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Just-In-Time Algebra and Trigonometry for Early Transcendentals Students taking calculus with Early Transcendentals. Strong ... MORE="width:100%" />Strong algebra and trigonometry skills are crucial to success in calculus. This text is designed to bolster these skills while readers study calculus. As readers Numbers and Their Disguises:Multiplying and dividing fractions, adding and subtracting fractions, parentheses, exponents, roots, percent, scientific notation, calculators, rounding, intervals.Completing the Square: Completing the square in one and two variables.Solving Equations:Equations of degree 1 and 2, solving other types of equations, rational equations, the zero-factor property.Functions and Their Graphs:Introduction, equations of lines, power functions, shifting graphs, intersection of curves.Cyclic Phenomena: The Six Basic Trigonometric Functions:Angles, definitions of the six trigonometric functions, basic identities, special angles, sum formulas.Exponential Functions:The family of exponentials, the function.Composition and Inverse Functions:Composite functions, the idea of inverses, finding an inverse offgiven by a graph, finding the inverse offgiven by an expression.Logarithmic Functions:Definition of logarithms, logs as inverses of exponential functions, laws of logarithms, the natural logarithm.Inverse Trigonometric Functions:The definition of arcsinx, the functions arctanxand arcsecx, inverse trigonometric identities.Changing the Form of a Function:Factoring, canceling, long division, rationalizing, extracting a factor from under a root.Simplifying Algebraic Expressions:Working with difference quotients and rational functions, canceling common factors, rationalizing expressions.Decomposition of Functions: Inner, outer, and outermost functions, decomposing composite functions.Equations of Degree 1 Revisited:Solving linear equations involving derivatives.Word Problems, Algebraic and Transcendental:Algebraic word problems, the geometry of rectangles, circles and spheres, trigonometric word problems, right angle triangles, the law of sines and the law of cosines, exponential growth and decay.Trigonometric Identities:Rewriting trigonometric expressions using identities. For all readers interested in algebra and trigonometry in early transcendentals calculus. |
Engaging, accessible, and extensively illustrated, this brief, but solid introduction to modern geometry describes geometry as it is understood and used by contemporary mathematicians and theoretical scientists. Basically non-Euclidean in approach, it relates geometry to familiar ideas from analytic geometry, staying firmly in the Cartesian plane. It uses the principle geometric concept of congruence or geometric transformation--introducing and using the Erlanger Program explicitly throughout. It features significant modern applications of geometry--e.g., the geometry of relativity, symmetry, art and crystallography, finite geometry and computation. Covers a full range of topics from plane geometry, projective geometry, solid geometry, discrete geometry, and axiom systems. For anyone interested in an introduction to geometry used by contemporary mathematicians and theoretical scientists. |
Lakeland Community College: Free algebra textbook getting raves
Related Links
In response to rising prices and the falling quality of college textbooks, a Lakeland Community College professor and a Lorain County Community College have done their part to make textbooks more affordable to students.
Lakeland Mathematics Professor Dr. Carl Stitz, of Painesville Township, was recently named among the outstanding faculty at University System of Ohio institutions who have creatively integrated digital content into their courses.
The Faculty Innovation Award was created by Chancellor Eric Fingerhut in 2009 to stimulate the creation of innovative and affordable instructional materials for students in the University System of Ohio.
Printed versions are available through at lulu.com for the cost of printing and binding, which is less than $20 per book as opposed to more than $100 for traditional textbooks.
They felt that much of the mathematical rigor in traditional textbooks diminished over the years, thereby robbing students of valuable mathematical learning.
Their solution was to co-author their own college algebra book, offer it free to students and faculty, and develop it in a way for anyone in the world to adapt it to their needs.
Stitz and Zeager have received positive feedback from colleagues across the state, nation, and from as far away as The Netherlands.
"The college is very proud of Dr. Stitz and his noble cause to publish such a high calibre electronic algebra textbook and offer it to anyone free of charge," said Dr. Frederick Law, executive vice president and provost at Lakeland.
"By declining offers from publishers, he is committed to providing students with free access to the book."
Several national college textbook outlets have pursued the authors to publish their work.
However, they have declined all offers in order to maintain their original vision of creating a high-quality, content textbook that is within reach and accessible to the average college student. |
ADVICE]BSIT Stutent.
Modern computing has its roots from Mathematics so there is always Math involved. These days you probably won't need them since there are a bunch of libraries and frameworks that will handle mathematical operations for you should you write high level applications. HOWEVER, if you want to be on top of your game you should definitely know your Math eg: Discrete Structures, Linear Algebra, Number Theory, Combinatronics, etc. You will frequently encounter those in graphics development, compiler design, analysis of algorithms, network communications, AI, and several other fields. |
Common Sense Problem Solving
and Cognitive Research
To solve the typical textbook problem, an experienced person will scan the
problem, make a mental marker that places the problem in the appropriate
field of knowledge (for example, kinematics, electricity and magnetism, quantum mechanics, or some other field). Continuing the scan, the expert makes another mental marker for the next more precise area (perhaps Newton's second law, Faraday's law... ).
As the scan goes on, there may be a number of such markers further
refining the concepts needed to solve the problem. These markers
are held in the expert's mind, usually without that person being consciously
aware of what's happening. The trained mind is very powerful.
When the specific parameters of the problem are reached, the expert
begins making notations and works back up through the hierarchy
which has been marked out during the scanning. This results in presenting the solution in reverse order from the actual solution that was
done. The examples in textbooks are therefore very natural presentations from the expert's point of view.
The inverted presentation is confusing to the novice who has indeed had considerable training in non-inverted processes. Since problem solving is a linear process, even though the ideas that evolve in the process of solving a problem are far from linear, it is necessary to present problem solutions linearly. Doing so involves the use of linguistics and semantics.
The student, however, does not yet have the ability or resources to
make these mental markers and carry them along in the mind. The
student needs to see these guideposts written in the order in which
they are encountered. Each new branch that narrows the area of
investigation is actually a subproblem of the broader level concept and
needs to be recognized as such.
The problem solution presentations included here are a sample of solutions designed to provide students with problem solving that is more
representative of the process an expert actually goes through than the
abbreviated, inverted presentations shown in textbooks and solution
manuals. These are a small part of a substantial database of problem
solutions currently being edited into publishable form.
The references listed below are not complete but serve to indicate
the dimensions of the research and experience that are the basis for the manner in which these solutions are presented. The process of solving problems is well understood, since research in problem solving is substantial. The results of that research are not commonly used in textbooks and other teaching materials.
The difficulty students have in learning to solve problems limits the effectiveness of problem solving as a tool in exploring, using, and thoroughly understanding the concepts of their subject matter. These solution presentations address several of those difficulties.
The most important idea illustrated here is the development of problem
solutions through using concepts of the subject matter. This premise
means starting the problem solution by explicitly stating the law,
definition or principle that directly responds to the question asked.
Such a beginning is in contrast to the typical textbook presentation in
which the solution proceeds as if the student has already mastered the
subject and developed the sophistication of the expert. In textbooks
the guiding principle being used in solving the problem makes its first
appearance at the end. Thus the first marker the expert made in solving the problem is the last to appear in the presentation of the solution.
At that point various numerical values that have been obtained in the
early part of the solution are substituted and the problem is considered solved. Some observations on this have been reported by
Dall'Al-ba et al (1993).
After the initial statement of the law, definition or principle that will
solve the problem, the solutions attached here proceed in a logical,
step-by-step manner with successive steps being guided by cues derived from the current state of the solution. This is similar to computer
methods that apply artificial intelligence to problem solving. (Soar is
an example. See Newell (1990); also Newell and Simon (1972).)
The problem solution continues to evolve in a cues - to - pattern - to -
cues - to - pattern process such as described by Margolis (1987). The
solution emphasizes using the concepts to provide the production rules
to move from one state of the solution to another. In the typical problem these production rules make use of additional physics or mathematical concepts.
The presentations provided here show the formal reasoning that occurs in problem solving. They do not, of course, show the internal reasoning. They provide an environment in which the problem and
associated concepts can be explored and internal reasoning promoted.
The problem solutions illustrated in this presentation make strong use of verbalization. The
value of this has been demonstrated by Whimbey (1984) with TAPS
(Think Aloud Pair Solving), and by others. It is well known that students are quite capable of solving problems without understanding the
concepts. (Halloun & Hestenes (1987)). Verbalization is a necessary part
of coming to understand concepts. Formally including this in the solution organization, as shown in the examples, provides an avenue for
exercising verbalization.
The verbal statements are similar to the explanations a person would
make when explaining a step to someone else. In that way understanding the ideas (or lack of that understanding) comes strongly into play. This
communication between the problem solver and his "self" is actually
essential but is slighted in the teaching/learning process.
In the problem solutions shown the first statement is in essence the
answer to the question. It provides a means of starting a solution: simply respond to what the problem asks for with no attention paid to the
particulars of the problem. This response then asks for additional information.
The solution evolves by recursively applying this process. It follows
the selective encoding and selective combination described by Sternberg (1984). This reinforces and further
defines the four step problem solving process described by Polya.
There may well be several appropriate starting points for the solution
of a problem. Solving a problem by starting with the various appropriate concepts is valuable to development of problem-solving and thinking skills as well as to development of an understanding of the concepts employed and their interaction.
Different starting points generate different paths through problem
space and draw on different elements of knowledge space. Solving a
problem using various solution paths provides a means of exploring
the problem. This process leads to understanding the problem and the
ideas that support its solution.
A problem solution consists of a set of nested solutions of subproblems,
shown in the presentations by indenting the subproblems. This logical
organization is widely used in such common things as outlines, tables
of contents, organizational charts, and computer programming.
Recognizing the existence of subproblems addresses the situation described by Staver (1986), in which students have increasing difficulty
with problems as the number of independent variables and conditions
is increased. The resulting overload of the working memory defeats
both the solution of the problem and the development of an appreciation for the concepts that are involved.
Making use of the fact that problem solving has a grammar, and that
this grammar leads naturally to an indented structure, does much to
alleviate this overload. Students can solve simple problems involving
only one variable or condition. More complex problems are simple
problems combined in an interacting, dynamic manner.
It is therefore possible to handle a complex problem because each subproblem is a simple problem. Subproblems themselves may lead to additional sub-subproblems. Solving any level of subproblem supplies
results to the superior level.
The process is quite similar to functions in a computer program which
supply results to the calling function and so on up to the main program.
The subproblem is not involved in knowing the whole problem. It
needs only to supply results to the calling problem.
Although problem solving has long been widely assumed to be an important part of the transfer of knowledge, the validity of this assumption has little research basis other than the striking results in science
and technology that have resulted from the accomplishments of people
trained under that assumption.
Some question about the effectiveness
of good problem solving procedure has been pointed out by Heller and Reif (1984) and Costa (1993).
Inadequate problem-solving skills are amplified by the existence of
sketchy examples in textbooks. Sound problem-solving principles are
not widely available.
Students are exposed to fragmentary problem solving. The
fragmented, inverted solutions in textbooks and answer books are the models presented to them. The
opportunity to make contact with the much broader schema that the
expert actually uses is not made available to students. Indeed even a
casual examination of textbooks shows readily identifiable instances
in which deliberate efforts have been made to protect the student from being
confronted with a broader schema.
The student just does not know what steps to take when confronted
with a problem, or is confused by conflicting examples. That this
should be the case when such a substantial understanding of problem
solving actually exists is unfortunate.
Physics has been said to be "common sense represented in mathematical terms." With the problem solving presentations shown here we can bring common sense into mathematical representations for physics and other subjects.
References
Victoria Brookhart Costa, "School Science as a Rite of Passage; A New
Frame for Familiar Problems," J. of Research in Science Teaching, 30,
(7), 649-668 (1993). Return to text.
J. R. Staver, "The effects of problem format, number of independent variables, and their interaction on student performance on a control of
variable reasoning problem," J. of Research in Science Teaching, 23, (6),
533-542 (1986). Return to text.
NOTE: The example problems referred to in this document would be selected
problem solutions contained in these web pages. A variety of hardcopy material and
material on floppy disks concerning problem solving are also available from the author.
Material on these web pages can be downloaded for individual use that is in accord with
copyright law. For other uses contact the author. |
COMPASS Study Guide Math
Significance of a Study Guide for Math Prep
Preparing for the COMPASS using a math study guide might seem to be preposterous for you, but they turn out to be efficient time savers in the long run. They give an overview of the entire math section in less time. Most guides also present tips and tricks to take care of, in the COMPASS test. But care should be taken when attempting to cover your entire syllabus from one guide. You shouldn't consider it as a one stop solution for your exam. Treat math guides more as workbooks.
How math guides are useful:
They cover almost all topics
They provide helpful tricks and tips
They provide cheat sheets that help you revise math formulae in less time
They are helpful before beginning a focussed math prep
How math guides can be misleading:
They can assume a "know-it-all status", leaving out the particulars
They can be devoted only for tips and tricks, not focussing much on practice
They cannot simulate the adaptive nature of the test
They are not focussed on developing an understanding, but simply as workbooks
In all, studying from a COMPASS study guide math can be both advantageous as well as a frustrating experience. The differentiator is therefore the kind of guide you choose, and how you work through each type of problem. A frustrating COMPASS study guide math is a book that focuses simply on providing answers without explanations or walkthroughs. Beware of books that focus only on tips and don't provide exhaustive exercises or practice tests.
To help you in selecting a COMPASS study guide math here's a review of 3 books that are available in the market. Two are from established publishers, while the third book is an eBook that is downloadable freely from the net.
Study Guide 1:
A guide that is available in the market is "COMPASS Math Test Success: 150 COMPASS Math Problems & Solutions". It is a decent book from a good publisher. It costs about 15 USD, and is a book that gives you value for money. It consists of some good practice questions that are also relevant for the exam. It includes 150 math problems and solutions as the title suggests, but the solutions are not very well explained. However, it turns out to be the best COMPASS study guide math available in its price range.
Study Guide 2:
Another guide that is a winner among students is "Chart Your Success on the COMPASS Test" by Carol Callahan. The guide is best placed in the refresher category. Students who have left their studies long time back find it extremely useful. The guide is not without its share of fallacies, one being that the answers might not be absolutely correct. But the tips section focussed on the COMPASS test is valuable and a good read and it turns out to be a good COMPASS study guide math included.
Study Guide 3:
This book for the COMPASS study guide math is a book that's freely available for download on the net. Here's a link that points to the book.
It is free, and so you might think, "Why not!" The problem with thinking this way is that reading through a free eBook can be a frustrating experience. Some students waste a lot of time not buying a book and simply thinking that they will download an eBook from the net and practice eventually. This is not wise, because wasting time on a bad guide is akin to penalising your time to study for the exam. However, this particular book is from a good source, and previews almost 90% of the topics that are relevant for the exam. Studying from this book will be like skimming through all the questions relevant for the exam. This is valuable when you are not sure which topics you should be concentrating on, and going through all the topics in this book will make you accustomed to the type of questions you can expect, and make you aware of the kind of questions you are weak at. A more focussed approach can be made once you are aware of what topics you must concentrate on while studying from a COMPASS study guide math.
In conclusion, beware of wasting time on eBooks, focus more on practice, and if you do pick a guide, choose one which has a lot of practice questions and a detailed answer key in case you get stuck on one question. Remembering to practice and not simply reading should be a sure shot way to success in the COMPASS |
... read more
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Our Editors also recommend:Sieve Methods by Heine Halberstam, Hans Egon Richert This text by a noted pair of experts is regarded as the definitive work on sieve methods. It formulates the general sieve problem, explores the theoretical background, and illustrates significant applications. 1974 An Algebraic Approach by Ethan D. Bolker This text uses the concepts usually taught in the first semester of a modern abstract algebra course to illuminate classical number theory: theorems on primitive roots, quadratic Diophantine equations, and more.
Topics in Number Theory, Volumes I and II by William J. LeVeque Classic 2-part work now available in a single volume. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes problems and solutions. 1956 editionFundamentals of Number Theory by William J. LeVeque Basic treatment, incorporating language of abstract algebra and a history of the discipline. Unique factorization and the GCD, quadratic residues, sums of squares, much more. Numerous problems. Bibliography. 1977 edition.
An Adventurer's Guide to Number Theory by Richard Friedberg This witty introduction to number theory deals with the properties of numbers and numbers as abstract concepts. Topics include primes, divisibility, quadratic forms, and related theorems.
Product Description:
problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problems—some computational and some classical, many original, and some with complete solutions. The opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamental properties of integers and congruences. Subsequent chapters present proofs of Fermat's and Wilson's theorems, introduce number theoretic functions, and explore the quadratic reciprocity theorem. Three independent sections follow, with examinations of the representation of numbers, diophantine equations, and primes. The text concludes with 260 additional problems, three helpful appendixes, and answers to selected exercises and problems.
Reprint of the W. H. Freeman and Company, San Francisco, second 1978 edition.
A solutions manual to accompany this text is available for free download. Click here to download PDF version now.
Bonus Editorial Feature:
Underwood Dudley: Cranking Out Classics
Any editor involved with publishing in mathematics for any length of time is familiar with the phenomena — the receipt, usually via snail mail, of generally handwritten, and generally interminable, really, really interminable, theses on some bizarre and unprovable point — theses hoping, trying against all hope, demanding in fact, to prove the unprovable, to rewrite some fundamental part of mathematics, often in my experience to demonstrate for one final time that, for example, Einstein didn't know what he was talking about — in short, the work of a mathematical crank!
Underwood Dudley (Woody to everyone in the math world), Professor Emeritus, Depauw University, provided an inestimable service to all math editors in the universe by demonstrating that they are not alone in their experience. His unique and wonderful book Mathematical Cranks (The Mathematics Association of America, 1992) is a readable feast, especially for those who have been on the receiving end of mathematical crank mail. We're all in Woody's debt for having assembled this collection of failed squared circles, angle trisections, and much, much more.
However, chronicling the cranks — as enjoyable as it may have been to the rest of us — is hardly a career, Woody has written many other books as well. And any reader who wants to check out a totally uncranky, reader- and student-friendly, time-tested basic text in Elementary Number Theory could hardly do better than to look at the Dover edition of Woody's book by that name, which started its career with Freeman in 1969 and which Dover was pleased to reprint in 2008 |
Interactive Algebra II tutorial and testing package for individual e-learning and home schooling with emphasis on building problem-solving skills. Java- and web-based math course includes theoretical concepts, hands-on examples featuring animated graphics and live formulas, problem-solving lessons, and customizable real time tests with solutions and evaluationsMath Function Mania is a fun multimedia game for grades 7-12 that teaches functions, algebra and problem solving skills. You must first detect which function is being used, and then solve it by clicking on the correct answer. Includes a head-to-head combat option for two-player competition. This game will take some of the mystery out of functions. |
Discrete Mathematics its Applications, Seventh Edition, is intended one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a discrete mathematics course demonstrates the relevance practicality of discrete mathematics to a wide a wide variety of real-world applications
Multiplying dividing large numbers. Simplifying fractions converting percentages. Hling square roots exponents. These other skills are the veritable foundation on which all of mathematics rests. To master them is to unlock the door to more advanced areas of study
This comprehensive introduction to the calculus of variations its main principles also presents their real-life applications in various contexts: mathematical physics, differential geometry, optimization in . Based on the authors' original work, it provides an overview of the field, with examples exercises suitable graduate students entering research.
The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms cracks.
This text is designed to help teachers work with beginning intermediate ESL ELL students in grades 5 to 12. It provides lessons activities that will develop the students' vocabulary, English usage, mathematical understing. A balance of high-interest activities, cultural sidebars, vocabulary review, chapter tests reince mathematical concepts in English. |
In Classic mode, the TI-34 MultiView can be used in the same classrooms as the TI-34 II Explorer PlusTM as the screen appears identical to the TI-34 II Explorer Plus in this mode
Features
Designed for Middle School Math, Pre-Algebra, Algebra I & II, Trigonometry, General Science, Geometry and Biology
The multi-view display allows you to view multiple calculations on a 4-line display and scroll through entries with ease - See math expressions and symbols, including stacked fractions, exactly as they appear in textbooks
Up to 4 lines of display lets you enter multiple calculations to compare results and explore patterns, all on the same screen
Data List Editor - Enter statistical data for 1- and 2-var analysis as well as explore patterns via list conversions to see different number formats like decimal, fraction and percent side-by-side |
2011The perfect companion for beginners and experts alike, Geometry is the ideal guide to the mathematics of size and shape, from ancient times to the present day. It conveys the basic elements of geometry in a way that is clear and accessible, no matter your level of mathematical ability |
Math 51 Fall 2013
Completing homework assignments is an integral part of
this course. Problems are designed to reinforce concepts covered in
lecture as well as to encourage students to explore implications of
the results discussed in class. Very few students will be able to go
through the entire course without struggling on many problems, so do
not be discouraged if you do not immediately know how to solve a
problem. In confronting difficult questions you should consider how
the problem at hand connects to topics, definitions and/or theorems
discussed in class.
When you have
worked on a problem for a while and remain
stuck,
you are encouraged to ask for hints from your instructor or
TA. Students may also discuss problems with one another, but must
write solutions on their own. In particular if you have taken notes
while discussing homework problems with friends or instructors, you
must put these notes away when writing your solution.
The Honor Code applies to this and all other written aspects of the course.
Be warned:
watching someone else solve a problem will not make homework a good
preparation for tests. Don't get caught in the trap of relying on
others to get through homework assignments.
Students are
expected to take care in writing their
assignments. For instance,
never forget to put your name, your section number and your TA's name on the top of your work;
assignments
should be written neatly;
assignments
should contain clear, complete
solutions; and
completed assignments
which contain multiple pages should
be stapled for easy grading -- one point will be deducted for not doing
this.
Partial progress
toward solutions on problems will be
awarded
partial credit, but simply writing answers down without justification
will receive zero credit. Please note that usually only a portion of
each week's problems will be scored; the selection of problems chosen
to be graded will not be announced in advance.
Logistics for Weekly Homework:
Assignments must be turned in to your TA (discussion section leader) during your enrolled section -- you will not receive credit for work turned into another section leader or section time.
no Please attach a written explanation of the regrade request to your assignment. If more than a week has passed since an assignment was returned in section, your CourseWork score entry for that assignment can no longer be changed. |
Using and Understanding Mathematics : A Quantitative Reasoning premiere text for the emerging Quantitative Reasoning/Quantitative Literacy Course offers an innovative approach for Liberal Arts/Survey Math. It provides a legitimate alternative to algebra and math appreciation courses for non-quantitative majors, helping to reduce math anxiety, emphasizing practicality, and focusing on the use of mathematics in college, career and life. 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 ma... MOREthematics 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, essential uses of math. |
Homework on Autopilot
Why teach calculus students what a revolutionary software system can
solve automatically?
August 30, 2000--Wolfram Research has announced the release of a
stand-alone version of Calculus WIZ, a revolutionary software
product for
first-year
calculus students. With Calculus WIZ, students' computers can now
solve
over 90 percent of the homework problems assigned in a typical calculus
course. Just as the
introduction of the pocket calculator led to serious debate among math
instructors, Calculus WIZ raises serious questions about how
mathematics
should be taught in the
age of the computer.
Calculus WIZ was conceived by Keith Stroyan, Professor of
Mathematics at
the University of Iowa and long-time crusader in the cause of calculus
reform, a movement in
math education that stresses conceptual understanding over rote "cookbook"
calculations.
"Traditional calculus instruction is dominated by the 'template examples
and exercises' paradigm," says Stroyan. "Students work three sets of five
exercises each, just like
the three examples a few pages earlier in the text. This activity has some
value--it builds confidence through practice--but it doesn't do anything
to
develop a deep
understanding. That means it leaves a big gap in the students' ability to
apply calculus to more open-ended problems."
In a typical introductory calculus sequence, so much time is spent
learning and practicing specific pencil-and-paper techniques that the
underlying theory is often
shortchanged. "The traditional courses tend not to have any time left
after students work all the template exercises," Stroyan notes.
However, the templates themselves have become standardized through
hundreds of years of math education, a fact that makes it possible for
Calculus WIZ to contain over
a hundred "solvers," each one addressing a different exercise template. To
solve a given homework problem, the student needs only to fire up
Calculus
WIZ, find the
appropriate solver, type in the details of the exercise, and then sit back
as the computer solver does the work.
A complete electronic calculus textbook, including exercises, is another
part of Calculus WIZ, making it an effective tool for self-study.
However,
what sets it apart from
every other calculus study aid is the problem-solving power it gets from
Mathematica, the leading technical computing system. Calculus
WIZ includes
a special version of
Mathematica's "brain," the extraordinary collection of mathematical
algorithms and knowledge that is the heart of Mathematica's
computational
power.
Will Calculus WIZ change the way that calculus is taught? Probably
not all
by itself--but anyone who remembers how pocket calculators changed math
education can see
the signs of a similar revolution taking shape.
The stand-alone edition of Calculus WIZ is available for Windows
95/98/NT/2000. It requires 160 MB of
disk space for hard-disk
installation. The suggested retail price is $69.50 (U.S. and Canada). For
more information about Calculus WIZ, visit |
Product Details
Learning Modern Algebra From Early Attempts to Prove Fermat's Last Theorem
by Al Cuoco and Joseph J. Rotman
Learning Modern Algebra aligns with the CBMS Mathematical Education of Teachers-II recommendations, in both content and practice. It emphasizes rings and fields over groups, and it makes explicit connections between the ideas of abstract algebra and the mathematics used by high school teachers. It provides opportunities for prospective and practicing teachers to experience mathematics for themselves, before the formalities are developed, and it is explicit about the mathematical habits of mind that lie beneath the definitions and theorems.
This book is designed for prospective and practicing high school mathematics teachers, but it can serve as a text for standard abstract algebra courses as well. The presentation is organized historically: the Babylonians introduced Pythagorean triples to teach the Pythagorean theorem; these were classified by Diophantus, and eventually this led Fermat to conjecture his Last Theorem. The text shows how much of modern algebra arose in attempts to prove this; it also shows how other important themes in algebra arose from questions related to teaching. Indeed, modern algebra is a very useful tool for teachers, with deep connections to the actual content of high school mathematics, as well as to the mathematics teachers use in their profession that doesn't necessarily "end up on the blackboard.'' |
MAZ431: Mathematics 10 (2012-2013)
Major Concepts/Content: The -Mathematics 9 - 12 courses are designed to facilitate student mastery of the DoDEA Mathematic standards and essential objectives. These courses are designed for students needing reinforcement in estimation, computation, basic measurement, and abstract reasoning skills. Technology is utilized to provide support and reinforce math skills. Accommodations and modifications of content, instructional activities, evaluation techniques, and essential objectives are implemented as appropriate for students with disabilities in support of their Individualized Education Program (IEP).
Major Instructional Activities: Instructional activities are provided in individual, small group, and whole class settings. Student activities involve students in a step-by-step process to perform computations mentally, with paper and pencil, and with calculators or computers. Additionally activities use proper instruments for geometric constructions and measurement and apply mathematical concepts to everyday situations. Problem-solving strategies teach students to read, analyze, plan, solve, and check multi-step problems.
Major Evaluative Techniques: Students will be evaluated through informal and formal assessments. Multiple authentic assessments will be used as students perform, produce and otherwise demonstrate skill growth and improvement. Individual student progress is based on understanding and applying the concepts taught.
Course Objectives: The essential objectives of -Mathematics 9 – 12 courses are designed to facilitate learning outcomes appropriate to the instructional need of each student. Instructional priorities are based on the needs of the individual students |
drawn upon their successes in the classroom and the lab as inspiration for MyMathLab for Prealgebra . This new MyMathLab® eCourse offers students a guided learning path through content that has been organized into small, manageable mini-modules. This course structure includes pre-made tutorials and assessments for every topic in the course, giving instructors an eCourse that can be easily set up and customized for a variety of learning environments.
28.2 Simplifying Complex Rational Expressions by Multiplying by the LCD
28.3 Solving Rational Equations
28.4 Applications of Rational Equations: Solving Formulas for a Variable
28.5 Applications of Rational Equations: Work Problems
28.6 Applications of Rational Equations: D = RT
Mini-Module 29: Variation
29.1 Direct Variation
29.2 Inverse Variation
29.3 Joint and Combined Variation
29.4 Applications of Variation
Mini-Module 30: Roots and Radicals
30.1 Square Roots
30.2 Higher-Order Roots
30.3 Simplifying Radical Expressions
30.4 Rational Exponents
30.5 More on The Pythagorean Theorem
30.6 The Distance Formula
Mini-Module 31: Operations of Radical Expressions
31.1 Introduction to Radical Functions
31.2 Adding and Subtracting Radical Expressions
31.3 Multiplying Radical Expressions
31.4 Dividing Radical Expressions
31.5 Rationalizing the Denominator
31.6 Solving Radical Equations
Mini-Module 32: Solving Quadratic Equations
32.1 Introduction to Solving Quadratic Equations
32.2 Solving Quadratic Equations by Factoring
32.3 Solving Quadratic Equations using the Square Root Property
32.4 Solving Quadratic Equations by Completing the Square
32.5 Solving Quadratic Equations using the Quadratic Formula
32.6 Applications with Quadratic Equations
Mini-Module 33: Complex Numbers and More Quadratic Equations
33.1 Complex Numbers
33.2 The Discriminant in the Quadratic Formula
33.3 Solving Quadratic Equations with Real or Complex Number Solutions
33.4 Solving Equations Quadratic in Form
33.5 Complex and Quadratic Applications
Mini-Module 34: Graphing Quadratic Functions
34.1 Introduction to Graphing Quadratic Functions
34.2 Finding the Vertex of a Quadratic Function
34.3 Finding the Intercepts of a Quadratic Function
34.4 Graphing Quadratic Functions Summary
34.5 Applications with Quadratic Functions
Mini-Module 35: Compound and Nonlinear Inequalities
35.1 Interval Notation
35.2 Graphing Compound Inequalities
35.3 Solving Compound Inequalities
35.4 Solving Quadratic Inequalities
35.5 Solving Rational Inequalities
Mini-Module 36: Absolute Value Equations and Inequalities
36.1 Introduction to Absolute Value Equations
36.2 Solving Basic Absolute Value Equations
36.3 Solving Multiple Absolute Value Equations
36.4 Solving Absolute Value Inequalities
Mini-Module 37: Conic Sections
37.1 Introduction to Conic Sections
37.2 The Circle
37.3 The Parabola
37.4 The Ellipse
37.5 The Hyperbola
Mini-Module 38: Logarithmic and Exponential Functions
38.1 Composite Functions
38.2 Inverse Functions
38.3 Evaluating Exponential and Logarithmic Expressions
38.4 Graphing Exponential Functions
38.5 Converting Between Exponential and Logarithmic Forms
38.6 Graphing Logarithmic Functions
Mini-Module 39: Solving Logarithmic and Exponential Equations
39.1 Properties of Logarithms
39.2 Common and Natural Logarithms
39.3 Change of Base of Logarithms
39.4 Solving Simple Exponential Equations and Applications
39.5 Solving Exponential Equations and Applications
39.6 Solving Simple Logarithmic Equations and Applications
39.7 Solving Logarithmic Equations and Applications
Appendix A: U.S. and Metric Measurement
A.1 U.S. Length
A.2 U.S. Weight and Capacity
A.3 Metric Length
A.4 Metric Mass and Capacity
A.5 Converting Between U.S. and Metric Units
A.6 Time and Temperature
Appendix B: More on Functions
B.1 Using a Graphing Calculator
B.2 Algebra of Functions
B.3 Transformations of Functions
B.4 Piecewise Functions
B.5 Graphing Piecewise Functions
Appendix C: More on Systems
C.1 Systems of Linear Inequalities
C.2 Systems of Non-Linear Equations
C.3 Matrices and Determinants
C.4 Solving Systems of Linear Equations Using Matrices
C.5 Cramer's Rule
Appendix D: Additional Topics
D.1 Sets
D.2 The Midpoint Formula
D.3 Surface Area
D.4 Synthetic Division
D.5 Balancing a Checking Account
D.6 Determining the Best Deal when Purchasing a Vehicle, and she was recently awarded a 2011 AMATYC Teaching Excellence Award. |
Transform methods provide a bridge between the commonly used method of separation of variables and numerical techniques for solving linear partial differential equations. While in some ways similar ... |
019853261 Course in Number Theory (Oxford Science Publications)
Ideal for undergraduate and graduate students in pure mathematics, this new text introduces the central, fundamental topics in number theory, including: divisibility and multiplicative functions; congruence and quadratic residues; continued fractions, diophantine approximation and transcendence; partitions; and diophantine equations and elliptic curves. In addition, some more advanced results are given, such as the Gelfond-Schneider theorem, the prime number theorem, and the Mordell-Weil theorem. Based on 20 years of teaching number theory, the approach is thoroughly classroom tested. Each chapter concludes with an extensive selection of sample problems, and an appendix contains hints, sketch solutions, and useful tables, making this the perfect self-contained tool for teaching and learning number |
More About
This Textbook
Overview
Almost every student has to study some sort of mathematical proofs, whether it be in geometry, trigonometry, or with higher-level topics. In addition, mathematical theorems have become an interesting course for many students outside of the mathematical arena, purely for the reasoning and logic that is needed to complete them. Therefore, it is not uncommon to have philosophy and law students grappling with proofs.
This book is the perfect resource for demystifying the techniques and principles that govern the mathematical proof area, and is done with the standard "Demystified" level, questions and answers, and accessibility.
Meet the Author
Stan Gibilisco is one of McGraw-Hill's most prolific and popular authors. His clear, reader-friendly writing style makes his math and science books accessible to a wide audience, and his background in research makes him an ideal editor for professional handbooks. He is the author of Geometry Demystified; Trigonometry Demystified; Statistics Demystified; Everyday Math Demystified; Physics Demystified; Electronics Demystified; Electricity Demystified; The TAB Encyclopedia of Electronics for Technicians and Hobbyists; Teach Yourself Electricity and Electronics; and The Illustrated Dictionary of Electronics. Booklist named his McGraw-Hill Encyclopedia of Personal Computing a "Best Reference" of reviewer
This book is different from any other math proofs book I have found. It teaches you how to think logically. So many people can't do that these days. If you are an advanced student and you want to see how the most complicated proofs are done, you probably don't need this book. But if you're an average person, and you have to work with 'or argue with' people logically, this is a great book. I have also spoken with several beginning geometry and algebra students who were helped by this book, especially when they went on to 'Geometry Demystified.'
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
Anonymous
Posted February 17, 2008
A reviewer
I'm currently enrolled into geometry honors and was desperately in need of proof practice. This book provided weak or nearly any knowledge that could have helped me during class. I would not recommend this book to any readers. The algebra book was fine, but the proof and geometry demystified books are horrible. Please consider saving your money and not spending it on worthless books.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. |
Learner Note: Trigonometry is an extremely important and large part of Paper 2.
... In this session, you will be concentrating on Grade 12 ... be integrated with the
trigonometry you studied in Grade 11.
Grade 12 Mathematics .... to digitally pin your question to a page and see what
questions and ..... 10 Trigonometry. 148 ..... the arithmetic and quadratic
sequences studied in earlier grades, to geometric.
This book basically consists of my lecture notes from teaching trigonometry at ....
Trigonometry is the study of the relations between the sides and angles of
triangles. The ... Trigonometry is distinguished from elementary geometry in part
by its ...
After studying this chapter you should. • be able to ... encountered many of the
elementary results concerning the ..... Chapter 1 Trigonometry. 12. Note that the
inverse functions are denoted here by sin. |
The intelligent reader of a mathematical book desires two things:
First, to see that the present step of the argument is correct.
Second, to see the purpose of the present step.
Everyone in college knows how to read.
We've been reading for a long time.
But it takes a while to learn that there are
different kinds of reading,
as well as more and less effective ways of reading.
You already have your own ``way of reading
mathematics,''
even if you aren't particularly aware of it.
The advice here is aimed to help you
think about how you read mathematics
and (hopefully!) help you to
read it more effectively.
Read the authors' advice.
It's in the section labelled something like,
``How to use this book:
notes for students,''
usually located before the table of contents.
First Reading: look for the Big Picture.
It's easy to get bogged down with details in a math book.
No doubt about it.
So, it's helpful to let yourself skim through a section
your first time through it.
Just get a sense for what's there and maybe why.
Try to see where the authors are taking you,
and worry about the details later.
Second Reading: with paper, pen(cil), and calculator.
Now start worrying about details.
Try, as much as you can, to verify everything
that is in your text.
In other words, make sure YOU think each step is
correct.
Many results must be given of which the details
are suppressed...
These must not be taken on trust by the student,
but must be worked out by his [her] own pen,
which must never be out of his [her] own hand while
engaged in any mathematical process.
Notice that last line: the pen must always be in
your hand ``while engaged in any mathematical process.''
To a great extent, people think mathematically
through writing.
It's hard to do in your head.
Continually ask: What is the Point?
The only way you will learn mathematics is to make it
your own.
It has to become part of you-not in some weird way,
where you suddenly start wearing pocket protectors-but
in the way that ``1+1 = 2'' is just a part of what
you know.
It's not alien.
Asking the question, ``Why is this here?'' or ``What is
the point of this?'' can help the process
of making the mathematics your own.
It is a particularly good question to ask of examples,
which are almost always in the text for a specific
reason.
The reason isn't always stated,
but if you look for it, often it isn't too hard to find.
The same advice applies on a smaller scale,
and I think that's what Polya had in mind.
As you read through an example or proof of a theorem
and are checking each step (remember the Second Reading!),
try to be thinking of what the point or purpose is
of each step.
Why do they calculate this here?
Another way of saying the same thing is,
``Keep your head up out of the sand.''
Don't get buried too deep in calculations.
Learn the vocabulary.
Mathematics obtains much of its power
by constructing a very precise
vocabulary.
When learning new mathematical vocabulary,
it's helpful to distinguish between
formal and informal definitions.
Informal ones are good for getting a feeling
for what the word means.
They help to build up your intuition.
Formal definitions are also important for building
intuition.
What does this mean?
Just that working with a formal definition
will help you to develop correct mathematical
intuition for the concept.
It comes from no other place-mathematicians
(usually!) aren't born with an intuitive knowledge
of, say, continuous functions.
They develop it by working with the formal
definition.
Because formal definitions are precise, they
are one of the few places in mathematics where
memorization can be useful.
So, during your second reading-with pen
or pencil in hand-look for both formal and
informal definitions and rewrite them someplace.
(Rewriting is one way to memorize.
It gets your hands involved.)
It may be worth collecting them in one
place, to build up a calculus glossary.
Learn the Theorems.
Theorems are another source of power for mathematics.
Why?
Because a theorem is something
we know for sure.
Working from precise definitions,
mathematicians prove consequences of those
definitions,
and in doing so, they create theorems.
There are few things in life as certain
as a good theorem.
Like definitions, theorems are stated precisely
and should be rewritten and remembered in the same way.
Read backwards and forwards.
Think of your knowledge of calculus as an organic,
growing thing.
A beast, if you like.
Beasts do not grow in a straight line.
They grow in all directions, at different rates in
each direction.
Your knowledge is like that.
You may not fully learn something in Chapter 1 until
we are halfway through Chapter 3.
That's ok.
But to facilitate such things, it's a good idea to
look back once in a while over previous sections.
See if things are getting any clearer.
Look a bit more at the things you were most puzzled by.
It helps if you're aware of what you were puzzled by,
so we'd better add:
Mark things you find puzzling.
But don't just mark them.
They may be puzzling you for a reason.
Maybe there's something wrong in the text.
Maybe the material is hard.
Guess what?
It is hard!
And that leads to my last piece of advice.
Ask for help.
I'm thinking here especially of things that are hard
with the reading,
but the advice applies to every aspect of the course.
If you're stuck somewhere, the odds are good that
you're not alone.
See if anyone else you know is having the same trouble-you
might have better luck together.
Or ask your professor, ask the SI, ask the tutors at
the Center for Academic Excellence.
But don't be afraid to ask. |
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Starting at $1510Int New!Interactive Exercisesappear at the beginning of an objective's exercise set (when appropriate), and provide students with guided practice on some of the objective's underlying principles. New!Think About ItEx New!Important Pointshave been highlighted to capture students' attention. With these signposts, students are able to recognize what is most important and to study more efficiently. New!A Concepts of Geometry section has been added to Chapter 1. New!Coverage of operations on fractions has been changed in Section 1.3 so that multiplication and division of rational numbers are presented first, followed by addition and subtraction New!A Complex Numbers section has been added to Chapter 11, "Quadratic Equations." New Media!Two key components have been added to the technology package: HM Testing (powered by Diploma) and, as part of the Eduspace course management tool, HM Assess, an online diagnostic assessment tool.
Table of Contents
Prealgebra Review
Introduction to Integers
Operations with Integers
Rational Numbers
Exponents and the Order of Operations Agreement
Concepts from Geometry
Variable Expressions
Evaluating Variable Expressions
Simplifying Variable Expressions
Translating Verbal Expressions into Variable Expressions
Solving Equations and Inequalities
Introduction to Equations
General Equations
Inequalities
Solving Equations and Inequalities: Applications
Translating Sentences into Equations
Integer, Coin, and Stamp Problems
Geometry Problems
Markup and Discount Problems
Investment Problems
Mixture Problems
Uniform Motion Problems
Inequalities
Linear Equations and Inequalities
The Rectangular Coordinate System
Graphs of Straight Lines
Slopes of Straight Lines
Equations of Straight Lines
Functions
Graphing Linear Inequalities
Systems of Linear Equations
Solving Systems of Linear Equations by Graphing
Solving Systems of Linear Equations by the Substitution Method
Solving Systems of Linear Equations by the Addition Method
Application Problems in Two Variables
Polynomials
Addition and Subtraction of Polynomials
Multiplication of Monomials
Multiplication of Polynomials
Integer Exponents and Scientific Notation
Division of Polynomials
Factoring
Common Factors
Factoring Polynomials of the Form x2 + bx + c
Factoring Polynomials of the Form ax2 + bx + c
Special Factoring
Solving Equations
Rational Expressions
Multiplication and Division of Rational Expressions
Expressing Fractions in Terms of the Least Common Multiple of Their Denominators |
Basic College Basic College Mathematics, Beginning Algebra, and Intermediate Algebra courses including lecture-based, self-paced, discussion oriented, and modular classes.This clear, accessible treatment of mathematics features a building-block approach toward problem solving and realistic, diverse applications. Students practice problem solving and decision making with interesting applications throughout the text. The Putting Your Skills to Work and new chapter-end feature, Math in the Media, present students with opportunities to utilize critical think... MOREing skills, analyze and interpret data, and problem solve using applied situations encountered in daily life.The problem solving strategy, highlighted by *A Mathematics Blueprint for Problem Solving, helps students determine where to begin the problem-solving process, as well as how to plan subsequent problem-solving steps. Chapter organizers help students focus their study on the concepts and examples. Developing Your Study Skills boxes throughout the text give students tips to help them improve their study skills. These features, together with the applications and emphasis on problem solving, help students to become effective and confident problem solvers.*Please note: Intermediate Algebra includes a similar feature called Problem Solving Procedure. This clear, accessible treatment of mathematics features a building-block approach toward problem solving, realistic and diverse applications, and chapter organizer to help users focus their study and become effective and confident problem solvers. The Putting Your Skills to Work and new chapter-end feature, Math in the Media, present readers with opportunities to utilize critical thinking skills, analyze and interpret data, and problem solve using applied situations encountered in daily life. Chapter 7, Geometry, has been extensively revised and re-organized to include a new section 7.1 on angles and new section 7.4 devoted to triangles. Increased coverage of estimating with fractions and decimals with new "To Think About" exercises in Sections 2.5, 2.8, and 3.3 and a new lesson in Section 3.7. Coverage of fractions in Chapter 2 has been expanded as follows: Section 2.6 now begins with a discussion of least common multiples so that the subsequent coverage of least common denominators is more complete; a new lesson on order of operations in Section 2.8 offers readers additional review of these rules and practice applying them to fractions; and a new mid-chapter test on fractions appears after Section 2.5. Percent applications are now covered in two sections (Sections 5.4 and 5.5) to allow for a more patient presentation of this important topic. |
Avancemos! cuatro by Ana C Jarvis(
Book
) 1
edition published
in
2010
in
English
and held by
10
libraries
worldwide
Geometry : concepts and skills(
Book
) 1
edition published
in
2010
in
English
and held by
10
libraries
worldwide
The Concepts and Skills program is committed to meeting the needs of all learning levels by providing an accessible approach that helps prepare students for success in algebra and geometry. Build a Solid Foundation in the Fundamentals. Built-in learning support helps students master concepts one at a time. The texts include visual learning strategies, easy-to-follow examples, and help notes for homework, vocabulary, and problem solving. Count on Flexibility and Manageable Pacing. A variety of teaching tools and the focused presentation of the material aid you in the development of active learners. Practice problems gradually increase in difficulty, and Geometry presents a paced approach to proofs. Prepare Students with Abundant Practice. Numerous exercises reinforce concepts and ensure that your students are ready for assessment success. Guided practice targets specific skills. - Publisher. |
Discrete Mathematics
9780198534273
ISBN:
0198534272
Publisher: Oxford University Press, Incorporated
Summary: This text is a carefully structured, coherent, and comprehensive course of discrete mathematics. The approach is traditional, deductive, and straightforward, with no unnecessary abstraction. It is self-contained including all the fundamental ideas in the field. It can be approached by anyone with basic competence in arithmetic and experience of simple algebraic manipulations. Students of computer science whose curric...ulum may not allow the study of many ancillary mathematics courses will find it particularly useful. Mathematics students seeking a first approach to courses such as graph theory, combinatorics, number theory, coding theory, combinatorial optimization, and abstract algebra will also enjoy a clear introduction to these more specialized fields. The main changes to this new edition are to present descriptions of numerous algorithms on a form close to that of a real programming language. The aim is to enable students to develop practical programs from the design of algorithms. Students of mathematics and computer science seeking an eloquent introduction to discrete mathematics will be pleased by this work.
Biggs, Norman L. is the author of Discrete Mathematics, published under ISBN 9780198534273 and 0198534272. Twenty four Discrete Mathematics textbooks are available for sale on ValoreBooks.com, thirteen used from the cheapest price of $0.01, or buy new starting at $101.45 |
Navigating the Hypertextbook
Since we have all of the flexibility and tools of the web at our disposal, we are constructing the hypertextbook to be accessible to students at all academic levels. There are thus three tracks through the hypertextbook for novice, intermediate, and advanced students, respectively.
Ski Slope Model
To make navigation of the hypertextbook through these various levels intuitive and clear, we have adopted the international ski terrain symbols and colors as identifying elements throughout to help you choose and stay on the right path.
In general, the various tracks through the hypertextbook have features or content more relevant to the level of the presentation.
Green Circle Track (Novice)
The green circle level is designed for novice students. It has
more intuitive explanations of important concepts
little emphasis on mathematical rigor
less jargon, or when jargon is used, it is well defined
Blue Square Track (Intermediate)
The blue square level is for intermediate students. It features
dependence on concepts that should have been learned in freshman and sophomore level courses
discussions of mathematical underpinnings of the topics as relevant
free use of standard notation and jargon that students should be acquainted with from prior courses
Black Diamond Track (Advanced)
The black diamond level is designed for advanced students. It promotes |
Modern Geometry / With CD - 02 edition
Summary: Modern Geometry was written to provide undergraduate and graduate level mathematics education students with an introduction to both Euclidean and non-Euclidean geometries, appropriate to their needs as future junior and senior high school mathematics teachers. Modern Geometryprovides a systematic survey of Euclidean, hyperbolic, transformation, fractal, and projective geometries. This approach is consistent with the recommendations of the National Council of Teachers...show more of Mathematics (NCTM), the International Society for Technology in Education (ISTE), and other professional organizations active in the preparation and continuing professional development of K-12 mathematics teachers. ...show less
The Concept of Parallelism. Points, Lines, and Curves in Poincare's Disc Model. Polygons in Hyperbolic Space. Congruence in Hyperbolic Space.
4. TRANSFORMATION GEOMETRY.
An Analytic Model of the Euclidean Plane. Representing Linear Transformations in 2-space with Matrices. The Direct Isometries: Translations and Rotations. Indirect Isometries: Reflections. Composition and Analysis of Transformations. Other Linear Transformations.
5. FRACTAL GEOMETRY.
Introduction to Self-similarity. Fractal Dimension. Iterated Function Systems. From Order to Chaos. The Mandelbrot Set.
Book has a small amount of wear visible on the binding, cover, pages. Selection as wide as the Mississippi.
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<< I choose the topic of Algebra with a concentration on graphing and functions. However, as a requirement we are to write one multicultural lesson. >>
One type of Islamic art is very geometric. Its base is lines and circles. The artists start with two lines that intersect at right angles. Then they draw a circle with its center as the intersection point of the two lines. More circles and lines are drawn from there. The centers of the circles are always the intersection points of circles and circles or circles and lines. Lines are drawn from points where circles intersect circles or other lines. Once they have drawn many lines and circles, they start erasing pieces of the lines and circles until they create a unique pattern.
This type of art can be used in conjunction with your lesson. Have your students make a piece of art using this method. Then have them place the art on a graph. The students can find the equations of the lines and circles in their drawings and their starting and ending points. If you have computers available, the students can program the computer to make their pattern.
As a start to the lesson, I would suggest finding photographs of this type of Islamic art for your students to view. It will give them some idea of what they are shooting for. At that time you can give some background information about this art, tieing in the cultural aspect. |
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Essentials of Discrete Mathematics65.93
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About the Book
The Second Edition of David Hunter's Essentials of Discrete Mathematics is the ideal text for a one-term discrete mathematics course to serve computer science majors, as well as students from a wide range of other disciplines. The material is organized around five types of mathematical thinking: logical, relational, recursive, quantitative, and analytical. This presentation results in a coherent outline that steadily builds upon mathematical sophistication. Graphs are introduced early and are referred to throughout the text, providing a richer context for examples and applications. Students will encounter algorithms near the end of the text, after they have acquired enough skills and experience to analyze them properly. The final chapter contains in-depth case studies from a variety of fields, including biology, sociology, linquistics, economics, and music. |
From the Publisher: The farther the car goes, the more gas it uses. Makes sense -- until you try to do the math! Helping your students represent everyday actions mathematically, this book supports the NCTM's call for a more visual approach to learning algebra. These supplementary exercises develop an understanding of relations and functions in the real world by asking the student to picture a visual image (a graph) of the situation before tackling the equation -- an approach that benefits students who have difficulty with the abstract nature of algebra. |
Courses in
Mathematics
and Statistics
Timetable
MT1002 MATHEMATICS
Aims
This module is designed to introduce students to the ideas, methods and techniques which they will need for applying mathematics in the physical sciences or for taking the study of mathematics further.
It aims to extend and enhance their skills in algebraic manipulation and in the differential and integral calculus; to develop their geometric insight and their understanding of limiting processes and to introduce them to complex numbers and matrices. |
Math
The mathematics curriculum is designed to provide a rigorous foundation in the basics of mathematics and the tools to foster logical thought and analysis. We want students to appreciate the nature, beauty, and scope of mathematics and to understand its potential in dealing with the world's increasing technological complexities. Critical thinking, collaboration and mathematical modeling are emphasized at all levels. In all mathematics courses, faculty help students develop successful study skills and effective test-preparation techniques.
For students whose backgrounds and aptitudes are strong, there are advanced sections of courses in our core curriculum. These include A.P. Calculus BC, Multivariable Calculus with Differential Equations, Advanced Math/Science Research, and A.P. Computer Science. Each of these courses allow students who are passionate about mathematics to pursue excellence in the subject at the highest level.
Dr. April Burch, Director of Berkshire's Advanced Math Science Research program, talks about this year's INTEL submissions. See more here about this science competition and the extraordinary Berkshire students who are taking part in it. |
Elementary Mathematics Is Anything but Elementary: Content and Methods From A Developmental Perspective: Content and Methods From A Developmental Perspective, 1st Edition
Making sure you are well prepared for the classroom, ELEMENTARY MATHEMATICS IS ANYTHING BUT ELEMENTARY: CONTENT AND METHODS FROM A DEVELOPMENTAL PERSPECTIVE is a comprehensive program that equips you with both a content and a methods text. Serving as a professional development guide for both pre-service and in-service teachers, this text''s integrated coverage helps dissolve the line between content and methods—and consequently bolsters your confidence in your delivery of math instruction. The text''s comprehensive coverage includes pre-K information. Its strong emphasis on the National Council of Teachers of Mathematics five core standards—Number and Operations, Algebra, Geometry, Measurement, and Data Analysis & Probability—provides key information common to most state curricula relative to NCTM standards for grades pre-K through 6. Text content is based on thorough elementary mathematical scope and sequences that have been shown—and class-tested by the authors—to be effective means for guiding the delivery of curriculum and instruction. With its solid coverage and emphasis on student thinking, ELEMENTARY MATHEMATICS inspires, empowers, and prepares preservice teachers for today''s classroom41.49
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Algebra I Teacher Resources
Find Algebra I educational ideas and activities
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Here is an excellent, detailed resource that builds on prior work done in Algebra I on domain and range of a function. Learners review the concepts of domain and range, then work in pairs to complete a worksheet of exercises in which they determine domain and range of a relation given its graph and state whether the relation is a function. After discussing their solutions with the class, each pair then selects an item from a grab bag which contains exercises with instructions to sketch possible graphs for a given domain and range. Note that solutions to exercises are not included.
Using a regression applet, your class can predict and explore the shape of the residuals of linear and non-linear data. Then through discussion, these learners can generate rules on how to analyze residual plots to recognize non-linear data. Round out the lesson with an investigation regarding SAT scores and best fit regression models. For an extra challenge, have the class use the regression applet to try to generate scatter plots to match given residual plots. Note: the Data Sets for Algebra I Handout mentioned as an optional resource is not availableStudents participate in a lesson that reviews the concept of linear functions in connection with preparation for an exam. The teacher reviews problems with the students for scaffolding. Students practice graphing linear functionsThis activity takes you from the basics of equations of lines (slope and intercepts) to scatter plots and lines of best fit. Interpret the slope using the context of the problem and use the regression line to extrapolate values. Included in the detailed lesson plans are a warm-up activity and a link for pre-lesson review on slopes of lines. Unfortunately, the link to the end of lesson PowerPoint evaluation does not work.
Mathematicians use an inquiry method to solve linear equations. In this linear equations lesson plan, students practice solving equations using addition, subtraction, multiplication and division. They solve multi-step equations and equations with variables on both sides of the equal sign. Each section features a class discussion, and work sample questions. The final activity requires students to work in small groups to plan a one-day trip to France.
Students explore multi-step equations. In this pre-algebra/algebra I lesson, students use the TI-nspire computer algebra system to check the steps they used to solve multi-step equations and equations with variables on both sides.
High schoolers gather data by experimentation or observation in one of nine activities. Each group models the data they gathered, creates a display, and presents results to the class using an overhead projector. explore the concept of patterns. In this patterns instructional activity, students use their Ti-Nspire to determine linear, quadratic, and geometric patterns. Students notice that the area of a rectangle creates a quadratic width v. area graph.
Students discuss what good presentation looks like. In this geometry lesson, students discuss the 7 important steps required to be a good presenter. They start with their names and what they will be discussing and end with a thank you to all who helped with the creation of their work. They may work in groups.
Students read and discuss two poems for meaning. In this language arts/math lesson, student count the number of letters in the poem, and then count the number of vowels and consonants. Additionally, students discuss how to turn their counts into percentages.
Students investigate the formula used to solve quadratic equations. In this algebra lesson, students solve quadratic equations using the quadratic formula and the discriminant to tell where the graph will intercept the x-axis. They set the equation to zero and solve for x.
Students investigate the different hormone contaminants in the water supply. In this math lesson, students analyze data tables and graphs. They demonstrate exponential growth and decay using frog populations.
Students examine linear and non-linear functions. In this Algebra I or II activity, students investigate the realtionship between numerical (table), graphic, and symbolic representation. The use of a graphing calculator is needed to complete the activity.
Students decompose a larger geometric shape into smaller parts. In this Algebra I/Geometry lesson plan, students examine the Orion spacecraft to determine its area. Students apply the area formulas for the various geometric shapes found in the decomposition model to estimate the area of the spacecraft.
Learners create a proposal to solve Wake County's problem with losing the North Wake landfill in such a way that: a new landfill site is agreed upon, Solid-wase disposal is in compliance with Local and State landfill regulations and waste disposal is safe and convenient. |
Vector calculus
Vector calculus is a branch of mathematics that investigates vector fields and how they change over time. Vector calculus usually studies two- or three-dimensional vector fields, but can be used in higher dimensions, too. It is a part of the study of multivariable calculus. Vector calculus is useful in physics and engineering because of how it can look at electromagnetic and gravitational fields. |
books.google.com - A thorough introduction to Borel sets and measurable selections, acting as a stepping stone to descriptive set theory by presenting such important techniques as universal sets, prewellordering, scales, etc. It contains significant applications to other branches of mathematics and serves as a self-contained... Course on Borel Sets |
Mathematics in the real world Inspired by Évariste Galois's attempts to express symmetry using mathematical equations, Professor Marcus du Sautoy explores the inextricable link between the physical world and mathematics. Author(s): Marcus du Sautoy
1 Learning to learn Debate 1: use of female protagonistGame Theory This course is an introduction to game theory and strategic thinking. Ideas such as dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, and signaling are discussed and applied to games played in class and to examples drawn from economics, politics, the movies, and elsewhere. Author(s): jsl57
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2.4 A comparison of Sunset Song and its literary predecessors12.333 Atmospheric and Ocean Circulations (MIT) In this course, we will look at many important aspects of the circulation of the atmosphere and ocean, from length scales of meters to thousands of km and time scales ranging from seconds to years. We will assume familiarity with concepts covered in course 12.003 (Physics of the Fluid Earth). In the early stages of the present course, we will make somewhat greater use of math than did 12.003, but the math we will use is no more than that encountered in elementary electromagnetic field theor Author(s): Plumb, R. Alan253J Transportation Policy and Environmental Limits (MIT) Through a combination of lectures, cases, and class discussions this subject examines the economic and political conflict between transportation and the environment. It investigates the role of government regulation, green business and transportation policy as facilitators of economic development and environmental sustainability. It analyzes a variety of international policy problems including government-business relations; the role of interest groups, non-governmental organizations, and the pub Author(s): Salvucci, Frederick,Coughlin1 Why plan a piece of writing2 'Good enough' is OK Estimating the time for the taskO_1:// the hypertextu(r)al matrix Founded in 1995 LAB[au], laboratory for architecture and urbanism, links theoretic research LAB[a+u] to concrete works of conception and realisations LA.BAU. LAB[au] elaborates a ?hyperdesign? investigating the implications of new technologies of communication and computation in spatiotemporal and social processes and their forms of representation as architecture and urbanism. The transposition of the hypertext model to architectural and urban concepts question the mutation of the spatial and se Author(s): Abendroth, M., Decock, J. and Mestaoui, N. a Author(s): No creator set |
Elementary Algebra W/PAC-Now
9780495389606
ISBN:
0495389609
Edition: 4 Pub Date: 2008 Publisher: Cengage Learning
Summary: This text blends instructional approaches that include vocabulary, practice, and well-defined pedagogy, along with an emphasis on reasoning, modeling, and communication skills. With an emphasis on the 'language of algebra', the author's foster students' ability to translate English into mathematical expressions and equations.
Tussy, Alan S. is the author of Elementary Algebra W/PAC-Now, published 2008 under ...ISBN 9780495389606 and 0495389609. One hundred forty two Elementary Algebra W/PAC-Now textbooks are available for sale on ValoreBooks.com, forty two used from the cheapest price of $6.95, or buy new starting at $80 slightly worn, cover scuffed/smudged |
Calculator for statistic, function plottting, vectors, matrices, complex numbers, coordinates, intersections. For objects like point, line, plane and sphere distances, intersections, volume, area of squeres, area of a triangle can be calculatedase 1.0 - Middle-School (grades 5 through 9) math program written to provide skills in context. Students are shown a Cartesian plane across which a small dot moves. Students try to "capture" the dot by typing in its current or anticipated coordinates. |
The math department recommends the purchase of either the TI-83 or TI-84 Plus caclulator for all students taking Algebra II or above. Please see the following link for details regarding these two models. Texas Instrument
Scientific calculators are sufficient for all other courses. It would be helpful to have a scientific calculator with the capability of performing operations with fractions. |
Product Description
This answer key contains answers for the Primary Mathematics textbooks and workbooks for both the U.S. Edition and 3rd Edition Books 4A-6B. These answers are already contained in the Home Educators and Teacher's Guides, and do not need to be purchased if the instructor already owns either of the other guides. 71 pages, softcover.
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Singapore Math, Primary Math Answer Key Booklet 4A-6B
5
5
1
1
great savings if you just need the answers
I don't need the instructors guide for this age group so the answer key for 4-6 saves me a great deal of money as well as time ( I can just look up the answers and move on ). If I have trouble explaining a problem ( usually a word problem ) I have used the Singapore math web site to ask the experts.
March 23, 2011 |
56,"ASIN":"0395977223","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":4.75,"ASIN":"0446310786","isPreorder":0}],"shippingId":"0395977223::l95vz7flkdRwHW4j2nWsrrmdz02rBOfXtqR0y3mxg9Xxwazifhryqml%2Fhdu20f7022JJUO%2BvCDQ1cyzxVh4TlQZpvTNOKoQOY8P%2FMha5KZk%3D,0446310786::932mSMIf0D0uEHj%2FDPWmJaCqq0FpqhQ%2FaUI5KgaHNsLNrrgU9kbGkTD6ctmFTFfRBvKecBKWAQqmclJdsbdR18h4xeUHiDQH4tHnzfJs0 thought out Algebra textbook. I started teaching from it earlier this year and have grown to appreciate it very much. I am especially pleased the more I compare this to other books. Most math books these days are little more than pretty colors, crazy fonts, neat pictures, lots of distractions, and very little actual math instruction. This book, on the other hand, actually focuses on the math, explains it reasonably well, and has great sets of real example problems and practice problems of all difficulty levels, including lots of practical problems that aren't forced or contrived. It is not perfect, but it is the best I have seen.
Pros: *Lots of math rather than lots of silly distractions *Appropriate difficulty level - not "dumbed down" *Good examples worked out and explained *Good problem sets for homework and practice
Cons: *Some explanations are just a bit short, although most are good *Factoring, the hardest topic, is early in the book, which makes it difficult for some students
This is one of only a handful of books that actually covers Algebra 1 in detail, and in an order that builds a strong foundation along the way. Sure, there will be students who find this book hard to understand -- they are the ones who are not really ready for algebra and should be either taking pre-algebra or one of the many "algebra lite" books that are available. Well-prepared students will find this book a great resource, and should find themselves extremely well-prepared for future classes in mathematics.
It is arguably one of the best algebra books available, and is one of the top algebra textbooks as rated by Mathematically Correct, a group that is concerned with the quality of mathematics instruction in California (and beyond).
This is a pretty good comprehensive textbook for students of all levels. There are twelve chapters in the book, plus a glossary, various helpful appendices, and an index. The book contains "A" (easy), "B" (intermediate), and "C" (challenging( problem sets for every topic covered. Also, enrichment topics are included, including "Extra," "Challenge," "Historical Note," "Application," and "Career."
Like any other book, this book does, however, isn't absolutely perfect. One thing about this book is that the explanations in this book at the top of every section summarizes important concepts and gives some examples and definitions; however, the examples often only cover the "A" and half of the "B" problem sets, and the "C" problems are often unexplained. Also, the textbook seems to be designed for slightly more advanced students, as the problems and pace of the text isn't for beginning or struggling students.
One note is that this book isn't the best tool to teach yourself math, although it is an excellent source for problem sets, and also serves as an excellent reference for algebraic concepts. I would recommend "CliffsStudy Solver Algebra I" if you are having trouble with Algebra I or if you want to teach yourself math, because this textbook is not designed to be a tutorial. I have tried to teach myself many new math concepts, but this book didn't always help - though I did some new problem solving strategies from here. Sometimes the explanations were simply skimmed over too quickly.
Overall, this is a great book. It's really helped me with my math grade, but this is just one of my math books which helped me. With teacher guidance, one or two more study guides, and most importantly, a dedicated self-motivated mind, you are bound to be a success in algebra.
I think overall, the book, Algebra Structure and method is wonderful. The book provides the odd answers to the problems, in the back, which is nice, because it gives me sense of if I'm getting the problems correct, without telling me all the answers. I also like how the difficulty of problems is catagorized, with "a" problems being the easiest, "b"problems, in the middle and "c" problems the hardest. Sometimes the explanations of how to do the problem are a little confusing,though. All in all, this book is a good teacher.
I am currently an eigth grader using this book in the challengers program at my school. It is an informative textbook, filled with lots of examples on how to solve mixture problems, polynomials, etc. But, I warn you, if you do not master the concepts in the previous chapters, you will have a hard time understanding the material from Chapter 7 on.
This book is a comprehensive algebra 1 course despite the implications of the words "Book 1" in its title. You can use it for self-instruction, because the answers to the odd-numbered problems are given at the back of the book -- and there are lots of problems. It is also a great source of supplementary material for students who are taking algebra 1 in school. Supplementary material is necessary because most algebra 1 courses these days are "dumbed down." The District of Columbia Public Schools, for example, uses a book (ISBN 0618250182) that has been stripped of traditional problems that show students the power of algebra -- "work problems," "mixture problems," "age problems" and so on. And it has been stripped of difficult problems in all of the topics that remain. The book under review here covers the traditional topics and has difficult problems in all topics. The book would be good for a differentiated course, because the problems in each section are grouped into three levels of difficulty, labeled A, B and C. |
Word problems are the most difficult part of any math course –- and the most important to both the SATs and other standardized tests. This book teaches proven methods for analyzing and solving any type of math word problem. |
Logic forms the basis of mathematics and is a fundamental part of any mathematics course. This book provides students with a clear and accessible introduction to this important subject, using the concept of model as the main focus and covering a wide area of logic. The chapters of the book cover propositional calculus, boolean algebras, predicate calculus and completelness theorems with answeres to all of the exercises and the end of the volume. This is an ideal introduction to mathematics and logic for the advanced undergraduate student.
Logic forms the basis of mathematics and is a fundamental part of any mathematics course. This book provides students with a clear and accessible introduction to this important subject, using the concept of model as the main focus and covering a wide a
In an elegant and concise fashion, this book presents the concepts of functional analysis required by students of mathematics and physics. It begins with the basics of normed linear spaces and quickly proceeds to concentrate on Hilbert spaces, specifically the spectral theorem for bounded as well as unbounded operators in separable Hilbert spaces. |
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Mathematics and Logic by Mark Kac, Stanislaw M. Ulam Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, more. Includes 34 illustrations. 1968 edition.
Great Ideas of Modern Mathematics by Jagjit Singh Internationally famous expositor discusses differential equations, matrices, groups, sets, transformations, mathematical logic, and other important areas in modern mathematics. He also describes their applications to physics, astronomy, and other fields. 1959 edition.
Product Description:
invariably leads to interesting questions that would never have otherwise arisen. With puzzles involving coins, postage stamps, and other commonplace items, students are challenged to account for the simple explanations behind perplexing mathematical phenomena. Elementary methods and solutions allow readers to concentrate on the way in which the material is explored, as well as on strategies for answers that aren't immediately obvious. The problems don't require the kind of sophistication that would put them out of reach of ordinary students, but they're sufficiently complex to capture the essential features of mathematical discovery. Complete solutions appear at the end |
#1 MIT
The Massachusetts Institute of Technology offers so many free mathematics courses online that it would be difficult to post them all here. But with more than 100 courses to choose from, MIT definitely belongs at the top of this list. Most of the school's free math courses include lectures, assignments, exams and a wide array of multimedia materials.
#2 The Open University
Britain's renowned Open University offers nearly 30 free mathematics courses online. From basic math to working your own math, The Open University has you covered. Most courses are text based and can be viewed online or downloaded to your computer.
#3 UMass, Boston
The Mathematics Department of the University of Massachusetts, Boston, provides several high-quality calculus courses that provide complete instruction for students at any level. All three of the free courses feature multiple lessons, calculus problems, assignments and tests.
#4 Capilano College
Canada's Capilano College offers two free math courses at this time. One is for students who are new to calculus, and the other is for students who have advanced calculus knowledge. Both courses include instruction, worksheets and exams.
#5 Dixie State College
Utah's Dixie State College offers two free calculus courses through its new OpenCourseWare program. Courses are designed for students at the introductory and intermediate levels and include instruction, notes, exams and other resources.
#6 Temple University
Although Temple University doesn't offer free mathematics courses in the strictest sense of the term, the school does offer free access to math textbooks that cover a wide range of topics. If you are an accomplished self-learner, you can utilize these books the same way you would use a formal course.
#7 UC Berkeley
The University of California, Berkeley, offers only one free mathematics course, but it is very good. The course covers topics that would be of interest to computer science students, such as statistics, elementary number theory, algebra and discrete probability. An audio and video version of the course is available.
#9 Carnegie Mellon
Carnegie Mellon University offers an excellent statistics course through its Open Learning Initiative. The free online course is comparable to the one on campus and includes expository text, case studies, interactive learning exercises and tests.
#10 Whatcom Community College
Whatcom Community College offers free access to a brief trigonometry course. The course is designed for trig beginners and is viewable in PDF format. Simple expository text and accompanying illustrations make navigating this course on your own a breeze. |
Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory
The History of Mathematics: An Introduction, Sixth Edition, is written for the one- or two-semester math history course taken by juniors or seniors, and covers the history behind the topics typically covered in an undergraduate math curriculum or in elementary schools or high schools.
Mathematics for Economics and Business provides a thorough foundation in mathematical methods for economics, business studies and account |
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collection of resources is designed to supplement a modern algebra course. They are designed to help students visualize many of the important concepts from a first semester undergraduate abstract algebra course.
This article explores how mathematical techniques, digital images, and dynamic geometry software can be used to analyze a real-world situation originating from poultry science. The topic is mathematical modeling of the shape of an egg, where the underlying question is: What is the volume and surface area of a hen's egg?" |
Oak Brook MathOr if they are a visual learner, I try to provide visual examples that they would likely be more interested in and understand easier. Finally, I always try to provide value. Learning becomes much easier when you understand the value of why you are learning a specific topicWhile Algebra 1 typically deals with linear relationships, Algebra 2 introduces the non-linear relationships that can better model the business and physical worlds. With the right perspective, it can be a mind-broadening experience. Calculus is the mathematics of change and variation which is fundamental to Physics, Chemistry, Biology, and Engineering. |
The MathWorks at MIT IAP 2010
The MathWorks is hosting 10 sessions during MIT's Independent Activities Period (IAP). Please join us to learn more about how you can use MathWorks products as a flexible environment for technical computing and application development in engineering, math, and science curricula and research. Attend as many sessions as you wish.
Session Descriptions and Presenter Information
Parallel Computing Master Class
Monday, January 11
10:00 a.m.–12:00 p.m.
Room 4-237
In this session, you will learn how to perform parallel computing in MATLAB using either your desktop machine or a computer cluster. You will discover how to utilize the full capabilities of your multicore machine through the parallelism capabilities of MATLAB 7.9 and Parallel Computing Toolbox 4.2 (both part of Release 2009b). You will also learn how to use the parallel computing products on a computer cluster to speed up your algorithms and handle larger data sets.
Highlights include:
Using the built-in parallel options for toolboxes
Developing task-parallel applications
Developing data-parallel applications
Converting interactive applications to scheduled applications
About the presenter: Sarah Wait Zaranek, Ph.D.
Sarah is an application engineer (MATLAB geek) at The MathWorks. Her work focuses on distributed computing and the efficient use of core MATLAB. She has been using MATLAB since her early undergraduate days and enjoys applying her experiences to help people use MATLAB to forward their science and research. Sarah has a Ph.D. in geology and a master's degree in applied mathematics from Brown University.
Advanced Programming Techniques in MATLAB
Monday, January 11
2:00–4:00 p.m.
Room 56-114
In this master class, you will learn how using the right MATLAB function type can lead to more robust and maintainable code. Through demonstrations, you will discover how to use MATLAB functions to solve optimization problems and make it easier to program GUIs. This session will also provide you with an understanding of how different MATLAB data types are stored in memory. Experienced MATLAB programmers will receive the most benefit from this session.
About the presenter: Loren Shure, Ph.D.
Loren is a principal MATLAB developer and has worked at The MathWorks for more than 20 years. She has coauthored several MathWorks products in addition to adding core functionality to MATLAB. Loren currently works on the design of the MATLAB language. She graduated from MIT with a B.S. in physics and has a Ph.D. in marine geophysics from the University of California, San Diego, Scripps Institution of Oceanography. Loren writes about MATLAB on her blog, Loren on the Art of MATLAB.
Assessing Alternative Energy Designs with Simulink
Tuesday, January 12
10:00 a.m.–12:00 p.m.
Room 4-231
In this session, we will demonstrate the use of MATLAB and Simulink in assessing the designs of new technologies for generating electricity using examples that include solar and wind power generation. We will show how MATLAB and Simulink can be used develop controls that maximize power generation and transmission and ensure that the generated AC power is synchronized in frequency and phase with the national electric grid. We will feature the use of SimPowerSystems, SimElectronics, and SimMechanics for modeling the electrical and mechanical components that make up these systems.
About the presenter: Terry Denery
Terry is currently the marketing manager for the physics-based modeling and simulation tools at The MathWorks. Before joining The MathWorks in 2004, he worked at MSC.Software as an engineer in the sales organization, supporting the products ADAMS, visualNastran 4D, Dynamic Designer, and CATIA v5i. At Knowledge Revolution, which was acquired by MSC.Software and produced the motion simulation tools Working Model and Interactive Physics, Terry founded the Technical Services group, which served customers through technical support, training, and consulting. Before working at Knowledge Revolution, Terry developed solid rocket propulsion systems at Hercules, Inc.
Terry has degrees in chemical and mechanical engineering from the University of Virginia as well as a Ph.D. in aeronautics and astronautics, focusing on fluid dynamics and thermodynamics, from Stanford University.
We will look at practical hardware examples that demonstrate state logic, motor (closed-loop) control, and signal processing. We will also provide hardware recommendations.
About the presenter: Sam Mirsky
Before joining The MathWorks in May 2007, Sam worked for 14 years in the defense industry, where he was involved in hardware-in-the-loop testing of advanced electro-optical and infrared weapon systems, including real-time, closed-loop simulation incorporating sensors such as GPS, accelerometers, gyros, and autopilots. He has a B.S. in aerospace engineering (fluid dynamics) from Syracuse University and an M.S. in aerospace engineering (combustion) from the Georgia Institute of Technology.
Doing Twisted Things to Images: Spatial Image Transforms in MATLAB
Wednesday, January 13
10:00 a.m.–12:00 p.m.
Room 4-237
Spatial transforms can make thumbnail views, fix slanted horizon lines, align multiple images of a scene, or warp images in bizarre and creative ways. MATLAB and Image Processing Toolbox offer tools to do all these things and more.
In this session, you will learn the essential and practical concepts you need to understand and apply spatial image transforms. For example, where does a transformed image go? Why are spatial transforms implemented backwards? You'll find out how to align and overlay transformed images, define your own transforms, and troubleshoot when things go awry. You will see how to have a little fun with some oddball transforms, including polar-coordinate image twisting and randomized image melting.
About the presenter: Steve Eddins, Ph.D.
Steve is an electrical engineer–turned–software developer. He manages the image processing and geospatial computing development team at The MathWorks. Before joining The MathWorks, Steve was on the faculty of the Electrical Engineering and Computer Science Department at the University of Illinois at Chicago, where he taught graduate and senior classes in digital image processing, computer vision, pattern recognition, and filter design, and performed research in image compression.
Steve coauthored the book Digital Image Processing Using MATLAB and writes regularly about image processing and MATLAB in his blog, Steve on Image Processing. He holds a B.E.E. and a Ph.D., both in electrical engineering, from the Georgia Institute of Technology. He is a senior member of the IEEE.
Using MATLAB for Computational Finance
Wednesday, January 13
12:00–2:00 p.m.
Room 4-237
Finance professionals within industry and academia worldwide use MATLAB and other MathWorks tools to conduct research, rapidly prototype algorithms, and develop financial models. In this session, you will learn how you can reduce your computing time and complement your existing models by using MATLAB and other financial tools from The MathWorks. You will see how you can:
Access and rapidly analyze your data
Leverage the power of MATLAB in your academic research
Develop models and prototype applications quickly and accurately
Incorporate MATLAB and other financial tools from The MathWorks in your curriculum
About the presenter: Michael Weidman
Michael joined The MathWorks in 2007 and is focused on computational finance. Michael earned a B.A. in physics from Harvard University and completed Part III of the Mathematical Tripos from DAMTP at the University of Cambridge. His research focused on solid and fluid mechanics in biological settings.
How a Differential Equation Becomes a Robot: Expanding the Power of MATLAB with Simulink and Symbolic Math Toolbox
Thursday, January 14
10:00 a.m.–12:00 p.m.
Room 4-237
In this session, we will show how MathWorks products complement each other, and how when working with them together, users can unleash the full potential of our complete development environment. Starting from the underlying mathematical and physical principles, we will discuss the iterative process of analysis, design, and optimization involved in the development and implementation of a real-life practical application, starting from the underlying mathematical and physical principles. The demonstration example will examine how a simple second-order differential equation can evolve into a full-fledged dynamic model of a multiple-degrees-of-freedom robotic manipulator that includes the controls, electronics, and three-dimensional mechanics of the complete system.
About the presenter: Carlos Osorio
Carlos is an application engineer specializing in control systems for robotics and vehicle dynamics. Before joining The MathWorks in 2007, he worked in the Advanced Chassis Technology Department at Visteon Corporation, where he was involved in the development and implementation of prototype electronic active suspension, steer-by-wire, and brake-by-wire systems for passenger vehicles. Carlos received a B.S. from the Pontificia Universidad Catolica del Peru and an M.S. from the University of California at Berkeley, both in mechanical engineering.
MATLAB for Bioinformatics and Systems Biology
This two-part, hands-on session will introduce Bioinformatics Toolbox and SimBiology. The first part will provide an overview of the functionality in Bioinformatics Toolbox, with examples to perform:
Sequence alignment
Phylogenetic analysis
Microarray analysis
The second part of the session will introduce the graphical and tabular interface in SimBiology for building and configuring reaction networks. Specifically, you will learn how to create network models (add compartments, reactions, and species) and configure properties of the reaction network. Once we build a model, we will see how to perform tasks such as:
Simulating the model
Performing parameter scans
Creating custom HTML reports
Note: Attendees should bring a laptop for this hands-on lab.
About the presenter: Saket Kharsikar
Saket joined The MathWorks in 2008 as an application engineer for bioinformatics. He has a master's degree in biomedical engineering, with a specialization in bioinformatics and computational biology, from the University of Akron. He also worked as a research assistant at the university. Saket's primary research and thesis was in the field of computational genomics, where he contributed toward development of a novel protein function classifier.
All the Controls You Need: Learn Controls in the Context of MATLAB and Simulink
Tuesday, January 19
9:00 a.m.–12:00 p.m.
Room 56-114
Controls are one of the most common tools in an engineer's arsenal. MATLAB and Simulink provide a comprehensive and intuitive environment to model, analyze, design, and test controllers for a variety of applications. In this session, you will learn how to apply a control design workflow to model, tune, and verify common compensators to meet design requirements.
We will start with the basics of modeling LTI systems in MATLAB and Simulink and then discuss the use of Control System Toolbox to analyze those systems in both the time domain and the frequency domain. Finally, we will apply open-loop techniques such as root locus to understand the response of closed-loop systems to external disturbances. Key topics include:
Modeling transfer functions and state-space equations
Investigating the transient response characteristics of systems
Analyzing the frequency response of systems
Applying the root locus technique
Implementing common compensator structures
Designing, tuning, and verifying a PID controller Tzuliang Loh
A training engineer at The MathWorks, Tzuliang focuses on developing and delivering training solutions for academic users. He has played a key role in developing a series of interactive video tutorials that teach students how to use MATLAB and Simulink. Tzuliang has a B.S.E. in mechanical engineering from the University of Michigan. He also has an M.S. in mechanical engineering from MIT, where he designed, fabricated, and characterized BioMEMS and microfluidic devices. His work included implementing live image processing for thermal characterization of a MEMS device in MATLAB.
All the Signal Processing You Need: Learn Signal Processing in the Context of MATLAB and Simulink
Tuesday, January 19
1:00–4:00 p.m.
Room 56-114
The advent of high-speed computing has enabled the widespread application of digital signal processing applications to solve a multitude of engineering problems. MATLAB, Simulink, and associated products enable rapid design, simulation, analysis, and implementation of DSP algorithms. In this session, you will learn how to represent, analyze, and design signal processing systems in MATLAB and Simulink.
We will start by looking at how to work with signals in the MATLAB environment. We will then show how to analyze signal processing systems implemented in MATLAB and Simulink. Finally, we will discuss how to design classical IIR and FIR filters in MATLAB and implement them in Simulink. Key topics include:
Working with signals
Analyzing discrete-time LTI systems
Designing and implementing filters
Signal processing road map Kirtan Modi
Kirtan is an academic training engineer at The MathWorks. His role involves delivering MathWorks product–specific training to MATLAB and Simulink users in academia and industry, and developing content to help academic instructors leverage MathWorks products in teaching. Kirtan has a Ph.D. in electrical engineering from the University of Virginia. His research experience spans the areas of multiuser MIMO wireless communications, optical communications, networking, and signal processing education, while his teaching experience is primarily in the area of signal processing. |
Art And Craft of Problem Solving
9780471789017
ISBN:
0471789011
Edition: 2 Pub Date: 2006 Publisher: John Wiley & Sons Inc
Summary: You' ve got a lot of problems. That's a good thing. Across the country, people are joining math clubs, entering math contests, and training to compete in the International Mathematical Olympiad. What's the attraction? It's simple--solving mathematical problems is exhilarating! This new edition from a self-described "missionary for the problem solving culture" introduces you to the beauty and rewards of mathematical p...roblem solving. Without requiring a deep background in math, it arms you with strategies and tactics for a no-holds-barred investigation of whatever mathematical problem you want to solve. You'll learn how to: get started and orient yourself in any problem. draw pictures and use other creative techniques to look at the problem in a new light. successfully employ proven techniques, including The Pigeonhole Principle, The Extreme Principle, and more. tap into the knowledge gained from folklore problems (such as Conway's Checker problem). tackle problems in geometry, calculus, algebra, combinatorics, and number theory. Whether you're training for the Mathematical Olympiad or you just enjoy mathematical problems, this book can help you become a master problem-solver! About the Author Paul Zeitz studied history at Harvard and received a Ph.D. in mathematics from the University of California, Berkeley. He currently is an associate professor at the University of San Francisco. He won the USA Mathematical Olympiad (USAMO) and was a member of the first American team to participate in the International Mathematical Olympiad (IMO) in 1974. Since 1985, he has composed and edited problems for several national math contests, including the USAMO and helped train severalAmerican IMO teams, most notably the 1994 "Dream Team" which, for the first time in history, achieved a perfect score. In 2003, he received the Deborah Tepper Haimo award, a national teaching award for college and university math, given by the Math Association of America.
Zeitz, Paul is the author of Art And Craft of Problem Solving, published 2006 under ISBN 9780471789017 and 0471789011. Six hundred forty Art And Craft of Problem Solving textbooks are available for sale on ValoreBooks.com, one hundred forty one used from the cheapest price of $32.76, or buy new starting at $52 |
more practice than any other resource, unrivalled guidance straight from the IB and the most comprehensive and correct syllabus coverage, this student book sets learners up to excel. The only resource developed with the IB curriculum team, it fully captures the IB philosophy and integrates the most in-depth assessment support.
· Full syllabus coverage - the truest match to the IB syllabus, written with the IB to exactly match IB specifications · Free eBook - a complete interactive eBook on CD is included for free, for the most flexible learning · Complete worked solutions - a full set of worked solutions is included online, in addition to interactive worked solutions on CD, which take learners through problems step-by-step · The most practice - more practice than any other resource, with over 700 pages and an eBook · Up-to-date GDC support - take the confusion out of GDC use and help students focus on the theory · Definitive assessment preparation - exam-style papers and questions will build confidence · The Exploration - supported by a full chapter, to guide you through this new component · Real world approach - connect mathematics with human behaviour, language, morality and more
About the Series: Oxford's IB Diploma Course Books are essential resource materials designed in cooperation with the IB to provide students with extra support through their IB studies. Course Books provide advice and guidance on specific course assessment requirements, mirroring the IB philosophy and providing opportunities for critical thinking |
CliffsQuickReview Basic Math and Pre-Algebra
9780764563744
ISBN:
0764563742
Edition: 1 Pub Date: 2001 Publisher: Cliffs Notes
Summary: We take great notes - and make learning a snap When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core mathematical concepts - from fractions, decimals, and statistics to graphs, integers, and exponents - and get the best possible grade.At CliffsNotes, we're dedicated to helping you do your best, no matter how challeng...ing the subject. Our authors are veteran teachers and talented writers who know how to cut to the chase-and zero in on the essential information you need to succeed.Master the basics-fast Complete coverage of core concepts Accessible, topic-by-topic organization Free pocket guide for easy reference
Jerry Bobrow Ph.D. is the author of CliffsQuickReview Basic Math and Pre-Algebra, published 2001 under ISBN 9780764563744 and 0764563742. Two hundred seventy one CliffsQuickReview Basic Math and Pre-Algebra textbooks are available for sale on ValoreBooks.com, one hundred sixty eight used from the cheapest price of $0.01, or buy new starting at $2.49 |
Blue Peak High School
Math Disclosure
Name: ________________________________________________________ Period:________________
Mathematics is a class that requires practice in order to understand and remember
concepts. Your grade is a reflection of your achievement of course goals, timely
work on assignments, and test scores. Daily work is essential to understanding
mathematics. If you miss class you miss the opportunity to learn new material and
to work with others in the class. Therefore, you should do everything you can to
make sure you are in class every day.
Required Supplies
Students are required to bring a notebook and pencil to class every day. We will
take notes daily, and students should have a notebook in which they can write their
notes and keep them organized. Notebooks may be graded at any time without
prior notice, so students should have their notebooks ready to turn in at any time.
Students are not required to buy a calculator, but they may wish to do so. In class
we will use the TI 30x and/or the TI 83 plus calculators. Occasionally projects will
also be assigned, which may require additional supplies.
Grades
Assignments are given on a regular basis, and will be corrected and turned in the
following day in class unless otherwise indicated. Grades are weighted according to
the following scale:
Category Percentage
Assignments 30%
Starters and Quizzes 20%
Participation and Notebook 20%
Tests 30%
Academic help is available most Tuesdays and Thursdays after school from 2:35 to
3:30.
Citizenship Grades
Citizenship grades are based on student attendance, behavior, and attitude.
Excessive tardies and/or absences, an uncorrected series of negative behaviors, or
one serious incident could result in a failing citizenship grade. Serious behaviors
might include, but not be limited to conduct such as:
1. Obvious disrespect for school authority or staff members
2. Repeated use of vulgarity or profanity
3. Direct and willful disobedience of classroom rules and school policies
4. Disruption of classroom and/or school activities
5. Theft or destruction of property
6. Cheating on tests or assignments
Absences and Late Work
It is the student's responsibility to make up any work missed due to an excused
absence. Students may check the make up calendar to see what they missed, and
students are responsible to collect any worksheets missed due to their absence.
Students have one week from the day they return to school to turn in any work
missed when they were absent. After one week, their assignment is late and is
worth 70% of what the assignment would have been worth had it been turned in on
time. Late work from the first half of the quarter must be turned in by the midterm
deadline, and late work from the second half of the quarter must be turned in by the
end of quarter deadline. If a student is absent during a test, that student must make
arrangements with the teacher to make up the test. The student has one week to
make up a missed test, unless other arrangements are made with the teacher. Work
missed due to an unexcused absence cannot be made up.
Movies
Film clips are occasionally used to enrich the curriculum. Clips used in class may
include the following titles:
Aladdin (rated G) Stand and Deliver (rated PG)
The Incredibles (rated G) The Apple Dumpling Gang (rated G)
The Princess Bride (rated G) Monsters, Inc. (rated G)
Donald in Mathmagic Land (rated G)
If you do not want your student to participate in viewing any of these clips, please
indicate on the signature section of this disclosure.
I have read and reviewed this disclosure statement with my parent or
guardian. Student Name: _________________________________________________________________
Student Signature: _________________________________________________________________________
Student Email: ______________________________________________________________________________
Comments: __________________________________________________________________________________
_________________________________________________________________________________________________
I have read and reviewed this disclosure statement with my student.
Parent/Guardian Name: __________________________________________________________________
Parent/Guardian Signature: _____________________________________________________________
Parent/Guardian Email: __________________________________________________________________
Telephone: __________________________________________________________________________________
Comments: __________________________________________________________________________________
________________________________________________________________ |
Browse Results
Modify Your Results
This is the newly revised and expanded edition of the popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron. A new "Sources" chapter points to supplemental literature for readers needing more information on any topic. A novel aspect is the inclusion of working C code for many of the algorithms, with discussion of practical implementation issues. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The code in this new edition is significantly improved from the first edition, and four new routines are included. Java versions for this new edition are also available. All code is accessible from the book's Web site ( or by anonymous ftp.
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems.The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only). To obtain access, please e-mail: Vickie_Kearn@press.princeton.edu
Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers. With the help of 200 colour website, howtofoldit. org, has dynamic animations of many of the foldings and downloadable templates for readers to fold or cut |
Product Details:
GDZ1361: Assist students to easily transition from arithmetic to algebra! Teachers can use the Helping Students Understand series as a full unit of study or as a supplement to their curriculum while parents can use this series to help their struggling students grasp algebraic concepts. This book includes step-by-step instructions with examples, practice problems using the concepts, real-life applications, a list of symbols and terms, tips, answer keys, reference, and NCTM Standards and Expectations for 2004. 128 pages.
Description:
GDZ3779: Help students make the transition from Algebra to Algebra
II! Written for teachers to use as a full unit of study or as a supplement to their curriculum, this book helps simplify algebraic concepts. Parents and students can ... |
Holt Spanish 2 Expresate Workbook Answers
Where do you find the answers to mcdougal littell math course 2? the odd problems are at the back of the book, but i do not know where the answers are.
Click your algebra 2 textbook below for homework help. our answers explain actual algebra 2 textbook homework problems. each answer shows how to solve a textbook
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"TEAM-Math Curriculum Guide"
Please download to view full document
425995544551851
TEAM-Math
Curriculum Guide
DRAFT
July 8, 2003
Send Comments or Questions to:
TEAM-Math
5040 Haley Center
Auburn, AL 36849
(334) 844-6881
mail@TEAM-Math.net
Available online at
TEAM-Math Curriculum Guide (July 8, 2003) p. 1
Chapter 1
Introduction to the TEAM-Math Curriculum Guide
Transforming East Alabama Mathematics (TEAM-Math) is a partnership between Auburn
University and twelve school districts (Alexander City, Auburn City, Chambers County, Elmore
County, Lanett City, Lee County, Macon County, Opelika City, Phenix City, Russell County,
Tallapoosa County, and Tallassee City), along with Tuskegee University and other organizations.
The goal of the partnership is to systemically improve mathematics education in this region,
including increasing overall student achievement, addressing gaps in performance between
demographic groups, enhancing the professional knowledge of practicing teachers, developing a
cadre of knowledgeable teacher leaders, and improving the preparation of prospective teachers at
the university.
In addition, the school districts in the partnership are working collaboratively with Auburn
University and the other partners to develop curriculum guides and other policies that promote
student learning in mathematics. This document describes the first step in this process.
Development of the Curriculum Guide
One of the first steps in the TEAM-Math process has been to develop a partnership-wide
curriculum guide that can be used to guide both instruction and further decision-making for the
partnership related to teaching and learning. A Curriculum Writing Team, consisting of 60
teachers from across the Partnership, met on six occasions in May, June, and July of 2003 to
develop a first draft of this document. See a list of the committee members in Appendix A.
The group began with an examination of the "big ideas" to be addressed across the grades,
moved to a consideration of the central concepts for each strand, and finally worked at
identifying outcomes for each course and grade. Summaries of the working meetings can be
found on the TEAM-Math Web site at
In developing this document, the group considered a number of references, including:
• Alabama Course of Study: Mathematics. The newest version of this document was
released in April 2003, and is to be adopted in the 2003-2004 school year. In contrast to
past versions, the 2004 course of study is very stripped-down, with far fewer objectives
per grade level and no repeated content from year to year or course to course.
• Principles and Standards for School Mathematics. This document, published by the
National Council of Teachers of Mathematics, provides a vision of how mathematics
should be taught. It was used as the primary basis for the Alabama Course of Study:
Mathematics. The Curriculum Team used it as a reference to supplement its use of the
Course of Study.
TEAM-Math Curriculum Guide (July 8, 2003) p. 2
Chapter 1. Introduction
• SAT-10 test description. The committee found that the SAT-10 was in good alignment
with the Course of Study and Principles and Standards for School Mathematics. In
addition, the state of Alabama will be creating an "augmented" version of the test that
will be completely aligned with the Course of Study. It is this "augmented SAT-10" that
will be used as the state-wide accountability measure. However, the national SAT-10
scores will also be reported, so the group sought to ensure that the topics covered will
meet those requirements.
• Alabama High School Graduation Examination. In theory, this assessment should also be
in alignment with the Course of Study. However, it is not currently being revised to meet
the new guidelines, so the committee checked to be sure all its requirements were met.
• National Assessment of Educational Progress (NAEP) Mathematics Framework. NAEP
is the "nation's report card," designed to assess the overall national progress in
mathematics and other subject areas. Alabama's statewide progress is tracked using this
test, therefore we also reviewed their requirements.
In general, the group found good agreement in the recommendations from these various sources.
While the Course of Study was taken as the primary source, since those are the objectives for
which the teachers and students of our state are accountable, that document was limited in a
number of ways by the state requirements for the course of study. For example, only the content
for which students at a particular grade are accountable was included. However, we know that
this cannot be the only content that is addressed. There needs to be some revisiting of the content
from the year before and also attempts to set the stage for the next year. Thus, focusing only on
"testable content" will not provide an accurate description of the content to be covered. Also, the
authors of the Course of Study (three of whom were on the Curriculum Team) were limited in the
verbs they could use and in how they could say things. For example, anything that might be
judged to describe instruction was not permitted, a major limitation in a document intended to
guide teaching.
We did not have such limitations in developing our guides, as we made our own rules, so to
speak. Principles and Standards become a key source in "filling in the gaps" for what was not
considered in the state course of study. This worked particularly well since Principles and
Standards guided the development of the state course of study. This document was particularly
important in developing the underlying philosophy for the group, which is outlined in the next
chapter.
Uses of the Curriculum Guide
This curriculum guide is designed to provide a general view of what content is critical for each
grade and course to ensure that students are making the necessary mathematical progress from
grades K-12. This document is intended to be used in two ways:
• To help teachers make decisions about what they should teach during the 2003-2004
school year. Each teacher must be responsible for the material in the Curriculum Guide to
ensure that students are making the necessary progress.
TEAM-Math Curriculum Guide (July 8, 2003) p. 3
Chapter 1. Introduction
• To serve as a basis for the textbook adoption process, which will take place during the
2003-2004 school year. TEAM-Math will be organizing a collaborative review of
textbooks based on this curriculum guide.
Next Steps
This draft of the curriculum guide serves as a top-level description of what should happen in
each course and grade, with little day-to-day support for teachers. Following the adoption of
textbooks, which we hope will be consistent across the partnership, the Curriculum Writing
Team will reconvene to begin to make more specific recommendations, incorporating references
to the Partnership textbook series. Thus, we hope to have a unit-by-unit description of each
course and grade for the 2004-2005 school year which will incorporate guidance on sequencing
of lessons, provide sample activities, and suggest ways in which the textbook can be used as an
effective resource for instruction. We also plan to begin professional development for teachers
on how they can effectively implement this curriculum.
TEAM-Math Curriculum Guide (July 8, 2003) p. 4
Chapter 2
Curriculum Across the Grades
The following MISSION STATEMENT was adopted by the Curriculum Writing Team as
underlying the work of the Partnership:
To enable all students to understand, utilize, communicate, and appreciate
mathematics as a tool in everyday situations in order to become life-long learners
and productive citizens by Transforming East Alabama Mathematics (TEAM-
Math). The mission will be met by:
• Aligning the curriculum K-12
• Ensuring consistency in teaching
• Providing professional development
Organizing Principles
Several important points are raised in this statement, which are summarized in the following
sections. These points are consistent with the Principles found in Chapter 2 of the Principles and
Standards for School Mathematics.
Equity: The importance of meeting the needs of "all students". The statement begins, "To enable
all students…" The emphasis on the word "all" is particularly important, since there are huge
gaps in performance among different groups of students, particularly between white and minority
students and between poor and more affluent students. It is our responsibility to do our best to
meet the needs of all of our students. Only by holding all students to the highest expectations,
and giving them the support they need, can we truly improve performance across the Partnership.
Indeed, under the new federal legislation, No Child Left Behind, a school's accountability
includes the degree to which they address these gaps in performance between different groups of
students.
Learning: The importance of process. In accordance with Principles and Standards, the
document emphasizes students' understanding of mathematics and their ability to apply their
knowledge, rather than focusing on rote learning and memorization. While the focus of a
curriculum document tends to be the topics and ideas to be taught, it is equally important to
consider how students will learn those ideas. The group repeatedly returned to this saying:
It is not just what you teach; it is how you teach that content.
If students can only do what they are told, they will not be prepared to become productive
citizens. The Course of Study adopted the five "process standards" described in the national
Principles and Standards:
TEAM-Math Curriculum Guide (July 8, 2003) p. 5
Chapter 1. Introduction
• Problem solving
• Reasoning and proof
• Communication
• Connections
• Representation
Teachers must pay as much attention to the "how" as they do the "what." The writers of this
document did their best to incorporate attention to process throughout their work, and it is
reflected in the "umbrella statement" that is given at the beginning of each of the content strands
in this chapter.
The Process Standards (Problem Solving, Reasoning and Proof, Communication,
Connections, and Representation), estimation, reasonableness of answers, terminology,
and technology should be integrated throughout each content strand to help students
develop relational understanding (the "how" and the "why").
Curriculum: The importance of alignment K-12. The Curriculum Team did its best to ensure that
its recommendations will promote the mathematical growth of all students K-12. As previously
mentioned earlier, the number of objectives in the new Course of Study has been dramatically
reduced for each grade and course. This is intended to promote focus on what mathematics is
important for each grade, rather than repeating the same material each year. There needs to be
growth across the grades.
Thus, it is the intent of this document that all teachers do their best to help their students meet the
objectives in the grades or courses they teach. In this way, students will be prepared for the next
course and grade. Failure to meet those objectives means that students will not be ready for the
next year, meaning that they will fall further and further behind. The Curriculum Team discussed
the difficulties of dealing with students who come to a grade or course behind where they need to
be. We will need to continue to deal with effective ways to deal with this issue, but hopefully the
situation will improve over the next years as we all strive towards this goal.
Another result of the fewer objectives in the Course of Study is that there are sometimes "gaps"
across the grades, since only "testable content" is included, not content that is being developed.
That is, an idea or concept might be included at one grade level, where it will be tested at an
introductory level, and not appear again until two or more years later, where it will be tested at a
much more sophisticated level. This is a result of the way the Course of Study was designed: It
only describes the content for which students at a particular grade or course are accountable.
However, there needs to be a build-up across the grades to meet the objectives in the course in
which the idea will be tested. As someone said, "The success of fifth-grade students is not the
result of the fifth-grade teachers. It is the result of all the teachers that student has had since they
entered school." Thus, the writers worked hard at establishing a smooth learning trajectory
across the grades.
Technology: Appropriate uses. The use of technology (particularly calculators) raised heated
discussion among the group, to say the least. Many members raised the concern that technology
might become a replacement for learning the necessary basics. Others emphasized the potential
TEAM-Math Curriculum Guide (July 8, 2003) p. 6
Chapter 1. Introduction
value of technology in allowing students to explore new concepts and in allowing them to
address "messy" problems that don't have nice answers. While this will no doubt be an issue of
continuing discussion in the next years, the group consensus was that technology should be used
in ways that enhance student learning, not replace their learning. A teacher needs to make
judgments about what activities will be enhanced by calculator use, and in what activities
calculators will be a hindrance. However, the best research does demonstrate that calculators and
other technology have the potential to greatly increase student learning. (Notes from the
committee's discussion of this important issue can be found at
Assessment: Importance of multiple methods. While the group did not spend much time on
assessment, the importance of incorporating assessment beyond just quizzes and tests was
discussed on several occasions. When students are engaged in doing mathematics, rather than
just mimicking what the teacher does, the teacher has many opportunities to observe and assess
how his or her students are progressing.
The group also discussed the possibility of devising quarterly assessments to be used across the
Partnership, thus helping to determine whether students are making the progress they need.
Big Ideas K-12
The Curriculum Writing Team organized its work into four subcommittees by: K-2, 3-5, 6-8, and
9-12. This is consistent with both the state Course of Study and Principles and Standards. To
ensure that the goal of K-12 alignment was met, the group worked at developing a common
vision across the grades. As a part of that effort, each subcommittee identified "big ideas" for
their gradeband. The subcommittees then met with each other to ensure that clear developmental
paths were being established.
These "big ideas" are organized in five content strands that are used both in the Course of Study
and Principles and Standards:
• Number and Operations
• Algebra
• Geometry
• Measurement
• Data Analysis and Probability
While some of these strands are more important at some levels than others, efforts were made to
show how they developed across the grades. Charts for each of the strands follow.
TEAM-Math Curriculum Guide (July 8, 2003) -- Chapter 2. Across the Grades p. 7
Number place value; use money. 1. Order, compare, estimate, decimal 1. Order and compare real numbers
Model with objects, pictures, and/or and whole numbers not to exclude the emphasizing irrational numbers.
symbols. use of fractions and extend place
value. 2. Concept/properties of complex
2. Strong understanding of base ten numbers.
and number sense.
3. Distinguish between various
number sets. (real, complex, rational,
irrational, integers, whole)
3. Basic addition and subtraction facts 2. Have efficient and accurate 1. Use operations involving place 4. Simplify operations with:
with fluency and use problem solving. methods for computing. (add, subtract, value, fractions, decimals, percents, a. reals with radicals
multiply, divide and equivalency) irrational and rational numbers, b.polynomial expressions
4. Compose and decompose whole scientific notation, integers, and c. complex numbers
numbers. (Fact Families) estimation of a reasonable answer. d. vectors
-Exponents e. exponential and logarithmic
5. Model with objects, pictures, and/or -Sets f. matrices
symbols, addition and subtraction/ -Properties g. rational expressions
number patterns. -Order of Operations
-Compare and Order
-Real number line
6. Understand and use fractions. (1/2, 3. Fractions; Modeling concrete 2. Prime / composite for LCM, GCF, 5. Factoring polynomials
¼, 1/3) examples moving toward abstract and reducing fractions
thinking.
3. Understand and use proportional
reasoning
* Ratios, rates, proportions, scale
drawings
TEAM-Math Curriculum Guide (July 8, 2003) -- Chapter 2. Across the Grades p. 8
Algebra patterns, relations, 1. Understand and identify properties 1. Graphing of functions 1. Identify, interpret, and solve:
functions, and properties. and patterns using symbols, numbers, a. Range and domain graphically, numerically, and
- Extend Patterns and non-standard units. b. Notation: f(x) analytically.
c. Patterns a. Relations as functions
b. Linear, quadratic,
polynomial, rational,
exponential, inverse,
trigonometric, absolute value,
piecewise-defined*, and radical
c. Parametric shifts
d. Sequences and Series*
2. Use of number sentence symbols 2. Use a variety of strategies and 2. Solve simple equations and 2. Understand the meaning of
(+,-,=) methods to solve mathematical inequalities (2 variable equations) equivalent forms of expression,
- Understand use of symbols situations and structures. equations, inequalities, relations,
- Understand greater than (>), complex numbers, quadratic
less than (<), equal to (=) equations, vectors, matrices, and
number theory
* Covered in Precalculus
TEAM-Math Curriculum Guide (July 8, 2003) -- Chapter 2. Across the Grades p. 9
Geometry Analyze spatial relationships 1. Use visualization, spatial reasoning, 1. Classify and know properties for 1. Identify geometric figures from a
* Recognize and make and geometric modeling to solve various geometric shapes verbal description of its properties.
connections in their problems, rotational symmetry. a. Plane (flat)
environment. b. 3-D
* Demonstrat understanding that c. Angles
translating, rotating, and reflecting d. Transformations
of objects does not change shape. e. Pythagorean Theorem
* Understanding use of symmetry
-line symmetry
-rotational symmetry
* Spatial recall
* Problem solving
2. Understand geometrical shapes 2. Recognize and identify angles, 2. Understand and analyze properties
* Recognize, build, and create 2& 3 polygons, coordinate plans, and of transformations, similarity, and
dimensional shapes. rotations of symmetry. congruence.
* Sort and compare shaped by
attributes. 3. Analyze characteristics and
* Recognize shapes and properties of geometric figures.
relationships in the
environment.
3. Connections 2. Identify and plot points and lines on 3. Use Cartesian coordinates such as
* Within math the Cartesian Plane. navigational, polar to analyze
* Across the curriculum a. Slope geometric situations:
* Real world connections b. Distance -distance
- Interpret simple maps and - midpoint
grids. - slope
- Recognize changes made in
rearrangements of shapes.
TEAM-Math Curriculum Guide (July 8, 2003) -- Chapter 2. Across the Grades p. 10
4. Apply geometric properties and
relationships in solving multi-step
problems in 2 and 3 dimensions.
5. Emphasize proof by having
students communicate with each other
and justify methods of solving
problems.
6. Use trig to determine lengths and
angle measures.
TEAM-Math Curriculum Guide (July 8, 2003) -- Chapter 2. Across the Grades p. 11
Measurement Use standard and nonstandard 1. Convert one type of measurement 1. Identify the appropriate measure of 1. Analyze various problems to
linear measurement and choose to another within the same system. an object as well as which formula is determine which measurement and
correct tool. (time, capacity, length, etc.) ( metric appropriate. (polygons and 3-D tools are appropriate.
and customary) figures)
a. Stress units and conversions 2. Solve angle measure problems
b. Angle measurement including angles of triangles and other
polygons and parallel lines cut by a
transversal.
2. Understand and compare 2. Recognize, select, calculate, 2. Determine the appropriate measure 3. Solve problems involving area,
measurable attributes related to estimate, and use correct forms of for area, perimeter, circumference, perimeter, circumference, surface
weight, area, length, volume, and measurement. volume, length, and mass area, volume, arc length, and area of a
time. a. Apply formulas sector
b. Understand error
3. Develop understanding of 3. Be able to calculate and understand 4. Analyze accuracy and approximate
approximation. length, area, perimeter, volume, and error in situations.
elapsed time.
5. Understand properties of vectors as
magnitude and direction.
a. *Apply and use vectors
when appropriate in solving
problems.
TEAM-Math Curriculum Guide (July 8, 2003) -- Chapter 2. Across the Grades p. 12
Data Analysis and Probability reasonableness of answers,
terminology, notation, and technology should be integrated throughout each content strand to help students develop relational understanding (the "how" and the
"why").
1. Investigate, collect, organize, and 1. Investigate, collect, organize, and 1. Represent, interpret, and compare 1. Read and analyze various data
represent data demonstrate data. data in various ways displays graphs and tables and express
* using concrete objects a. Charts, tables, graphs the properties of these data displays as
* use and create pictures, graphs, b. Scatterplots and line of best fit. algebraic equations.
and tables c. Mean, median, mode, and range a. Linear, quadratic, exponential
d. Determine most appropriate b. Includes standard deviation
representations c. Construct sample space
d. Evaluate published reports
2. Make inferences and predictions 2. Use estimation as a tool to solve 2. Use estimates and predictions. 2. Making decisions and predictions
based on reading graphs. problems based on given information: graphical
or written.
3. Probability of something happening 3. Understand and apply basic 3. Find probability 3. Understand concepts of probability
concepts of probability using a. Independent and dependent events (independent and dependent) and
experiments and predictions. b. Experimental and theoretical compute probability using several
probability. methods.
TEAM-Math Curriculum Guide (July 8, 2003) p. 13
Chapter 2. Across the Grades
Conclusion
The Importance of the Partnership. By working together as a partnership, we can accomplish
much more than any one school or district can individually. It is our hope that this document is
the first step in the development of a collaborative and unified vision for mathematics education
in East Alabama.
We end by noting that the members of the Curriculum Writing Team did their best in pulling
together the best possible sources and their best possible professional wisdom in developing this
document. However, as always seems to be the case, we were pushed for time and never got as
far as we might have hoped. Thus, please send any comments or suggestions to
curriculum@TEAM-Math.net.
TEAM-Math Curriculum Guide (July 8, 2003) p. 14
Chapter 3. Curriculum for K-2
Chapter 3
Curriculum for Kindergarten-Grade 2
"Students enter school confident in their own abilities, and they are curious and eager to learn
more about numbers and mathematical objects. They make sense of the world by reasoning and
problem solving, and teachers must recognize that young students can think in sophisticated
ways. Young students are active resourceful individuals who construct, modify, and integrate
ideas by interacting with the physical world and with peers and adults. They make connections
that clarify and extend their knowledge, thus adding new meaning to past experiences. They
learn by talking about what they are thinking and doing and by collaborating and sharing their
ideas. Students abilities to communicate through language, pictures, and other symbolic means
develop rapidly during these years." (NCTM, 2000)
"All students need adequate time and opportunity to develop, construct, test, and reflect on their
increasing understanding of mathematics. Early education must build on the principle that all
students can learn significant mathematics." (NCTM, 2000)
The Process Standards, which include, Problem Solving, Reasoning and Proof, Communication,
Connections, and Representation are outlined in both national standards (NCTM, 2000) and in
the Alabama state standards, (ALSDE, 2003). These Standards are an integral part of students
reaching their educational goals and must be incorporated into the K-2 curriculum. In addition,
making sense of math and recognizing the reasonableness of answers should be stressed.
In grades K-2, students should be knowledgeable of, and become increasingly comfortable with,
using appropriate mathematical terminology and notation in communicating about mathematical
and real-world situations.
Appropriate technology should be integrated through out the K-2 curriculum to help students
explore, investigate, and solve mathematical problems. Technology should be used to enrich
mathematical understanding but does not replace sound, conceptual instruction.
The initial focus for K-2 is number and operations and additional focus on geometry. The six
"big ideas" focus on all content strands and include the following:
1. Develop understanding of the base ten number system including the sequence of
counting, composition of number, number relationships, and place value.
2. Develop strategies for whole number computations, problems solving with addition and
subtraction, and fluency of basic addition and subtraction facts.
3. Model and explain addition and subtraction of whole numbers using objects, pictures,
symbols, and extending patterns.
4. Recognize basic shapes, symmetry, and movement to build a foundation for the
development of visualization and spatial reasoning.
TEAM-Math Curriculum Guide (July 8, 2003) p. 15
Chapter 3. Curriculum for K-2
5. Compare measurable attributes of objects and use nonstandard and standard units for
linear measurements.
6. Collect and represent data in various ways using concrete objects, pictures, and symbols.
The K-2 K-2 by content strand. In the
following charts, the content for each grade is organized in these five strands. Each column in the
chart shows a particular course, and each row shows the relationship between concepts in the
courses, thus highlighting the vertical alignment across the courses.
TEAM-Math Curriculum Guide (July 8, 2003) p. 16
Chapter 3. Curriculum for K-2
Number Strand, K-2
Kindergarten Grade 1 Grade 2
1. Whole numbers 1. Develop an understanding of place 1. Extend an understanding of place
a. Demonstrate one-to-one value/base 10 to: value/base 10 to:
correspondence a. Compose and decompose whole a. Develop an understanding and use
b. Count with understanding and numbers using multiple of expanded notation
recognize "how many" in sets of representations b. Count by multiples to 100
objects b. Count by ones, fives, and tens to including 3's
c. Compare sets of objects using the 100 c. Know the value of 100 more or 100
appropriate terminology c. Know the value of 10 more or 10 less
d. Know the value of one more and less d. Represent whole numbers to 1000
one less d. Know what equals 10 e. Develop an understanding of the
e. Use multiple models to represent e. Connect number words and relationship between ordinal
single digit numbers numerals to the quantities they numbers and cardinal numbers
f. Recognize and connect numerals to represent f. Use models to develop and explain
quantities they represent f. Use models to develop and explain the value of a 3-digit number
g. Identify quarters, dimes, nickels, the value of a two-digit number g. Determine the monetary value of
and pennies g. Determine the monetary value of sets of coins and bills up to $5.00
individual coins and sets of coins up
to $1.00
2. Develop an understanding of addition 2. Develop an understanding of the 2. Extend an understanding of the
and subtraction to: operations of addition and subtraction to: operations of addition and subtraction to:
a. Relate real life situations to the a. Represent real life number stories a. Develop computational fluency
operations of joining and separating to the actions of joining and with sums through 18 and
sets separating sets using numbers differences with minuends through
b. Use multiple models to compose b. Model and explain addition and 18
and decompose single digit whole subtraction with manipulatives, b. Solve problems using separation
numbers pictures, and symbols (take-away), comparison (finding
c. Recognize missing numbers in c. Demonstrate an understanding of the difference), and part-whole
simple groupings up to 5 fact families and the commutative (missing addends)
d. Model single-digit (numbers to 5) property c. Use two or three digit addition and
addition and subtraction d. Demonstrate computational fluency subtraction to solve problems
TEAM-Math Curriculum Guide (July 8, 2003) p. 17
Chapter 3. Curriculum for K-2
with basic addition and subtraction d. Model and explain multiplication
facts through 10 as repeated addition with
e. Solve story problems and manipulatives, pictures, and
determine relevant/irrelevant symbols
information e. Model division as equal groupings
f. Use three or more addends with manipulatives, pictures, and
g. Solve addition/subtraction symbols
problems using 1 or 2-digit f. Solve story problems and
numbers distinguish relevant/irrelevant
information
3. Develop an understanding of fractions 3. Develop an understanding of fractions 3.Demonstrate an understanding of
to: to: fractions to:
a. Recognize that objects and sets can a. Connect everyday situations to a. Label parts of a whole using fraction
be divided into parts common fractions notation including ½, 1/3, 1/4
b. Compare parts of objects and parts b. Compare and represent fractions in b. Transfer fraction representation from
of sets multiple ways using manipulatives, one form to another
c. Identify parts of objects and parts pictures, and words (1/2, 1/3, ¼) c. Identify parts of a set as a fractional
of sets that appear equal c. Solve real life fraction problems ratio(3 parts out of 4)
using figures, sets of objects, d. Represent parts of a whole as a
and linear models quotient using real life situations (2
d. Identify parts of a whole with two, cookies divided among 4 people)
three,
or four equal parts
e. Divide an object or set of objects
into equal parts
TEAM-Math Curriculum Guide (July 8, 2003) p. 18
Chapter 3. Curriculum for K-2
Algebra Strand, K-2
Kindergarten Grade 1 Grade 2
1. Build knowledge and experience with 1. Understand patterns, relations, and 1. Apply an understanding of patterns,
patterns, relations, and functions to: functions to: relations, and functions to:
a. Sort objects by color, shape, size, a. Sort, classify, and order by size, a. Interpret and explain numeric
or other properties number, and other properties patterns
b. Identify, explain, and extend b. Recognize, describe, and extend • Sequence addition (If 32+18=50
repeating patterns and recognize shape-patterns, numeric-patterns, and 33+18=51, what would
the patterns using different and simple functions 35+18 be?)
materials c. Use graphic organizers to solve • Paired subtraction (If 24-15=9,
c. Interpret a pattern in more than one problems involving number patterns what is 24-16?
way and functions b. Use mathematical models to
d. Create patterns d. Identify patterns in the environment represent and understand
e. Create a pattern quantitative relationships
f. Translate patterns from one c. Identify missing elements in given
representation to another patterns
d. Extend a growing pattern
2. Use one-to-one correspondence and 2. Represent number sentences using 2. Extend use and understanding of
understanding of likenesses and differences algebraic symbols number sentences using algebraic
to: a. Understand the use of symbols (+, -, symbols:
a. Determine and explain elements =, <, and >) a. Apply concepts of > and <
that belong in a pattern, and those b. Solve problems using identity (+0) b. Introduce concepts of x and /
that do not belong and commutative property c. Solve problems using associative
b. Identify and explain equality using and commutative properties
concrete materials (example: six d. Solve missing addend problems
green triangles in pattern blocks are
"the same as" one yellow hexagon)
3. Describe qualitative change (students 3. Describe change over time (qualitative
growing taller) and quantitative)
TEAM-Math Curriculum Guide (July 8, 2003) p. 19
Chapter 3. Curriculum for K-2
Geometry Strand, K-2
Kindergarten Grade 1 Grade 2
1. Recognize and name two-dimensional 1. Describe characteristics and properties 1. Analyze geometric relationships using
shapes to: of two and three-dimensional geometric 2D and
a. Identify shapes in the environment shapes to: 3D geometric shapes to:
b. Create combinations of rectangles, a. Understand similarities and a. Describe attributes of 2-
squares, circles, and triangles using differences between plane and solid dimensional (plane) and 3-
drawings or concrete materials shapes (sort by attribute) dimensional (solid) figures using
b. Recognize and name shapes in the terms: side, surface, edge, vertex,
environment angle
c. Build 3D shapes using 2D picture b. Categorize 2D and 3D shapes and
d. Investigate putting together and explain groupings according to the
taking apart two and three- properties
dimensional shapes c. Predict the results of putting
together and taking apart 2D and
3D shapes
2. Develop an understanding of movement: 2. Develop an understanding of positions, 2. Apply concepts of positions, directions,
a. Demonstrate knowledge of relative directions, and distance to: and distance to:
position and use vocabulary such as a. Describe and name relative a. Describe the route from one
over, under, near, far, between, and positions in space using location to another
other appropriate terminology positional terms b. Follow multi-step directions to
b. Recognize movement of objects b. Describe movement using locate objects
from one location to another directional terms c. Create and read simple maps
c. Follow simple directions to move c. Draw or build maps of familiar d. Use grids to show movement
from one location to another space between intersecting points
d. Describe movement of objects
from one place to another
TEAM-Math Curriculum Guide (July 8, 2003) p. 20
Chapter 3. Curriculum for K-2
3. Develop an understanding of 3. Use transformations and symmetry to: 3. Analyze mathematical situations by
transformation and symmetry to: a. Identify and create shape applying transformations and using
a. Solve puzzles and manipulate compositions symmetry to:
shapes in combinations b. Demonstrate the concept that a. Apply slides, flips, or turns to
b. Experiment and predict results of changing position does not change create designs that exhibit line
folding and cutting two- the properties of a shape or an symmetry
dimensional materials object b. Recognize and create lines of
c. Identify real-life examples of line symmetry using everyday objects
symmetry and geometric figures
4. Develop visualization and spatial 4. Use visualization and spatial reasoning 4. Demonstrate visualization and spatial
reasoning to: to: reasoning to:
a. Recognize the number in simple a. Create mental images of geometric a. Identify images of a simple 3D
groupings up to five without shapes using spatial memory and structure from different
counting (example: domino dots) visualization perspectives
b. Locate items in the environment b. Recognize and represent shapes b. Predict resulting image of
from physical descriptions from a different perspective manipulated figures and objects
(puzzles)
c. Locate shapes and structures in the
environment
TEAM-Math Curriculum Guide (July 8, 2003) p. 21
Chapter 3. Curriculum for K-2
Measurement Strand, K-2
Kindergarten Grade 1 Grade 2
1. Compare objects according to length, 1. Compare measurable attributes of 1. Apply appropriate techniques, tools and
height, weight, and volume objects to: formulas in measurement to:
a. Demonstrate and use nonstandard a. Measure using nonstandard,
and standard units of linear standard customary and metric
measurement units
b. Compare objects according to b. Understand the comparison of
weight, area, length, and volume customary units and metric units to
familiar objects
c. Demonstrate use of customary and
metric units in linear measurement
d. Compare and order objects
according to related attributes of
weight, area, length and volume
2. Use vocabulary associated with the 2. Analyze and use analog and digital 2. Tell time to the minute using analog and
measurement of time, including words clocks to: digital clocks
related to clocks and calendars a. Identify hour and half hour • Hour, half hour, quarter, 5 minutes
(intervals)
• Elapsed time
3. Compare everyday experiences to
reinforce concepts of time (Example: It
takes about the same amount of time to
watch a movie as it does to watch a
football game.)
3. Use calendar math
a. Identify day, date, month, day
before, day after, yesterday, today,
tomorrow
TEAM-Math Curriculum Guide (July 8, 2003) p. 22
Chapter 3. Curriculum for K-2
Data Analysis and Probability Strand, K-2
Kindergarten Grade 1 Grade 2
1. Develop an understanding of data 1. Collect, organize, and display data 1. Collect, organize, and display data in
collection to: collected from one's environment to: multiple ways from self-generated
a. Respond to prepared data collection a. Collect data for given questions questions to:
models (yes/no charts, single Venn using multiple display models a. Use multiple display models
diagrams, bar graphs, and other (yes/no charts; single, double, and (yes/no charts; single, double, and
models) double over-lapping Venn double over-lapping Venn
b. Use real objects, representative diagrams, bar graphs, tallies, and Diagrams; circle graphs;
concrete objects, pictures, or other models) vertical/horizontal bar graphs,
symbols to gather data from one's b. Organize and display data with frequency tables; tallies; and other
immediate environment many materials including real models)
c. Sort and classify data collected objects, representative concrete b. Organize, plan, collect, and
from the environment objects, pictures/drawings, interpret data to answer self-
d. Make observations about data symbols, and numbers generated questions or to make
collected c. Make observations, identify decisions
e. Pose questions about oneself or patterns, pose additional questions, c. Recognize patterns in data
one's surroundings that can be and make predictions from data collected
answered with the collection of collected d. Represent data in multiple ways
data d. Generate questions and determine
the data needed to arrive at answers
2. Communicate possible and impossible 2. Communicate events and outcomes of 2. Communicate events and outcomes in
outcomes in a given concrete situation everyday events and simple investigations appropriate probability terminology
as possible/impossible; or as (certain, likely, equally likely, unlikely,
likely/unlikely possible, impossible, fair)
3. Evaluate and redefine predictions using
cognitive benchmarks
TEAM-Math Curriculum Guide (July 8, 2003) p. 23
Chapter 4
Curriculum for Grades 3-5
"Most students enter grade 3 with enthusiasm for, and interest in, learning mathematics. They
find it practical and believe that what they are learning is important. Instruction at this level must
be active and intellectually stimulating and must help students make sense of mathematics.
In grades 3-5, multiplicative reasoning, equivalence, and computational fluency should be the
focus. (NCTM, 2000)
The Process Standards, which include Problem Solving, Reasoning and Proof, Communication,
Connections, and Representation, are outlined in both the national standards (NCTM, 2000) and
in the Alabama state standards (ALDSE, 2003). These standards are an integral part of students
reaching their educational goals and must be incorporated into the 3-5 curriculum. In addition,
estimation and recognizing the reasonableness of answers should be stressed.
In grades 3-5, students should become knowledgeable of and begin the use of appropriate
mathematical terminology in communicating about mathematical and real-world situations.
Appropriate technology should be integrated throughout the 3-5 curriculum to help students see
the real-world connections of the mathematics they are studying and to develop understanding of
the mathematical concepts. This will also help prepare them for the demands of technology in the
workplace.
The 3-5 group identified the following big ideas that should guide instruction in those grades:
1. Establish computational fluency, equivalency, and multiplicative reasoning (Algebra,
Number & Operations)
2. Correlate patterns between geometry, algebra, and other areas. (Algebra, Geometry,
Connections)
3. Use questioning, justifying, and communicating to develop mathematical reasoning.
(Reasoning, Communication, Connections, Problem Solving)
4. Investigate, collect, organize, and demonstrate data. (Data Analysis, Communication,
Representation, Number & Operations, Measurement)
5. Understand measurable attributes of objects, unit systems, and the process of
measurement. (Measurement, Geometry, Algebra, Number & Operations, Reasoning,
Connections)
6. Recognize, identify, and classify geometric figures. (Geometry, Connections, Reasoning,
Representation, Communication)
The 3-5 curriculum is organized into five strands that are consistent with both national and state
standards: Number, Algebra, Geometry, Measurement, and Data Analysis. While these strands
TEAM-Math Curriculum Guide (July 8, 2003)
Chapter 4. Curriculum for 3-5
are useful as an organizational device, they are interconnected, and teachers should help students
see those connections.
TEAM-Math Curriculum Guide (July 8, 2003) p. 25
Chapter 4. Curriculum for 3-5
Number Strand, 3-5
Grade 3 Grade 4 Grade 5
1. Order, compare… 1. Order, compare… 1. Compare, order…
a. Compare, order, round, and expand a. Compare, order, and expand whole a. Compare, order, round, and expand
whole numbers to thousands numbers to millions whole numbers through millions and
b. Demonstrate and understand place value b. Understand and demonstrate place value decimals to the thousandths
from hundredths to 9999 by using from hundredths through hundred b. Determine the value of a whole number
words, models, and pictorial thousands using words, models, and to the millions and decimals to the
representations, including the use of pictorial representation, including thousandths
coins to make change. money in dollars and cents c. Determine equivalency between
c. Understand the use of decimals when c. Determine place value in a decimal fractions, decimals, and percents
writing dollar amounts through hundredths d. Identify numbers less than zero on a
d. Demonstrate computational fluency in d. Demonstrate an understanding and use number line and in real life situations
addition, subtraction, and basic of equivalency in fractions and decimals
multiplication and division e. Rename improper fractions as mixed
e. Demonstrate and understand addition numbers and mixed numbers as
and subtraction of fractions with like improper fractions
denominators f. Demonstrate and understand addition
and subtraction of fractions with like
and unlike denominators
2. Computation 2. Computation 2. Computational Methods
a. Regroup two and three digit numbers a. Demonstrate computational fluency in a. Identify and use relationships between
in addition and subtraction and basic addition, subtraction, operations such as inverse operations
multiply two digit numbers by a one multiplication, and division b. Multiply larger whole numbers with two
digit number b. Regroup in subtraction and addition digit multipliers
b. Divide two digit dividends by one problems with hundreds, through c. Divide larger whole numbers by two
digit divisors with and without hundred thousands digit divisors
remainders c. Divide using one digit divisors with d. Multiply and divide decimals
c. Solve real life problems involving and without remainders
numerical and/or rounding concepts d. Multiply using two digit multipliers
and using estimation, mathematical
reasoning, appropriate and non-routine
strategies
3. Estimate sums and differences by using 3. Round whole numbers to nearest ten, 3. Fractions
compatible numbers and front-end estimation hundred, and thousands a. Adding, subtracting, and multiplying
TEAM-Math Curriculum Guide (July 8, 2003) p. 26
Chapter 4. Curriculum for 3-5
fractions with common and uncommon
denominators
b. Changing mixed numbers to improper
fractions and improper fractions to
mixed numbers
c. Simplifying fractions, making
equivalent fractions
d. Identify and use order of operation rules
4. Number Theory
a. Find and use the least common multiple
(LCM) by listing multiples of the
numbers involved and greatest common
factor (GCF) by listing factors of the
numbers involved
b. Determine divisibility of numbers 2, 3,
4, 5, 6, 9, and 10
c. Introduce prime and composite numbers
4. Demonstrate number sense by comparing, 4. Solve real life problems using: 5. Problem solving
ordering, and expanding whole numbers • Basic operations • Solve problems using basic operations
• Estimating on whole numbers, fractions, and
• Reasoning decimals
• Solve problems by estimating sums,
differences, products, and quotients
5. Fractions 5. Extend to notions of equivalence (50/100 = 6. Convert fractions to decimals and percents
• Introduce representations for common ½ = 50%)
fractions of 10 x 10 grids and interpret
display as decimals and percents (10th
and 100th)
• Recognize understanding and use of
equivalency sentences and fractions
6. Introduce ratios in problem solving 6. Extend the understanding of ratios and 7. Use ratios and proportions in real life
situations develop the concept of proportions in problem applications such as scale drawings:
solving: • Equivalent fractions
• Equivalent fractions • Unit rate
• Unit rate • Factor of change
• Factor of change
TEAM-Math Curriculum Guide (July 8, 2003) p. 27
Chapter 4. Curriculum for 3-5
Algebra Strand, 3-5
Grade 3 Grade 4 Grade 5
1. Identify properties of operations, such as 1. Understand and use the associative, 1. Demonstrate the use of commutative,
commutative, associative, and distributive and distributive, and commutative properties to distributive, associative, and identity properties
use them to compute whole numbers, including solve problems of addition and multiplication
the inverse relationships between
addition/subtraction and multiplication/division 2. Complete and extend patterns with symbols,
numbers, and units
2. Complete numeric, geometric, and symbolic
patterns
3. Model problem situations with objects and 3. Write a number sentence for a problem 2. Write a number sentence or sentences for a
use representation such as graphs, tables, and expressed in words problem expressed in words involving multiple
equations to draw conclusions steps
4. Complete an addition or subtraction number 4. Solve number sentences for a missing 3. Realize a variable is an unknown quantity
sentence with missing addend or subtrahend addend, subtrahend, or factor represented by a letter or a symbol
4. Solve simple algebraic equations
5. Express mathematical relationships using
equations
6. Find the output of functions (number
machines)
TEAM-Math Curriculum Guide (July 8, 2003) p. 28
Chapter 4. Curriculum for 3-5
Geometry Strand, 3-5
Grade 3 Grade 4 Grade 5
1. Identify, compare, classify, and analyze 1. Identify, compare, classify, and analyze 1. Identify figures that have a rotational
attributes of two and three dimensional shapes: geometric solid and plane figures including: symmetry
• Congruency and similarity • Symmetry (rotational and mirror for
• Horizontal, vertical, and diagonal lines plane figures) 2. Identify and explore geometric shapes in
and line segments • Congruency terms of their angles and sides:
• Lines of symmetry within given • Identify angles as right, obtuse, acute
shapes or straight
• Classify triangles as equilateral,
isosceles, or scalene
• Components of a circle: center,
radius, diameter, and introduce
circumference
2. Predict and describe the results of sliding, 2. Identify reflection (flip), rotation (turn), and 3. Use either transformations (slides, flips, or
flipping, and turning two-dimensional shapes translation (slide) and make predictions turns) or measurements to determine the
congruence of angles, line segments, and
polygons
3. Find the distance between points along 3. Locate and name coordinates on a grid 4. Identify the x-axis, y-axis, origin, and
horizontal and vertical lines on a coordinate (ordered pairs): quadrants on the Cartesian Plane
system • Parallel and perpendicular lines
• Edges 5. Locate points on the coordinate grid using
4. Describe location and movement using • Vertices ordered pairs
common language and geometric vocabulary • Angles
• Surfaces
5. Build and draw geometric shapes 4. Identify and build a three-dimensional 6. Identify the nets (combination of two-
object from a two-dimensional object dimensional shapes to make three-dimensional
shapes) for three-dimensional shapes
6. Problem solving using geometric models in 5. Solve problems using: 7. Recognize geometric ideas and relationships
other areas of mathematics • Predicting and apply them to other disciplines and to
• Estimating problems that arise in the classroom or in
• Spatial reasoning everyday life
TEAM-Math Curriculum Guide (July 8, 2003) p. 29
Chapter 4. Curriculum for 3-5
Measurement Strand, 3-5
Grade 3 Grade 4 Grade 5
1. Understand the need for measuring with 1. Identify appropriate units and tools of 1. Use appropriate units and tools of
standard units and become familiar with measurement in customary and metric units measurement in customary and metric units
standard units in the customary and metric
systems
2. Select and apply appropriate units and tools
of measurement based on given attributes
(length, area, weight, volume)
3. Carry out simple unit conversions (cm-m) 2. Convert units of measurement within the 2. Convert a larger unit of measurement into a
within a system same system smaller unit of measurement and vice versa
(length, capacity, time, weight)
4. Find and estimate perimeter and area of 3. Determine and use estimated and exact 3. Develop and use formulas to find and/or
given geometric shapes measurement of perimeter and area in real life estimate the perimeter of all shapes and area of
situations parallelograms
4. Calculate the area and perimeter of
measured dimensions
5. Solve problems involving elapsed time, 4. Calculate elapsed time, minutes, hours, 5. Solve problems using elapsed time and
temperature, spatial reasoning, and calendar days, and so forth to solve problems money
concepts
TEAM-Math Curriculum Guide (July 8, 2003) p. 30
Chapter 4. Curriculum for 3-5
Data Analysis and Probability Strand, 3-5
Grade 3 Grade 4 Grade 5
1. Collect and represent data using a variety of 1. Collect, represent, interpret, and analyze 1. Collect data through investigating and be
tables, graphs, and charts data using a variety of tables, graphs, charts, able to organize and demonstrate the data in a
and grids variety of ways: charts, tables, graphs, and
grids
2. Develop an understanding of mean, median,
and range 2. Analyze data using measures of central
tendency: mean, median, mode, and range
2. Recognize data as either categorical or 3. Determine if an outcome of simple events
numerical are likely, certain, or impossible
3. Predict the probability of outcomes of 4. Understand the concept of probability and 3. Apply and understand concepts of
simple experiments and test the predictions use it to predict outcomes of a given situation probability using experiments and predictions
TEAM-Math Curriculum Guide (July 8, 2003) p. 31
Chapter 5
Curriculum for Grades 6-8
"Middle grades students experience physical, emotional, and intellectual changes that mark the
middle grades as a significant transition point in their lives. During this time, many students will
solidify conceptions about themselves as learners of mathematics – about their competence, their
attitude, and their interest and motivation. These conceptions will influence how they approach
the study of mathematics in later years, which will in turn influence their life opportunities."
(NCTM 2000).
The Process Standards, which include Problem Solving, Reasoning and Proof, Communication,
Connections, and Representation are outlined in both national standards (NCTM 2000) and in the
Alabama state standards (ALSDE 2003). These standards must be integrated into the 6-8
curriculum in order to "deepen students' understanding of mathematical concepts." (ALSDE
2003). Along with these standards, estimating and recognizing the reasonableness of answers
should be stressed.
Students in grades 6-8 should be expected to use appropriate mathematical terminology when
communicating about mathematics and explain their reasoning. Students should be encouraged
to "verbalize, illustrate, or record their mathematical thought processes" (ALSDE 2003).
Appropriate technology should be integrated throughout the 6-8 curriculum to help students see
the real-world connections of the mathematics they are studying and to develop understanding of
the mathematical concepts. This will also help prepare them for the demands of technology in
the workplace.
Five "big ideas" provide focus for the 6-8 curriculum. Through their study in these courses,
students should be able to:
1. Represent numbers in a variety of ways.
2. Apply proportional reasoning in a variety of contexts including unit rates and
slope.
3. Solve linear and nonlinear equations.
4. Recognize and classify geometric figures.
5. Interpret, analyze, compare, and represent data using probability and statistics.
The 6-8TEAM-Math Curriculum Guide (July 8, 2003) p. 32
Chapter 5. Curriculum for 6-8
Number Strand, 6-8
Grade 6 Grade 7 Grade 8 (Pre-algebra)
1. Use operations involving place value, 1. Use operations involving fractions, 1. Use operations involving real numbers,
fractions, decimals, common percents, rational decimals, percents, introduce irrationals, percents, scientific notation, and determine the
numbers, and determine reasonableness of an scientific notation, integers, and determine reasonableness of an answer:
answer: reasonableness of an answer: • Exponents
• Exponents • Exponents • Sets
• Distributive • Sets • Properties (substitution principle)
• Real number line (including integers) • Properties • Order of operations
• Integers (add) • Order of operations • Compare and order
• Order of operations (+, -, x, /) • Compare and order • Real number line
• Compare and order • Real number line
2. Introduce prime factorization 2. Use prime factorization to find LCM and 2. Apply LCM, GCF, and prime/composite in
GCF various contexts:
3. Use divisibility rules or prime factorization • Simplifying fractions
to determine if a number is prime or composite • Simplifying algebraic expressions
• Solving real world problems
4. Convert terminating decimals to fractions 3. Extend computation to percents greater than 3. Determine percent of change
and percents 100 and less than 1
4. Apply percents and proportions to real
5. Solve problems involving decimals, 4. Expand problem solving situations to world situations and in multi-step problems
fractions, percents, and proportions include:
• Discounts
• Taxes
• Commissions
• Simple interest
6. Extend strategies for solving proportions to 5. Use proportional reasoning to solve 5. Apply proportional reasoning to real world
using cross products problems situations:
• Ratios and rates
7. Select appropriate strategies for solving • Properties
proportions • Comparing quantities
• Scaling ratios up or down
• Similarity
TEAM-Math Curriculum Guide (July 8, 2003) p. 33
Chapter 5. Curriculum for 6-8
Algebra Strand, 6-8
Grade 6 Grade 7 Grade 8 (Pre-algebra)
1. Determine a verbal rule for a function when 1. Explore Functions 1. Extend working knowledge of Functions:
given the input and output • Represent and determine a rule for data • Determine the range for a given
that appears with tables, graphs, charts, domain
2. Solve problems using geometric and and mappings • Introduce and use function notation:
numeric patterns • Determine the range and domain f(x)
• Investigate the role of functions in real • Patterns
world situations • Independent/dependent variables
• Apply to real world situations
2. Relations
• Linear; slope, and y-intercepts
• Nonlinear
3. Solve one-step equations 2. Solve one and two step equations and 3. Solve multi-step equations and inequalities,
inequalities including the distributive property
3. Inequalities-graph on number line
Geometry Strand, 6-8
Grade 6 Grade 7 Grade 8 (Pre-algebra)
1. Based on attributes, properties, and 1. Recognize, compare, and draw two- 1. Develop mathematical arguments about the
component parts (sides, angles, parallel and dimensional and three-dimensional objects relationships among types of quadrilaterals and
perpendicular lines) identify and classify: triangles:
• Quadrilaterals and triangles 2. Investigate properties and relationships • Identify angle bisectors, perpendicular
• Circles among similar and congruent figures bisectors, congruent angles, and
• Prisms and pyramids congruent figures
• Cylinders and cones • Constructing congruent and similar
polygons, congruent angles, congruent
segments, and parallel and perpendicular
lines
2. Identify transformations on coordinate plane 3. Graph the transformations and dilation of
geometric figures in the Cartesian plane
TEAM-Math Curriculum Guide (July 8, 2003) p. 34
Chapter 5. Curriculum for 6-8
3. Identify line and rotational symmetries of 4. Determine the types of symmetry (rotational
polygons or line) found in a reflection or rotation
5. Use networks to represent and solve
problems
2. Derive, justify, and apply the Pythagorean
Theorem (distance formula)
Measurement Strand, 6-8
Grade 6 Grade 7 Grade 8 (Pre-algebra)
1. Convert units of length, width, or capacity 1. Convert units of length, width, or capacity 1. Convert between systems
within the same system (Example: cups to from metric to customary and from customary
gallons) to metric 2. Convert between units in area and volume
2. Determine unit rates
2. Estimate, measure, and classify angles 3. Determine the measures of special angle 3. Investigate the measures of special angle
pairs including: pairs formed by two or more lines cut by a
• Adjacent transversal including:
• Vertical • Corresponding
• Supplementary • Alternate Interior
• Complementary • Alternate Exterior
• Consecutive Interior/Exterior
3. Develop and apply formulas (perimeter and 4. Develop and apply the concept of pi and the 4. Find the perimeter and area of regular and
area): formulas for circumference and area for circles irregular plane figures
• Triangles and trapezoids
• Understand error 5. Develop and apply the formula for the 5. Develop and apply the surface area and
volume of a prism and cylinder volume of prisms, cylinders, pyramids, and
4. Develop and apply the volume of a cones
rectangular prism (area of base multiplied by
height)
5. Use scale drawings and proportions to 6. Determine the lengths of missing sides and 6. Apply concept of similar and congruent
determine distance measures of angles in similar and congruent figures to real world situations, such as
figures indirect measurement
TEAM-Math Curriculum Guide (July 8, 2003) p. 35
Chapter 5. Curriculum for 6-8
Data Analysis and Probability Strand, 6-8
Grade 6 Grade 7 Grade 8 (Pre-algebra)
1. Interpret and represent data from charts and 1. Interpret and represent data using and 1. Interpret, represent, and compare data sets:
tables in bar graphs, line graphs, and circle creating histograms, frequency tables, stem- • Box-and-whisker plots
graphs (1/2 and ¼ of a circle) and-leaf, and circle graphs (using angle • Scatter plot
measures) • Circle graph
2. Find the mean, median, mode, and range • Determine the measure of center that
from a list of data 2. Determine measures of central tendency is most appropriate for a given
(mean, median, and mode) and the range, situation
given a set of data or graphs
3. Make estimates or predictions based on 3. Determine the validity of data, estimation, 2. Make predictions and estimations for a set
given data and predictions of data, including using the line of best fit
4. Find the probability of a simple event using 4. Determine the probability of compound 3. Determine the theoretical probability of
ratios, percents, and decimals events: events:
• Represent outcomes as a list, chart, • Complementary and mutually
picture, or tree diagram (fundamental exclusive events
counting principle) • Two independent or two dependent
• Model problem events
4. Determine the experimental probability of
an event through simulation and compare the
theoretical probabilities
TEAM-Math Curriculum Guide (July 8, 2003) p. 36
Chapter 6
Curriculum for 9-12
"The high school years are a time of major transition. Students enter high school as young
teenagers, grappling with issues of identity and with their own mental and physical capacities. In
grades 9–12, they develop in multiple ways—becoming more autonomous and yet more able to
work with others, becoming more reflective, and developing the kinds of personal and
intellectual competencies that they will take into the workplace or into postsecondary education."
(NCTM, 2000)
The Process Standards, which include Problem Solving, Reasoning and Proof, Communication,
Connections, and Representation, are outlined in both national standards (NCTM, 2000) and in
the Alabama state standards (ALSDE, 2003). These Standards are an integral part of students
reaching their educational goals and must be incorporated into the 9-12 curriculum. In addition,
estimation and recognizing the reasonableness of answers should be stressed.
In grades 9-12, students should be knowledgeable of, and become increasingly comfortable with,
using appropriate mathematical terminology and notation in communicating about mathematical
and real-world situations.
Appropriate technology should be integrated throughout the 9-12 curriculum to help students see
the real-world connections of the mathematics they are studying and to develop understanding of
the mathematical concepts. This will also help prepare them for the demands of technology in the
workplace.
The initial focus of this chapter is on Algebra I, Geometry, and Algebra II with Trigonometry, as
the basic foundation for high school mathematics. At a later point, this chapter will be extended
to include additional courses as needed.
Six "big ideas" provide focus for Algebra I, Geometry, and Algebra II with Trigonometry.
Through their study in these courses, students should be able to:
1. Analyze and graph relations and functions, including direct and indirect variation,
trigonometric relationships, and exponential functions.
2. Solve linear and nonlinear equations and inequalities in one, two, and three variables,
including applications of matrices.
3. Explore the properties of and relationships among number systems (whole numbers
through real and imaginary numbers), among types of geometric figures (two- and three-
dimensional), and among families of functions (including trigonometric identities).
4. Explore geometric patterns and relationships, including transformations, similarity, and
congruence.
5. Interpret, compare, analyze, and represent data using probability and statistics.
TEAM-Math Curriculum Guide (July 8, 2003)
Chapter 6. Curriculum for 9-12
6. Solve problems using estimation and measurement, algebraic notation, modeling, and
other techniques, enhancing students' ability to justify answers and prove results.
The 9-12 9-12 by content strand. In the
following charts, the content for each course is organized in these five strands. Each column in
the chart shows a particular course, and each row shows the relationship between concepts in the
courses, thus highlighting the vertical alignment across the courses.
TEAM-Math Curriculum Guide (July 8, 2003) p. 38
Number Strand, 9-12
Algebra I Geometry Algebra II with Trigonometry
1. Order and compare real numbers
emphasizing irrational numbers.
2. Distinguish between various number sets:
Complex (Course of Study #1)
3. Distinguish between number sets: real, 3. Understand and apply concepts and
rational, irrational, whole, integer. properties of complex numbers (Course of
Study #2)
4. Perform operations involving 4. Apply operations involving radicals and 4. Perform operations involving:
• Real numbers including radicals introduce operations with vectors. • Reals with radicals
• Exponents • Complex numbers (Course of Study
(Course of Study #1) #2)
• Common logarithms
• Rational expressions (Course of Study
#6)
• Calculate a determinate for a 2x2 and
3x3 matrix (Course of Study #8)
Algebra Strand, 9-12
Algebra I Geometry Algebra II with Trigonometry
1. A. Identify and graphically represent: 1. A. Extend solving equations and 1. A. Identify and graphically represent:
(Course of Study #4) inequalities to applications. (Course of Study #3)
• x=constant B. Reinforce and apply operations on • y=kx
• y=constant polynomials • y=ax
• y=x (identity) • y=k/x
• y= x • y=x3
• y=logax
• y= x 2
• y=[x]
• y= x • y=sin x
B. Investigate and translate vertically and • y=cos x
horizontally: • y=tan x
• x=constant • Constructing graphs by analyzing their
TEAM-Math Curriculum Guide (July 8, 2003) p. 39
Chapter 6. Curriculum for 9-12
• y=constant functions as sums, differences, or
• y=x (identity) products (Course of Study #6 c)
• y= x B. Translate, rotate, dilate, and reflect linear,
quadratic, cubic, rational, exponential,
• y= x 2 logarithmic, trigonometric, absolute value, and
• y= x radical functions. (Course of Study #3)
C. Analyze linear functions from their slopes, C. Analyze families of functions including:
equations, and intercepts: (Course of Study # • Domain (Course of Study #3)
2) • Range
• Find slope of a line form equation or • Restricted domains
using slope formula. • Roots (Course of Study #4)
• Determine the equations of linear • Maximum and minimum values
functions given 2 points, a point and (Course of Study #5)
slope, tables of values, graphs, and Given a graph, table of values, or its
ordered pairs. equation.
• Graph two-variable linear equations D. Determine period and amplitude of sine,
and inequalities on the Cartesian plane. cosine, and tangent functions from graphs or
D. Determine the equation of a line parallel or basic equations. (Course of Study #9)
perpendicular to a second line through a given E. Solve equations and inequalities including:
point (Course of Study # 7) • Quadratics
E. Determine the characteristics of a relation, • Absolute value
including: (Course of Study #3) • Radical
• Domain • Exponential
• Range • Common logarithmic
• Whether it is a function when given • Linear systems in 2 and 3 variables,
graphs, tables of functions, mappings, including matrices. (Course of Study #
or sets of ordered pairs. 8)
F. Solve equations and inequalities including: • Develop quadratic formula
(Course of Study #7)
• Multi-step linear
• Radical
• Absolute value
• Literal
• Linear systems in two variables
(Course of Study #8)
TEAM-Math Curriculum Guide (July 8, 2003) p. 40
Chapter 6. Curriculum for 9-12
• Factorable quadratics (Course of Study
#9)
• Using the quadratic formula
G. Write in set notation and graph solutions of
an equation or inequality (Course of Study #7)
2. Model real world problems by developing 2. Solving word problems involving real life
and solving equations and inequalities situations. (Course of Study #8)
including inverse and direct variation, systems
of equations, and simple number theory.
(Course of Study #7 & #8)
3. Perform operations on polynomial 3. Applying factoring when problem solving. 3. Perform operations on functions:
expressions: (Course of Study #5)` • +
• + • -
• - • x
• x • /
• / by a monomial • Composition
• factor (not sum and difference of • Inverse
cubes) • Factor polynomials including sum and
difference of cubes
(Course of Study #6)
Geometry Strand, 9-12
Algebra I Geometry Algebra II with Trigonometry
1. Identify geometric figures from a verbal
description of its properties. (Course of Study
#3 & #14)
2. Understand and analyze properties of
transformations, similarity, and congruence.
(Course of Study #8 & #13)
3. Calculate length, midpoint, and slope of a 3. Apply distance, midpoint, and slope
line segment given coordinates. (Course of formulas to solve problems and to confirm
Study #10) properties of polygons. (Course of Study #12)
4. Apply geometric properties and
relationships in solving multi-step problems in
2 & 3 dimensions. (Course of Study #5 & #6)
TEAM-Math Curriculum Guide (July 8, 2003) p. 41
Chapter 6. Curriculum for 9-12
5. Derive the distance, midpoint, and slope 5. Emphasize proof by having students 5. Verify simple trigonometric identities using
formulas. (Course of Study #10) communicate with each other and justify Pythagorean and/or reciprocal identities.
theorems and methods of solving problems. (Course of Study #12)
(Course of Study #2 & #8)
6. Determine lengths of sides and angle 6. Solve general triangles, mathematical
measures of triangles (including the use of problems, and real-world applications
trigonometry) (Course of Study #4 bullet & using the Law of Sines and the Law of
Course of Study #7 & Course of Study #10) Cosines.
• Deriving formulas for Law of Sines
and Law of Cosines
• Determining area of oblique triangles
(Course of Study #10)
7. Define the six trigonometric functions using
ratios of the sides of a right triangle,
coordinates on the unit circle, and the
reciprocal of other functions.
(Course of Study #11)
Measurement Strand, 9-12
Algebra I Geometry Algebra II with Trigonometry
1. Analyze various problems to determine 1. Analyze various problems to determine 1. Analyze various problems to determine
which measurement and tools are appropriate which measurement and tools are which measurement and tools are appropriate
in relation to Algebra I topics, including appropriate in relation to Geometry topics, in relation to Algebra II topics, including
analyzing accuracy and approximate error. including analyzing accuracy and analyzing accuracy and approximate error.
approximate error.
2. Determine the measure of interior and
exterior angles associated with polygons.
• Verifying the formulas for the
measures of interior and exterior
angles of polygons inductively and
deductively
(Course of Study #4)
3. Solve problems algebraically that involve 3. Determine the areas and perimeters of
area and perimeter of a polygon, area and regular polygons, including inscribed or
TEAM-Math Curriculum Guide (July 8, 2003) p. 42
Chapter 6. Curriculum for 9-12
circumference of a circle, and volume and circumscribed polygons, given the coordinates
surface area of right circular cylinders or right of vertices or other characteristics.( Course of
rectangular prisms. Study #11)
• Applying formulas to solve word 4. Calculate measures of arcs and sectors of a
problems circle from given information.
Example: finding the radius of a • Examples: finding the area of a sector
circle with area 75 square given its arc length and radius, finding
inches the arc length of a sector given its area
(Course of Study #11) and radius, finding the area or arc
length given the measure of the central
angle and the radius (Course of Study
#15)
5. Calculate surface areas and volumes of solid
figures, including spheres, cones, and
pyramids.
• Developing formulas for surface area
and volume of spheres, cones, and
pyramids
• Calculating specific missing
dimensions of solid figures from
surface area or volume
• Determining the relationship between
the surface areas of similar figures and
volumes of similar figures
(Course of Study #16)
6. Identify the coordinates of the vertices of the
image of a given polygon that is translated,
rotated, reflected, or dilated.
Example: using a translation vector,
rotating a triangle a given
number of degrees around a
specific point
(Course of Study #13)
TEAM-Math Curriculum Guide (July 8, 2003) p. 43
Chapter 6. Curriculum for 9-12
Data Analysis and Probability Strand, 9-12 Tuesday, June 24, 2003
Algebra I Geometry Algebra II with Trigonometry
1. Compare various methods of data reporting,
including scatterplots, stem-and-leaf plots,
histograms, box-and-whisker plots, and line
graphs, to make inferences or predictions.
• Determining effects of linear
transformations of data
• Determining effects of outliers
• Evaluating the appropriateness of the
design of a survey
(Course of Study #12)
2. Distinguishing between conclusions drawn 2. Use different forms of representation to
when using deductive and statistical reasoning compare characteristics of data gathered
(Course of Study #17a) from two populations.
• Evaluating the appropriateness of the
design of an experimental study
• Describing how sample statistics
reflect values of population parameters
(Course of Study #13)
3. Use a scatterplot and its line of best fit or a 3. Construct with precision a circle graph to 3. Determine an equation of linear regression
specific line graph to determine the represent data from given tables or classroom from a set of data.
relationship existing between two sets of experiments. (Course of Study #18) • Examining data to determine if a
data, including positive, negative, or no linear, quadratic, or exponential
relationship. (Course of Study #14) relationship exists and to predict
outcomes
(Course of Study #14)
4. Identify characteristics of a data set, 4. Analyze sets of data from geometric
including measurement or categorical and contexts to determine what, if any,
univariate or bivariate. relationships exist.
(Course of Study #13) (Course of Study #17a)
5. Estimate probabilities given data in lists or 5. Calculating probabilities arising in 5. Calculate probabilities of events using the
graphs. geometric contexts (Course of Study #17b) laws of probability.
• Comparing theoretical and • Using permutations and combinations
experimental probabilities to calculate probabilities
TEAM-Math Curriculum Guide (July 8, 2003) p. 44
Chapter 6. Curriculum for 9-12
(Course of Study #15) • Calculating conditional probability
• Calculating probabilities of mutually
exclusive events, independent events,
and dependent events
(Course of Study #15)
TEAM-Math Curriculum Guide (July 8, 2003) p. 45
Appendix A
Members of the Curriculum Writing Team
According to TEAM-Math records, the following persons attended at least two of the Curriculum
Writing Team's meetings:
Name District Name District
Michele Barnes Chambers County Carol McDaniel Tallassee City
Sara Boone Lee County Angelika McGuire Auburn City
Evelyn Boyd Elmore County Sharon Minnifield Macon County
Karen Brooks Phenix City Donna Nall Alexander City
Teresa Burns Tallapoosa County Pam Norris Opelika City
Terrica Carlisle Tallassee City Kimberly Nunes-Bufford Opelika City
Shirley Carter Lanett City Barbara Pickard Tallassee City
Frazelma Crittenden-Lynn Opelika City Beverly Price Tallapoosa County
Tammy Culbertson Chambers County Equvia Rhodes Opelika City
Donna Cunningham Tallassee City Jeannie Riddle Alexander City
Jackie Deen Lanett City Stacy Royster Opelika City
Christie Drury Lee County Greg Sanders Russell County
Leigh Ann Flemming Phenix City Becky Scarborough Auburn City
Lew Germann Phenix City Melissa Smith Lanett City
Kimberly Harris Lee County Theressa Stanford Barnes Chambers County
Donna Henderson Lanett City Rosa Stokes Elmore County
Beth Hickman Lee County Rhonda Strickland Alexander City
Lasisi Hooks Macon County Darrell Thomas Auburn City
Amy Hopkins Russell County Vanessa Tolbert Tallapoosa County
Jackie Jackson Chambers County Allison Tuthill Phenix City
Yvette Johnson Elmore County Bertha Walker Macon County
Catherine Jones Elmore County Nancy Washburn Alexander City
Debbie Kielwein Alexander City Cynthia Weaver Phenix City
Lisa Lishak Russell County Judy Welch Elmore County
Kristy Mann Tallassee City Teresa Williams Alexander City
Michele Matin Opelika City Sandi Woods Alexander City
Jerrie Mattox Alexander City Anna Wright Auburn City
Robin McCoy Russell County
The following faculty members and graduate students from Auburn University and Tuskegee
University also participated in the process:
Joy Black Leslie Sitton
Dr. Gary Martin Dr. Marilyn Strutchens
Dr. Mohammed Qazi Dr. Steve Stuckwisch
Dr. Chris Rodger Kathy Westbrook
Dr. Betty Senger Dr. Phil Zenor |
The methodology of economics employs mathematical and logical tools to model and analyze markets, national economies, and other situations where people make choices. Understanding of many economic issues can be enhanced by careful application of the methodology, and this in turn requires an understanding of the various mathematical and logical techniques. This course reviews concepts and techniques usually covered in algebra, analytical geometry, and the first semester of calculus. It also introduces the components of subsequent calculus and linear algebra courses most relevant to economic analysis. The course emphasizes the reasons economists use mathematical concepts and techniques to model behavior and outcomes.
The course will meet three times a week, twice for lectures and once in discussion section conducted by a teaching assistant. Lectures will demonstrate the power of math to answer economic questions, stressing the reasons economists use math and explaining mathematical logic and techniques. Discussion sections will demonstrate solutions for problems, answer questions about material presented in the lectures or book, and focus on preparing students for exams.
Students should be prepared to devote at least 4 hours per week outside class meetings, primarily working on problem sets as well as reviewing materials and practicing. Students with weak math skills will need to spend additional time mastering techniques.
Course objectives
Each student should be able by the end of the semester to
Recognize and use the mathematical terminology and notation typically employed by economists
Explain how specific mathematical functions can be used to provide formal methods of describing the linkages between key economic variables
Employ the mathematical techniques covered in the course to solve economic problems and predict economic behavior
Problems Sets
There are six problem sets. Answers will be posted after the due date at the following links: PS1, PS2, PS3, PS4, PS5, PS6. If it is after the due date and you still see "Suggested Answers are not yet available." then press F5 to refresh the page.
Class Schedule and Materials
Note well: the schedule may change as a result of snow events and other factors. Please watch your email for notification of such changes, which will then be reflected below once you press F5 to refresh the page. |
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Mathomatic
Mathomatic is a free, portable, general-purpose Computer Algebra System (CAS) that can automatically solve, differentiate, simplify, combine, and compare algebraic equations, perform standard, complex number, modular, and polynomial arithmetic, etc. It does some calculus and is very easy to learn and use. Plotting expressions with gnuplot is also supported (requires gnuplot |
Business Math is a business course designed to prepare students for roles as entrepreneurs, producers, and business leaders by developing abilities and skills that are part of any business environment. A solid understanding of math including algebra, basic geometry, statistics and probability provides the necessary foundation for students interested in careers in business and skilled trade areas. The content includes mathematical operations related to accounting, banking and finance, marketing, and management. Instructional strategies should include simulations, guest speakers, tours, Internet research, and business experiences. Fulfills a Mathematics requirement for the General diploma only or counts as an Elective for the Core 40, Core 40 with Academic Honors and Core 40 with Technical Honors diplomas |
Algebra 1: 270 Fractional Equations
Presentation (Powerpoint) File
Be sure that you have an application to open this file type before downloading and/or purchasing.
0.43 MB
PRODUCT DESCRIPTION
Mr. Appledorf's On-Line PowerPoint Math Lessons
Fractional Equations
Objectives:
Students will explain similarities and differences between equations with fractional coefficients and fractional equations and will solve fractional equations.
NCTM Standards:
Students recognize and use connections among mathematical ideas.
Students understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
California Content Standards:
(13.0) Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques.
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This is a collection of activities for use in precalculus and single variable calculus. It is prefaced by a brief summary of...
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This is a collection of activities for use in precalculus and single variable calculus. It is prefaced by a brief summary of what I know about group learning and how I use the activities. Many activities are quick combinations of discovery and practice. The statistics gets a bit lengthy, but I thought I'd include it anyway. As far as I recall, my text is only mentioned once and this posting should not be considered a commercial. Use the activities any way you wantFlash program that tests students' graphical understanding of addition or subtraction of functions. Uses two...
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Flash program that tests students' graphical understanding of addition or subtraction of functions. Uses two randomly generated trig graphs that students then need to add and subtract to find the new graph. Appropriate for use when discussing special cases of graphing trig functions or for use when discussing algebra of functions in a precalculus class even if students are not yet familiar with trig.trigonometry, college algebra, math, precalculus, algebra of functions, addition of ordinates, subtraction of ordinates
Allows the student to practice finding various radian measures on the unit circle, both in terms of multiples of key values...
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Allows the student to practice finding various radian measures on the unit circle, both in terms of multiples of key values and in decimal format.trig, trigonometry, unit circle, radian, radian measure, precalculus, math, mathematics |
Demonstrations to Enhance the Conceptual Understanding of Engineering Lectures
engineering classes are often taught in large lecture halls, but due to a lack of laboratory apparatus, professors use chalk or erasers to demonstrate physical principles. "Imagine this chalk is a Gaussian sphere" is a phrase underclassmen hear and are expected to learn by. Clearly, easily accessible, illustrative instructional aids could facilitate learning complex engineering concepts. This paper describes a set of 5-minute demonstrations that are simple to execute, require very little equipment, and can be used to increase students' conceptual understanding. Each activity demonstrates a basic engineering principle taken from courses, such as Differential Equations, Physics, Circuits, and Thermodynamics - topics that are required classes for all disciplines. Emphasis is placed on convenience and ease of use by the professor, with most equipment small enough to carry in a pocket or briefcase. These demonstrations introduce a laboratory element into the lecture without the necessity of having a laboratory onsite.Fri, 14 Oct 2011 03:00:02 -0500Web-based Are You Ready quiz/reviews
for students about to start first and second year courses in Mathematics. Students can test themselves to see whether they are ready for intermediate algebra, college algebra, business calculus, calculus I, II, or III, or ordinary differential equations.Fri, 12 Aug 2011 03:00:04 -0500EqWorld: The World of Mathematical Equations
site contains methods and exact solutions for a multitude of mathematical equations, including algebraic, differential, partial differential, integral, and functional equations.Fri, 6 May 2011 03:00:02 -0500Differential Equations
series of lectures, created by Salman Khan of the Khan Academy, focuses on topics covered in a first year course in differential equations. A basic understanding of differentiation and integration from Calculus before starting here is necessary. Overall, the collection features 45 videos and is a quintessential guide to this broad topic.Tue, 26 Apr 2011 03:00:01 -0500Computational Science and Engineering I
course, presented by MIT and taught by professor Gilbert Strang, provides a review of linear algebra. Topics include differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications. MIT presents OpenCourseWare as free educational material online. Video lectures, assignments and exams are included. No registration or enrollment is required to use the materials.Wed, 12 Jan 2011 03:00:03 -0600Introduction to Numerical Analysis
course, presented by MIT and taught by Professor Alar Toomre, provides an introduction to numerical analysis. The material looks at the basic techniques for the efficient numerical solution of problems in science and engineering. Topics include root finding, interpolation, approximation of functions, integration, differential equations and direct and iterative methods in liner algebra. Lecture notes are included on the site. MIT presents OpenCourseWare as free educational material online. No registration or enrollment is required to use the materials.Wed, 12 Jan 2011 03:00:02 -0600Linear Partial Differential Equations
course, presented by MIT and taught by professor Matthew Hancock, covers the partial differential equations of applied mathematics, including diffusion, Laplace/Poisson, and wave equations. Methods and tools for solving these equations are also taught. The course includes lecture notes as well as assignments and exams with solutions. MIT presents OpenCourseWare as free educational material online. No registration or enrollment is required to use the materials.Tue, 11 Jan 2011Differential Equations
Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODEs) deal with functions of one variable, which can often be thought of as time.Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams.Wed, 8 Dec 2010 03:00:02 -0600Computational Science and Engineering I
series of lectures, created by Gilbert Strang of the Massachusetts Institute of Technology, provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.Wed, 8 Dec 2010 03:00:01 -0600Nano-Scale Device Simulations Using PROPHET-Lab Exercise 1
two lectures are aimed to give a practical guide to the use of a general device simulator (PROPHET) available on nanoHUB. PROPHET is a partial differential equation (PDE) solver that offers users the flexibility of integrating new models and equations for their nano-device simulations. The first lecture covers the basics of PROPHET, including the set-up of simulation structures and parameters based on pre-defined PDE systems. The second lecture uses examples to illustrate how to build user-defined PDE systems in PROPHET.Fri, 22 Oct 2010 03:00:03 -0500Experiments with Fourier Series
by Lang Moore and David Smith for the Connected Curriculum Project, the purpose of this module is to study convergence of Fourier approximations of periodic functions. This is one lesson within a much larger set of learning modules hosted by Duke University.Thu, 2 Sep 2010 03:00:03 -0500Review of Fourier Series
by Lang Moore of the Connected Curriculum Project, the purpose of this module is to review Fourier approximations of periodic functions. This is one lesson within a larger set of learning modules hosted by Duke University.Tue, 31 Aug 2010 03:00:02 -0500Introduction to the One-Dimensional Heat Equation
by Lang Moore of the Connected Curriculum Project, the purpose of this module is to provide a qualitative introduction to a simple second-order linear partial differential equation. In this module we will concentrate on graphical representations of the solutions of appropriate initial and boundary value problems; we examine symbolic solutions in other modules. This is one lesson within a larger set of learning modules hosted by Duke University.Mon, 30 Aug 2010 03:00:02 -0500Experiments With the Laplace Transform
by Lang Moore for the Connected Curriculum Project, the purpose of this module is to study the Laplace transform and use it to examine both an ordinary differential equation problem and a problem for the one-dimensional heat equation on a semi-infinite rod. This is one of a much larger set of learning modules hosted by Duke University.Wed, 25 Aug 2010 03:00:02 -0500 |
Integrated Mathematics for Middle School: International Impressions
by Donna F. Berlin January 2001
Support for moving beyond the separate-subject approach toward a holistic mathematical curriculum has a long tradition. As early as 1899, the Chicago Section of the American Mathematical Society endorsed the "correlation of work" for the subjects of arithmetic, geometry, and algebra. Variously called composite, correlated, general, or unified courses, the movement toward integrated mathematics gained momentum with the design of junior high schools in the 1920s. The appropriateness of integrated mathematics for adolescent learners was further advanced with the middle school movement of the 1970s and 1980s. An integrated view of mathematics is consistent with two key components of the middle school philosophy: interdisciplinary teaching and coherent learning.
In the United States, the National Council of Teachers of Mathematics (NCTM) has closely aligned the term connections with integrated mathematics. NCTM's Principles and Standards for School Mathematics (Reston, Va.: NCTM, 2000) recommends the following:
Instructional programs from prekindergarten through grade 12 should enable students to—
recognize and use connections among mathematical ideas;
understand how mathematical ideas interconnect and build on one another, producing a coherent whole; and
recognize and apply mathematics in context outside of mathematics courses.
To obtain an accurate international perspective of integrated mathematics at the middle school level, a series of questions was posed to mathematics educators throughout the world. They were asked to share relevant sections of their national curriculum, textbooks, and lessons and activities. The following three-part vision emerged:
Integrated mathematics programs should—
emphasize the interrelatedness of mathematical topics—for example, number, operations, algebra, geometry, measurement, data analysis, and probability—and provide a view of mathematics as a coherent, holistic field of study;
connect mathematics with other subjects in the curriculum so that students engage in mathematics in context, extend and apply their knowledge, and experience coherent learning; and
connect mathematics with students' interests, experiences, and real life to emphasize the pervasiveness of mathematical knowledge and the power of mathematical modeling.
The pedagogical approaches of problem-based, project-based, or thematic inquiry and investigation were most often represented in the integrated mathematics lessons and activities. Similarly, in the United States, these approaches are embodied in the National Science Foundation–sponsored comprehensive, Standards-based middle school curriculum programs: Connected Mathematics, Mathematics in Context, MathScape: Seeing and Thinking Mathematically, MATHThematics, and Middle-School Mathematics through Applications Project.
Internationally, most national curricula—for example, those of Canada, the Czech Republic, Israel, Italy, the Netherlands, Sweden, and the United Kingdom—endorse the vision of integrated mathematics, whereas other areas, for example, Palestine, plan to include this perspective in the near future. The national curriculum of Japan is moving toward a compulsory period for integrated study by 2002, consistent with the second part of the vision of integrated mathematics.
Although most national curricula are compulsory, I asked colleagues to reflect on the relationship between the intended curriculum and actual classroom practice. The overwhelming response was that the relationship depends on the teacher. Teachers' content knowledge, pedagogical knowledge, beliefs about the nature of mathematics, and availability of resources are essential elements in implementing integrated mathematics.
Clearly there is worldwide interest in, and attention to, integrated mathematics. Perhaps the International Association for the Evaluation of Educational Achievement should include "integrated mathematics" in its next cross-national analysis of mathematics and science curriculum guides, textbooks, and classroom practice.
Donna F. Berlin, professor in mathematics, science, and technology education at Ohio State University, served as codirector of the 1991 Wingspread Conference on Integrated Science and Mathematics Teaching and Learning, is research coordinator for integration at the National Center for Science Teaching and Learning, and is the mathematics education associate for the Eisenhower National Clearinghouse for Mathematics and Science Education. Her professional interests include elementary and middle school mathematics education, the integration of mathematics and science education, and classroom-based research.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research. |
About the Mathematics Department
Mathematics is one of the oldest learned disciplines, and continues to be a vital and developing topic of research. It is the basis for understanding much of the physical world, and it has become essential for the study of modern developments in the social sciences. Mathematics graduates are very much in demand in teaching, the business world, and the computing professions. The Vassar Mathematics Department offers a flexible major, enabling students to tailor their course of study for a range of interests, as well as a correlate sequence for students concentrating in other disciplines. Our biweekly colloquium, the annual Asprey Lecture, and participation in URSI are extracurricular opportunities to get a glimpse of the living subject that is present-day mathematics.
Mathematics begins with the notions of number, shape, function, and data and through the process of formal, logical reasoning discovers the patterns and relations between these ideas to articulate mathematical truths. These truths are rigorously derived through proof, the language of mathematics.
The study of mathematics at Vassar develops a precision of thought and articulation that is valued highly outside of mathematics, for example, in law or in science. The curriculum ranges over a large portion of the landscape of mathematical ideas from symmetries to measures of randomness, from the calculus to abstract vector spaces. Developing a student's intuition about new mathematical objects is a goal of our courses, accomplished through lecture, workshop, assignments, and oral and written presentations.
There are many paths through the mathematics major with emphases on algebra, analysis, geometry, and statistics. Extracurricular opportunities to learn about mathematics can be found in the various series of lectures and conversation hosted by the department, and the summer research program URSI (Undergraduate Research Summer Institute) at Vassar. Faculty research ranges from algebra, analysis, topology, and statistics to dynamical systems and logic.
Graduates with mathematics majors are in high demand in graduate programs in economics, business, and engineering, and in education, law, and computing. The demands of critical thinking, precise reasoning and effective communication that mathematics requires are also central to the goal of a liberal arts education and they apply in almost every activity in life. |
Algebraic statistics is a rapidly developing field, where ideas from statistics and algebra meet and stimulate new research directions. One of the origins of algebraic statistics is the work by Diaconis and Sturmfels in 1998 on the use of Gröbner bases for constructing a connected Markov chain for performing conditional tests of a discrete exponential family. In this book we take up this topic and present a detailed summary of developments following the seminal work of Diaconis and Sturmfels. This book is intended for statisticians with minimal backgrounds in algebra. As we ourselves learned algebraic notions through working on statistical problems and collaborating with notable algebraists, we hope that this book with many practical statistical problems is useful for statisticians to start working on the field. |
Mathematics for AQA GCSE (modular) for an Amazon.co.uk gift card of up to £1.90, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Learn more
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I purchased this book for use during an access to higher education course. We actually had to work through this book in our lessons so for us it was very relevant. The book contains
Collection and organisation of data, Pictograms and bar charts, Averages and range, Pie charts and stem and leaf diagrams, Time series and frequency diagrams, Scatter graphs, Probability, Whole numbers, Decimals, Approximation and estimation, Negative numbers, Fractions, Working with numbers, Percentages, Time and money, Personal finance, Ratio and proportion, Speed and other compound measures, Introduction to algebra, Solving equations, Further equations, Formulae, Sequences, Coordinates and graphs, Using graphs, Inequalities, Quadratic graphs, Angles, Triangles, Symmetry and congruence, Quadrilaterals, Polygons, Direction and distance, Circles, Areas and volumes, Loci and constructions, Transformations, Enlargements and similar figures, Pythagoras's theorem and Understanding and using measures.
All of the answers are in the back and there are also review sections to go over what you have learnt. I found this book really helpful. I personally did not notice any wrong answers as the previous reviewer has commented.
Dear All, You might find me harsh to put this review but A BOOK suppose to teach you anything should have the right/correct answer all thew way through. My GF is strudying math as a part opf Nursing course and she left school early so she is studying math again. I have had University education so I do understand a little bit of math(I am a japanese...lol Yes our eyes are made out of numbers.lol) and the Page157 - Exercise12.5 Question 5 (A)-(E)..... the answer on the page 493 are wrong. Page159 - Exercise12.6 Question 1 (J) Only.... The answer on the page 493 is wrong as well.
Like the earlier reviewer's p[artner suggested, this really needs to be double checked for your kids or partner on this. I really recommend refund for this book. We haven't but I am going to send a letter to the publisher. This autrhers are sorry to say, very Irresponsible and Disappointing authors. How can you make a mistake answer in MATH! Unbelievabvle!
I am not sure if the publisher has corrected this or issued a insert page to retailer selling this book.
This only causes problems to all studewnts who can only relyon books and not their teachers or not good at asking questinos.
I would like to hear what Amazon have to say as a retailer, they should also hold responsible to sell something that they are confident with.
Therefore the very low star!
Whoever it is the publisher really need to wake up and slap their own face. And make sure you do that on both sides!!!
I have just started an evening class to resit my Maths G.C.S.E. The lecturers recommended that we get this book. I have been working through each chapter at home to help with what we were taught in the lesson. However, I have found that a couple of questions in the book have wrong answers.
I thought I just needed a little help. I asked my partner to help, we looked on the Internet for help and I asked my lecturer to go through them. They are wrong. A word of warning, the questions I found to have wrong answers, were from: Chapter 12 Fractions exercise 12.5 question 5. I have noticed another couple of errors.
This book has helped me, though I am a little wary now. My lecturer suggested double checking everything on the calculator just to make sure. I do feel that this book is a good study aid, just watch out for the answers in the back! |
A Geometer's Sketchpad tool for constructing distorted images that can be viewed undistorted with a cylindrical mirror. The file contains tabbed pages with several images, a grid for students to draw... More: lessons, discussions, ratings, reviews,...
Students test a variety of figures for symmetry by actually constructing reflections and rotations. The link to the tool itself is to a zip file that contains both the sketch and a pdf file of the... More: lessons, discussions, ratings, reviews,...
Students test a variety of figures for symmetry by actually constructing reflections and rotations. The link to the tool itself is to a zip file that contains both the activity in pdf format and t... More: lessons, discussions, ratings, reviews,...
This activity has students explore and construct several different types of tessellations. The first part of the activity uses only regular polygons to create pure and semi-pure tessellations; therefo... More: lessons, discussions, ratings, reviews,...
Students explore what happens when they reflect a figure over a line and then reflect the image over a second line that intersects the first. The link to the activity itself is to a zip file that c... More: lessons, discussions, ratings, reviews,...
This "lab" contains seven "experiments" in which students perform different geometric transformations on an object to determine whether, or under what conditions, the transformations commute. More: lessons, discussions, ratings, reviews,...
The 56 activities in this collection give students the opportunity to directly experience, through dynamic visualization and manipulation, the topics covered in precalculus. It finishes with a dynami explore various triangle properties, such as scalene, isosceles, equilateral, acute, right, and obtuse. The link to the tool itself is to a zip file that contains both the sketch and a pdf |
realgebra
The Rockswold/Krieger algebra series fosters conceptual understanding by using relevant applications and visualization to show students why math ...Show synopsisThe Rockswold/Krieger algebra series fosters conceptual understanding by using relevant applications and visualization to show students why math matters. It answers the common question "When will I ever use this?"Hide synopsis
Description:New. 0321567994 Instructor's edition. Identical to student...New. 0321567994 Instructor's edition. Identical to student edition. May have extra/answers for the professor. Great way to save money! WE SHIP DAILY |
Pre-Algebra
9780078651083
ISBN:
0078651085
Pub Date: 2005 Publisher: Glencoe/McGraw-Hill School Pub Co
Summary: "Glencoe Pre-Algebra" is focused, organized, and easy to follow. The program shows your students how to read, write, and understand the unique language of mathematics, so that they are prepared for every type of problem-solving and assessment situation.
Glencoe McGraw-Hill Staff is the author of Pre-Algebra, published 2005 under ISBN 9780078651083 and 0078651085. One thousand one hundred fifty seven Pre-Alge...bra textbooks are available for sale on ValoreBooks.com, one thousand fifty five used from the cheapest price of $5.95, or buy new starting at $55.00.[read more Glencoe: Pre-Algebra, Student Edition [Hardcover]. Copyright-2005, ISBN:0078651085. These books are |
REA's newest ACT test prep helps high school students master math and get into the college of their dreams!
Bob Miller has taught math to thousands of students at all educational levels for 30 years. His proven teaching methods will help you master the math portion of the ACT and boost your score!
Written in a lively and unique format that students embrace, Bob Miller's Math for the ACT prepares ACT test-takers with everything they need to know to solve the math problems that typify the math portion of the ACT. Unlike some dull test preps that merely present the material, Bob actually teaches and explains math concepts and ideas. His no-nonsense, no-stress style and decades of experience as a math teacher help students boost their ACT math score.
In this new test prep, Bob breaks down math and puts it back together in an easy-to-follow, step-by-step format. Each chapter is devoted to a specific topic and is packed with examples and exercises that reinforce math skills.
Related Subjects
Meet the Author
Bob Miller — Author, Teacher, and Renowned Mathematician
Bob Miller received his B.S. in the Unified Honors Program sponsored by the Ford Foundation and his M.S. in math from Polytechnic University. After the first class he taught (as a substitute for a full-time professor), he overheard one student say to another, "At least we have someone who can teach the stuff." From that moment on, he was hooked on teaching.
Since then, Bob has taught at virtually every educational level, and has brought his math skills to classrooms at C.U.N.Y., Westfield State College, Rutgers, and Poly. Bob says, "I always feel great when students tell me they used to hate math or couldn't do math and now they like it more and can do it better."
Bob considers teaching to be exceptionally rewarding, and he has broadened his teaching horizons to include math students beyond the classroom. His math test preps are specifically written in a fun and easy-to-follow style that students embrace.
Bob says his goal as an author, teacher, and mathematician is to help students understand math so they can get the scores they need to excel on the ACT exam. With his numerous success stories, best-selling test preps, and over 30 years of experience, Bob has proven that his teaching methods get results!
Read an Excerpt
Congratulations!!!!
You are about to enter the second part of your education, and for you, the ACT is the first step toward college.
I've written this book as if you were in front of me and I was teaching you personally. I teach some of the areas in greater detail than others because I have found many students have problems with these topics. They include factoring, algebraic fractions, trig, and, yes, percentage problems. Chapter 17 presents four sample practice tests so you know you'll have improved your skills.
If you want any topics explained more fully than this book presents, you might want to check one of my other books. If you want any questions explained or something added to the book, please send your question to REA along with your e-mail address, and I'll respond to you. E-mail: info@rea |
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary...
This course, authored by Denis Auroux of Massachusetts Institute of Technology, covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices...
This unit from Illuminations provides students with the opportunity to learn about the mathematical properties of rotations. These lessons investigate rotational symmetry by fixing the center of an object and then... |
is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference. less |
EasyTrigFunctions 2.0 description
EasyTrigFunctions is designed to show students what happens when the amplitude, or phase of a Sine, Cosine, Tangent, Secant,Cosecant, and Cotangent function is changed.Students can compare the Sine and Cosine functions and see how they differ.
Stu...read more
This bilingual problem-solving mathematics software allows you to work through 19292 trigonometric equations with guided solutions, and encourages to learn through in-depth understanding of each solut Free Download |
Wolfram Algebra Course Assistant
iPhone Screenshots
iPad Screenshots
- Evaluate any numeric expression or substitute a value for a variable.
- Simplify fractions, square roots, or any other expression.
- Solve a simple equation or a system of equations for specific variables.
- Plot basic, parametric, or polar plots of the function(s) of your choice.
- Expand any polynomial.
- Factor numeric expressions, polynomials, and symbolic expressions.
- Divide any two expressions.
- Find the partial fraction decomposition of rational expressions.
The Wolfram Algebra Course Assistant is powered by the Wolfram|Alpha computational knowledge engine and is created by Wolfram Research, makers of Mathematica---the world's leading software system for mathematical research and education.
The Wolfram Algebra Course Assistant draws on the computational power of Wolfram|Alpha's supercomputers over 2G, 3G, or WiFi connection |
Warren Wilson College Catalog 07-08
MAT 111 Mathematics for Liberal Arts
4cr
An introductory investigation of mathematics from some of the following- points of view: historical,
philosophical, computational, and aesthetic. Theory and applications will be explored as a means for
understanding the world. Individual faculty members choose topics from his/her fields of expertise and interests.
Such topics may include history and philosophy of mathematics, systems of numeration, logic, mathematical modeling,
space-time and the Theory of Relativity, probability, logarithms and musical scales, mathematics in art, non-Euclidean geometry,
fractals, cryptography, and mathematical puzzles. (Please consult the department chairperson or course instructor for a specific
description of the topics to be presented each semester.) Upon successful completion of this course the student will have
an enhanced knowledge of how math is used in society and appears in nature. The student will also gain proficiency in
mathematical problem solving through extensive reading and writing of mathematics and mathematical explorations. A
working knowledge of algebra and geometry is assumed.
Triad:
Mathematics
Prerequisite:
Two years of high school algebra and one year of high school geometry. |
97803872017ers, Polynomials, and Rings: A Course in Algebra (Undergraduate Texts in Mathematics)
This introduction to modern algebra differs from texts in this area in fundamental ways. The author's primary goal is to have the reader learn to work with mathematics through reading, writing, speaking, and listening. The choice of content is important, but he regards it as a vehicle, not as an end in itself. It is the raw material through which the readers develop the ability to understand and communicate mathematics. One non-standard feature of the book is that the author proves only a few of the theorems. Most proofs are left as exercises, and these exercises can form the core of a course based on this |
Synopses & Reviews
Publisher Comments:
As part of the market-leading Graphing Approach Series new edition, intended for precalculus courses that require the use of a graphing calculator, includes a moderate review of algebra to help students entering the course with weak algebra skills.Enhanced accessibility to students is achieved through careful writing and design, including same-page examples and solutions, which maximize the readability of the text. Similarly, side-by-side solutions show algebraic, visual, and numeric representations of the mathematics to support students' various learning styles.New! The Library of Functions thread throughout the text provides a definition and list of characteristics for each elementary function and compares newly introduced functions to those already presented to increase students' understanding of these important concepts. A Library of Functions Summary also appears inside the front cover for quick reference.New! Technology Support notes provided at point-of-use throughout the text guide students to the Technology Support Appendix, where they can learn how to use specific graphing calculator features to enhance their understanding of the concepts presented. These notes also direct students to the Graphing Technology Guide on the textbook web site for keystrokesupport.New! Technology Tips, also provided at point-of-use, call attention to the strengths and weaknesses of graphing technology. Some of these tips offer alternative methods for solving or checking a problem using technology.New! Because students are often misled by the jagged nature of graphs generated by graphing calculators, this text frequently highlights the path of a function in color on the calculator image. This unique design feature enables students to visualize the mathematical concepts clearly and accurately and avoid common misunderstandings.Study Tips at point-of-use throughout the text reinforce concepts and help students learn how to study mathematics.New! Checkpoint questions appear after each worked-out solution, directing students to work a similar exercise for further practice or concept reinforcement. These can be used by instructors in class to quickly check student understanding or by students to practice and study concepts.Chapter Review exercises, Chapter Tests, and periodic Cumulative Tests offer students frequent opportunities for self-assessment and help them to develop strong study- and test-taking skills.The Student Success Organizer is a valuable note-taking guide that helps students organize their class notes and create an effective study and review tool.New! Text-specific Tutorial Support is provided in numerous additional resources designed to help students succeed. These resources include live online tutoring, instructional DVDs and videos, and algorithmic tutorial support and self-assessment available on CD-ROM and the web.Explorations provided at point-of-use throughout the text can help instructors provide a quick introduction toconcepts or reinforce student understanding.Modeling Exercises are integrated throughout the text to motivate students and allow them to see the usefulness of the concepts being presented.Assignments are easily customized to the difficulty level of the instructor' s choice. Exercises are carefully graded in difficulty from mastery of basic skills to more challenging. For example, Review Exercises in each section reinforce previously learned skills in preparation for the next lesson. Synthesis Exercises combine skills and check for conceptual understanding. For those instructors wanting to incorporate more theory, Proofs in Mathematics, allowing instructors to incorporate more theory, are provided for selected theorems in Appendix B.A variety of exercise types is included in each exercise set. Questions involving skills, writing, critical thinking, problem solving, applications, and real data sets are included throughout the text. Exercises are presented in a variety of question formats, including free response, true/false, and fill-in the blank.New! Vocabulary questions at the beginning of every exercise set help students learn proper mathematical terminology.New! Houghton Mifflin' s Eduspace online classroom management tool offers instructors the option to assign homework and tests online, provides tutorial support for students needing additional help, and includes the ability to grade any of these assignments automatically.New! Digital Lessons and Digital Figures in PowerPoint provide instructors editable electronic instructional resources. These pre-created lessons and textbook figures make it easier than ever for instructors to present in-class examples andgraphics. In addition, for instructors with limited office hours, the full-color presentation helps promote better understanding among students, who can access these slides online to review lectures and prepare for exams.The Instructor Success Organizer includes suggested lesson plans for each section of the text and is an especially useful tool for larger departments that want all sections of a course to follow the same outline.The Instructor' s Edition of the Student Success Organizer can serve as a lecture outline for every section of the text and includes additional examples for classroom discussion. This is another valuable resource for schools promoting consistent instruction or to support less-experienced instructors.New! Eduspace is Houghton Mifflin' s online learning tool. Powered by Blackboard, Eduspace is a customizable, powerful and interactive platform that provides instructors with text-specific online courses and content. The Larson/Hostetler/Edwards Precalculus with Limits: A Graphing Approach course features algorithmic exercises, test bank content in question pools, author-produced tutorials for all sections, video explanations and eSolutions interactive odd-numbered solutions manual (optional).
Synopsis:
For a full description, see Larson et al., College Algebra: A Graphing Approach, 3/e.
Synopsis:
About the Author
Dr. Ron Larson is a professor of mathematics at The Pennsylvania State University 2012 William Holmes McGuffey Longevity Award for PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE and the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS (a complete text on CD-ROM that was the first mainstream college textbook to be offered on the Internet.) The intermediate algebra textbooks. His teaching specialties include remedial algebra, calculus, and math education, and his research interests include mathematics education and textbooks. Bruce
"Synopsis"
by Netread,
For a full description, see Larson et al., College Algebra: A Graphing Approach, 3/e.
"Synopsis"
by Netread, |
Numerical Analysis A Mathematical Introduction
9780198502791
ISBN:
0198502796
Publisher: Oxford University Press, Incorporated
Summary: 'Numerical Analysis' explains why numerical computations work or fail. These are mathematical questions, and the text provides students with a complete and sound presentation of the interface between mathematics and scienctific computation.
Schatzman, Michelle is the author of Numerical Analysis A Mathematical Introduction, published under ISBN 9780198502791 and 0198502796. Fifteen Numerical Analysis A Mathe...matical Introduction textbooks are available for sale on ValoreBooks.com, thirteen used from the cheapest price of $29.07, or buy new starting at $103.650198502796 LIKE NEW/UNREAD! ! ! Text is Clean and Unmarked! --Be Sure to Compare Seller Feedback and Ratings before Purchasing--Has a small black line on bottom/exterior edge [more]
0198502796 |
1662933 / ISBN-13: 9780471662938 ...Show more levels: highlights algebraic concepts throughout the text and includes additional supporting information; provides enhanced coverage of order of operations, Z scores, union of two events, Least Common Multiple, and Greatest Common Factor; focuses on solid mathematical content in an accessible and appealing way; offers the largest collection of problems (over 3,000!), worked examples, and problem solving strategies in any text of its kind; and includes a comprehensive, five chapter treatment of geometry based on the van Hiele model |
January 1998:Lopaka's WWW Math
Projects - Robert Garry
Garry's pages offer rich mathematics projects and science projects that
use mathematics, with links to suggested Internet resources for
background explorations. In Lopaka's notebook you'll find
links, WWW lectures and assignments, E-Zine articles from CCMATH, the
Problem Zone (games and puzzles on the WWW), and current activities such
as Hawai'i STTP, a Calculus-Physics enrichment program.
February 1998:Algebra I:
Graphing Linear Equations: - Tim O'Brien
A project created for a Master's Degree in mathematics. Topics covered:
Ordered Pairs; Graphing Equations 1 and 2; Horizontal Lines; Vertical
Lines; Slope; Equations and Slope; Find Equation of Line; Scatter Plots;
Parallel Lines; Perpendicular Lines; Solving a System. Also Quizzes and
Tests; Ask the Teacher (email a question); a Discussion Room, Glossary,
Index, and Message Board; a Crossword Puzzle and Word Search; an
Internet project predicting the number of people who will vote in the
year 2004; a simple scientific calculator; and a plotter that can plot
functions, differentials, and integrals, including trigonometric
functions.
March 1998:MathsNet
- Bryan Dye
A British site for mathematics, education, information technology, and
the Internet. Pages on logo, spreadsheets, and graphs, and areas for
specific educational software and articles. MathsNet also offers a
selection of mathematical
puzzles of various kinds.
April 1998:Polls:
What do the Numbers Tell Us? - Annenberg/CPB
Take part in a survey; then follow a year in a fictitious election
campaign for an inside look at the mathematics behind the polls and the
statistics affecting the political news you hear every day. This exhibit
explores well-known statistical concepts - random sampling, margin of
error, and confidence - through activities where YOU play the pollster.
Also included is a page of pointers to other Web sites related to
statistics. The site is part of the Annenberg/CPB Projects Exhibits
Collection, and is inspired by the PBS video Against All Odds.
May 1998:Triangle Centers
- Prof. Clark Kimberling
"Aside from the centroid, the ancient Greeks also marveled at three
other triangle centers: incenter, circumcenter, and orthocenter.
Centuries passed before a fifth triangle center surfaced: the Fermat
point. During the nineteenth century, more triangle centers entered the
literature, and then the subject died for a while. Now as we near the
year 2300 AE, new triangle centers are once again popping out, often
with the help of computers..." Prof. Kimberling offers descriptions,
illustrations, and commentary on 20th-century and Classical triangle
centers, from Schiffler and Hofstadter to Fermat and Napoleon.
June 1998:Aunty
Math - Angela Giglio Andrews
An every-other-week math challenge for grades K-3 from "Aunty Math."
Each challenge is presented in the form of a story taken from the life
of Aunty Math, her two nephews Barney and Danny, and her niece Gina.
Students with questions or suggestions can e-mail Aunty Math directly,
and a Tips for the Current
Challenge page provides parents and teachers with suggestions for
modifying or extending each problem. Students may also submit solutions
and read what others have written from Aunty Math's Solutions page.
July 1998:The
Show-Me Center
A National Science Foundation project supporting the implementation of
standards-based middle grades mathematics curricula. The site features a
searchable calendar of professional development opportunities; the
Show-Me Project center and satellites, with related NSF-sponsored
implementation and curriculum projects; and the Mathematics Curricula
Showcase: a tool for comparing five curricula on such key features as
content goals, process goals, learning environment, and use of
technology. These projects were funded in 1992 by the NSF to develop
comprehensive standards-based curricula: Connected Math; Math in
Context; MathScape; MathThematics; MMAP. Also related literature:
selected articles and papers on mathematics curriculum reform.
August 1998:Project Interactivate -
The Shodor Foundation
Project Interactivate is part of the Presidential Technology Initiative.
The materials it develops are designed to be adapted easily to any NCTM
Standards-based middle school mathematics text. Middle school
lessons cover probability, statistics, functions, and fractals. Discussions
on these subjects range from the probability of simultaneous events and
introducing elementary set operations through Internet search, to
histograms vs. bar graphs and recursion in fractals. Applets that
provide computer simulations present opportunities for group work as
well as individual investigation.
September 1998:Secondary
Mathematics Assessment and Resource Database (SMARD)
This Queensland, Australia site offers an opportunity for secondary
maths teachers to share assessment tools and other resources, including
classroom activities. Much of the assessment is alternative assessment,
known as 'authentic assessment' in the United States. The searchable and
browseable database is
divided into six main sections: Junior mathematics (years 8-10), Senior
Mathematics (years 11-12), Puzzles, Competitions, Teaching Mathematics,
and Mathematics for Leasure. In addition there are more than 220 annotated links,
organized by topic, to Web pages that support secondary mathematics.
October 1998:The
Perfect Number Journey - Heng O. K.
Math facts and exercises that address the following questions: How to
find perfect numbers? What are Mersenne numbers? How are Mersenne primes
related to perfect numbers? How to find Mersenne primes? How were the
larger perfect numbers found? Are there any odd perfect numbers? Some
properties of perfect numbers. How are perfect numbers and triangular
numbers related? Are all perfect numbers hexagonal? What is the largest
known prime? Also from the same author: The Maths Room,
offering selected sites in a variety of mathematical categories.
November 1998:The
Amazing Mathematical Object Factory (AMOF)
Part encyclopedia and part calculator, a teaching tool that generates
mathematical permutations for some combinatorial object types: subsets,
combinations, permutations, 8-queens problem, pentominoes, permutations
of a multiset, partitions, Fibonacci sequences, and magic squares; with
a link to the higher-level Combinatorial Object Server
(COS).
December 1998:Through
the Glass Wall - TERC
Looking at
how girls and boys play mathematical computer games in order to
answer such questions as: How can children learn significant mathematics
from computer games? Descriptions of over 50 games, with reviews, sample
dialogues of children playing and interacting with games, and suggested
Web links and print resources. Topics include: gender and technology,
mathematics, and play; technology in education and in the classroom;
technology and popular culture, "games for girls"; advice on choosing
software, with links to reviewers and sellers. The project's research
questions and outcomes also offer links to papers written to date, and
an essay
on the reviews onsite exploring such questions as What does it mean
to be a good computer game? |
40 million students have trusted Schaumís Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaumís Outlines cover everything from math to science, nursing to language. The main feature for all these books is the solved problems. Step-by-step, authors walk readers through coming up with solutions to exercises in their topic of choice.
387 solved problems
Covers all probability fundamentals
No calculus needed
Supports and supplements the leading probability and statistics textbooks
Appropriate for the following courses: Introduction to Probability and Statistics, Probability, Statistics, Introduction to Statistics
Detailed explanations and practice problems in probability and statistics
Comprehensive review of specialized topics in probability and statistics
Seymour Lipschutz is on the mathematics faculty of Temple University. He has taught at the Polytechnic Institute of Brooklyn and was visiting professor in the computer science department of Brooklyn College. He received his Ph.D. in 1960 at the Courant Institute of mathematical Sciences of New York University. He is the author of Schaum's Outline of Beginning Linear Algebra, Schaum's Outline of Discrete Mathematics, and Schaum's Outline of Linear Algebra.
John J. Schiller is an associate professor of mathematics at Temple University. He received his Ph.D. at the University of Pennsylvania and has published research papers in the areas of Riemann surfaces, discrete mathematics, and mathematical biology. He has also coauthored texts in finite mathematics, precalculus, and calculus |
The Matrix Multiplication simulation aims to help students learn how to multiply two matrices and what conditions need to be...
see more
The Matrix Multiplication simulation aims to help students learn how to multiply two matrices and what conditions need to be fulfilled for the product of two matrices to exist. Students can choose different dimensions for matrices A and B, and the product C=AB is displayed if it exists. Student can select an element of the matrix C to see how it is calculatedThis site hosts software that allows for the visualizatoin of finite groups using Pascal's Triangle. The software is...
see more
This site hosts software that allows for the visualizatoin of finite groups using Pascal's Triangle. The software is supported by dozens of labs that introduce the students to the relationship between groups and Pascal's Triangle, and assist them in a visual exploration of groups, subgroups, cosets, and other aspects of groups.
Change the values in the left matrix and click the INVERT button. The values in the right matrix are rounded to the 4th digit...
see more
Change the values in the left matrix and click the INVERT button. The values in the right matrix are rounded to the 4th digit (x.xxxx) to fit the text fields. If you want to use a n x n matrix with n6 you need to set the remaining diagonal elements=1.
The following applet allows users to plot three 2x1 vectors in 2-Space and gain insight about their linear independence and...
see more
The following applet allows users to plot three 2x1 vectors in 2-Space and gain insight about their linear independence and linear span. Two vectors are denoted as v1 and v2. The third is b. When possible the applet shows the linear combination of v1 and v2 necessary to form b. |
MATH 1112 COLLEGE TRIGONOMETRY (45-0-3)
Prerequisite: MATH 1111 with a grade of C or better
This course emphasizes techniques of problem solving using trigonometric concepts. Topics include trigonometric functions, properties of trigonometric functions, vectors and triangles, inverse of trigonometric functions and graphing of trigonometric functions, logarithmic and exponential functions, and complex numbers.
MATH 1113 PRECALCULUS (45-0-3)
Prerequisite: Regular Admission and MATH 1111 with a grade of C or better
Prepares students for calculus. The topics discussed include an intensive study of polynomial, rational, exponential, logarithmic, and trigonometric functions and their graphs. Applications include simple maximum and minimum problems, exponential growth and decay. |
f... read more familiarity with calculus and linear algebra. This text's introductions to several branches of geometry feature topics and treatments based on memorability and relevance. The author emphasizes connections with calculus and simple mechanics, focusing on developing students' grasp of spatial relationships. Subjects include classical Euclidean material, polygonal and circle isoperimetry, conics and Pascal's theorem, geometrical optimization, geometry and trigonometry on a sphere, graphs, convexity, and elements of differential geometry of curves. Additional material may be conveniently introduced in several places, and each chapter concludes with exercises of varying degrees of difficulty |
Book DescriptionEditorial Reviews
From the Back Cover
Just the critical concepts you need to score high in pre-algebra
This
Get down to the basics — get a handle on the basics of math, from adding, subtracting, multiplying, and dividing to exponents, square roots, and absolute value
Conquer with confidence — follow easy-to-grasp instructions for working with fractions, decimals, and percents in equations and word problems
Take the "problem" out of word problems — learn how to turn words into numbers and use "x" in algebraic equations to solve word problems
Formulate a plan — get the lowdown on the essential formulas you need to solve for perimeter, area, surface area, and volume
Open the book and find:
How to find the greatest common factor and least common multiple
Tips for adding, subtracting, dividing, and multiplying fractions
How to change decimals to fractions (and vice versa)
Algebraic expressions and equations
Essential formulas
How to work with graphs and charts
Learn to:
Work with and convert fractions, decimals, and percents
Solve for variables in algebraic expressions
Get the right answer when solving basic math problems
About the Author
Mark Zegarelli is a math tutor and author of several books, including Basic Math & Pre-Algebra For Dummies.
I teach a GED class but I happen to have been hired because of my expertise in English and reading rather than math.Because of that, I'm not sure of my math-teaching efforts, so I look for books and ideas that add to my basic knowledge. This book was really useful for my beginning algebra students. Algebra is a scary word for most GED students because math was often the reason they dropped out of school (or convinced themselves of this). This book puts the instruction in plain language that makes sense to most of my students.
Pre algebra for dummies answered questions I didn't know to ask. It is very helpful and easy to understand! I needed it to supplement my child's homeschool curriculum. It covered everything I needed. I had searched the Internet for tools to help me help my daughter, this is the best one to assist my classroom needs.
this seems to be an interesting and educational book, the problem with the digital version studying algebra, it doesn't show exponents properly. when it tries to show 5 squared it shows 52. it can be very difficult to try to decipher.
Let's get a few things straight: I haven't had a math class since eleventh grade, and that was more years ago than I'd care to admit. In fact, I took "lab science" courses as an undergraduate to avoid taking math in college, and I never had to touch a math class for my Masters. Even so, I found myself having to cram for a GRE to get into a doctoral program--and I'd forgotten how to do math without a calculator!
Pre-Algebra Essentials for Dummies is usually spot-on with its explanations, and it's well-written and accessible, but I'm one of those "learn by doing" people, and I simply didn't find enough practice problems to really drive home what I was learning. This may have been my own confidence issue, but a few more problems at the end of each section (with answers and explanations) would have been much more helpful. As a refresher, it may be enough--but I was reteaching myself, and more practice was definitely necessary.
That said, the word problem chapters are excellent. For the first time, I really felt like I understood the concept behind a word problem, and I found using the methods in the book sincerely helped.
This is a great book for keeping the mind active in retirement. Math has changed to some degree since I went to grade school in the 50's, and I was never very good at it anyway. This book has also clarified and explained many principles from my high school algebra class. It was a used book but its condition was like new.
I am a late in life student who still has a fear of math. I ordered this book as a way of refreshing my mind prior to taking a college placement test. Im still studying but the book is very helpful and easy to understand.
More About the Author
Mark Zegarelli is the author of Logic For Dummies. He holds degrees in both English and math from Rutgers University. He has earned his living for many years writing vast quantities of logic puzzles, a hefty chunk of software documentation, and the occasional book or film review. Along the way, he's also paid a few bills doing housecleaning, decorative painting, and (for ten hours) retail sales. He likes writing best, though. |
Basic Math Textbooks
Basic mathematics textbooks are introductory textbooks for the study of mathematics. A great resource for ground-level mathematic concepts like logic, arithmetic, statistics and probability, basic mathematics textbooks are essential for students developing key mathematic skills. Basic mathematics textbooks include lots of equations and exercises. Textbooks.com has the basic mathematics textbooks and advanced mathematics textbooks you need for your classes |
Equation Calculator
Por Ron Avitzur
Abre Mac App Store para comprar y descargar apps.
Descripción
Equation Calculator is a scientific calculator which does symbolic and algebraic manipulation, algebra and calculus as well as numeric computation. You can define variables and functions, evaluate symbolic derivatives, numeric integrals and matrix operations. |
Advanced Algebra
This 900 page advance algebra text is well written with detailed examples; it was written by nine teachers and includes topics such as: equations, graphs, linear relationships, matrices, parabolas, quadratic equations, functions, exponents, logarithms, trigonometry, statistics, and others. Most |
Algebra and Trigonometry With Analytic Geometry - 13th edition
Summary: Clear explanations, an uncluttered and appealing layout, and examples and exercises featuring a variety of real-life applications have made this book popular among students year after year. This latest edition of Swokowski and Cole's ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY retains these features. The problems have been consistently praised for being at just the right level for precalculus students. The book also provides calculator examples, including specific keystrokes that...show more show how to use various graphing calculators to solve problems more quickly. Perhaps most important--this book effectively prepares readers for further courses in mathematicsOversized, Edition: 13, Hardcover, Fast shipping! Access codes and CDs are not guaranteed with used books!
$160.34 +$3.99 s/h
Good
Campus_Bookstore Fayetteville, AR
Used - Good Hardcover. Textbook only! 13th Edition May contain highlighting/underlining/notes/etc. May have used stickers on cover. Ships same or next day. Expedited shipping takes 2-3 business days; ...show morestandard shipping takes 4-14 business days. ...show less
$175183.65214.06 +$3.99 s/h
New
Stork Group Phoenix, MD
Brand new and unread! Join our growing list of satisfied customers!
$230.21 |
More About
This Textbook
Overview
Introductory Technical Mathematics, 5th Edition provides current and practical vocational and technical math applications for today's sophisticated trade and technical work environments. Each unit delivers practical math concepts alongside step-by-step examples and problems drawn from various occupations. The plentiful examples and problem sets emphasize on-the-job applications of math. Enhancements to the fifth edition include improved algebra coverage, a new section on basic statistics, new material on conversions from metric to customary systems of measure, and a section that supplements the basics of working with spreadsheets for graphing |
Internet Explorer 10 & 11 Users : If you are using Internet Explorer 10 or Internet Explorer 11 then, in all likelihood, the equations on the pages are all shifted downward. To fix this you need to put your browser in Compatibility View for my site. Click here for instructions on how to do that. Alternatively, you can also view the pages in Chrome or Firefox as they should display properly in the latest versions of those browsers without any additional steps on your part.
In this chapter we will start looking at the next major
topic in a calculus class. We will be
looking at derivatives in this chapter (as well as the next chapter). This chapter is devoted almost exclusively to
finding derivatives. We will be looking
at one application of them in this chapter.
We will be leaving most of the applications of derivatives to the next
chapter.
Chain
Rule The Chain Rule is one of the more important
differentiation rules and will allow us to differentiate a wider variety of
functions. In this section we will take
a look at it.
Implicit Differentiation In this section we will be looking at implicit
differentiation. Without this we won't
be able to work some of the applications of derivatives.
Related Rates In this section we will look at the lone
application to derivatives in this chapter.
This topic is here rather than the next chapter because it will help to
cement in our minds one of the more important concepts about derivatives and
because it requires implicit differentiation.
Logarithmic
Differentiation The topic of logarithmic differentiation is
not always presented in a standard calculus course. It is presented here for those who are
interested in seeing how it is done and the types of functions on which it can
be used. |
ED350 Teaching of Elementary Math
Subject:ED
Course Number:350
Credits:2 Credits
Available Online:No
In a laboratory setting, students actively explore mathematical concepts and skills in the area of geometry, measurements, estimation, logical thinking, computers, computation and problem solving. Topics such as evaluation, testing, learning theory and instructional techniques as they relate specifically to elementary mathematics are also studied. (Prerequisite: admission to Teacher Education Program) Enrollment is concurrent with ED371 Teaching Practicum. |
Math 330 (formerly 102)
Our Math 330 page contains five topics that instructors at Solano believe our students need to already know in order to be successful in this course.
If you find from going through the videos that you are ready for Elementary Algebra (Math 330), but would like it presented at a slower pace, consider taking the course in two semesters, which involves taking Math 330A (formerly Math 107, the first half of Elementary Algebra), and then Math 330B (formerly 108, the second half of Elementary Algebra).
If you find that the material on this page is too difficult for you, our Math 320 (Pre-Algebra) course may be better suited for you. Here's what you need to do:
1) Watch each video (they are between five and ten minutes each).
2) Work on the sample problems linked underneath each video.
3) Check your solutions using the link underneath each video.
4) At the bottom of the page is sample final for our Pre-Algebra course, Math 320. If you take this exam, and find that you have a good knowledge of all the material, you have a good chance of being successful in Math 330. |
A unit that introduces elementary ideas included in probability theory, defining important words and ideas, presenting formulas for solving problems, and discussing permutations, combinations, and compound probability.... |
Trigonometry - With Access - 10th edition
Summary: Trigonometry, Tenth Edition , by Lial, Hornsby, Schneider, and Daniels, engages and supports students in the learning process by developing both the conceptual understanding and the analytical skills necessary for success in mathematics. With the Tenth Edition , the authors adapt to the new ways in which students are learning, as well as the ever-changing classroom environment.
4-24-12 other 10 |
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