softcover and spiral bound; answer booklet; 4 CDs. 116 lessons and 19 quizzes.
Teaching Textbooks is designed for independent students, with the "teacher" and "textbook" elements combined. The textbook offers detailed instructions, fun illustrations, real-world examples, extensive review and already high-lighted important concepts; and if your student gets stuck, there's always the audiovisual step-by-step solutions for every one of the homework problems and quizzes!
Teaching Textbooks uses the review method, helping students through difficult or new concepts, and increasing long-term retention. Another unusual and extremely helpful feature are the audiovisual lecture, practice, and solution CDs for every chapter, homework and test problem. With such a support network, you'll never be stumped again!
Extraordinarily clear illustrations, examples and graphs have a non-threatening, hand-drawn look, and engaging real life questions make learning algebra practical and applicable! Not only is their textbook clear, but their audiovisual support includes lecture, practice and solution CDs for every chapter, homework and test problem! With such a supporting, review-centered method, you'll never be stumped again!
Illustrations, examples and graphs have a hand drawn look to them, and problems often use engaging real life illustrations. Not only is the textbook well done, but there are audiovisual lecture, practice, and solution CDs for every chapter, homework and test problem. Definitions, theories and more have their own reference portion in the back of the text.
All together, this kit includes:
768 page spiral bound softcover textbook
164 page test book with answer key
1 test solution CD
6 homework solution CDs with step by step explanations for every problem
Designed specifically for homeschoolers, this packet includes a spiral bound 753 page teaching textbook, Answer Key & Test Bank Workbook, set of 4 Lecture and Practice CD's, set of 6 Solutions CD's, and a test solutions CD. |
ISBN: 1441912959 / ISBN-13: 9781441912954
A Problem Book in Real Analysis
This book systematically solves the problems related to the core concepts of most analysis courses. The wide variety of exercises presented in this ...Show synopsisThis book systematically solves the problems related to the core concepts of most analysis courses. The wide variety of exercises presented in this book range from the computational to the more conceptual and vary in difficulty.Hide synopsis
...Show more history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.Hide
Description:New. This book systematically solves the problems related to...New. This book systematically solves the problems related to the core concepts of most analysis courses. The wide variety of exercises presented in this book range from the computational to the more conceptual and vary in difficulty |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). |
More About
This Textbook
Overview
Vita Mathematica will enable teachers to learn the relevant history of various topics in the undergraduate curriculum and help them incorporate this history in their teaching. It contains articles dealing not only with calculus, but also with algebra, combinatorics, graph theory, and geometry, as well as more general articles on teaching courses for prospective teachers, and describes courses taught entirely using original sources. Judith Grabiner shows us how two important eighteenth century mathematicians, Colin Maclaurin and Joseph-Louis Lagrange, understood the calculus from these different standpoints and how their legacy is still important in teaching calculus today. We learn from Hans Nils Jahnke why Lagrange's algebraic approach dominated teaching in Germany in the nineteenth century. Wilbur Knorr traces the ancient history of one of the possible foundations, the concept of indivisibles. This volume demonstrates that the history of mathematics is no longer tangential to the mathematics curriculum, but in fact deserves a central role.
Editorial Reviews
Booknews
Brings together a group of 30 papers addressing the history of mathematics and its integration with mathematical pedagogy. Topics include historiography and sources, historical studies from antiquity to the present, the integration of history with mathematics teaching, and the origins and teaching of calculus. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Related Subjects
Table of Contents
Part I. Histiography and Sources: 1. New trends and old images in the history of mathematics David E. Rowe; 2. The role of problems in the history of mathematics and mathematics teaching Evelyne Barbin; 3. Dramatising the birth and formation of mathematical concepts: two dialogues Gavin Hitchcock; Part II. Studies in the History of Mathematics: 4. The four sides and the area: oblique light on the prehistory of algebra Jens Hoyrup; 5. The method of indivisible in ancient geometry Wilbur Knorr; 6. The enigmas of Chinese mathematics Frank Swetz; 7. Combinatorics and induction in medieval Hebrew and Islamic mathematics Victor Katz; 8. The earliest correct algebraic solutions of cubic equations Barnabus Hughes; 9. Early geometrical works of Marin Getaldic Zarko Dadic; 10. Abolition of the slave trade: empowerment through modelling John Fauvel; 11. The calculus as algebra, the calculus as geometry: Lagrange, Maclaurin, and their legacy Judith Grabiner; 12. The development of algebraic analysis from Euler to Klein and its impact on school mathematics in the nineteenth century Hans Nils Jahnke; 13. The mathematics seminar at the University of Berlin: origins, founding and the Kummer–Weierstrass years Ronald Calinger; 14. Kovalevskaya's research on the rotation of a rigid body Roger Cooke; 15. Mathematics education at nineteenth-century German technical colleges Susan Hensel; 16. American mathematics viewed objectively: the case of geometric models Peggy Kidwell; 17. The social and intellectual shaping of a new mathematical discipline: the role of the National Science Foundation in the rise of theoretial computer science and engineering William Aspray, Andrew Goldstein, and Bernard Williams; Part III. Integration of History of Mathematics Teaching: 18. History of mathematics and the teacher Torkil Heide; 19. Ethnomathematics: an explanation Ubiratan D'Ambrosio; 20. The necessity of history in teaching mathematics Frederick Rickey; 21. Mathematical masterpieces: teaching with original sources Richard C. Laubenbacher; A history of mathematics course for teachers based on great quotations Israel Kleiner; 22. Measuring an arc of meridian Michelle Gregoire; 23. From Egypt to Benjamin Banneker: African origins of false position solutions Beatrice Lumpkin; 24. Mary Everest Boole (1832–1916) Karen Dee Michalowicz; 25. Pupil's perception of the continuum Peter Bero; Historical motivation for a calculus course: Barrow's theorem Martin Flashman; 26. The history of the concept of function and some implications for classroom teaching Manfred Kronfellner; 27. Integration in finite terms: from Liouville's work to the calculus classroom of today M. K. Siu; 28. How many people ever lived James Tatters |
the mathematical foundations of numerical methods and demonstrates their performance on examples, exercises and real-life applications. This is done using the MATLAB software environment, which allows an easy implementation and testing of the algorithms for any specific class of problems. The book is addressed to students in Engineering, Mathematics, Physics and Computer Sciences. In the second edition of this extremely popular textbook on numerical analysis, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been |
More About
This Textbook
Overview
The world of mathematics is probably one of the most fascinating creations of mankind. The world of mathematics with a Computer Algebra System, like MuPAD, is even more fascinating. With MuPAD, we can develop mathematical concepts, explore them and visualize them with just a few simple commands.
This book is a gentle introduction to MuPAD – a modern Computer Algebra System. The author introduces MuPAD step by step and shows how we can use it in various areas of mathematics. A large chapter of the book is devoted to the graphical visualization of mathematical concepts, and MuPAD graphics are also used extensively throughout the rest of the book.
Each chapter of the book should be considered as a single workshop for MuPAD beginners. The whole book is a perfect resource for conducting workshops on using Computer Algebra Systems to explore, experiment with, and visualize mathematical concepts.
Related Subjects
Table of Contents
to MuPAD.- Mathematical graphics with MuPAD.- to calculus of one variable.- Multivariable calculus.- Algebra with MuPAD.- Data visualization and elementary statistics.- A brief introduction to |
Algebra II—Semester A
You had so much fun in Algebra that you had to come back for more? Yeah, we don't blame you.
Algebra II has all the expressions and equations you've seen before…and then some. You're sure to see some old familiar friends along the way (we're looking at you, polynomials), along with a few unfamiliar faces (we're looking—or at least trying to look at you, imaginary numbers).
Semester A starts off with expressions, polynomials, and a beautiful thing we've all seen before: factoring. After being able to rearrange polynomials in more ways than a contortionist, we'll venture into the land of the imaginary. (Feel free to extend an invite to your imaginary childhood friend, Maurice.) We'll finish up the semester by working with more equations and inequalities than you can shake a dotted line at.
Course Breakdown
Unit 1. Seeing Structure in Expressions
We'll start the course off by diving headfirst into expressions! With the help of factoring, radicals, and even sequences and series, we'll be able to pluck out different parts of an expression and figure out if two expressions are two peas in a pod or two peas in…separate pods. Because sometimes, one pod is just too cramped.
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Unit 2. Arithmetic with Polynomials and Rational Expressions
You may have dealt with polynomials and rational expressions in the past, but you ain't never seen 'em like this before. Not only will we gain some new tips and tricks to help us deal with these pesky expressions, we'll learn and even prove a few theorems along the way. Yeah, we mean business.
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Unit 3. The Complex Number System
You might think imaginary numbers are about as helpful as Maurice, your imaginary friend from kindergarten. We'll fill you in on a little secret: while Maurice can't deal with negatives under the radical or tell you about the Fundamental Theorem of Algebra, imaginary numbers can—and will. Then again, Maurice can make a mean imaginary apple cobbler. We all have our strengths.
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Unit 4. Creating Equations
This unit is all about using the magic of the equal sign to create and solve problems. (We'd use the magic of Houdini, but we're still working on that rope escape trick.) By creating and graphing every type of equation you can possibly think of, we'll learn how to tell them apart and understand which type of equation is applicable to which situation.
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Unit 5. Reasoning with Equations and Inequalities
For this unit, we're going how to put all the equations we created to use. We're going to graph our creations—both separately and together—and see how to use them to solve problems. More often than not, they can do a significant portion of the work for us, and who doesn't love outsourcing their work? So put your feet up, grab a piña colada, and let equations and inequalities do the work for you. (Not really.) |
Using and Understanding Mathematics - 4th edition
Summary: Most students taking this course do so to fulfill a requirement, but the true benefit of the course is learning how to use and understand mathematics in daily life. This quantitative reasoning text is written expressly for those students, providing them with the mathematical reasoning and quantitative literacy skills they'll need to make good decisions throughout their lives. Common-sense applications of mathematics engage students while underscoring the practical, esse...show morential uses of math.
Features
Practical Matters. Focusing on matters of high practical importance, this feature highlights common-sense applications of math such as avoiding credit card trouble and spotting a bad cell phone deal.
A Brief Review. This feature reviews key mathematical skills students should have learned previously, but which many students still need review and practice. They appear in the book wherever a particular skill is first needed, and exercises based on the review boxes can be found at the end of the unit.
Thinking About. Building upon the main narrative, this feature reaches beyond to a deeper level of mathematical understanding. Examples include boxes on the proof of the Pythagorean theorem and on Zeno's paradox.
Time Out to Think. Appearing throughout the book, the Time Out to Think features pose short conceptual questions designed to help students reflect on important new ideas. They also serve as excellent starting points for classroom discussions.
Margin Features. A wide margin leaves room for students to make notes while studying. The margin also contains material that spurs student interest in three basic forms:
By the Way features contain interesting notes and asides relevant to the topic at hand
Historical Note remarks give historical context to the ideas presented in the chapter
Technical Notes contain details that are important mathematically for students looking for more depth
Now Try Exercises. At the end of every in-text example students are directed to Now Try a specific exercise, immediately testing their comprehension of the material.
Does It Make Sense? These qualitative exercise questions test conceptual understanding by asking whether given statements are sensible and asking students to explain why or why not.
Basic Skills and Concepts. Covering concepts from the unit, these exercises can be used for homework assignments or for self-study. Answers to most odd-numbered exercises appear in the back of the book.
Web Projects. The Web Projects require students to search for data or other information online. They can be used for extended projects, discussions, group activities, or essays.
In the News. In these exercises, students are challenged to find examples of unit concepts in the news or in their daily lives. These questions may be assigned as homework or used for class discussions |
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