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Buy Used Textbook Buy New Textbook eTextbook Downloadable Offline Access Duration Price 180 day subscription $81.88 $81.88 More New and Used from Private Sellers Starting at $3926Linear Algebra with Applications Linear Algebra With Applications Student Study Guide for Linear Algebra with Applications Customer Reviews An easy understanding of Linear AlgebraAugust 8, 2011 by William Byrd A very good undergraduate textbook dealing with Linear Algebra. The text is very clear on the subject. But, the real strength of this textbook is the examples is using the MatLab computer program. I have been able to duplicate the problems using Octave computer program. Linear Algebra With Applications: 4 out of 5 stars based on 1 user reviews. Summary This book is for sophomore-level or junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite. This thorough and accessible text from one of the leading figures in the use of technology in linear algebra gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualization play in understanding linear algebra. This edition will continue to be packaged with the ancillary ATLAST computer exercise guide, as well as new MATLAB and Maple guides, which also come with the package. One of the longer sections in the previous edition was the section on matrix algebra in Chapter 1. The material in that section has been expanded further for the current edition. Rather than include an overly long revised section, we have divided the material into sections titled Matrix Arithmetic and Matrix Algebra. 2. New Exercises After seven editions it was quite a challenge to come up with additional original exercises. This eighth edition has more than 130 new exercises. The new exercises are not evenly distributed throughout the book. Some sections have many new exercises and others have few or none. 3. New Subsections and Applications A new subsection on cross products has been included in Section 3 of Chapter 2. A new application to Newtonian Mechanics has also been added to that section. In Section 4 of Chapter 6 (Hermitian Matrices), a new subsection on the Real Schur Decomposition has been added. 4. New and Improved Notation The standard notation for the jth column vector of a matrix A is aj , however, there seems to be no universally accepted notation for row vectors. In the MATLAB package, the ith row of A is denoted by A(i, :). In previous editions of this book we used a similar notation a(i, :), however, this notation seems somewhat artificial. For this edition we use the same notations as for a column vector except we put a horizontal arrow above the letter to indicate that the vector is a row vector (an horizontal array) rather than a column vector (a vertical array). We have also introduced improved notation for the standard Euclidean vector spaces and their complex counterparts. 5. Other Revisions Various other revisions have been made throughout the text. Many of these revisions were suggested by reviewers. 6. Special Web Site and Supplemental Web Materials Pearson has developed a special Web site to accompany the 8th edition. This site includes a host of materials for both students and instructors. Author Biography Steven J. Leon is a Chancellor Professor of Mathematics at the University of Massachusetts Dartmouth. He has been a Visiting Professor at Stanford University, ETH Zurich (the Swiss Federal Institute of Technology), KTH (the Royal Institute of Technology in Stockholm), UC San Diego, and Brown University. His areas of specialty are linear algebra and numerical analysis. Leon is currently serving as Chair of the Education Committee of the International Linear Algebra Society and as Contributing Editor to Image, the Bulletin of the International Linear Algebra Society. He had previously served as Editor-in-Chief of Image from 1989 to 1997. In the 1990's he also served as Director of the NSF sponsored ATLAST Project (Augmenting the Teaching of Linear Algebra using Software Tools). The project conducted 18 regional faculty workshops during the period from 1992–1997.
6.2 Learning about Rate of Change in Linear Functions Using Interactive Graphs Beginning to understand the relationship between change and accumulation is a precursor to understanding calculus. This example illustrates the use of dynamic graphs to learn about change and linear relationships, as described in the Algebra Standard. Explore a linear function or a piecewise function comparing units vs. cost per unit in order to find the total cost of a phone plan. The e-example below contains the original applet which conforms more closely to the pointers in the book. In this two-part example, users can drag a slider on an interactive graph to modify a rate of change (cost per minute for phone use) and learn how modifications in that rate affect the linear graph displaying accumulation (the total cost of calls). 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.
Discrete Mathematical Structures - 6th edition Summary: Key Message: Discrete Mathematical Structures Sixth Edition offers a clear and concise presentation of the fundamental concepts of discrete mathematics. This introductory book contains more genuine computer science applications than any other text in the field and will be especially helpful for readers interested in computer science. This book is written at an appropriate level for a wide variety of readers and assumes a college algebra course as the only prerequisite. Key Topics: Fu...show morendamentals; Logic; Counting; Relations and Digraphs; Functions; Order Relations and Structures; Trees; Topics in Graph Theory; Semigroups and Groups; Languages and Finite-State Machines; Groups and Coding Market: For all readers interested in discrete mathematics
This activity would be done at the end of the school year in a pre-algebra class. It is a way to introduce algebra and its... see more This activity would be done at the end of the school year in a pre-algebra class. It is a way to introduce algebra and its history, putting some personality into the abstractness of the subject by researching the individuals behind algebraic concepts. It was initially found on the following site five years ago when I first did it with my classes: It has since disappeared, however, so the specific modifications I made at the time are fuzzy at best, but I have made recent adjustments to every portion.Introduction:Algebra, what does it mean? Where did it come from? Who thought up this stuff? Have you ever wondered what the word algebra means or when and where algebra was developed or who developed algebraic concepts? In this project your group will go on a journey through time and the history of mathematics to discover the answers to these questions.Task:Each group will go on a quest to find the mathematicians' histories that have named as being the fathers or founders of algebra. On this journey your group will collect information about the mathematician responsible for developing the algebraic concept assigned to your group, create a timeline to show when the concept was developed in relation to other significant events in history, and find examples of the algebraic concept. Each group will prepare a Powerpoint to present the information to the class.Group I The Father of Algebra (Algebraic thought and equations)Group II Founder of Cartesian Plane and Graphing EquationsGroup III Developer of PolynomialsGroup IV Set Notation and Venn Diagrams DesignerEach group will need a Researcher, Recorder, Mathematician, and a Reporter.Researcher - Using the resources below, work with the Recorder to find and record needed information for your topic.Recorder - Record information on your topic and citation for where the information was found. Work with the Researcher and the Reporter to prepare a report of the findings of your group.Mathematician - Work with the Researcher and the Recorder to find examples of mathematical problems from your assigned topic. Choose two examples that you can share, with which you can demonstrate the topic for the class.Reporter - Work with the other members of your group to create a presentation, using PowerPoint, which you will present to the class. StAIR (Stand Alone Instructional Resource) that can be used to teach the laws of the exponents to independent learners. Can... see more StAIR (Stand Alone Instructional Resource) that can be used to teach the laws of the exponents to independent learners. Can also be used as a review for students who have been introduced to the topic in previous math classes. Integrates video, audio, music, text, games, and practice problems.It was not mentioned in the introduction, but the student is not expected to complete all activities, though that is certainly an option. Rather the student is expected to choose those activities that best help him/her to thoroughly understand the topic. Assists teachers in understanding and interpreting the properties of numbers and provides a background to the numerous proofs... see more Assists teachers in understanding and interpreting the properties of numbers and provides a background to the numerous proofs and solutions to various mathematical equations. Material is crucial for the teaching of secondary school mathamatics.Compulsory Readings for Mathematics II: Number Theory (PDF) This course includes lecture notes, assignments, problems for group work in recitation, and a full set of lecture videos.... see more This course includes lecture notes, assignments, problems for group work in recitation, and a full set of lecture videos. These video lectures of Professor Arthur Mattuck teaching 18.03 were recorded live in the Spring 2003. Professor Mattuck has inspired and informed generations of MIT students with his engaging lectur
Product Details The strength of the Pollatsek book lies in its many exercises and its many opportunities for students to explore ideas that arise during the development of Lie theory... --The UMAP Journal Can be used as supplementary reading in a linear algebra course, or as a primary text in a "bridge" course that helps students make the transition to courses that emphasize definition and proofs, as well as for an upper level elective. The work of the Norwegian mathematician Sophus Lie extends ideas of symmetry and leads to many applications in mathematics and physics. Ordinarily, the study of the "objects" in Lie's theory (Lie groups and Lie algebras) requires extensive mathematical prerequisites beyond the reach of the typical undergraduate. By restricting to the special case of matrix Lie groups and relying on ideas from multivariable calculus and linear algebra, this lovely and important material becomes accessible even to college sophomores. Working with Lie's ideas fosters an appreciation of the unity of mathematics and the sometimes surprising ways in which mathematics provides a language to describe and understand the physical world. Lie Groups is an active learning text that can be used by students with a range of backgrounds and interests. The material is developed through 200 carefully chosen problems. This is the only book in the undergraduate curriculum to bring this material to students so early in their mathematical careers. Solutions to selected problems. An instructor's manual comes with the adoption of this title.
This activity consists of three exercises in which learners sketch the graphs of various power functions on the same axes. They use their sketches to make comparisons and observations which lead to generalizations about the graphs of power functions. To aid them in their exploration, students compute specified function values at key points and find points of intersection of the graphs. The graphs can be sketched by hand or with the use of a graphing calculator. Students compare and contrast exponential and power functions. In this precalculus lesson, students identify the value of x, using the graph as a visual. They compare functions with base of greater than one, to base of less than one. In this power functions worksheet, students read about determining the brightness of stars using a magnitude scale. Students solve 4 problems including finding the magnitude differences of stars and determining equivalent magnitudes. Learners identify the different properties of exponential functions. In this algebra lesson plan, students graph and analyze exponential functions as it relates to growth and decay. They apply the laws of exponents to add, subtract, multiply and divide exponential functions. Texas Instruments has composed yet another lesson to get your class using the TI-Inspire calculator to solve power and root functions. They find similarities and differences in the graphs of even and odd power and root functions then group them as families of functions. They then examine the inverse relationship among these functions. Students explore a variety of ways of solving quadratic equations. Students choose from graphing, factoring, finding square roots, completing the square and using the Quadratic formula. They ponder in the end on polynomial equations. Young scholars define rational functions and solve to find the long run behavior. In this algebra lesson, students identify functions by the given formula, from a graph or from a horizontal asymptote describing the long run behavior of a rational function. Students add subtract and multiply rational functions. For this algebra lesson, students identify the domain and range of each function. They predict the end behavior of the graph based on the power of the polynomial. Students investigate scatterplots for the-line of best fit or linear regression. In this statistics lesson, students collect data, graph and analyze it using graphs. They differentiate between inductive and deductive reasoning. Pupils graph polynomial functions and analyze the graphs. They identify the inverse of the functions and find the domain and range. Learners will then label the functions as one to one and use the horizontal and vertical line test to verify functions. Learners describe the end behavior of polynomial functions. Pupils relate the behavior of the graph to the exponent of the graph. They differentiate graphs with odd-exponent and graphs with even exponents. Ideal for your electricity unit, especially with middle schoolers, this lesson plan gets engineers using multimeters in electrical circuits to explore the relationships among voltage, current, and resistance. Older learners may even plot data on graphs to see the E-I curves. It's a full-fledged resource for your physical science learners! What's my function? Your class will work in pairs to determine which type of function is described in 14 different scenarios. Linear, quadratic, exponential and power functions are represented in a variety of ways: numerically, graphically, verbally, and analytically. Included are complete lesson plans, an activity sheet with answers, and a quick assessment to use at the end of the lesson plan. In some ways, the digital world is a living, evolving organism. Take a look at a popular theory that helps to explain some big questions about connections. The video defines networks, power functions, nodes and hubs, and includes an example for each term. Class members can watch the vibrantly animated video and then complete the provided questions. In this graphing calculator learning exercise, students explore the necessary steps in using a graphing calculator to simply square root, cubed root, and xth root functions. Afterwards, they independently solve three story problems involving roots and powers. One problem is multiple choice, and the other problems are multi-step and open ended.
Functions Modeling Change -Text Only (Cloth) - 2nd edition Summary: This fai...show morelure rates. A large number of real-world examples and problems enable students to create mathematical models that will help them understand the world in which they live. The focus is on those topics that are essential to the study of calculus and these topics are treated in depth. Linear, exponential, power, and periodic functions are introduced before polynomial and rational functions to take advantage of their use to model physical phenomena. Building on the Consortium's Rule of Four: Each function is represented symbolically, numerically, graphically, and verbally where appropriate
Rent Textbook Buy New Textbook Used Textbook We're Sorry Sold Out eTextbook We're Sorry Not Available More New and Used from Private Sellers Starting at $195This package consists of the textbook plus an access kit for MyMathLab/MyStatLab. The Sullivan/Struve/Mazzarella Algebraprogram is designed to motivate students to "do the math"— at home or in the lab—and supports a variety of learning environments. The text is known for its two-column example format that provides annotations to the left of the algebra. These annotations explain what the authors are about to do in each step (instead of what was just done), just as an instructor would do. MyMathLab provides a wide range of homework, tutorial, and assessment tools that make it easy to manage your course online. Author Biography Michael Sullivan, III is a full-time professor of mathematics at Joliet Jr. College. His training is in mathematics, statistics, and economics and he has more than 18 years experience as an instructor. His publications with Pearson cover developmental math, precalculus, and introductory statistics. Most recently, Mike has been highly involved in Course Redesign at Joliet Junior College. His experience in course redesign and writing texts for the college-level math and statistics courses gives him a unique insight into where students are headed after the developmental math track, and what they need to do to be successful. Mike is the father of three children and an avid golfer. Katherine Struve is a full-time instructor with Columbus State Community College and has more than 30 years experience in the classroom. She is in tune with the challenges of teaching mathematics at a large, urban community college. She has served as the Lead Instructor of Developmental Mathematics and has been involved in the recent course redesign effort at Columbus State. Janet Mazzarella is a full-time instructor at Southwestern College and has more than 18 years experience teaching a wide range of courses from arithmetic through calculus. She helped develop the self-paced developmental math program and spent two years serving as its director. Along with Mike and Kathy, Janet has also been active in the course redesign initiative at her institution. Table of Contents Preface 1. Operations on Real Numbers and Algebraic Expressions 1.1 Success in Mathematics 1.2 Fractions, Decimals, and Percents 1.3 The Number Systems and the Real Number Line 1.4 Adding, Subtracting, Multiplying, and Dividing Integers 1.5 Adding, Subtracting, Multiplying, and Dividing Rational Numbers Putting the Concepts Together (Sections 1.2-1.5) 1.6 Properties of Real Numbers 1.7 Exponents and the Order of Operations 1.8 Simplifying Algebraic Expressions Chapter 1 Activity: The Math Game Chapter 1 Review Chapter 1 Test 2. Equations and Inequalities on One Variable 2.1 Linear Equations: The Addition and Multiplication Properties of Equality
book containing over 200 problems spanning over 70 specific topic areas covered in a typical Algebra II course. Learners can encounter a selection of application problems featuring astronomy, earth science and space exploration, often with...(View More) more than one example in a specific category. Learners will use mathematics to explore science topics related to a wide variety of NASA science and space exploration endeavors. Each problem or problem set is introduced with a brief paragraph about the underlying science, written in a simplified, non-technical jargon where possible. Problems are often presented as a multi-step or multi-part activities. This book can be found on the Space Math@NASA website.(View Less) In this problem set, learners will consider the temperature in Kelvin of various places in the universe and use equations to convert measures from the three temperature scales to answer a series of questions. Answer key is provided. This is part of...(View More) Earth Math: A Brief Mathematical Guide to Earth Science and Climate Change.(View Less) This is a booklet containing 37 space science mathematical problems, several of which use authentic science data. The problems involve math skills such as unit conversions, geometry, trigonometry, algebra, graph analysis, vectors, scientific...(View More) notation, and many others. Learners will use mathematics to explore science topics related to Earth's magnetic field, space weather, the Sun, and other related concepts. This booklet can be found on the Space Math@NASA website.(View Less) In this problem set, learners will refer to the tabulated data used to create the Keeling Curve of atmospheric carbon dioxide to create a mathematical function that accounts for both periodic and long-term changes. They will use this function to...(View More) answer a series of questions, including predictions of atmospheric concentration in the future. A link to the data, which is in an Excel file, as well as the answer key are provided. This is part of Earth Math: A Brief Mathematical Guide to Earth Science and Climate Change.(View Less) In this problem set, learners will create and use a differential equation of rate-of-change of atmospheric carbon dioxide. They will refer to the "Keeling Curve" graph and information on the sources and sinks of carbon on Earth to create the...(View More) equation and apply it to answer a series of questions. Answer key is provided. This is part of Earth Math: A Brief Mathematical Guide to Earth Science and Climate Change booklet containing 87 problem sets that involve a variety of math skills, including scale, geometry, graph analysis, fractions, unit conversions, scientific notation, simple algebra, and calculus. Each set of problems is contained on one...(View More) page. Learners will use mathematics to explore varied space science topics in the areas of Earth science, planetary science, and astrophysics, among many others. This booklet can be found on the Space Math@NASA website.(View Less)
studymaths.co.uk - Jonathan Hall Free help on your maths questions. See also the bank of auto-scoring GCSE maths questions, games, and resources such as revision notes, interactive formulae, and glossary of terms. ...more>> Success for All Curriculum driven by co-operative learning that focuses on individual pupil accountability, common goals, and recognition of team success, all with the aim of getting learners "to engage in discussing and explaining their ideas, challenging and teaching ...more>> Syzygy Shareware - Thomas C. Bretl A source of math freeware for both Mac and PC, appropriate for grades K-12. Includes games, simulations, and skill-building programs. Explore, see in new ways, discover patterns, and solve problems. ...more>> Teaching Mathematics - Daniel Pearcy Pearcy has used this blog, subtitled "Questions, Ideas and Reflections on the Teaching of Mathematics," as a "journal of ideas, lessons, resources and reflections." Posts, which date back to October, 2011, have included "New Sunflower Applet: Fibonacci ...more>> ThinkQuest An international contest designed to encourage students from different schools and different backgrounds to work together in teams toward creating valuable educational tools on the Internet while enhancing their ability to communicate and cooperate in ...more>> Ti 84 Plus Calculator Instructional videos include using the parametric function to construct a pentagram, hypothesis testing, sketching polynomial functions, finding critical points of a function, and using the TVM (Time Value of Money) Solver method. The site also offers ...more>> TI-89 Calculus Calculator Programs TI-89 calculator programs for sale. Enter your variables and see answers worked out step by step: a and b vectors, acceleration, area of parallelogram, component of a direction u, cos(a and b), cross product, curl, derivative, divergence of vector field, ...more>> Title III MSS Final Performance Report - Dana Lee Ling Dana Lee Ling is a mathematics and science software specialist at the College of Micronesia-FSM. Articles document the College's attempts to increase the success of pre-algebra and algebra students through "conceptual" and technology-based approaches. ...more>> To Accumulate a Rate — Integrate! - Kaleb Allinson Allinson teaches trigonometry and AP Calculus AB at Lake Stevens High School (WA), where he also serves as the math department head. He describes his blog as a venue to "help me reflect on my teaching.... and record the unique [ideas] I came up with for ...more>> TutorTeddy.com Online tutoring sessions across grades in arithmetic, algebra, statistics, probability, calculus, geometry, and trigonometry. The TutorTeddy.com site also freely offers more than a hundred chalkboard video lectures and worked problems. ...more>> Utah Elementary Mathematics - David A. Smith Blog of conceptual frameworks and other classroom resources for Utah educators implementing the Utah Core State Standards. Smith, the Elementary Mathematics Specialist at the Utah State Office of Education (USOE), has posted since October, 2013; and also ...more>> Varsity Tutors - Chuck Cohn, founder and CEO Varsity Tutors is a private tutoring service in Chicago (with tutors there and in Houston, New York City, Phoenix, St. Louis, and Tucson) that provides premium at-home (or mutually agreed location) academic assistance in math-related subjects. Varsity ...more>> WebGrapher - Tom Cooper This page contains a graphing applet that can be used online or downloaded. The applet can create dynamic graphs with sliders that can be saved as web pages. Users can plot points, functions, parametric functions, polygons, vectors and more. There ...more>> When Am I Going to Use This? - Column Five Media This graphic plots popular career choices on axes of "number of math concepts" and "median average salary" to illustrate the basic math, algebra, geometry, or trigonometry required of athletes, cosmetologists, carpenters, pilots, psychologists, lawyers, ...more>> Wild About Math! - Sol Lederman Math posts, which date back to October, 2007, have included "10 ways to get wild about Math," "How to square large numbers quickly (part 1)," "26 tips for using learning styles to help your kids with Math," "The algebra of cross-multiplication," "Flexagon ...more>>
Courses & Curriculum SuccessMaker®: A Digital Learning Curriculum SuccessMaker Mathematics Course Overview SuccessMaker Mathematics is an interactive, standards-based course designed to develop and maintain fundamental concepts taught in mathematics in grades K through 8. The student experience begins with Initial Placement which identifies the appropriate starting point for instruction and then moves the student seamlessly into the courseware. As learners navigate the content, the experience is highly visual and engaging. Learners work at their own pace aided by full audio support and online manipulatives. The course includes real-world contexts for problem solving and guided interactive practice and assessment to reflect the best practice recommendations of the National Council of Teachers of Mathematics while aligned to the Common Core State Standards. SuccesMaker Mathematics A Strong Start The SuccessMaker curriculum is well-correlated to the Common Core State Standards, and students leave junior high with skills derived from strong work on phonics, fluency, vocabulary and comprehension even if it's multiple levels below grade. Algebra Readiness Content throughout grade levels addresses Algebraic concepts such as functions, relations, variables, and patterns, preparing students for the algebra demands of middle school and high school. Problem Solving A Personalized Path to Success SuccessMaker keeps learners on the road to success. At every turn, the program helps students break through roadblocks by delivering tutorials, prerequisite instruction, and other scaffolded interventions based on their individual needs. Program Facts Response to Intervention (RTI) RTI is an ongoing instructional process of using assessments to inform instruction that leads to improved student performance. Pearson's Response to Intervention solution provides a continuum of accelerated intervention strategies that assess, instruct, and monitor at every level for the best possible outcome. Unlike other modular solutions, Pearson's combination of continual progress monitoring and instruction ensure long-term, sustained results. STEM Pearson offers customizable, integrated K-12 science, technology, engineering, and mathematics (STEM) solutions to support states seeking to implement standards-based STEM curricula and meet the Federal Department of Education's Race to the Top and Invest in Innovation (I3) grant priorities. Only Pearson provides a fully integrated approach to STEM curriculum, including courses, training, and community partnerships that will help promote relevant and effective learning and teaching. Funding Funding Your Pearson sales representative is ready to partner with you to create a customized curriculum and professional development plan to help your struggling students and schools achieve success. Visit Pearson's Grants and Funding Web site to find useful links to identify possible grants and resources for grant applicants applying for Pearson's products.
Enter an equation and this works out the solution. It basically does just what it says on the tin. So if you have homework that you need to check, then look no further. The widget tool is taken from the selection of tools that appears on my live worksheet apps solve cuadratic equations, cubic equations or real polynomials up to degree 99. Systems of 2 equations, systems of 3 equations or systems up to 99 real equations. It's very helpful in your homeworks or any important project. All your calculations are automatically saved, so you can check them out in the built-in calculations history at any time. The interface allows you to write the equations and see results just like you we're doing it in a paper, all variables and results are generated automatically. When editing a system of equations if you type a wrong equation you can use our modify system to change the wrong equations without needing to start again from scratch the whole system. And for those who want to go pro, Science Formula Calculator Pro is available. It includes the full versions of both Physics and Chemistry Formula Calculators. Just search "Science Formula Calculator Pro" in the market.Circuit solving app with basic features of DC and AC 1-frequency calculations. "Solve circuits the simple way. Draw them and tap Solve to get them solved." This application uses Kirchoff's Voltage Law and common concepts of mesh analysis to solve circuits. Just draw the circuit, and for each loop, keep adding in whatever is needed (R,L,C,V) via the blue dots until they meet and become black. No blue dots mean all loops are complete. Features in version 1.0 - 1. Draw-it-yourself approach to make the circuit. 2. DC calculations for complex-interlinked loops. 3. AC calculations for single frequency circuits, which can be easily solved via phasor interpretation. 4. AC results shown in A < B format where A is the magnitude of phasor and B is angle of phasor with reference. 5. Components available - inductor, capacitor, resistor, DC source, AC source. 6. Reset circuit option. **Advice for use New connecting wire can be drawn only from where you ended the last connection. More in the next version! Please do mail me and tell me what changes do you want in this version, or upcoming ones.Free physics formula calculators app is an awesome app for all students and is designed and developed for school/college students . This app has many sections on physics and is very helpful during the exam period. This app has over 80 formulas that allow the user to solve for not one, but all of the variables in each formula. Much more useful than a basic app.Perfect for Physics Related Calculation. Topics Cover: -Electricity and Magnetism -Mechanism -Dynamics -Fluid Mechanics -Thermal Physics -Atomic and Nuclear Physics -Waves and Optics -Modern Physics Features: 1.It is designed to give all the possible answers, as quickly as possible. 2.This helps any student check their answer easily. 3.no internet connection required. Please feel free to send us your comments on how to improve this app This
Thank you for your consideration. Algebra 1 is a textbook title or the name of a course, but it is not a subject. It is often the course where students become acquainted with symbolic manipulations of quantities.
A plain-English guide to the basics of trig Trigonometry deals with the relationship between the sides and angles of triangles... mostly right triangles. In practical use, trigonometry is a friend to astronomers who use triangulation to measure the distance between stars. Trig also has applications in fields as broad as financial analysis, music... more... This is the Proceedings of the ICM 2010 Satellite Conference on "Buildings, Finite Geometries and Groups" organized at the Indian Statistical Institute, Bangalore, during August 29 - 31, 2010. This is a collection of articles by some of the currently very active research workers in several areas related to finite simple groups, Chevalley... more... The second volume of this modern, self-contained account of Kaehlerian geometry and Hodge theory continues Voisin's study of topology of families of algebraic varieties and the relationships between Hodge theory and algebraic cycles. Aimed at researchers, the text is complemented by exercises which provide useful results in complex algebraic geometry. more...
Annie's Sketchpad Activities - Annie Fetter Handouts for activities that incorporate JavaSketchpad, including: making a presentation sketch; investigating the properties of quadrilaterals; the Euler segment; morphing a simple figure to a circle; Napoleon's theorem; drawing a box and its net; and ...more>> Annual Pi Day - The Exploratorium, San Francisco, CA "Founded by the the Exploratorium's own Prince of Pi, physicist Larry Shaw, Pi Day has become an international holiday, celebrated live and online all around the world." Read a brief history of pi; find activities for cutting π and wearing π; and ...more>> Another Record Prime - Ivars Peterson (MathLand) This time, it didn't take a supercomputer. The new record for the largest known prime number goes to someone using a Pentium-powered desktop machine. Joel Armengaud, a computer programmer working for Apsylog in Paris, made the discovery on Nov. 13 and ...more>> Answer Ace - MathSupport Co. A Windows 95/98/NT math problem solver that helps students learn or review arithmetic, pre-algebra, and basic algebra skills. Students enter specific problems and the software provides answers along with step-by-step help. A free trial is available for ...more>> ap-calc - The College Board, Math Forum The Advanced Placement Calculus mailing list is hosted by The College Board and archived by the Math Forum. Designed for pre-college students preparing for AP tests, the level of discussion and the explicit relation to the college sequence may also make ...more>> AP Calculus TI 89 Program - Nils Hahnfeld Calculator program for the TI 89 which animates calculus concepts and computes answers. Covers the entire AP Calculus (AB & BC) curriculum. Screen shots and a list of functions available at the site, as well as documentation. ...more>> AP Computer Science - College Board Online General information about exams and courses (A and AB), links to archives of free-response questions in C++, the AP CS mailing list, development committee access, related websites, and an on-line store for College Board books. Maintained by the College ...more>> Aplusix: Software for Learning Algebra Software for helping students learn algebra. In English, French, Portuguese. Includes classical exercises and word problems, with various levels of assistance. It contains 400 patterns of exercises for numerical calculation, expansion, factorization, ...more>> APlusStudent Online Learning Interactive math lessons with graphics, animation, and audio, based on Micromedia Flash technology. Teacher-designed, standards-based lessons. Parents can monitor the progress of their children. There is also homework help and an online gallery where ...more>> Appealing Numbers - Ivars Peterson (MathTrek) A short history of amicable numbers - pairs in which each number is the sum of the proper divisors of the other. The smallest such pair is 220 and 284. The number 220 is evenly divisible by 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110, which add up to ...more>> AP Statistics - BB&N Upper School A course from the Buckingham Browne & Nichols School. Advanced Placement Statistics acquaints students with the major concepts and tools for collecting, analyzing, and drawing conclusions from data, featuring work on projects involving the hands-on ...more>> Archimedes - Chris Rorres, Drexel University A collection of information on Archimedes' life and achievements, complete with historical quotes, illustrations, and animations. The site covers Archimedes' inventions and accomplishments: Archimedes' Claw, Burning Mirrors, the Golden Crown, the Archimedes ...more>> Archimedes Palimpsest - The Walters Art Gallery An introduction to the people, places, times, and historical significance of the Archimedes Palimpsest, a compendium of mathematical treatises by Archimedes of Syracuse. The manuscript itself includes the only copy of the treatise Method of Mechanical ...more>>
Course Description Prerequisite: MATH 099 or equivalent. Prepares students for an understanding of arithmetic, algebra, geometry, data analysis, and quantitative reasoning. Students will show competence in these skill areas with additional support using the computer software including the resources available on the internet. Three class hours weekly.
This training is the first of a two-part program. The course will help anyone within the extrusion industry looking to expand or fine-tune his or her math skills. Topics start with the basics of using whole Numbers, negative numbers, and decimals; then continues on to refining the use of a calculator. Addition, subtraction, multiplication and division are reviewed before learning the benefits of rounding numbers and using significant figures. Finally, formulas, equations, and order of operations is defined
A large collection of multimedia lessons and instructional resources devoted to algebra education, covering the basics of algebra, the foil method, exponents of numbers, variables and polynomials, study tips, buying a calculator for school and much more..
The Algebra 1: The Complete Course DVD Series will help students build confidence in their ability to understand and solve algebraic problems. In this episode, concrete examples and practical applications show how the mastery of fundamental algebraic concepts is the key to success in today's technologically advanced world. Students will also learn the development of algebraic symbolism as well as the geometric and numeric currents. Grades 5-9. 30 minutes on DVD.
College Mathematics for offers a "six-step approach" to problem solving, numerous tips, and clear, concise explanations that explore the concepts behind mathematical processes. Simplified language appeals to a variety of learning styles, and promotes active, independent, and lifelong learning -- while strengthening critical thinking and writing skills. This book addresses curriculum and pedagogy standards that are initiatives of the American Mathematical Association of two-year Colleges (AMATYC), the National Council of Teachers of Mathematics (NCTM), and the Mathematics Association of America (MAA). It focuses on number, symbol, spatial and geometric, function, and probability and statistical sense. Other features include career applications, and mathematics in the workplace articles that demonstrate the relationship of chapter concepts to highly sought after job skills -- such as computational, research, and critical thinking/decision-making.
Find a Glen Ellyn StatisticsIn our data-driven age, applications of linear algebra are ubiquitous. Linear algebra applies math to such matrices as any Excel spreadsheet, and using the power of matrices, you can calculate millions of values or solve billions of equations simultaneously. I have used linear algebra in such a...
TI-84 Graphing Calculator Basics Related Topics There's no fraction key on the TI-84 Plus calculator, per se, but many fraction tools are built into this calculator. For starters, isn't a fraction just division in disguise? So, pressing / between two[more…] The functions housed in the Angle menu on your TI-84 Plus calculator enable you to convert between degrees and radians or convert between rectangular and polar coordinates. To convert degrees to radians[more…] The functions available in the TI-84 Plus calculator's Angle menu enable you to convert between decimal degrees and DMS (degrees, minutes, and seconds). You can also override the angle setting in the Mode[more…] The often overlooked Test menu on the TI-84 Plus enables you to use your calculator in creative ways to solve problems. Do you want to do better on your next standardized test? Some of these tips just[more…]
Soal Soal Un Matematika Smp Kelas 9
In short, the aim of this beautiful monograph on analytic number theory may best be described by the beginning of the preface of this book. " 'In order to become proficient in mathematics, or in any subject,' writes André Weil, 'the student must realize that most topics involve only a small number of basic ideas.' After learning these basic concepts and theorems, the student should 'drill in routine exercises, by which the necessary reflexes in handling such concepts may be acquired. ...There can be no real understanding of the basic concepts of a mathematical theory without an ability to use them intelligently and apply them to specific problems.' Weil's insightful observation becomes especially important at the graduate and research level. ...Our goal is to acquaint the student with the methods of analytic number theory as rapidly as possible through examples and exercises." Of course, it is not possible to describe adequately the wealth of material covered in this book. The reviewer thinks that every adept of number theory ought to work by himself through the problems of this monograph – certainly he will gain large benefits.
It can be used in sequence with FUNDAMENTAL METHODS, or independently, at the advanced undergraduate or a beginning graduate level. It is written at the same analytical level, with the same care, as the other Chiang text.
Linear Programming Basics HOW MAY WE HELP YOU? Optimizing LP problems A primer on the basics of linear programming Linear Programming Basics Linear programming (LP) is a powerful framework for describing and solving optimization problems. It allows you to specify a set of decision variables, and a linear objective and a set of linear constraints on these variables. To give a simple and widely used example, consider the problem of minimizing the cost of a selection of foods that meets all the recommended daily nutrient guidelines. The LP model would have a set of decision variables that capture the amount of each food to buy, a linear objective that minimizes the total cost of purchasing the chosen foods, and a linear constraint for each nutrient, requiring that the chosen foods together contain a sufficient quantity of that nutrient. Using linear algebra notation, a linear program can be described as follows: Objective: minimize cTx Constraints: A x = b (linear constraints) l ≤ x ≤ u (bound constraints) When described in this form, the vector x represents the decision variables, the vector c captures the linear objective function, the matrix equation Ax = b specifies the linear constraints on x, and the vectors l and u give the lower and upper bounds on x. The set of applications of linear programming is literally too long to list. It includes everything from production scheduling to web advertising optimization to clothing manufacturing. LP touches nearly every commercial industry in some way. LP Algorithms The first algorithm for solving linear programming problems was the simplex method, proposed by George Dantzig in 1947. Remarkably, this 65 year old algorithm remains one of the most efficient and most reliable methods for solving such problems today. The primary alternative to the simplex method is the barrier or interior-point method. This approach has a long history, but its recent popularity is due to Karmarkar's 1984 polynomial-time complexity proof. Interior-point methods have benefited significantly from recent advances in computer architecture, including the introduction of multi-core processors and SIMD instructions sets, and are generally regarded as being faster than simplex for solving LP problems from scratch. However, the sheer variety of different LP models, and the many different ways in which LP is used, mean that neither algorithm dominates the other in practice. Both are important in computational linear programming. Computational Linear Programming Given the age of these algorithms (65 years for the simplex method, and 28 years for interior point methods), you might expect that the implementation issues associated with the methods would be well understood, and that different implementations would give similar results. Surprisingly, this is far from true. Computational benchmarks across a range of models show wide performance and robustness variations between different implementations. For example, the open-source simplex solvers CLP and GLPK are on average a factor of 2.5 and 58 times slower than the Gurobi simplex solver, respectively. What explains such wide disparities between implementations of such old and well-established methods? The differences primarily come down to three factors. Sparse Linear Algebra The first factor is sparse linear algebra. The constraint matrices that arise in linear programming are typically extremely sparse. Sparse matrices contain very few non-zero entries. It is not unusual to find constraint matrices containing only 3 or 4 non-zero values per columns of A. The steps of both the simplex and interior-point algorithms involve a number of computations with extremely sparse matrices and extremely sparse vectors. Sparse matrices must be factored, systems of sparse linear equations must be solved using the resulting factor matrices, the factor matrices must be modified, etc. It takes years of experience in sparse numerical linear algebra and linear programming to understand the computational issues associated with building efficient sparse matrix algorithms for LP. Dense Matrix Sparse Matrix Numerical Errors The second factor is careful handling of numerical errors. Whenever you solve systems of linear equations in finite-precision arithmetic, you will always get slight numerical errors in the results. A crucial part of building an efficient LP algorithm is to design effective strategies for managing such errors — failing to do so can mean the difference between a model solving in a fraction of a second and not solving at all. Heuristic Strategies The third factor is developing effective heuristic strategies for making the variety of choices that arise in the course of the solution process. To give one example, the simplex algorithm must repeatedly pick one variable from among many to enter the basis. The strategy used can have a profound effect on the runtime of the algorithm. Differences between the different strategies are often quite subtle, and in many cases they are simply based on empirical observations about which schemes are most effective in practice. Again, choosing effective strategies takes years of experience. Benchmark Results Public benchmarks of different commercial LP solvers demonstrate the effectiveness of the approaches that Gurobi has taken for each of these issues. For both the simplex and barrier methods, the Gurobi solvers provide both higher performance and better numerical robustness than competing solvers. This difference is of course relevant when you are solving LP models, but more importantly, it also provides a more solid foundation on which to build the many algorithms that rely on LP as a subroutine. One very important example is the branch-and-bound algorithm that is used for solving Mixed Integer Programming (MIP) models. References If you would like more information on these methods, we refer you to the following books:
Add song and dance to your mathematics lessons with this exercise, in which students discover the various covert mathematical relations hidden in the lyrics to the song ?The Twelve Days of Christmas.? In addition to ... This website applies virtual reality to calculus in order to illustrate mathematical concepts more clearly to students. While many courses utilize computers via computer algebra systems and graphing tools to... This handy program will solve any function equation entered into its screen, and provide tips for solving a similar problem on paper. After providing the answer, the program then provides further information on the key... Rice University provides this website, which is an introduction to key concepts in Calculus, from a high school level to advanced college math. Students can learn about major Calculus subjects and teachers can use the... Go with Alice to a wonderland of math! This website utilizes Lewis Carroll?s bright universe and most-recognizable character in order to teach mathematical concepts. Many students may feel as though they have s...
No, seriously, I also like Vellemans book more. It's true that it has more emphasis on set theory, but this is in fact a very good thing. Many people find mathematics difficult because they don't understand set theory well, so the faster you'll be introduced to set theory and the likes, the better for you. Also, I found "100% mathematical proof" too chaotic. And a lot of the book is concerned with stuff you'll never need again...
Customers Who Bought This Also Bought... Connect the process of problem solving with the content of the Common Core. The first of a series, this book will help mathematics educators illuminate a crucial link between problem solving and the Common Core State Standards. AntThis book focuses on essential knowledge for teachers about proof and the process of proving. It is organized around five big ideas, supported by multiple smaller, interconnected ideas—essential understandings. The study of geometry—whether taught as a stand-alone or as a series of topics integrated within other courses—develops core ideas, concepts, and habits of mind that students will need as users of mathematics and as lifelong learners. A valuable resource to any mathematics teacher, this rich collection of mathematical tasks will enliven students' engagement in mathematical thinking and reasoning and help them succeed in the classroom. Award-winning author Page Keeley and mathematics expert Cheryl Rose Tobey apply the successful format of Keeley's best-selling Science Formative Assessment to mathematics. They provide 75 formative assessment strategies and show teachers how to use them to inform instructional planning and better meet the needs of all students. Research shows that formative assessment has the power to significantly improve learning, and its many benefits include: 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.
Colma, CA AlgebraAlgebra 2 is the time in the development of our curriculum that takes the basic skills and puts them into context. More types of functions are introduced and applied during this year. It is important at this time to connect all topics to an overarching understanding of the meaning of each in depth
North Houston SAT MathThe course of study is designed to extend the development of numbers to include the study of the complex numbers as a mathematical system, to expand the concept of functions to include quadratic, exponential and logarithmic functions, to analyze the concepts, and to develop additional problem-sol
SolidWor­ks is a powerfu­l 3D solid mode­ler used in com­puter-aided des­ign (CAD). Popu­lar for its dra­g-and-drop, poi­nt-and-click, a­nd cut-and-past­e functions, So­lidWorks is com­plex, and the d­etail found in ­these two compr­ehensive guides­ gives new user­s everything th­ey need to beco­me productive w­ith the program­. This e-book s­et features in-­depth instructi­on and complete­ tutorials on p­arts (making pa­rt models and... Finally,­ this brand new­ book exposes t­he secrets of c­omputers for ev­eryone to see. ­Its humorous ti­tle begins with­ the punch line­ of a classic j­oke about someo­ne who is baffl­ed by technolog­y. It was writt­en by a 40-year­ computer veter­an who wants to­ take the myste­ry out of compu­ters and allow ­everyone to gai­n a true unders­tanding of exac­tly what comput­ers are, and al­so what they ar­e not. Years of­ writing, diagr­amming, pilotin­g and editing... This non-­traditional int­roduction to th­e mathematics o­f scientific co­mputation descr­ibes the princi­ples behind the­ major methods,­ from statistic­s, applied math­ematics, scient­ific visualizat­ion, and elsewh­ere, in a way t­hat is accessib­le to a large p­art of the scie­ntific communit­y. Introductory­ material inclu­des computation­al basics, a re­view of coordin­ate systems, an­ introduction t­o facets (plane­s and triangle ­meshes) and an ­introduction to­ computer graph­ics. The scient­ific computing...
Peyton Statistics education has provided me with an extensive knowledge of mathematics. Differential equations are commonly used throughout all areas of physics. For instance, one cannot solve the Schrodinger equation in quantum mechanics without knowledge of differential equations.
Basic Mathematics Description This work-text gives a strong review of all arithmetic concepts and skills with an emphasis upon mastering and applying percentages. Other branches of mathematics introduced are algebra, plane and solid geometry, statistics, and trigonometry. Two units on basic algebra give the junior-high student the foundation he needs to enjoy and succeed in high school algebra. Practical topics such as adjusting recipes, banking, and budgeting are taught. Helpful features include problem solving strategies, charts, glossary, and index. Designed to be used in grade 7. Consumable, 416
Differential equations This unit extends the ideas introduced in the unit on first-order differential... This unit extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equations which has a variety of applications. The unit assumes that you have previously had a basic grounding in calculus, know something about first-order differential equations and some familiarity with complex numbers. After studying this unit you should: be able to solve homogeneous second-order equations; know a general method for constructing solutions to inhomogeneous linear constant-coefficient second-order equations; know about initial and boundary conditions to obtain particular values of constants in the general solution of second-order differential equations. Contents Differential equations Introduction This unit extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equation which has a variety of applications. The unit assumes that you have previously had a basic grounding in calculus, know something about first-order differential equations and have some familiarity with complex numbers. This study unit is an adapted extract from the Open University course MST209 Mathematical methods and models, which is no longer taught by the University. If you want to study formally with us, you may wish to explore other courses we offer in this subject area [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .
we dont use log books during math exams anyway; those are for physics mainly. as far as trigonometry is concerned we're not required to find out the values of any angle other than 0, 30, 45, 60, 90, their sums/differences and multiples. the questions have more to do with proofs with variable angles though. Also, people get good at copying stuff when you give them log books- they used to cover the pages we were not allowed to look at and tape them down or something. Or just give us a photocopy of the relevant information.not that cbse is much better. the entire indian education system is in desperate need of an overhaul. and it might be coming, what with kapil sibal making board exams for 10th optional and all and the constant changes in curriculum. baby steps.
Geometry Seeing, Doing, Understanding 9780716743613 ISBN: 0716743612 Edition: 3 Pub Date: 2003 Publisher: W H Freeman & Co Summary: Jacobs innovative discussions, anecdotes, examples, and exercises to capture and hold students' interest. Although predominantly proof-based, more discovery based and informal material has been added to the text to help develop geometric intuition. Jacobs, Harold R. is the author of Geometry Seeing, Doing, Understanding, published 2003 under ISBN 9780716743613 and 0716743612. One hundred sixty Geometry Seein...g, Doing, Understanding textbooks are available for sale on ValoreBooks.com, nineteen used from the cheapest price of $54.57, or buy new starting at $166.58.[read more] Ships From:Tempe, AZShipping:StandardComments:WE HAVE NUMEROUS COPIES -HARDCOVER, Mild shelf wear to cover, edges, and corners, a ding to the ... [more]WE HAVE NUMEROUS COPIES -HARDCOVER, Mild shelf wear to cover, edges, and corners, a ding to the top and bottom of spine, otherwise book is NEW. [less]
HIGH SCHOOL MATH LEARNING DIFFERENCES BUNDLE HIGH... Overview - HIGH with all the concepts and skills they need to succeed in a first-year algebra course. Algebra 2 allows learners to apply intermediate-level algebra concepts to everyday problems. Geometry offers short, lively lessons students can grasp easily and explores geometric solids, triangles, the Pythagorean Theorem, quadratic equations, length, area, and volume. ÿ Includes:
ALEX Lesson Plans Title: Systems of Equations: What Method Do You Prefer? Description: TheStandard(s): [MA2013] (8) 10: Analyze and solve pairs of simultaneous linear equations. [8-EE82 ALC (9-12) 2: Solve application-based problems by developing and solving systems of linear equations and inequalities. (Alabama) (8 - 12) Title: Systems of Equations: What Method Do You Prefer? Description: The Thinkfinity Lesson Plans Title: Least Squares Regression Description: In Standard(s): the Least Squares RegressionTitle: Whelk-Come to Mathematics Description: In Standard(s): AM1 (9-12) 12: Calculate the limit of a sequence, of a function, and of an infinite series. (Alabama) Subject: Mathematics,Science Title: Whelk-Come to Mathematics Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Northwestern Crows Description: In PRE (9-12) 50: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. [S-MD1] Subject: Mathematics,Science Title: Northwestern Crows Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Road Trip! Description: In this Illuminations lesson, students investigate the famous Traveling Salesman Problem by considering the shortest route between five northeastern cities. Three different algorithms for finding the shortest route are explored, and students are encouraged to look for others2 (9-12) 46: (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [S-CP9 Road Trip! Description: In this Illuminations lesson, students investigate the famous Traveling Salesman Problem by considering the shortest route between five northeastern cities. Three different algorithms for finding the shortest route are explored, and students are encouraged to look for others Make a Conjecture Description: In this lesson, one of a multi-part unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart. Standard(s): 39: Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [F-LE3 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [MA2013] ALC (9-12) 5: Determine approximate rates of change of nonlinear relationships from graphical and numerical data. (Alabama) 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1] hand in simple cases and using technology for more complicated cases.* [F-IF7] [MA2013] AL2 (9-12) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6] [MA2013] AL2 (9-12) 38: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7] [MA2013] ALT (9-12) 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1] [MA2013] ALT [MA2013] ALT (9-12) 37: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. [S-ID4 ALT (9-12) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6] [MA2013] ALT (9-12) 42: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7] Health,Mathematics Title: Make a ConjectureThinkfinity Learning Activities Title: Isosceles Triangle Investigation Description: This student interactive, from an Illuminations lesson, allows students to investigate the relationship between the area of the triangle and the length of its base. Standard(s): [MA2013] GEO (9-12) 6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. [G-CO6] [MA2013] GEO (9-12) 10: Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180o, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, and the medians of a triangle meet at a point. [G-CO10] [MA2013] GEO (9-12) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [G-CO12] [MA2013] GEO (9-12) 17: Prove theorems about triangles. Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity. [G-SRT4 Isosceles Triangle Investigation Description: This student interactive, from an Illuminations lesson, allows students to investigate the relationship between the area of the triangle and the length of its base. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
... More About This Book text then serves as a resource for further investigation, explanation, and clarification. Unlike most texts, which present exercises very similar to examples, Bassarear demonstrates how real-life problems are generally complex and often filled with ambiguity and that non-routine and multistep problems are the norm. Students learn that there may be more than one way to find an answer and even more than one answer. A special 16-page insert includes actual pages from Houghton Mifflin's best-selling K-6 basal series, demonstrating material currently used in the classroom. Related Subjects Meet the Author Tom Bassarear is a professor at Keene State College in New Hampshire. He received his BA from Claremont-McKenna College, his MA from Claremont Graduate School, and was awarded an Ed.D degree from the University of Massachusetts. Tom's complementary degrees in mathematics and educational psychology have strongly influenced his convictions about education—specifically, mathematics education. Before teaching at the college level, he taught both middle school and high school mathematics. Since arriving at Keene State College, Tom has spent many hours in elementary classrooms observing teachers and working with them in school and workshop settings, plus, he has taught 4th grade math every day for a semester at a local elementary school
The Application of Algebra Algebra is always a subject questioned by students, but here are my thoughts on it after being clarified by my teacher. Submitted:Apr 26, 2012 Reads: 437 Comments: 2 Likes: 2 People often question the subject Algebra. They often ask why it's essential to learn it, and at one point, I did as well. But during a class discussion in Algebra, my teacher enlightened us on how it can be applied in real life. Now, I wish to share his knowledge on this subject and give an answer to those questions. We don't apply algebra directly. Algebra is everywhere.. It's all in the way you apply what you've learned in real life situations. We would probably forget that "if x=3 then x+2=5 and x-2=1," but your way of thinking to analyze and solve the problem stays with you (hopefully). If you ask me how algebra could apply in instances such as law, I can answer that. And answer I will.. Anyway, when in law, you'd need to have an analytic mind to piece together the parts to solve a case. In medicine, you can apply algebra as well. When in cases that you have to save a person's life, critical thinking is needed. In daily things, algebra is applied as well. Even at school, especially when we're asked to hold a debate about things on occasion. You may not notice it, but math is everywhere, just not directly applied as I've said over and over. Though it would be really weird if algebra was directly applied. I imagine daily conversations to be something like: ♣: Hey, how much did you buy that car for? ♠: I bought it for x, where x is equal to y^2 + z(y-z). ♣: That's cool. Have you seen my house? It's ab - cd + c^6 square meters. ♠: Wow, that's big.. Anyway, I'll see you later. My sister's coming home today, and I have to get ready in about qx minutes and 4y seconds. ♣: Alright. See ya! Anyway, my point is, algebra is everywhere, but we don't see how it's really applied. That's probably why people get tired of it too easily. The things you pick up along the way (patience, analytic skills, critical thinking, etc.) are the things that we really use. Also, I'm sorry if this isn't a formal essay. I just didn't know what category this would fit into, lol.
Unit 5 Grade 9 Applied Linear Relations: Constant Rate of Change, Initial Condition, Direct and Partial Variation Lesson Outline BIG PICTURE Students will: • connect physical movement to resulting distance/time graphs; • describe linearly related data graphically, in words and algebraically; • describe linearly related data using initial condition and constant rate of change. Day Lesson Title Math Learning Goals Expectations 1 Match Me! • Use Calculator Based Ranger (CBR™) and graphing calculators LR4.02, LR4.05 to analyse motion graphs in terms of starting position, direction of CGE 5a, 7i motion, and rate of change (speed). 2 Story Graphs • Write stories related to piecewise graphs; demonstrate the LR4.02, LR4.05 connection between the position, direction, speed, and shape of CGE 2d the graph. • Investigate a variety of graphs in contexts with respect to rate of change, e.g., filling containers, raising a flag, temperature. 3 Ramps, Roofs, and • Examine rate of change in a variety of contexts. NA1.06, LR3.01 Roads • Calculate rate of change using rise and connect to the unit rate of run CGE 2c, 3c, 5a Presentation file: change. Rate of Change • Convert fractions ↔ decimals ↔ percents. 4 Models of Movement • Use rate of change to calculate speed in distance-time graphs. NA1.06, LR3.01, • Write stories with speed calculations. LR4.02 CGE 3c, 5g 5 The Bicycle Trip • Assess students' ability to connect representations of linear LR4.02, LR4.05 relations and solve problems using a quiz. CGE 5a, 5e • Write a story to make literacy connections. 6 Tables of Values, • Make tables of values, equations, and graphs from descriptions of LR3.03, LR3.04 Equations, Graphs situations. CGE 5b • Compare the properties of direct and partial variation in applications and identify the initial value. 7 Walk the Line • Use the graphing calculator and CBR™ to collect linear motion LR3.03, LR3.04, data in order to determine the equation using the starting distance LR3.05 and walking rate. CGE 5a, 7i • Use technology to verify the equation. • Model linear relations with equations using the initial value and rate of change. 8 Modelling Linear • Write equations representing linear relations from descriptions, LR3.03, LR3.04, Relations with tables of values, and graphs. LR3.05, LR4.03 Equations • Review concepts of continuous and discrete data. CGE 5a, 5b 9 Graphing Linear • Given an equation in context, graph the relationship. LR2.01, LR3.03, Relations in Context • Graph linear relations using initial value and rate of change. LR3.04, LR3.05, LR4.03 • Identify initial value and rate of change from equations representing linear relations. CGE 3c, 5a, 5e 10 Instructional Jazz 11 Assessment TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 1 Unit 5: Day 1: Match Me! Grade 9 Applied Math Learning Goals Materials • Use Calculator Based Ranger (CBR™) and graphing calculators to analyse • viewscreen • graphing calculators motion graphs in terms of starting position, direction of motion, and rate of • BLM 5.1.1, 5.1.2 change (speed). 75 min Assessment Opportunities Minds On ... Whole Class Demonstration Using the CBR™ (motion detector), graphing calculator, and viewscreen, with a student volunteer demonstrate connections between the shape and position of the graph and the direction, speed (including stopped), and starting position of their walk. Before each walk, students predict what they think the graph will look like and draw the actual graph after the walk (BLM 5.1.1). Action! Pairs Peer Coaching Students investigate the connection between the shape and position of the graph and the direction, speed, and starting position by using the "DIST MATCH" application of the Ranger program (BLM 5.1.2). One student reads the graph and gives walking instructions to a partner who cannot see the graph. They reverse roles. Students match as many graphs as possible in the allotted time. Consolidate Whole Class Summarizing Debrief Discuss the key understandings involving the starting position relative to the CBR™, direction of walk, speed of the walk. Whole Class Exploration Learning Skill (Teamwork/Initiative)/Observation/Rating Scale: Assess students' ability to work collaboratively and to take initiative. Check that students understand the difference between the path walked and shape of the graph by asking students to predict which alphabet letters can be walked, e.g., a student could make the letter "w" but the letter "b" is not possible. Ask students to explain why. Discuss which letters of the alphabet can be "walked" using the CBR™. Students use a CBR™ to verify/disprove predictions about the shape of distance time graphs. Home Activity or Further Classroom Consolidation Application Draw a graph to match the following descriptions: Concept Practice • Stand 4 metres from the CBR™ and walk at a constant rate towards the CBR™ for 5 seconds. Stand still for 3 seconds then run back to the starting position. • Begin 0.5 metres from the CBR™, run away for 3 seconds at a constant rate, then gradually slow down until you come to a complete stop. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 2 5.1.1: Walk This Way 1. Student walks away from CBR™ (slowly). 2. Student walks towards CBR™ (slowly). 3. Student walks very quickly towards CBR™. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 3 5.1.1: Walk This Way (continued) 4. Student increases speed while walking towards the CBR™. 5. Student decreases speed while walking away from the CBR™. 6. Student walks away from ranger, at 2 metres stops for 5 seconds, then returns at the same pace. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 4 5.1.2: CBR™: DIST MATCH Setup Instructions You will need: • 1 CBR™ with linking cable • 1 graphing calculator Insert one end of linking cable FIRMLY into CBR™ and the other end FIRMLY into graphing calculator. Setting up the DIST MATCH Application Press the APPS key Select 2: CBL/CBR Press ENTER Select 3: RANGER Press ENTER You are at the MAIN MENU Select 3: APPLICATIONS Select 1: METERS Select 1: DIST MATCH Follow the directions on the screen. If you are not happy with your graph, Press ENTER Select 1: SAME MATCH to try again If you would like to try a different graph to match, Press ENTER Select 2: NEW MATCH Select 5: Quit to quit TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 5 5.1.2: CBR™: DIST MATCH Setup Instructions (continued) Part One: Walk the height as the rise and the base as the run. Show the lengths of each. Calculate the rate of change of your walk using the formula: rate of change = rise run Complete 6 5.1.2: CBR™: DIST MATCH Setup Instructions (continued) Describe your walk. Use your starting position and rate of change to write a walking description statement: I started ____metres from the CBR™ and walked away from it at a speed of ____metres per second. After 10 seconds, I was ____ __ from the motion detector. At this rate, estimate how far you would have walked after 30 seconds. Construct an equation to model your walk. Read this walking statement: A student started 0.52 metres from the CBR™ and walked away at a speed of 0.19 metres/second. The equation D = 0.52 + 0.19t models the student's distance, D, from the CBR™ after t seconds _____ metres/sec. The equation __________________________ models my position from the CBR™. The graphing calculator equation is ____________________. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 7 5.1.2: CBR™: DIST MATCH Setup Instructions (continued) Verify your equation of your walk using the graphing calculator. Turn off the STATPLOT Type your equation into the Y = editor Graph your equation ( 8 5.1.2: CBR™: DIST MATCH Setup Instructions (continued) Use the equation to solve problems. The equation D = 0.52 + 0.19t models the student's position from the CBR™. We can calculate the student's distance from the CBR™ after 30 seconds: D = .052Calculate your position from the CBR™ after 30 seconds: a) The equation ____________________ models your position from the CBR™ (from previous page). b) Calculate your distance from the CBR™ after 30 seconds.________________________________________________________________ How does this answer compare with your estimate at the beginning of the activity? ________________________________________________________________ TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 9 5.1.2: CBR™: DIST MATCH Setup Instructions (continued) Part Two: Walk AnotherHint: The rise will be a negative number! Draw a large right-angled triangle under the graph and label it with the rise and run values. Calculate the rate of change using the formula: rate of change = rise . run Complete the following: The rate of change of my walk is ________________. The speed of my walk is ________________ m/s away from the CBR™. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 10 5.1.2: CBR™: DIST MATCH Setup Instructions (continued) Describe your walk. Use your initial position and rate of change to write a walking description statement: I started ______metres from the CBR™ and walked towards it at a speed of _____metres per second. After 10 seconds, I was ______from of 0.32 metres/second. The equation D = 4 – 0.32t models the student's position from the CBR™. To graph it on the graphing calculator use: Y = 4 – 0.32x. Write a walking statement and equation for your walk: _______________ started ____ metres from the CBR™ and walked towards it at a speed of _____ metres per second. The equation ___________________________ models my position. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 11 Unit 5: Day 2: Story Graphs Grade 9 Applied Math Learning Goals Materials • Write stories related to piecewise graphs; demonstrate the connection between • overhead projector • BLM 5.2.1, 5.2.2, the position, direction, speed, and shape of the graph. • Investigate a variety of graphs in contexts with respect to rate of change, e.g., 5.2.3, 5.2.4 filling containers, raising a flag, temperature. 75 min Assessment Opportunities Minds On ... Whole Class Discussion Explain the activity on BLM 5.2.1. Answer any questions. Use BLM 5.2.2 to discuss what their stories must include. Stress the difference between constant rate of change and variable rate of change. Action! Pairs Note Making/Presentation Using one of the graphs from BLM 5.2.3, students work in pairs to write a An alternative is to story and orally present it to the class. have students copy the graph onto chart Encourage students to think beyond the distance-time graphs done on the paper and write their CBR™ and think about raising a flag, filling containers, etc. Show some story next to the examples. graph. Note: Most students will find it easier to think of time as the independent Students may wish variable rather than some other measure. to act out their story as well as give their Curriculum Expectation/Observation/Checklist: Use BLM 5.2.2 as a tool oral presentation. to assess communication. Consolidate Whole Class Discussion Debrief Review the graphs with students and clarify any information that students A common student may have misinterpreted (BLM 5.2.3). interpretation of these graphs Curriculum Expectations/Observation/Checklist: Assess student ability to involves going up and down hills. use proper conventions for graphing. Explain that a hill is not necessary to explain the graph. Word Wall increasing rapidly increasing slowly decreasing rapidly decreasing slowly constant rate of change varying rate of change See Think Literacy, Mathematics, pages 62–68 for more information on reading graphs. Home Activity or Further Classroom Consolidation Complete worksheet 5.2.4, Interpreting Graphs. NCTM has many Concept Practice activities that relate Application to rates of change and graphs at TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 12 5.2.1: Graphical Stories Below the following graphs are three stories about walking from your locker to your class. Two of the stories correspond to the graphs. Match the graphs and the stories. Write stories for the other two graphs. Draw a graph that matches the third story. 1. I started to walk to class, but I realized I had forgotten my notebook, so I went back to my locker and then I went quickly at a constant rate to class. 2. I was rushing to get to class when I realized I wasn't really late, so I slowed down a bit. 3. I started walking at a steady, slow, constant rate to my class, and then, realizing I was late, I ran the rest of the way at a steady, faster rate. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 13 5.2.2: Writing Stories Related to a Graph Names: As you create your story: Focus on the rate of change of each section of the graph and determine whether the rate of change is constant, varying from fast to slower or slow to faster or zero. Criteria Yes Does your story include: • the description of an action? (e.g., distance travelled by bicycle, change of height of water in a container, the change of height of a flag on a pole) • the starting position of the action? • the ending position of the action? • the total time taken for the action? • the direction or change for each section of the action? • the time(s) of any changes in direction or changes in the action? • the amount of change and time taken for each section of the action? • an interesting story that ties all sections of the graph together? Scale your graph, and label each axis! TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 14 5.2.3: Oral Presentation Story Graphs TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 15 5.2.4: Interpretations of Graphs Sunflower Seed Graphs Ian and his friends were sitting on a deck and eating sunflower seeds. Each person had a bowl with the same amount of seeds. The graphs below all show the amount of sunflower seeds remaining in the person's bowl over a period of time. Write sentences that describe what may have happened for each person. a) b) c) d) Multiple Choice Indicate which graph matches the statement. Give reasons for your answer. 1. A bicycle valve's distance from the ground as a boy rides at a constant speed. a) b) c) d) 2. A child swings on a swing, as a parent watches from the front of the swing. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 16 Unit 5: Day 3: Ramps, Roofs, and Roads Grade 9 Applied Math Learning Goals Materials • Examine rate of change in a variety of contexts. • computer/data rise projector • Calculate rate of change using run and connect to the unit rate of change. • BLM 5.3.1 • Convert fractions ↔ decimals ↔ percents. 75 min Assessment Opportunities Minds On ... Whole Class Demonstration Rate of Change.ppt Review converting between fractions, decimals, and percents. Show the Rate of Change electronic presentation, summarizing the main If a projection unit is ideas. Students make notes. not available, the pages in the With the students, complete the first example, Ramps, and the first two table electronic rows on Roads (BLM 5.3.1). presentation can be made into transparencies. Action! Pairs Problem Solving Students complete each page of BLM 5.3.1 in pairs and share answers in groups of four. Word Wall pitch Learning Skill (Work habits)/Observation/Anecdotal: Observe students' grade work habits and make anecdotal comments. ramp incline rate of change = rise run Consolidate Whole Class Sharing Debrief Select students to share their answers to BLM 5.3.1. Draw out the mathematics, and clear up any misconceptions. Home Activity or Further Classroom Consolidation Concept Practice • Complete rate of change practice questions. Provide students Journal • In your journal, give an example of where rate of change occurs in your with practice home. questions. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 17 5.3.1: Ramps, Roofs, and Roads Ramps Rise Run Types of inclines and recommendations by Rate of (Vertical (Horizontal rehabilitation specialists Change Distance) Distance) The recommended incline for wheelchair uses is 1:12. For exterior ramps in climates where ice and snow are common, the incline should be more gradual, at 1:20. For unusually strong wheelchair users or for motorized chairs, the ramp can have an incline of 1:10. The steepest ramp should not have an incline exceeding 1:8. Building Ramps Which of four ramps could be built for each of the clients below? 1. 2. 3. 4. Choice of Ramp Clients and Reason Client A lives in a split-level town house. He owns a very powerful motorized chair. He wishes to build a ramp that leads from his sunken living room to his kitchen on the next level. Client B requires a ramp that leads from her back deck to a patio. She is of average strength and operates a manual wheelchair. Client C lives in Sudbury where ice and snow are a factor. She is healthy, but not particularly strong. Her house is a single level bungalow but the front door is above ground level. Client D will not get approval because the design of his ramp is too dangerous. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 18 5.3.1: Ramps, Roofs, and Roads (continued) Roofs Calculate the rate of change (pitch) of each roof. Answer the questions that follow the diagrams. 1. If all four roofs were placed on the same-sized foundation, which roof would be the most expensive to build? Hint: Steeper roofs require more building materials. 2. Why do you think apartment buildings have flat roofs? What is the rate of change of a flat roof? 3. In the winter snow builds up on the roof. Sometimes, if the snow builds up too high, the roof becomes damaged. Which roof would be the best for areas that have a large amount of snowfall? Why? TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 19 5.3.1: Ramps, Roofs, and Roads (continued) Roads The inclination of a road is called "percent grade." Severe grades (greater than 6%) are difficult to drive on for extended amounts of time. The normal grade of a road is between 0% and 2%. Warning signs are posted in all areas where the grades are severe. Rate of change Percent grade Fraction Rise Run (decimal form) A 1% B 1 50 C 0.035 D 4% E 525 10 000 3 F 50 G 0.1 H 1 2 I 0.75 J 1 3 2 K 5 L 8.25% Which of the roads, A–L, would require a warning sign? Some of the values in the table are fictional. There are no roads that have grades that are that severe. Which roads, A–L, could not exist? Explain your reasoning. Describe a road with a 0% grade. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 20 Rate of Change (Presentation software file) Rate of Change.ppt 1 2 3 4 5 6 7 8 9 10 11 12 TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 21 Unit 5: Day 4: Models of Movement Grade 9 Applied Math Learning Goals Materials • Use rate of change to calculate speed on distance-time graphs. • BLM 5.4.1, 5.4.2, • Write stories with speed calculations. 5.4.3 75 min Assessment Opportunities Minds On ... Whole Class Demonstration Demonstrate how to calculate rate of change on a distance-time graph using rate of change BLM 5.4.1 BC = 160 m/min First complete the scale to reinforce that each unit is not worth 1, as in the rate of change previous lesson. CD = 80 m/min rate of change For example, the first calculation would be DE = 0 m/min rate of change AB = 800 m = 160 m/min or 9.6 km/h rate of change 5 min EF = -280 m/min 800 m = 160 m 5m 1m 160 × 60 = 9600 m 1× 6 1h = 9.6 km/h Reinforce that they must look at the scale, rather than count the squares. Action! Individual/Pairs Problem Solving Students complete BLM 5.4.2 individually, then they compare their answers with their partner. Learning Skill (Works Independently)/Observation/Anecdotal: Observe students' ability to work independently. Consolidate Whole Class Connections Debrief Review students' answers. Make a connection between the rate of change of the graph and the speed and direction of motion. Guiding questions: • If the rate of change is negative, what does that tell us about the direction The negative rate of the person is moving? change represents • If the rate of change is zero, what does that tell us about the motion? changing direction • What does the point (20, 600) represent? back towards the starting point. • What does the graph look like if the rate of change is constant? • Ask a student to read their story about Micha's journey. With students, sketch a graph. Example: A flag is at half mast and is lowered at 85 cm/min. Together, describe the effect on the graph of: a) lowering the flag at 50 cm/min. b) starting the flag at the top of the flag pole and lowering at 85 cm/min. Home Activity or Further Classroom Consolidation Concept Practice Complete worksheet 5.4.3, The Blue Car and the Red Car. Create a practice sheet involving rate of change. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 22 5.4.1: A Runner's Run Chris runs each day as part of his daily exercise. The graph shows his distance from home as he runs his route. Calculate his rate of change (speed) for each segment of the graph. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 23 5.4.2: Models of Movement 700 Distance vs. Time At 11 o'clock, Micha's mother sends him to the corner store for milk and tells him to be D E back in 30 minutes. Examine the graph. 600 Distance from Home (m) F 500 400 C 300 200 B 100 A G 4 8 12 16 20 24 28 32 36 40 44 48 Time (min) 1. Why are some line segments on the graph steeper than others? 2. Calculate the rate of change (speed) of each of the line segments: Rate of change AB = Rate of change BC = Rate of change CD = Rate of change DE = Rate of change EF = Rate of change FG = TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 24 5.4.2: Models of Movement (continued) 3. Over what interval(s) of time is Micha travelling the fastest? the slowest? Compare steepness, not direction. 4. How long did it take Micha to reach the store? How do you know? 5. How long did Micha stay at the store? 6. How long did it take Micha to get home from the store? 7. How can you use the graph to tell which direction Micha is travelling? 8. Did Micha make it home in 30 minutes? How do you know? 9. Using the information the graph provides, write a story that describes Micha's trip to the store and back. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 25 5.4.3: The Blue Car and the Red Car Two friends are leaving a parking lot at the same time. They agree to meet later at the home of a friend who lives 400 km from the parking lot. One friend drives a blue car and the other a red car. The blue car is labelled B and the red car, R. Answer the questions below using the following graph. 400 Distance from parking lot (km) 300 B R 200 100 1 2 3 4 5 6 Time (h) 1. At what time do the cars pass each other? How far are they from the parking lot? 2. Which car stopped and for how long? How far from the parking lot did the car stop? 3. Suggest reasons for the car stopping. 4. Which car got to the final destination first? Explain. 5. The posted speed limit was 80 km/h. If you were a police officer, could you stop either of the cars for speeding? Explain. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 26 Unit 5: Day 5: The Bicycle Trip Grade 9 Applied Math Learning Goals Materials • Assess students' ability to connect representations of linear relations and solve • BLM 5.5.1 • BLM 5.5.2 (quiz) problems using a quiz. • Write a story to make literacy connections. 75 min Assessment Opportunities Minds On ... Whole Class Discussion Take up the students' work from the Home Activity, The Blue Car and the Red Car (BLM 5.4.3). Students mark their own work. Describe the assessment task (BLM 5.5.1 and 5.5.2) and answer any questions. Action! Individual Assessment For some students Curriculum Expectations/Quiz/Marking Scheme: Assess students' you may want to understanding of concepts. accept oral answers to some questions. Students complete the quiz independently (BLM 5.5.2). Circulate to give support. Use a coloured pen to identify what you Once students have handed in the quiz, they can start writing their bicycle trip helped the student story (BLM 5.5.1). with. Consolidate Pairs Check for Understanding Debrief Students will give feedback on how to improve their story by peer editing each other's work. Provide criteria for editing this graphical story. Suggested criteria: • Does the story include references to position, direction, speed, and time? • Does the story indicate when the rate of change is constant? • Does the story make sense? • Does the story include reasons to explain each segment of the graph? In providing feedback, peers suggest one criterion that was well done and one criterion for improvement. Home Activity or Further Classroom Consolidation Concept Practice Revise your bicycle trip story and make a final copy. Collect the stories to give feedback to students. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 27 5.5.1: The Bicycle Trip Mary and Carolyn set out for a bicycle trip. The distance-time graph shows their progress as they reach their destination. 70 60 Distance from home (km) 50 40 30 y ar olyn 20 M 10 Car 0 1 2 3 4 Time (h) Write a story that describes their trip. This could be a play-by-play sportscast. Details you should include: • times they were together/apart, stopped, or going faster/slower • possible events explaining the different sections of the graphs • references to time and distance, as well as your calculations of speeds in a narrative style • comparisons and contrasts Write a creative story as you use the information in the graph. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 28 5.5.2: Quiz Rate of Change and Story Graphs Name: ____________________________ 1. Devin went for a bicycle ride. The graph below shows his trip. Note: Distance is the number of kilometres from home. C D 15 E Distance from home (km) B 10 5 F A 1 2 3 4 5 Time (h) (4) a) Calculate his speed during the first hour (AB) and the second hour (BC). Show your work. (2) b) How does the speed between A and B compare with the speed between B and C? (2) c) Explain what segment CD tells you about Devin's motion. (2) d) Which section of the graph shows that Devin was changing speeds? Explain. (2) e) What information can you determine from segment EF? TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 29 5.5.2: Quiz (continued) (10) 2. Sketch the graph that is described in each story. Distance from sensor (m) a) Begin 5 metres from the sensor. Walk towards the sensor for 6 seconds at a steady rate of 1 metre in 2 seconds. Stop for 5 seconds. Run back to your starting position at a steady rate of 1 metre per second. Time (s) Stop. b) Begin at the sensor. Walk very slowly at a steady rate away from the sensor for 3 Distance from sensor (m) seconds. Increase your speed and walk at this new speed for 3 seconds. Stop for 3 seconds. Walk very slowly at a steady rate towards the sensor for 3 seconds. Time (s) Gradually increase your speed to a run and go back to the sensor. (3) 3. If a wheelchair ramp has a rate of change (incline) greater than 0.1, then it is considered unsafe. Determine whether or not each of the following ramps is safe. Show your work and explain your reasoning. 20 cm 15 cm 210 cm 120 cm TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 30 Unit 5: Day 6: Tables of Values, Equations, Graphs Grade 9 Applied Math Learning Goals Materials • Make tables of values, equations, and graphs from descriptions of situations. • BLM 5.6.1, 5.6.2 • overhead projector • Compare the properties of direct and partial variation in applications and identify the initial value. 75 min Assessment Opportunities Minds On ... Pairs Brainstorm Brainstorm scenarios in which there is an initial condition and a rate. For example: Taxis charge a base amount, plus a cost per kilometre. Brainstorm everyday situations where there is an initial condition and a rate. Examples that students may suggest: • ice cream cone plus extra scoops • pizza (pizza plus toppings) • rentals (item plus time or distance) • repairs and service (base amount plus hourly rate) • memberships (membership plus user fees) Work through the questions with the students (BLM 5.6.1). Action! Pairs Applying Knowledge Students work in pairs to complete BLM 5.6.2. Students should connect the verbal description, the calculations in the table, the graph, and the equation. Learning Skill//Observation/Checklist: Assess student ability to choose an appropriate scale for their graph. Consolidate Whole Class Connecting Debrief Using BLM 5.6.1, connect each of the models to one another. Description: Highlight the base fee and the fee per hour. Table of Values: Show how the numbers increase and connect to rate. Graph: Identify the initial value and calculate the rate of change. Equation: Connect the numbers to the description. Reinforce the fact that the rate is the one with the variable. Home Activity or Further Classroom Consolidation Concept Practice Highlight the connections you made on worksheet 5.6.2 during the class Refection discussion. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 31 5.6.1: Outfitters Jaraad wants to rent a canoe for a day trip. He gathers this information from two places and decides to make a table of values and graph each of these relationships. • Big Pine Outfitters charges a base fee of $40 and $10 per hour of use. • Hemlock Bluff Adventure Store does not charge a base fee, but charges $30 per hour to use the canoe. Jaraad's Working Sheet 1. a) What is the cost of each canoe if Jaraad cancels his reservation? b) Compare the rate of change of cost for Big Pine and for Hemlock Bluff to the cost per hour for each outfitter. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 32 5.6.1: Outfitters (continued) 2. Which graph illustrates a proportional relation? How do you know? This is called a direct variation. 3. Which graph has an initial value other than zero? This is called a partial variation. 4. Which outfitter company should Jaraad choose if he estimates he will canoe for 0.5 h?…1.5 h?…2.5 h? Time (h) Big Pine Cost ($) Hemlock Bluff Cost ($) 0.5 1.5 2.5 Explain how you determined your answers. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 33 5.6.1: Outfitters (continued) 5. Write an equation to model the cost for each outfitter. Let C represent the cost in dollars and h represent the time in hours. Big Pine C= Hemlock Bluff C= 6. If Big Pine Outfitters decided to change its base fee to $50 and charge $10 per hour, what effect would this have on the graph? a) Draw a sketch of the original cost and show the changes on the same sketch. b) Write an equation to model the new cost. 7. If Hemlock Bluff Adventure Store decided to change its hourly rate to $40, what effect would this have on the graph? a) Draw a sketch of the original cost and show the changes on the same sketch. b) Write an equation to model the new cost. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 34 5.6.1: Outfitters (continued) 8. For Big Pine Outfitters, how are the pattern in the table of values, the description, the graph, and the equation related? Description Big Pine Outfitters charges a base fee of $40 to deliver the canoe to the launch site and $10 per hour of use. Table of Values Graph Time (h) Cost ($) 0 40 1 50 2 60 3 70 4 80 Equation C = 40 + 10h 9. For Hemlock Bluff, how are the pattern in the table of values, the description, the graph, and the equation related? Description Hemlock Bluff charges $30 per hour. Table of Values Graph Time (h) Cost ($) 0 0 1 30 2 60 3 90 4 120 Equation C = 30h TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 35 5.6.2: Descriptions, Tables of Values, Equations, Graphs 1. A rental car costs $50 per day plus $0.20 for each kilometre it is driven. a) What is the dependent variable? b) Make a table of values for the rental fee up to 1000 km. c) Graph the relationship. Number of Cost ($) Kilometres Cost vs. Number of Kilometres 0 260 100 240 220 200 200 180 160 Cost ($) 140 120 100 80 60 40 20 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 Number of Kilometres d) Write an equation to model the relationship. C is the cost and n is the number of kilometres. ____ = _______________ e) Does this relation represent a partial or direct variation? Explain. f) Determine the rental fee for 45 km. Show your work. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 36 5.6.2: Descriptions, Tables of Values, Equations, Graphs (continued) 2. There is $500 in Holly's bank account. She takes out $50 from her account each month but doesn't put any back in. a) Make a table of values for up to 6 months. b) Graph the relationship. Balance vs. Number of Months 600 500 Balance ($) 400 300 200 100 2 4 6 8 10 12 14 Number of Months c) Write an equation to model the relationship. ____ = ______________ d) Does this relation represent a partial or direct variation? Explain. e) How much will Holly have in her account after 8 months? Show your work. f) How many months will have passed when Holly has $50 in her account? Show your work. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 37 5.6.2: Descriptions, Tables of Values, Equations, Graphs (continued) 3. Nisha is just learning how to snowboard. White Mountain charges $10/hour for lessons and $40 for the lift ticket and snowboard rental. a) Make a table of values for up to 6 hours. b) Graph the relationship. 150 100 50 2 4 6 8 10 12 14 c) Write an equation to model the relationship. ___ = _________________ d) Does this relation represent a partial or direct variation? Explain. e) How much will it cost in total for Nisha to take 2.5 hours of lessons? Show your work. f) If Nisha paid $75, how long was she at the White Mountain getting lessons? Show your work. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 38 5.6.2: Descriptions, Tables of Values, Equations, Graphs (continued) 4. Ishmal sells high-definition televisions. He is paid a weekly salary of 20% commission of his total weekly sales. a) Complete the table of values. b) Graph the relationship. Weekly Total Pay ($) Sales ($) 0 1000 2000 1800 1600 2000 1400 1200 3000 1000 800 4000 600 400 200 5000 2000 4000 6000 8000 10000 12000 c) Write an equation to model the relationship. ___ = _________________ d) Does this relation represent a partial or direct variation? Explain. e) Determine Ishmal's pay if his sales for the week were $8000. Show your work. f) Ishmal made $975. How much were his weekly sales? Show your work. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 39 Unit 5: Day 7: Walk the Line Grade 9 Applied Math Learning Goals Materials • Use the graphing calculator and CBR™ to collect linear motion data in order • CBR™, graphing to determine the equation using the starting distance and walking rate. calculator • metre sticks • Use technology to verify the equation. • BLM 5.7.1 • Model linear relations with equations using the initial value and rate of change. 75 min Assessment Opportunities Minds On ... Whole Class Discussion With the help of a student volunteer (the walker), demonstrate walking away Emphasize the care from a CBR™ to create a linear graph of a 10-second walk. Using the and precision viewscreen calculator, project the graph for student viewing. Trace the graph, needed to copy the axes, and scale onto the paper. Demonstrate the construction of a right-angled graph from the calculator to the triangle showing the rise and run under the graph. Mark the start and finish handout. position using the coordinates (time, distance) of the points. Join the first and last point with a straight line. Discuss how to: • calculate the rate of change using the rise formula. run • use the graph to extrapolate the distance from the CBR™ after 20 seconds. Action! Pairs Investigation Learning Skill (Teamwork)/Observation/Checklist and Curriculum Expectations/Observation/Mental Note: Observe students as they complete their investigations. Use the TRACE key Pairs support each other with the operation of the CBR™ experiment, e.g., to move to the right running the Ranger Program, making sure the walking alley is clear as they along the line and complete BLM 5.7.1. Students write the motion equations using x for time read the position and time display at and y for distance. Explain that they must write the equation in the form: the bottom of the distance = initial value + (rate of change) x, so that the graphing calculator screen. can be used. Discuss the issues that arise when collecting motion data when the walker is moving towards the CBR™. Note that data cannot be collected when the walker is behind the CBR™. Consolidate Whole Class Connecting Debrief Discuss what changes the students made to their equations in order to make a better match between the equation and the graph. Determine an equation for the demo graph constructed at the start of the lesson. Students exchange their work with a peer to verify their walking description statements match with their equations. Verify their understanding of "starting position" and "walking rate" by locating the graph and equation among the class set of work that begins the closest/farthest from the CBR™. Represent the fastest/slowest walk. Summarize how to model linear motion with an equation. Home Activity or Further Classroom Consolidation Record the walking description statements of five of your classmates. Concept Practice Application Create the graph and equation for each. Use the information to determine the distance each classmate would be from the CBR™ after 30 seconds if they walked at a constant rate. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 40 5.7.1: Walk the Line: Setup Instructions You will need: • 1 CBR™ • 1 graphing calculator • 1 ruler Connect your calculator to the CBR™ with the Link cable and follow these instructions: Setting up the RANGER Program Press the APPS key Select 2: CBL/CBR Press ENTER Select 3: RANGER Press ENTER You are at the MAIN MENU. Select 1: SETUP/SAMPLE Use the cursor → and ↓ keys and the ENTER key to set-up the CBR: MAIN MENU START NOW REAL TIME: no TIME(S): 10 DISPLAY: DIST BEGIN ON: [ENTER] SMOOTHING: none UNITS: METERS Cursor up to START NOW Press ENTER to start collecting data 1. Walk away at a steady pace. 2. Press ENTER then 5: REPEAT SAMPLE if necessary. 3. Press ENTER then 7: QUIT when you are satisfied with the graph. 4. Press GRAPH. This is the graph you will analyse. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 41 5.7.1: Walk the Line: Setup Instructions (continued) Part One: Draw your graph. Stand about 0.5 metres from the CBR™. Walk slowly away from the CBR™ at a steady pace. • Copy the scale markings on the distance and time• Draw a right-angled triangle under the graph and label it with the rise and run values. • Calculate the rate of change of your walk using the formula rate of change = rise . run • Complete 42 5.7.1: Walk the Line: Setup Instructions (continued) Describe your walk. Use your starting position and rate of change to write a walking description statement: I started ____ metres from the CBR™ and walked away from it at a speed of ____ metres per second. After 10 seconds, I was ____ __ from the motion detector. At this rate, how far would you have walked after 30 seconds? Construct an equation to model your walk. Read this walking statement: A student started 0.52 metres from the CBR™ and walked away at a speed of 0.19 metres/second. The equation D = 0.52 + 0.19t models the student's position from the CBR™ _____ metres/sec. The equation __________________________ models my distance from the CBR™. The graphing calculator equation is ____________________. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 43 5.7.1: Walk the Line: Setup Instructions (continued) Verify your equation with your walk using the graphing calculator. Turn off the STATPLOT. Type your equation into the Y= editor Graph your equation ( 44 5.7.1: Walk the Line: Setup Instructions (continued) Use the equation to solve problems. The equation D = 0.52 + 0.19t models the student's distance away from the CBR™, over time. We can calculate the student's distance from the CBR™ after 30 seconds: D = 0.52Now, calculate your distance from the CBR™ after 30 seconds: (Use the best equation that matches your walk.) a) The equation ____________________ models your distance from the CBR™. b) Calculate your distance from the CBR™ after 30 seconds:How does this answer compare with your estimate at the beginning of the activity? Use your equation to calculate how long it will take to walk 1 km from the CBR™. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 45 5.7.1: Walk the Line: Setup Instructions (continued) Part Two: Draw your graph. Stand about 3 metres from the CBR™. Walk slowly towards the CBR™ at a steady pace. • Copy the scale markings on the distance and time rise and run values. Calculate the rate of change using the formula: rate of change = rise . run The rate of change of my walk is ________________. Hint: The rise will be a negative number! Why? The speed of my walk is ________________ m/s away from the CBR™. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 46 5.7.1: Walk the Line: Setup Instructions (continued) Describe your walk. Use your initial position and rate of change to write a walking description statement: I started ______metres from the CBR™ and walked towards it at speed of _____metres per second. After 10 seconds, I was ______ from of 0.32 metres/second. The equation D = 4 – 0.32t models the students position from the CBR™. To graph it on the graphing calculator use: Y = 4 – 0.32x. Write a walking statement and equation for your walk: _____________started ____ metres from the CBR™ and walked towards it at a speed of _____ metres per second. The equation ___________________________ models my distance TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 47 Unit 5: Day 8: Modelling Linear Relations with Equations Grade 9 Applied Math Learning Goals Materials • Write equations representing linear relations from descriptions, tables of • BLM 5.8.1 values, and graphs. • Review concepts of continuous and discrete data. 75 min Assessment Opportunities Minds On ... Whole Class Discussion Discuss some of the student responses to the Home Activity and point out the range of the CBR™ and how close to the CBR™ students should stand. Using some of the examples generated in the brainstorming session (Day 6 and BLM 5.6.1), identify the initial values and the rates of change from the descriptions. Briefly describe the activity (BLM 5.8.1) and answer any questions. Complete the first page with the students. Action! Pairs Peer Coaching Students work in pairs to complete BLM 5.8.1. A coaches B and B coaches A. Students write the equation in the same manner that the line was described. Continuous data is (Dependent variable = initial value + rate of change × independent variable) data that is measured, and Whole Class Check for Understanding discrete data is data Take up examples from the peer coaching activity. that is counted. Ask guiding questions: When both variables • Notice that some graphs had dotted lines, while some had solid lines. in a relationship are continuous, a solid Why? line is used to model • If you graphed the data found in the tables of values for which ones would the relationship. If you use a dotted line? either of the variables in a relationship is discrete, a dashed line is used to model the relationship. Consolidate Individual Presentation Debrief Students create and answer their own questions (one description, one graph, and one table). Students present the graph of description and their equation to the class. Curriculum Expectations/Demonstration/Checklist: Assess the students' understanding as they present their graphs and equations. Home Activity or Further Classroom Consolidation Journal: A pizza costs $9 plus $2 per topping. Discuss the effect on the graph Concept Practice Application of changing the initial cost to $10 and lowering the cost per topping to $1.50. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 48 5.8.1: Modelling Linear Relations with Equations Food Frenzy Partner A: ______________________ Partner B: _______________________ A family meal deal at Chicken Deluxe 2. A Chinese food restaurant has a special costs $26, plus $1.50 for every extra price for groups. Dinner for two costs $24 piece of chicken added to the bucket. plus $11 for each additional person. 3. 4. 5. 6. Cost of Ice Number of Cost of a Large Number of Toppings Pizza ($) Cream with Scoops Sugar Cone ($) 0 9.40 0 1.25 1 11.50 1 2.00 2 13.60 2 2.75 3 15.70 3 3.50 4 17.80 4 4.25 TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 49 5.8.1: Modelling Linear Relations with Equations (continued) Planning a Special Occasion Partner A: ______________________ Partner B: _______________________ Write the equation for each relationship in the space provided. Show any calculations you made. Indicate if the relation is a partial or direct variation and describe why these variables are discrete. A coaches B B coaches A 1. A banquet hall charges $100 for the hall 2. The country club charges a $270 for their and $20 per person for dinner. facilities plus $29 per guest. 3. 4. 5. Cost of 6. Cost of Number of Attending a Number of Holding an Athletes Hockey People Athletic Tournament Banquet 0 0 0 75 1 255 20 275 2 450 40 475 3 675 60 675 4 900 80 875 TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 50 5.8.1: Modelling Linear Relations with Equations (continued) From Here to There Partner A: ______________________ Partner B: _____________________ Rent a car for the weekend costs $50 2. A race car travels at a constant speed of plus $0.16/km. 220km/h. Write an equation for the total distance travelled over time. 3. 4. 5. 6. Distance Cost of Bus Distance Cost of a Taxi (km) Fare ($) (km) Charter ($) 0 3.50 0 170 10 6.50 100 210 20 9.50 200 250 30 12.50 300 290 40 15.50 400 330 TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 51 Unit 5: Day 9: Graphing Linear Relations in Context Grade 9 Applied Math Learning Goals Materials • Given an equation in context, graph the relationship. • BLM 5.9.1, 5.9.2, • Graph linear relations using initial value and rate of change. 5.9.3 • Identify initial value and rate of change from equation representing linear relations. 75 min Assessment Opportunities Minds On ... Whole Class Discussion Using BLM 5.9.1, discuss with students how to: • write the equation given the description • graph the equation using the initial value as the starting point, then from this point use the rate of change rise to build two more points on the line. run • connect the points. BLM 5.9.2 Action! Pairs Investigation Golf x-scale: 1 Curriculum Expectations/Demonstration/Mental Note: Observe students' y-scale: $100 ability to identify the initial value and use the rate of change to locate two Repair It more points. x-scale: 1 y-scale: 5 Students work in partners to complete BLM 5.9.2. Movie House Whole Class Discussion x-scale: 1 Guide a class discussion about appropriate scales on the axes, referencing y-scale: 5 BLM 5.9.2. Kite x-scale: 1 Pairs Creating Graphs y-scale: 1 Students coach each other as they complete the task. (BLM 5.9.2) Shape Fitness Learning Skill (Initiative)/Observation/Rating Scale: Observe student x-scale: 1 y-scale: 5 initiative in taking responsibility for their learning and their partner's Repair Window learning. x-scale: 1 y-scale: 10 Yum-Yum & Toy Sub x-scale: 1 y-scale: 0.25 BLM 5.9.3 Consolidate Whole Class Connections Taxi Debrief Discuss the benefits of using this method of graphing. x-scale: 1 y-scale: 0.5 Help students articulate strategies for determining scales for the horizontal Bank Account and vertical axes that will facilitate graphing. x-scale: 1 y-scale: 10 Dino's x-scale: 1 y-scale: 2 Katie x-scale: 1 y-scale: 0.5 Home Activity or Further Classroom Consolidation Application Complete the worksheet 5.9.3, Relationships: Graphs and Equations. Concept Practice TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 52 5.9.1: Graphing Linear Relations A tennis club charges $25 initial membership fee plus $5 per day. The equation of this relation is C = 25 + 5d, where C is the cost and d is the number of days. Total Cost vs. Number of Day Passes 65 60 55 50 45 40 35 30 Total Cost ($) 25 20 15 10 5 0 1 2 3 4 5 6 7 8 Number of Day Passes Indicate where the rate of change is displayed on the graph. If the initial membership fee is changed to $15 and daily cost to $10, graph the new relation on the same grid. Indicate the procedure you followed to graph the line. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 53 5.9.2: The Speedy Way to Graph Partner A ___________________________ Partner B___________________________ Write the equation for the relationship and graph the relationship. 1. A golf club charges an annual membership 2. Repair-It charges $60 for a service call plus fee of $1000 plus $100 for a green fee to $25/h to repair the appliance. play golf. Equation: Equation: 3. Movie House charges $5 to rent each DVD. 4. A kite is 15 m above the ground when it descends at a steady rate of 1.5 m/s. Equation: Equation: TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 54 5.9.2: The Speedy Way to Graph (continued) Partner A ___________________________ Partner B___________________________ Write the equation for the relationship and graph the relationship. 1. The Recreation Centre charges a monthly 2. Repair Window charges a $20 service fee membership fee of $20 plus $5 per class. plus $10/h to fix the window pane. Show the relationship for one month. Equation: Equation: 3. Yum-Yum Ice Cream Shop charges $0.50 4. A submarine model starts 6.5 m above the for the cone plus $1 per scoop of ice bottom of the pool. It gradually descends cream. at a rate of 0.25 m/s. Equation: Equation: TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 55 5.9.3: Relationships: Graphs and Equations Write the equation for the relationship and graph the relationship. 1. A taxi cab company charges $3.50 plus 2. Shelly has $250 in her bank account. She $0.50/km. spends $10/week on snacks. Equation: Equation: 3. Dino's Pizza charges $17 for a party-sized 4. Katie sells programs at the Omi Arena. pizza plus $2 per topping. She is paid 50 cents for every program she sells. Equation: Equation TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 56 Unit 5 Test Name: ___________________ Date: ____________________ (2) 1. The graph describes Rami's walk with a motion detector. Distance (metres) Tell the story that describes this graph. Use distance away from the wall and times in your story. Time (seconds) 2. A story is described in each question. Sketch the graph that describes the story in the screen provided. (2) a) Begin 5 metres from the wall. Distance (metres) Walk towards the wall for 5 seconds. Stop for 5 seconds. Run back to your starting position. Stop. Time (seconds) (2) b) Begin at the wall. Distance (metres) Walk very slowly away from the wall for 3 seconds. Increase your speed for 3 seconds. Stop for 3 seconds. Walk very slowly towards the wall for 3 seconds. Run back to the wall. Stop. Time (seconds) (2) 3. Jen tried her new snowboard at the One Plank Only Resort. The graph shows her first run. Tell the story that describes Jen's first run. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 57 Unit 5 Test (4) 4. If a wheelchair ramp has a rate of change greater than 0.1 in size, then it is considered unsafe. Determine whether or not each of the following ramps is safe. Show your work and explain your reasoning. 20 cm 15 cm 210 cm 120 cm (2) 5. Calculate the rate of change of the staircase from A to B. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 58 Unit 5 Test 6. Arcadia charges players a $15 admission fee to their gaming centre. Arcadia also charges each player $5 per game. (2) a) Write an equation to model the cost of playing games at Arcadia. (2) b) What is the rate of change for this relation and how does it relate to the cost of playing games at Arcadia? (2) c) What is the initial value for this relation and how does it relate to the cost of playing games at Arcadia? (4) d) Graph the relation. (1) e) How many games can Jeremy play if he has saved $60 for a day at Arcadia? (1) f) How much will it cost Renay to spend a day at Arcadia if she plays 30 games? (2) g) How would the graph from a) change if Arcadia decreases the admission fee to $10? Write an equation that represents the new cost of a day spent gaming at Arcadia. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations 59 Unit 5 Test (2) h) How would the graph from a) change if Arcadia charges an admission of $10 and increases the cost per game to $7? Write an equation that represents the new cost of a day spent gaming at Arcadia. 7. The local swimming pool is open 5 days a week for 8 weeks during the summer holidays. The admission prices are displayed at the entrance. Splash World Swim Park Price List Season's pass ……… $60 plus $2 per day Daily swim pass …… $5 (2) a) How much will it cost one person to go to the pool every day the pool is open? i) with a season's pass? ii) with a daily pass? (2) b) Write an equation that represents the cost of a season's pass, and an equation that represents the cost of a daily pass. (4) c) Graph both relations on the same grid. (2) d) Which pass is better? Explain your reasoning. TIPS4RM: Grade 9 Applied – Unit 5: Linear Relations
Introduction to Mathematics for Economics introduces quantitative methods to students of economics and finance in a succinct and accessible style. The introductory nature of this textbook means a background in economics is not essential, as it aims to help students appreciate that learning mathematics is relevant to their overall understanding of the subject. Economic and financial applications are explained in detail before students learn how mathematics can be used, enabling students to learn how to put mathematics into practice. Starting with a revision of basic mathematical principles the second half of the book introduces calculus, emphasising economic applications throughout. Appendices on matrix algebra and difference/differential equations are included for the benefit of more advanced students. Other features, including worked examples and exercises, help to underpin the readers' knowledge and learning. Akihito Asano has drawn upon his own extensive teaching experience to create an unintimidating yet rigorous textbook. less
Calculus for Dummies (For Dummies) by Mark Ryan Publisher Comments The mere thought of having to take a required calculus course is enough to make legions of students break out in a cold sweat. Others who have no intention of ever studying the subject have this notion that calculus is impossibly difficult unless you...A History of Pi by Petr Beckmann Publisher Comments The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it didPre-Algebra Essentials for Dummies by Mark Zegarelli Publisher Comments Just the critical concepts you need to score high in pre-algebra This practical, friendly guide focuses on critical concepts taught in a typical pre-algebra course, from fractions, decimals, and percents to standard formulas and simple variable equations.... (read more) How to Lie with Statistics by Darrell Huff Synopsis Mr. Huff's lively, human-interest treatment of the dry-as-bones subject of statistics is a timely tonic. . . . This book needed to be written, and makes its points in an entertaining and highly readable manner.Illustrator and author pool their... (read more) The Education of T.C. Mits: What Modern Mathematics Means to You by Lillian R. Lieber Publisher Comments "I have studied with pleasure [this] new book. . . . Beautiful examples. . . . Illuminating. I am convinced that [Lieber's] original enterprise will get the recognition it so richly deserves."-Albert Einstein "This is quite different from any other book.... (read more) Mathematics-Grade 4: by School Specialty Pub Publisher Comments With Mathematics: A Step-By-Step Approach, Grade 4 Homework Booklet students will love building their mathematics skills while completing the fun activities in this great book Divided into four steps: addition and subtraction, multiplication, division... (read more) The Math Chat Book by Frank Morgan Publisher Comments Mathematics can be fun for everyone, and this book shows it. It grew out of the author's popularisation of mathematics via live, call-in TV shows and widely published articles. The questions, comments, and even the answers here come largely from the... (read more) Painless Math Word Problems (Barron's Painless Study) by Marcie F Abramson Publisher Comments (back cover) Really. This isn't going to hurt at all . . . Students discover interesting ways to see patterns in math word problems, and then make the correct computations to find solutions. In the process, they work with decimals and fractions, compare... (read more) Rapid Math Tricks & Tips: 30 Days to Number Power by Edward H Julius Publisher Comments Demonstrates a slew of time-saving tips and tricks for performing common math calculations. Contains sample problems for each trick, leading the reader through step-by-step. Features two mid-terms and a final exam to test your progress plus hundreds
08176419ical Olympiad Challenges Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory were selected from numerous mathematical competitions and journals. An important feature of the work is the comprehensive background material provided with each grouping of problems. The problems are clustered by topic into self-contained sections with solutions provided separately. All sections start with an essay discussing basic facts and one or two representative examples. A list of carefully chosen problems follows and the reader is invited to take them on. Additionally, historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on encouraging readers to move away from routine exercises and memorized algorithms toward creative solutions to open-ended problems. Aimed at motivated high school and beginning college students and instructors, this work can be used as a text for advanced problem- solving courses, for self-study, or as a resource for teachers and students training for mathematical competitions and for teacher professional development, seminars, and workshops
Understanding the Effects of Diet and Fitness on the Human Body through Mathematical Equations and Statistical Analysis on Calorie Intake and Calories Expended, by Ronald B. Coleman, Jr. Guide Entry to 12.03.03: This unit gives an interactive twist to the study of human anatomy and basic algebra for students in grades 5 and 6. Science and math are generally taught as separate subjects, yet mathematics is an integral part of scientific discovery. In this unit, students will study the basic function and developmental needs of three systems in the human body: the skeletal system, the muscular system, and the cardiovascular system. Students will work individually to understand their own personal nutritional needs, and they will work collectively to analyze hypothetical situations and compare the diets of several professional and Olympic athletes. After students have a clear, practical understanding of the nutritional values of proteins, carbohydrates, fats, and sugars they will track their own diet on a daily basis. Students will read and watch short films on the importance of combining a healthy diet with consistent exercise. Subsequently, individual students will showcase their knowledge through a self-exploration project that tracks their daily caloric intake and physical activity. Students will be able to apply their newly acquired skills towards improving their own physical and mental health. Once they are familiar with the mathematics involved in calculating net caloric intake, they will use Microsoft Excel and PowerPoint to create a final presentation. The hope is that students come away from the unit understanding the importance of proper diet and fitness in preventing disease and poor health. Finally, students will reflect on their own diet and level of physical fitness and make changes to become more confident, healthy individuals.
and Intermediate Algebra for College Students The Angel author team meets the needs of today's learners by pairing concise explanations with the new Understanding Algebra feature and an updated ...Show synopsisThe Angel author team meets the needs of today's learners by pairing concise explanations with the new Understanding Algebra feature and an updated approach to examples. Discussions throughout the text have been thoroughly revised for brevity and accessibility. Whenever possible, a visual example or diagram is used to explain concepts and procedures. Understanding Algebra call-outs highlight key points throughout the text, allowing readers to identify important points at a glance. The updated examples use color to highlight the variables and important notation to clearly illustrate the solution process32162091620927Good. 070 Item may show signs of shelf wear. Pages may include...Good. 070 a good book to start off with if you don't really understand math that well. the only problem with the book i reviced was the teacher edition and i asked for the student. but everything else is
College of Science and Mathematics Courses MATH 090. Introduction to Problem Solving (2) Introduction to problem-solving, with an emphasis on basic mathematics skills. Diagnostic tests enable students to identify specific topics for study. Involves collaborative learning, individualized advisement and instruction, and use of media and computers. Normally offered as a Summer Bridge course. Credit will not apply toward the Baccalaureate Degree, but will apply as two units of University credit. MATH 092. Developmental Mathematics I (3) First in a 2-semester sequence of developmental mathematics courses. Students scoring below 34 on the ELM need to complete MATH 092 and 093 successfully to be remediated. Credit will not apply toward the Baccalaureate Degree but will apply as 3 units of University Credit. Students who earn Credit in MATH 092 are eligible to enroll in MATH 093. Topics covered include fractions, decimal notation, percent, real numbers and algebraic expressions, equations and inequalities. (Credit/No Credit only) MATH 093. Developmental Mathematics II (5) Prerequisite: Score of 34 or above, but below 50 on the ELM Exam or credit in MATH 092. Credit will not apply toward the Baccalaureate Degree, but will apply as 5 units of University credit. Successful completion of MATH 093 qualifies students for entrance into MATH 102, 131, 140 and 210. Review of elementary algebra topics, such as equations and inequalities, polynomials, factoring, rational expressions, graphing, radical expressions, quadratic equations and functions. (Credit/No Credit only) MATH 099 Developmental Mathematics II Ð Accelerated (3) Prerequisite: A score of 40 or above but below 50 on the ELM Exam or credit in MATH 092. Credit will not apply toward the Baccalaureate Degree, but will apply as 3 units of University credit. Successful completion of MATH 099 qualifies students for entrance into MATH 102 and 103 (conditionally), 131, 140 and 210. This course is not open to students who are currently enrolled in or who have received credit in MATH 093. This is an accelerated review of elementary algebra topics, including equations and inequalities, polynomials, factoring, rational expressions, graphing, radical expressions, quadratic equations and functions. (Credit/No Credit only) MATH 102. College Algebra (3) Prerequisites: Listed in Table 1. Students who are conditionally prepared must have credit for or concurrently enroll in MATH 102L. Functions, linear equations, quadratic equations, theory of equations, progressions, inequalities, absolute value, logarithms, permutations, combinations, probability and determinants. Not open to students who have credit in MATH 103, 105 or 106. (Available for General Education, Basic Skills Mathematics.) MATH 102L. College Algebra Lab (1) Prerequisite: Required for all Conditionally prepared students enrolled in MATH 102. All students in MATH 102 are encouraged to enroll in this course. This is a Credit/No Credit hybrid enrichment laboratory for students in MATH 102. This course will include a self-paced, modular online component. 2 hours lab per week. (Credit/No Credit only) MATH 103. Mathematical Methods for Business (3) Prerequisites: Passing score on or exemption from the ELM Exam or credit in MATH 093; Passing score on the Mathematics Placement Test, Part I or credit or concurrent enrollment in MATH 103L. Concepts and applications of algebra and calculus to business. Topics include functions, systems of equations, matrices, the derivative and business-related topics in calculus. (Available for General Education, Basic Skills Mathematics.) MATH 103L. Mathematics for Business Laboratory (1) Prerequisite: Passing score on the ELM Exam. This self-paced, module-based laboratory is designed to give students additional exposure to the applications of college algebra to business and economics beyond what can be done in lecture. The additional hands-on problem-solving skills learned in this class enhance the lecture experience and strengthen the skills necessary for success in MATH 103 and subsequent courses in business majors. The lab environment allows students to both work at their own pace and receive small-group instruction with the laboratory instructor on all modules. Students with an MPT Part I score below 24 may enroll in MATH 103 only if they enroll in this course. 2 hours lab per week. (Credit/No Credit only) MATH 104. Trigonometry and Analytic Geometry (3) Prerequisites: Listed in Table 1. Students who are Conditionally prepared must have credit for or concurrently enroll in MATH 104L. Rectangular and polar coordinates; trigonometric functions, identities and equations; inverse trigonometric functions; conic sections; complex numbers. Not open to students who have credit in MATH 103, 105 or 106. MATH 104L. Trigonometry Lab (1) Prerequisite: Required for all conditionally prepared students enrolled in MATH 104. All students in MATH 104 are encouraged to enroll in this course. This is a Credit/No Credit hybrid enrichment laboratory for students in MATH 104. This course will include a self-paced, modular online component. w hours lab per week. (Credit/No Credit only) MATH 105. Pre-Calculus (5) Prerequisites: Listed in Table 1 above. Students who are Conditionally prepared must have credit for or concurrently enroll in MATH 105L. Number systems and their algebraic properties; systems of equations and inequalities; basic analytic geometry of lines and conic sections; elementary functions, including polynomial, rational, exponential and logarithmic, with emphasis on trigonometric functions; polar equations. Graphing calculators are used and the interplay between graphical and algebraic solutions is stressed. Not open for credit to students who have successfully completed MATH 150A.(Available for General Education, Basic Skills Mathematics) MATH 105L. PreCalculus Lab (1) Prerequisite: Required for all conditionally prepared students enrolled in MATH 105. All students in MATH 105 are encouraged to enroll in this course. This is a NC/CR hybrid enrichment laboratory for students in MATH 105. This course will include a self-paced, modular online component. 3 hours lab per week. (Credit/No Credit only) MATH 131. Mathematical Ideas (3) Prerequisites: Passing score on or exemption from the ELM Exam, or credit in MATH 093. General Education course intended to acquaint the student with basic mathematical ideas. (Available for General Education, Basic Skills Mathematics.) MATH 140. Introductory Statistics (4) Prerequisites: Passing score on or exemption from the ELM Exam, or credit in MATH 093. Methods for displaying, describing and producing data. Normal distribution. Correlation and regression. Sampling distributions and probability. Statistical inference for means and proportions. (Available for General Education, Basic Skills Mathematics.) MATH 150A. Calculus I (5) Prerequisites: Listed in Table 1. Students who are Conditionally prepared or who transfer the equivalent of MATH 105 or both MATH 102 and 104 must have credit for or concurrently enroll in MATH 150AL. Limits, derivatives, applications of differentiation. Definite and indefinite integrals, and the fundamental theorem of calculus. (Available for General Education, Basic Skills Mathematics.) MATH 150AL: Calculus I Laboratory (1) Prerequisite: Required for all Conditionally prepared students enrolled in MATH 150B or 255B. All students in MATH 150B and 255B are encouraged to enroll in this course. This is a NC/CR hybrid enrichment laboratory for students in MATH 150B and 255B. This course will include a self-paced, modular online component. 3 hours lab per week. (Credit/No Credit only) MATH 150B. Calculus II (5) Prerequisites: Listed in Table 1. Students who are Conditionally prepared must have credit for or concurrently enroll in MATH 150BL. Techniques of integration, numerical integration, improper integrals and applications of the integral. Taylor polynomials, sequences and series, and power series. MATH 150BL. Calculus II Laboratory (1) Prerequisite: Required for all Conditionally prepared students enrolled in MATH 150B or 255B. All students in MATH 150B and 255B are encouraged to enroll in this course. This is a Credit/No Credit hybrid enrichment laboratory for students in MATH 150B and 255B. This course will include a self-paced, modular online component. 3 hours lab per week. (Credit/No Credit only) MATH 210. Basic Number Concepts (3) Prerequisites: Passing score on or exemption from the ELM Exam or credit in MATH 093. Language of sets, systems of numeration, nature of numbers and fundamentals of operations, relations and functions, domain of integers, and field of rational and real numbers. Designed primarily for students intending to teach in elementary or junior high school. Not available for credit toward the Major or Minor in Mathematics. MATH 250. Calculus III (3) Prerequisite: Completion of MATH 150B with a grade of ÒCÓ or better. Continuation of MATH 150B. Solid analytic geometry, partial differentiation and multiple integrals with applications. MATH 255A. Calculus for the Life Sciences I (3) Prerequisites: Listed in Table 1. Students who are Conditionally prepared must have credit for or concurrently enroll in MATH 150AL. Knowledge of trigonometry is assumed. First semester of a short course in calculus. Topics in calculus of functions of one variable including techniques of differentiation, applications to graphing, extreme problems and an introduction to integration. Not open for credit to students who have successfully completed MATH 150A. (Available for General Education, Basic Skills Mathematics.) MATH 255B. Calculus for the Life Sciences II (3) Prerequisites: Listed in Table 1. Students who are Conditionally prepared must have credit for or concurrently enroll in MATH 150BL. Techniques of integration, series, applications, functions of several variables and partial differentiation. Not open for credit to students who have successfully completed MATH 150AB. MATH 262. Introduction to Linear Algebra (3) Prerequisite: MATH 150B. Systems of linear equations, matrices, determinants, eigenvalues, vector spaces and linear transformations, as well as introduction to inner products on Rn and spectral theorem for symmetric matrices. MATH 280. Applied Differential Equations (3) Prerequisite: MATH 150B. Recommended Corequisite or Preparatory: MATH 250. Ordinary differential equations, series solutions, systems of equations and Laplace transforms, with emphasis on applications and introduction to numerical techniques. Course is not open to students who have credit for MATH 351. MATH 310. Basic Concepts of Geometry, Probability and Statistics (3) Prerequisites: Passing score on or exemption from the ELM Exam or credit in MATH 093 and completion of MATH 210 with a grade of ÒCÓ or better. Articulated course from another college equivalent to MATH 210 may only satisfy the course prerequisite for MATH 310. Students passing such a course with a ÒCÓ or better will still need to fulfill the ELM Exam requirement. Second course for students intending to teach in elementary or junior high school. Geometry as a system; congruence and similarity through construction with straightedge and compass; transformational geometry; the nature of measurement, precision and accuracy; basic principles of probability and statistics. Not available for credit toward the Major or Minor in Mathematics. MATH 311. Basic Geometric Concepts (3) Prerequisites: Passing score on the ELM Exam and completion of MATH 210 and 310 with a grade of ÒCÓ or better, or instructor consent. Continuation of the investigation of elementary geometry begun in MATH 310. Topics selected from topology, motion geometry, metric geometry, geometry as a mathematical system, absolute geometry, Euclidean geometry and non-Euclidean geometry. Not available for credit toward the Math Major or Minor. MATH 312. Basic Algebraic Concepts (3) Prerequisites: Passing score on the ELM Exam and completion of MATH 210 and 310 with a grade of ÒCÓ or better, or instructor consent. Topics selected from: abstract algebra and applied algebra using elementary mathematical models. Not available for credit toward the Math Major or Minor. MATH 320. Foundations of Higher Mathematics (3) Prerequisite: MATH 150B. The goal of this course is to help students transition from a primarily computational mode of doing mathematics to a more conceptual mode. The emphasis will be on proofs, which are taught in the context of elementary number theory, combinatorics and analysis; the language of sets, relations, order, equivalence classes, functions and cardinality is introduced. Students are expected to write large numbers of proofs and communicate mathematical ideas clearly. MATH 326. Discrete Mathematics (3) MATH 331. Mathematical Explorations (3) Prerequisites: Passing Score on the ELM Exam; Completion of the Lower Division writing requirement; Upper Division standing. A course designed to give students an appreciation of the diversity of mathematics and the spirit in which it is employed in various applications. The character and origin of key topics from different branches of mathematics are explored. The contributions of various cultures to the field are studied, along with the use of mathematical models for physical problems. The development is conceptual rather than axiomatic, and includes several supervised reading and writing assignments. One significant writing assignment is required. Strongly recommended for prospective teachers in all fields. (Available for General Education, Basic Skills Mathematics.) MATH 341. Applied Statistics I (3) Prerequisite: MATH 150B. Introduction to the practice of statistics, emphasizing the role of probability. Includes basic probability, discrete and continuous probability distributions, expectation and variance, sample surveys and experiments, displaying and summarizing data, sampling distributions, central limit theorem, inference for proportions, chi-square test and least squares regression. Mathematics majors who are not in the Secondary Teaching Option may not receive credit for both MATH 340 and 341. MATH 370. Foundations of Geometry (3) Prerequisite or Corequisite: MATH 320. One of the goals of this course is to help students write rigorous proofs of results of plane Euclidean geometry. It is also expected that students visualize and develop geometric intuition through the use of dynamic geometry software. The content includes history, axiomatic structure and theorems of plane Euclidean geometry, geometric transformations of the plane, rigid motions, similarities, and inversion, coordinate geometry and an introduction to non-Euclidean geometries. MATH 382/L. Introduction to Scientific Computing and Lab (2/1) Corequisite: MATH 262. This course gives students an introduction to basic numerical techniques and to programming using some of the common software packages used in mathematics. Students apply these techniques in projects from different branches of mathematics.(This course does not replace a rigorous course in numerical analysis.) 2 hours lecture, 2 hours lab. MATH 390A-D. Mini-Courses in Mathematics for Pre and in Service Teachers (1) Prerequisites: MATH 210 with a grade of ÒCÓ or better or instructor consent; Passing score on ELM Exam. This course is intended for Liberal Studies Credential Candidates and in-service elementary- and middle-school teachers. Important concepts of mathematics that have particular application to the elementary-school curriculum, including: AÐHistory of Mathematics; BÐComputational Methods; CÐComputer-Assisted Instruction; and DÐStrategies in Problem Solving. (Credit/No Credit only) MATH 391. Field Experience in the Mathematics of the Public Schools (2) Prerequisites: Multiple Subject CandidatesÑMATH 210 and 310 or corequisite with 310; Passing score on the ELM Exam. Single Subject CandidatesÑMATH 150A, 150B; Junior standing. Field experience course designed to give the prospective teacher an appreciation of a quality mathematics program in public schools. Requirements include 45 hours of participation in an assigned school and regular group meetings to discuss the classroom experience. (Credit/No Credit only) MATH 440B. Mathematical Statistics II (3) MATH 441. Applied Statistics II (3) Prerequisite: MATH 341. Continuation of MATH 341 with emphasis on statistical inference. Includes design of surveys and experiments, the t-distribution, inference for means, correlation and regression with transformations, and inference for slope. MATH 481D. Topics in Numerical Mathematics (3) Prerequisite: MATH 481A. This course explores topics in numerical mathematics that have not been explored elsewhere in the sequence. These include, but are not limited to, topics from statistics and linear and non-linear optimization. The course may be taken twice for credit with the consent of an advisor. MATH 483. Mathematical Modeling (3) Prerequisites: MATH 340; 351. Applications of mathematical techniques to solve selected problems in ecology, biology, economics, finance, social sciences, life sciences, physical sciences and engineering. Models discussed include deterministic, stochastic, optimization, static and dynamic ones. Emphasis is placed on the initial phase of building mathematical models and the final phase of interpreting the solutions in terms of real-life applications. MATH 490. Capstone Course (3) Prerequisite: Senior standing. A course where prospective teachers see high-school level mathematics from a more advanced perspective, where there is considerably more emphasis on issues of pedagogy than in other content courses, and where students will see connections between the mathematics they have learned and some of the activities that they will themselves be engaged in as teachers. MATH 490 is required for the Secondary Teaching Option, but a student may choose, in consultation with his or her advisor, to take the course a second time as an elective. MATH 493. Undergraduate Seminar in Mathematics (3) Prerequisite: Junior standing in the major. Students will study current topics in mathematical and/or statistical literature and will prepare written summaries and give oral presentations to the class. Students will be active participants in all seminars by asking questions and providing written critiques and summaries of the presentations of other students. MATH 494. Practical Experience in Mathematics (3) Prerequisite: Junior standing in the major. Students will gain practical experience in the profession by either participating in an internship doing mathematical/statistical work at an outside organization or by doing directed research within the Department. All students are expected to work a minimum of 8 hours per week on this assignment and meet with the course instructor on a regular basis. All students are required to produce a written report on their work at the end of the semester. Students will give oral reports to the Department and their peers. MATH 501. Topology (3) MATH 510A/B. Algebra and Number Theory (3-3) Prerequisite: Admission to the Graduate Program. A 2-course sequence on integers and prime numbers, rational and complex algebraic numbers, symmetry and group theory, rings of polynomials and algebraic integers, basic algebraic geometry and algebraic extensions, elementary Galois Theory and the theory of equations. MATH 510A is the prerequisite for MATH 510B. These courses cannot be taken for credit toward the MasterÕs Degree in Options I and II. MATH 511A/B. Linear Algebra and Geometry (3-3) Prerequisite: Admission to the Graduate Program. A 2-course sequence on modern applications of mathematics that involve matrices, basic properties of vectors of R2 and R3, dot product, orthonormal basis, cross product, linear transformations of Euclidean 2- and 3-Space and the classification of its rigid motions, symmetric bilinear forms, conics and quadrics, basic topology of Rn, spherical geometry, PoincarŽÕs models of the hyperbolic plane and their isometries. MATH 511A is the prerequisite for MATH 511B. These courses cannot be taken for credit toward the MasterÕs Degree in Options I and II. MATH 512A/B. Concepts of Analysis (3-3) Prerequisite: Admission to the Graduate Program. A 2-course sequence on the real number system, countable and uncountable sets, cardinal numbers, Cantor diagonal argument, well-ordered sets, ordinal numbers, numerical sequences and numerical series of real numbers, continuity, differentiability and integration of functions of one variable, sequences and series of functions, uniform convergence and ordinary differential equations. MATH 512A is the prerequisite for MATH 512B. These courses cannot be taken for credit toward the MasterÕs Degree in Options I and II. MATH 514A/B. Probability and Statistics (3-3) Prerequisite: Admission to the Graduate Program. A 2-course sequence on probability rules, discrete and continuous random variables and their distributions, central limit theorem, and on elementary topics in statistics from the advanced point of view, including exploratory analysis, graphical display, random phenomena, probability distributions, simulation, correlation and regression, survey sampling and experimental design, sampling distributions, confidence intervals and significance tests for proportions and means, and chi-square tests. MATH 514A is the prerequisite for MATH 514B. These courses cannot be taken for credit toward the MasterÕs Degree in Options I and II. MATH 542A-D. Probability and Statistics (3-3-3-3) Prerequisite: MATH 340 or 440A. This course will cover topics in probability and statistics not covered elsewhere in the program. Part A is usually devoted to multivariate statistics, Part B to stochastic processes, and Part C to probability theory. Part D is left to a topic chosen by the individual instructor. MATH 560. Abstract Algebra III (3) MATH 570. Differential Geometry (3) Prerequisite: MATH 450. The local theory of regular curves in R3 and Frenet formulas. Regular surfaces in R3, the first and second fundamental forms, Gaussian and mean curvatures, and the Egregium Gauss theorem. Geodesics and the Gauss-Bonnet theorem. MATH 581. Numerical Methods for Linear Systems (3) Prerequisite: MATH 462. Methods for solving large linear problems and eigenvalue problems are presented at an advanced level. Direct methods such as LU factorization, Cholesky factorization and the Least Squares method, and Iterative methods, such as the Jacobi, Gauss-Seidel, SOR and conjugate Gradient methods, are discussed in detail. Eigenvalue problems are solved via power iteration, the QR method and the Jacobi method. MATH 582 A-D. Topics in Numerical Analysis (3-3-3-3) Prerequisite: MATH 581 or consent of instructor. The course will cover topics in numerical analysis which are important in many applications and which are not covered elsewhere in the program. Part A usually covers numerical methods in optimization, Part B covers numerical methods for ordinary differential equations ,and Part C covers numerical solution of partial differential equations. Part D covers a subject chosen by the instructor. MATH 589. Seminar in Mathematics (1) Prerequisite: Senior or graduate standing in the Mathematics Department. Students will read about advanced topics in the recent literature in mMathematics and report on them in a lecture. This course may be taken up to two times with the consent of the advisor. (Credit/No Credit only) MATH 592A-D. Topics in Applied Mathematics (3-3-3-3) Prerequisites: MATH 552 or consent of instructor. This course is devoted to a variety of important topics in applied Mmathematics that are not covered elsewhere in the Program. In particular, Part A will cover the mathematical theory of partial differential equations, Part B covers mathematical optimization and operations research, and Part C covers mathematical biology. The topic of Part D is left to the individual instructor. MATH 595A-Z. Experimental Topics (1-3) Prerequisite: Consent of instructor. Specialized topics from a concentrated field of current interest presented at an advanced level. MATH 625. Advanced Mathematical Modeling (3) Selected problems in ecology, biology, economics, finance, social sciences, life sciences, physical sciences and engineering are used to develop advanced techniques of mathematical modeling. Prerequisite: Consent of instructor. Advanced topics not covered in the previous classes on the subject. Part A covers topics in analysis, Part B covers topics in geometry, and Part C covers topics in topology. May be repeated with the consent of the advisor. MATH 655. Complex Analysis (3) Prerequisites: MATH 501, 455. Topics covered incluyde the general Cauchy theorem, power series and analytic continuation, series and product expansions, conformal mapping and the Dirichlet problem. Prerequisite: Consent of instructor. Advanced topics not covered in the previous classes on the subject. Part A covers topics in algebra, Part B covers topics in number theory, and Part C covers other topics in discrete mathematics. May be repeated with the consent of the advisor. MATH 680A/B. Applied Functional Analysis (3-3) Prerequisites: MATH 501, 552. This 2-semester sequence gives an introduction to Banach and Hilbert spaces and their applications. Fixed Point Theorems and their applications to differential and integral equations and variational principles. Adjoint and self-adjoint operators and spectral theory of linear operators. MATH 680A is a prerequisite for MATH 680B.
Elementary Numerical Analysis 9780471433378 ISBN: 0471433373 Edition: 3 Pub Date: 2003 Publisher: Wiley Summary: Offering a clear, precise, and accessible presentation, complete with MATLAB programs, this new Third Edition of Elementary Numerical Analysis gives students the support they need to master basic numerical analysis and scientific computing. Now updated and revised, this significant revision features reorganized and rewritten content, as well as some new additional examples and problems. The text introduces core areas... of numerical analysis and scientific computing along with basic themes of numerical analysis such as the approximation of problems by simpler methods, the construction of algorithms, iteration methods, error analysis, stability, asymptotic error formulas, and the effects of machine arithmetic. Kendall Atkinson is the author of Elementary Numerical Analysis, published 2003 under ISBN 9780471433378 and 0471433373. Four hundred fifty one Elementary Numerical Analysis textbooks are available for sale on ValoreBooks.com, one hundred thirteen used from the cheapest price of $70.00, or buy new starting at $144.35
books.google.com - Proof... Without Words Proofs Without Words: Exercises in Visual Thinking, Volume 1 Proof providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into five chapters: Geometry and algebra; Trigonometry, calculus and analytic geometry; Inequalities; Integer sums; and Sequences and series. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics. Geometric Series Part 3 Geometric Series Proofs: An Annotated Bibliography. We have seen a geometric proof and a classic algebraic proof for the sum of the geometric series, ... www41.homepage.villanova.edu/ robert.styer/ Bouncingball/ geometric_series_3.htm
Integration is one of the two cornerstones of analysis. Since the fundamental work of Lebesgue, integration has been interpreted in terms of measure theory. This introductory text starts with the historical development of the notion of the integral and a review of the Riemann integral. From here, the reader is naturally led to the consideration of the Lebesgue integral, where abstract integration is developed via measure theory. The important basic topics are all covered: the Fundamental Theorem of Calculus, Fubini's Theorem, \(L_p\) spaces, the Radon-Nikodym Theorem, change of variables formulas, and so on. The book is written in an informal style to make the subject matter easily accessible. Concepts are developed with the help of motivating examples, probing questions, and many exercises. It would be suitable as a textbook for an introductory course on the topic or for self-study. Graduate students and research mathematicians interested in mathematical analysis. Reviews From reviews for the first edition: "Distinctive features include: 1) An unusually extensive treatment of the historical developments leading up to the Lebesgue integral ... 2) Presentation of the standard extension of an abstract measure on an algebra to a sigma algebra prior to the final stage of development of Lebesgue measure. 3) Extensive treatment of change of variables theorems for functions of one and several variables ... the conversational tone and helpful insights make this a useful introduction to the topic ... The material is presented with generous details and helpful examples at a level suitable for an introductory course or for self-study." -- Zentralblatt MATH "A special feature [of the book] is the extensive historical and motivational discussion ... At every step, whenever a new concept is introduced, the author takes pains to explain how the concept can be seen to arise naturally ... The book attempts to be comprehensive and largely succeeds ... The text can be used for either a one-semester or a one-year course at M.Sc. level ... The book is clearly a labor of love. The exuberance of detail, the wealth of examples and the evident delight in discussing variations and counter examples, all attest to that ... All in all, the book is highly recommended to serious and demanding students."
Other Possible Workshops If you are interested in any of the workshop topics below, then that topic can be covered in the germane study session. For example, fractions, graphing, and factoring in M01 and M03 study sessions, probability in M15 study session, or trigonometry in M25A study session. All of these are on a as requested basis. Calculator While calculators are meant to be a tool to make mathematics easier, sometimes students have difficulty with using their calculators properly. This workshop covers correct calculator usage (to include Math M15 Statistics). Appropriate for all math classes. Conic Sections This workshops discusses both how to graph and solve analytically the four conic sections: circle, ellipse, parabola, and hyperbola. Appropriate for Math M03, Math M05, and Math M07. Dimensional Analysis (Unit Conversions) For the beginning chemistry student (Chem M01A, M11, M12) one of the most difficult aspects is dimensional analysis or unit conversions. This workshop was created with input from the Chemistry department and aims to help students with these fundamental chemistry problems. Appropriate for Chem M01A, Chem M11, and Chem M12. Exponential and Logarithmic Functions Exponential and logarithmic functions form an important part of both the pre-calculus and calculus curriculum. Thus, in this workshop we discuss the graphs and properties of these two types of functions as well as equations that contain these functions. Appropriate for Math M07, Math 25A, and Math 25B students. Factoring Factoring trinomials (i.e., algebraic expressions of the form ax^2-bx+c) is an integral part of algebra and it is difficult to succeed in algebra unless one is able to factor well. This workshop explores different methods of factoring through the use of common examples. Among the methods of factoring discussed are trial-and-check, factor-by-grouping, and using special products. Appropriate for Math M01, Math M03, Math M04, and Math M05 students. Fractions If fractions are the bane of your mathematical existence, then this workshop if for you. We will spend time with mixed numbers, but the emphasis will be on finding the least common denominator and dealing with improper fractions since those topics are most important for the study of algebra. Depending on the students who show up, the workshop may also cover how one approaches fractions when they are in algebraic expressions or equations. Appropriate for Math M09, Math M01, Math M03, Math M04, and Math M05 students. Graphing for Algebra This workshop is primarily for students in algebra classes who need help with graphing linear equations. The focus of this workshop is graphing as well as the equations that describe a linear equation of the form ax+by=c. Appropriate for Math M01, Math M03, Math M04, and Math M05 students. Math Anxiety & Test Taking Strategies If you have ever said that you hate math or that you know math until you take the test, then this workshop is for you. In this workshop, we discuss how to overcome math anxiety and how to prepare for and take a math exam. Appropriate for all Math Students. Probability This workshop is intended for students with difficulty with the counting and probability rules. Appropriate for Math M15. Radicals (Including Square Roots) Radicals form an important aspect of algebra. We begin with the study of square roots and then (depending on the interest of the students attending) proceed to other roots as well as describing how radicals can be written as fractional powers. Appropriate for Math M01, Math M03, Math M04, and Math M05 students. Reading Mathematics and Science This workshop approaches how to read a mathematical (or any science) text in order to increase one's understanding of the material. This workshop does not focus on word problems, though that is a topic that is discussed. (For help with word problems, see the Word Problems for Algebra Workshop). Reading math or science is often very difficult and in these workshop we discuss tools for making this necessary task easier. Appropriate for all Math and Science students regardless of level. Reading Math, Math Anxiety, & Test Taking Strategies This workshop is a combination of the Reading Mathematics and Science workshop and the Math Anxiety and Test Taking Strategies workshop. Appropriate for all Math Students. Trigonometry for Calculus The point-of-view of the workshop is based soundly on the unit circle. We will look at a number of example problems that require the use of right triangles as well as the unit circle. The goal is to leave the workshop with an understanding that the trigonometric functions are functions. As we progress through the semester, we will also introduce into the workshops calculus applications of trig that are appropriate for Math M25A and Math M25B. Appropriate for Math 25A or Math 25B, or even Math M06 or Math M07. Word Problems for Algebra Many students struggle with word problems or "problem solving" questions in algebra. The purpose of this workshop is to teach students how to translate from mathematical English into the symbolism of math in order to succeed at word problems. Appropriate for Math M01, Math M03, Math M04, and Math 5 students. All files on this page are .pdf files, which can be read by Adobe Acrobat. Download Adobe Acrobat.
Purchasing Options Features Looks at abstract algebra as the main tool underlying discrete mathematics and the digital world Uses semigroups and monoids as stepping stones to present the concepts of groups and rings Presents the fundamentals of abstract algebra, before offering deeper coverage of group and ring theory Provides examples of abstract algebra concepts in matrices and calculus Contains numerous exercises of varying levels of difficulty, chapter notes that point out variations in notation and approach, and study projects that cover an array of applications and developments of the theory Includes a solutions manual for qualifying instructors Summary Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles. A Quick Introduction to Algebra The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. The author also uses equivalence relations to introduce rational numbers and modular arithmetic as well as to present the first isomorphism theorem at the set level. The Basics of Abstract Algebra for a First-Semester Course Subsequent chapters cover orthogonal groups, stochastic matrices, Lagrange's theorem, and groups of units of monoids. The text also deals with homomorphisms, which lead to Cayley's theorem of reducing abstract groups to concrete groups of permutations. It then explores rings, integral domains, and fields. Advanced Topics for a Second-Semester Course The final, mostly self-contained chapters delve deeper into the theory of rings, fields, and groups. They discuss modules (such as vector spaces and abelian groups), group theory, and quasigroups. Editorial Reviews … The author goes the extra mile to build algebraic concepts by confronting the pedagogic and logical sequence groups-first or rings-first dilemma … a perfect pure math precursor to Grillet and Knapp's works. … The book's well-thought out sequence supports a set of useful statements on how to use its 11 chapters in a course … The book is also outstanding for self-study. … I recommend this book as second to none on abstract algebra for its content, style, and expository efficiency. —Computing Reviews, January 2011 … a careful treatment of the principal topics of abstract algebra … This is an attractive book which could be read by everybody because the author supposes not so much knowledge from the reader and gives all the necessary information to continue the reading from [one] chapter to the next. The approach used by the author to introduce modules and group actions is new and innovative. The book is well written … students and even experienced researchers may benefit strongly from this book. … —IACR Book Reviews, October 2010 … This compact book covers topics one would expect to find in an abstract algebra text. … Smith's approach is carefully implemented, and topics flow logically from one chapter to the next. The writing is careful and rigorous, yet accessible to hardworking students. The problems are collected at the end of each chapter in two sets, with one set made up of shorter exercises. … This is an ideal text for an abstract algebra course comprised of mathematics students or CS students who have either a strong minor or second major in mathematics. … —Computing Reviews, December 2009 One can trace the author's research interests to the border between algebra and category theory, which gives the textbook its unique flavour. —EMS Newsletter, March 2009 The book is well written and flows well. Readers looking for an alternative approach to abstract algebra should consider this volume. —J.R. Burke, Gonzaga University, CHOICE, July 2009, Vol. 46, No. 11 This book is well written, interesting to read, and the proofs and examples are clear and clean. —David F. Anderson, Mathematical Reviews, 2009e
Welcome to MathDL Mathematical Communication MathDL Mathematical Communication is a developing collection of resources for engaging students in writing and speaking about mathematics, whether for the purpose of learning mathematics or of learning to communicate as mathematicians. This site addresses diverse aspects of mathematical communication, including
A short article designed to provide an introduction to functional equations, those in which a function is sought which is to satisfy certain relations among its values at all points. For example, we may look for... Problems With a Point is a site developed for mathematics students and teachers in grades 6-12. The site contains practice problems on various topics that designed to help students understand mathematical concepts and... Provided by the University of Vienna?s futureMedia initiative, the Maths Online Gallery consists of a large collection of extremely useful interactive learning units that demonstrate mathematical concepts. A large n... While some may know fractals primarily from their use in abstract painting and African art, fractals are important elements within the world of mathematics. For those who seek to learn more about the construction of... This site highlights some of the conjectures and open problems concerning L-functions, with emphasis on the areas in which there has been recent progress using results from Random Matrix Theory. The main page's index...
Monmouth Junction TrigonometryAlgebra is the collection and categorization of many different rules, formulas and properties. A typical Algebra 1 course reinforces the very basics of solving, graphing, and writing linear equations and inequalities. The next step introduces powers and exponents, quadratic equations along with polynomials and factoringYou have to excel at one of the nation's top programs. That's why an outstanding score on the LSAT is more important than ever. The LSAT is a well-designed test of logic, critical reasoning, reading in detail, and mental speed and endurance.
More About This Textbook Overview A DIFFERENT WAY TO LEARN DIFFERENTIAL EQUATIONS Now anyone with an interest in stepping up to higher math can do so—without formal training, unlimited time, or a genius IQ. In Differential Equations Demystified, award-winning math professor Steven Krantz provides an effective, anxiety-free method to get past common obstacles on the road to success in higher math and science. With Differential Equations Demystified, you master the subject one step at a time—at your own speed. This self-teaching guide offers unique "Math Notes" and "You Try It" exercises, problems at the end of each chapter to pinpoint weaknesses, and a 100-question final exam to reinforce the great information in the entire book. If you want to master differential equations fearlessly, here's a fast and effective self-teaching course to help you do just that. Get ready to -- Editorial Reviews Sci-Tech Book News Krantz asserts that if calculus is the heart of modern science, differential equations are the guts. Writing for those who already have a basic grasp of calculus, Krantz provides explanations, models, and examples that lead from differential equations to higher math concepts in a self-paced format. He includes chapters on first-order and second-order equations, power series solutions and spatial functions, Fourier series, Laplace transforms, numerical methods, partial equations and boundary value problems. His models come from engineering, physics and other fields in math. He includes solutions to the exercises and a final exam. Meet the Author Steven Krantz, Ph.D., is Chairman of the Mathematics Department at Washington University in St. Louis. An award-winning teacher and author, Dr. Krantz has written more than 45 books on mathematics, including Calculus Demystified, another popular title in this series 23, 2009 bad book I agree with the other reviewer. The examples are very hard to understand, the author skips far too many steps, and the answers are not well explained at all. Not mention there are no answers for the "Now you try it" problems. How am I to know if I did it right? 1 out of 1 people found this review helpful. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. Anonymous Posted June 25, 2005 Good explanations poor examples You have to follow the author from beginning to end in order to understand the little steps involved, but all in all the explanations are very well written. The examples are inconsistent with variables, and often have integration errors. Also, the real-world examples should be sorted from examples that are meant to teach. I often found myself studying the real-world problems for hours at a time, not understand the ideas behind them, and yet still ace most of the tests. Needless to say, the book would have been great if the authors had double-checked their examples so I would not have to find where THEY went wrong. I would not recommend this book for anyone trying to understand differential equations. 1 out of 1 people found this review helpful. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
Unsolved problems on perfect graphs, a collection for people with at least a basic knowledge of the subject. Contents include: Perfection of special classes of Berge graphs; Recognition of special classes of Berge... A short article designed to provide an introduction to computational geometry, intended for topics whose geometric aspects are fairly straightforward, but for which the main questions involve efficient, accurate... In this activity, students will generate scatter plots and use regression and logarithms to explore a dataset with time and temperature data for an insulation pack. Questions about the exercise are given at the bottom... Combinatorial objects are everywhere. How many ways are there to make change for $1 using unlimited numbers of coins of all denominations? Each way is a combinatorial object. AMOF is part encyclopedia and part...
Focused on learning mathematics by working problems together, this course will explore how iterative processes can be used to investigate Fibonacci numbers, image processing, the calculation of square roots, and more. Focused on learning mathematics by working problems together, this course will use this theme as a springboard into investigations of the structure of different algebraic systems and geometric curves. This applied mathematics - choosing and designing tasks - is mathematics applied to the work teachers do. Focused on learning mathematics by working problems together, this course explores the fundamental mathematics on a topic that has its roots in secondary level, and is related to the mathematical theme of the Institute. Teachers in this course will look at some basic geometric habits of mind like studying continuous change and looking for things that don't change, and they'll apply these habits to a wide variety of situations. Focused on learning mathematics by working problems together, this course explores the fundamental mathematics on a topic that has its roots in the secondary level, and is related to the mathematical theme of the Institute. This course looks at how combinatorics itself can fit into the 5-12 program, but it also looks at how combinatorics and combinatorial thinking can be used to illuminate ideas from more mainstream courses like algebra, arithmetic, and geometry. Focused exclusively on learning mathematics by working problems together, this course explores the fundamental mathematics on a topic that is rooted at the secondary level but related to the mathematical theme of the Institute
have a TI-84 Plus Graphing Calculator, you have a powerful, sophisticated tool for advanced math. In fact, it's so sophisticated that you may not know how to take advantage of many of its features and functions. That's a good problem to have, and TI-84 Plus Graphing Calculator For Dummies is the right solution! It takes the TI-84 Plus to the next power, showing you how to: Display numbers in normal, scientific, or engineering notations Perform basic calculations, deal with angles, and solve equations Create and investigate geometric figures Graph functions, inequalities, or transformations of functions Create stat plots and analyze statistical data Create probability experiments like tossing coins, rolling dice, and so on Save calculator files on your computer Add applications to your calculator so that it can do even more TI-84 Plus Graphing Calculator For Dummies was written by C.C. Edwards, author of TI-83 Plus Graphing Calculator For Dummies, who has a Ph.D. in mathematics and teaches on the undergraduate and graduate levels. The book doesn't delve into high math, but it does use appropriate math examples to help you delve into: Using the Equation Solver Using GeoMaster and its menu bar to construct lines, segments, rays, vectors, circles, polygons, perpendicular and parallel lines, and more Creating a slide show of transformations of a graph Using the Inequality Graphing application to enter and graph inequalities and solve linear programming problems There's even a handy tear-out cheat sheet to remind you of important keystrokes and special menus, And since you'll quickly get comfortable with the built-in applications, there's a list of ten more you can download and install on your calculator so it can do even more! TI-84 Plus Graphing Calculator For Dummies is full of ways to increase the value of your TI–84 Plus exponentially
Free Algebra Lessons from Purplmath Lessons: "How do you really do this stuff?" — Purplemath's algebra lessons are written with the student in mind. These lessons emphasize the practicalities rather than the technicalities, demonstrating dependable techniques, warning of likely "trick" questions, and pointing out common mistakes. The lessons are cross-referenced to help you find related material, and a "search" box is on every page to help you find what you're looking for. You can access their preliminary through advanced Algebra lessons
MATH20201 - Algebraic Structures 1 Requisites Aims The course unit aims to introduce basic ideas group theory with a good range of examples so that the student has some familiarity with the fundamental concepts of abstract algebra and a good grounding for further study. Brief Description This course unit provides an introduction to groups, one of the most important algebraic structures. It gives the main definitions, some basic results and a wide range of examples. This builds on the study of topics such as properties of the integers, modular arithmetic, and permutations included in MATH10101/MATH10111. Groups are a fundamental concept in mathematics, particularly in the study of symmetry and of number theory. Learning Outcomes On completion of this unit successful students will be able to: Appreciate and use the basic definitions and properties of groups; Command a good understanding of the basic properties for a good range of examples;
Additionally every junior and senior physics course requires solving differential equations. Add to that all the graduate level physics courses (including mathematical methods) that I took and it is clear I understand differential equations. I have been using computers for more than 40 years.
I suggest you get a quick read on "Counting Techniques" and "Set Theory Basics" topics in a Finite Math (for business) type of book before you study probability. It would help a lot. – Emmad KareemFeb 11 '12 at 12:36 @EmmadKareem:Why these topics?Are they prerequisite?In what way?Would it be possible to elaborate on this in an answer perhaps? – JimFeb 11 '12 at 18:00 2 Answers It would help if you gave a little bit of background about yourself and your goals. Are you a math major or do you have some "mathematical sophistication?" Are you interested in learning probability for its own sake or for applications? I taught probability to undergraduate math majors recently and I used Chung's "Elementary Probability Theory." (You can check out the webpage for my course if you like.) I really like this book as a very gentle introduction to probability. Chung has a nice way of explaining the fundamental concepts in an intuitive yet rigorous manner. Also, this book has answers to many of the exercises in the back, which could be helpful for self-study, in case you get stuck. I don't believe there is a solutions manual, however. Also, I'm afraid some of my students were not very happy with the textbook (though that's typical no matter what book is used). Alternatively, "A First Course in Probability" by Sheldon Ross is an excellent introductory level textbook, with MANY examples to help you develop your intuition. If I were in your shoes, I would probably get myself a copy of Ross's book and then follow the syllabus of the MIT course based on this book here: I will check out these books thank you.One question though:from my experience (correct me here) topics that have other subjects as prerequisites are presented in the books as "refreshers chapters" and you don't really learn the material from there.You have to actually get another book since most of the intuitive explanation is assumed to be known or left out as "out of scope" for this book.I was wondering is this the same with Chung's book on counting and Sets? – JimFeb 12 '12 at 14:52 @Jim It seems to me that Chung's chapters on sets and counting are self-contained. However, it's hard for me to speak objectively about this, since I knew the subject before I ever opened Chung's book. I will say that one reason I chose Chung to teach from was because it was one of the only books to devote an entire chapter to sets. Also note: Chung calls the chapter "Set" -- not "Set Theory" -- probably to make it clear that this is not hard-core set theory. Rather, he just covers the very basics that you need for probability. So, yes, I think it's very elementary and self-contained. – William DeMeoFeb 15 '12 at 5:05 I suggest, based on my experience when I was a student, that you get a quick read on "Counting Techniques" and "Set Theory Basics" topics in a Finite Math (for business) type of book before you study probability. It would help a lot. Counting Techniques are important in solving probability problems based on counting. For example, what is the probability of getting a 1 when you throw a dice twice or what is the probability of pulling a number such as 123 form a list of random numbers. The knowledge of how to calculate combinations and permutations was poorly described in many of the probability books I used for study. Discrete Mathematics texts usually offer good presentation of Binomial theorem and the understanding of the properties of the Binomial coefficient is crucial for discrete counting techniques. Elementary set theory (set definition, union, intersection, Venn diagrams, etc.) gives a good background to understanding more about sample space construction. However, is is less important than counting techniques. I agree with your view that elementary set theory and counting techniques are critical for solving probability problems. This is one of the main reasons I chose Chung's book (mentioned in my answer above). Chapter 1 is called "Set." Chapter 3 is called "Counting." – William DeMeoFeb 12 '12 at 1:13 @williamdemeo, thank you for your comment. I must take a look at this book. I was not familiar with it before. – Emmad KareemFeb 12 '12 at 4:54 @Emmad Kareem:Do you have a recomended book on these topics? – JimFeb 12 '12 at 11:32 @Emmad Kareem:I will checkout the book mentioned by William Demeo of course.It is just that from my experience (correct me here) topics that have other subjects as prerequisites are presented in the books as "refreshers" and you don't really learn the material from there. – JimFeb 12 '12 at 14:50
More About This Textbook Overview ".makes it possible for a person to delve into the mystery of calculus without being mystified." --Physics Teacher Editorial Reviews Booknews Offers a set of DOS software tools with source code and explanations. Includes: directory management, dBase file manipulation, file security, printer control, system performance, and word processing. Glossary. No bibliography. A self-instructural guide for students who need additional help with calculus, or working professionals who need to brush up on the fundamentals. Contains frequent reviews, quizzes, examples, exercises and problems. Included are the elementary techniques of differential and integral calculus with a preliminary review of algebra and trigonometry. Annotation c. Book News, Inc., Portland, OR (booknews.com) Related Subjects Meet the Author DANIEL KLEPPNER is Lester Wolfe Professor of Physics at Massachusetts Institute of Technology. NORMAN RAMSEY is Higgins Professor of Physics at Harvard University and a recipient of the Nobel Prize for Physics
The Algebra 1: The Complete Course DVD Series will help students build confidence in their ability to understand and solve algebraic problems. In this episode, students will learn about the history of problem solving and the derivation of the algebraic equation by functional exploration and by symbolic manipulation. Grades 5-9. 30 minutes on DVD. Finally learn the language you've always wanted to learn with the Living Language Method!
... More About This Book problems, and practice exercises to test your skills. This Schaum's Outline gives you 885 fully solved problems Complete review of all course fundamentals Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time--and get your best test scores! Topics include: Fundamental Concepts; Polynomials; Rational Expressions; First-Degree Equations and Inequalities; Exponents, Roots, and Radicals; Second-Degree Equations and Inequalities; Systems of Equations and Inequalities; Relations and Functions; Exponential and Logarithmic Functions; and Sequences, Series, and the Binomial Theorem Schaum's Outlines--Problem Solved. Schaum's Outlines include basic theory, definitions, and hundreds of sample problems solved in step-by-step detail and supplementary problems with answers. Schaum's Outlines have been favorably received and widely adopted by numberous colleges and technical schools. Related Subjects Meet the Author Ray Steege received his B.A. in mathematics from the University of Wyoming and his M.A. in mathematics from the University of Northern Colorado. The first 20 years of his teaching career were at East High School in Cheyenne, Wyoming. He continued his professional career at Laramie County Community College in Cheyenne, Wyoming for an additional 25 years prior to his retirement in 1994. Among his many achievements and honors are: past president of the Wyoming Mathematics Association of Two-Year Colleges, Wyoming Mathematics Coalition Steering Committee member, newsletter editor, and recipient of the Outstanding Faculty Member of the Physical Science Division award at the college. Kerry Bailey received his B.A. in mathematics from San Diego State University and his M.A. in mathematics from the University of Colorado. He has been teaching at Laramie County Community College in Cheyenne, Wyoming for the past 14 years. Prior to this position, he taught for 10 years at Pikes Peak Community College in Colorado Springs, Colorado. Among his achievements and honors are: current inclusion in Who's Who in The West, Wyoming Mathematics Coalition Steering Committee member, newsletter editor, and recipient of the Outstanding Faculty member of the Physical Science Division award, and corecipient of the Outstanding Faculty Member award for the entire college at Laramie County Community
Intermediate Algebra "Intermediate Algebra" by Baratto/Kohlmetz/Bergman is part of the latest offerings in the successful Streeter-Hutchison Series in Mathematics. By ...Show synopsis"Intermediate Algebra" by Baratto/Kohlmetz/Bergman is part of the latest offerings in the successful Streeter-Hutchison Series in Mathematics. By popular demand, we are now offering an Intermediate Algebra book in the series again. This book combines the best of earlier versions of Intermediate Algebra, along with new material requested by a cross-section of Intermediate Algebra instructors across the country. This first edition maintains the hallmark approach of encouraging the learning of mathematics by focusing its coverage on mastering math through practice. This worktext seeks to provide carefully detailed explanations and accessible pedagogy to introduce are well-organized, and clearly labeled. Vocational and professional-technical exercises have been included throughout. Repeated exposure to this consistent structure should help advance the student's skills in relating to mathematics. The book is designed for a one-semester intermediate algebra course and is appropriate for lecture, learning center, laboratory, or self-paced courses. It is accompanied by numerous useful supplements, including McGraw-Hill's online homework management system, MathZone
John McGregor Secondary School COURSE STATEMENT COURSE NAME: Foundations of Mathematics, Grade 9 COURSE CODE: MFM 1P1 MINISTRY GUIDELINE: The Ontario Curriculum, Grades 9 and 10, Mathematics, 2005 (Revised) LEVEL OF DIFFICULTY: Applied CREDIT VALUE: 1 PREREQUISITE: none TEXTBOOK(s): Pearson 9 Value: $70 Course Description: This course enables students to develop an understanding of mathematical concepts related to introductory algebra, proportional reasoning, and measurement and geometry through investigation, the effective use of technology, and hands-on activities. Students will investigate real-life examples to develop various representations of linear relations, and will determine the connections between the representations. They will also explore certain relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. Students will consolidate their mathematical skills as they solve problems and communicate their thinking. Overall Learning Expectations: By the end of this course, students will: • solve problems involving proportional reasoning; • simplify numerical and polynomial expressions in one variable, and solve simple first-degree equations. • apply data-management techniques to investigate relationships between two variables; • determine the characteristics of linear relations; • demonstrate an understanding of constant rate of change and its connection to linear relations; • connect various representations of a linear relation, and solve problems using the representations. • determine, through investigation, the optimal values of various measurements of rectangles; • solve problems involving the measurements of two-dimensional shapes and the volumes of three-dimensional figures; • determine, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems. -2- Evaluation: Term Work 70% Knowledge / Understanding 35 % Inquiry / Thinking 15 % Communication 15 % Application / Making Connections 35 % Summative assessment activities during the course will be comprised of a variety of methods and strategies. (eg. Assignments, projects, tests, journals, performances, conferences, etc.) Final Evaluation 30% The final evaluation will consist culminating activities which include, but are not limited to:  a final examination, written during the examination schedule (15%)  the Grade 9 EQAO Assessment of Mathematics. (15%) Classroom Rules: Students are expected to follow these rules so that mathematics education can be successful. a) BE ON TIME b) COME PREPARED FOR CLASS c) PARTICIPATE IN CLASS - Keep good notes while the lesson is being taught, pay attention in class, ask questions and answer any questions the teacher asks, if possible. d) RESPECT THE RIGHTS OF OTHERS - Work quietly and co-operate so as not to disturb other students who are trying to learn. e) CATCH UP ON ANY WORK MISSED - When returning from an absence, catch up on missed work as quickly as possible. f) COMPLETE ANY HOMEWORK ASSIGNED - If work is not completed in class, complete it before the next class so that you may benefit from the discussions based on the homework. g) REMAIN IN YOUR DESK until the teacher dismisses the class. h) FOLLOW ESTABLISHED SCHOOL ROUTINES AND BEHAVIOUR CODES - see student handbook. Learning Materials Required:  Textbook: Number: __________  Notebook - 3 ring binder with lined and graph paper  Pencil, eraser, ruler  Scientific calculator (TI 83/84 preferred but not mandatory)  Student Handbook
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An Interactive Experience: Teaching Mathematics with Mathematica Eric Schulz, Walla Walla Community College This content requires JavaScript and Adobe Flash Player 10 or higher. If you are using a browser with JavaScript or Flash disabled, please enable them now. Otherwise, please install the latest version of the free Flash Player. Generates professional-looking documents that can include text, calculations, and interactive visualizations Provides a development environment to build flexible, structured courseware "There are other tools that on the surface appear equivalent to Mathematica, but I have yet to find anything that compares to Mathematica's breadth, depth, elegance, and consistency." Overview Teaching and Mathematica go hand in hand for Eric Schulz, a mathematics instructor at Walla Walla Community College. "Mathematica is more than it appears to be to the new user. It's not just a calculator. It's not just input/output. It's a tool where you can express yourself," says Schulz. "I use Mathematica to do all of my writing, in addition to lecture notes and handouts." Schulz also creates dynamic interfaces in Mathematica to visually enhance every lesson he teaches. He says, "I regularly think about how I can explain concepts visually because I know in the classroom I have students for which that would make sense. And then I can follow up and teach in the analytical mode."
Book summary This resource illustrates the mathematics that a game programmer would need to develop a professional-quality 3D engine. The book starts at a fairly basic level in each of several areas such as vector geometry, modern algebra, and physics, and then progresses to somewhat more advanced topics. Particular attention is given to derivations of key results, ensuring that the reader is not forced to endure "gaps" in the theory. The book discusses applications in the context of the OpenGL architecture. It assumes basic understanding of matrix algebra, trigonometry, and calculus, and concentrates on key math topics for programming game engines and computer graphics. Included are exercise sets which should allow the book to be used as a textbook. The book discusses applications in the context of the OpenGL architecture due to its cross-platform nature with references to certain 3D hardware such as the GeForce from Nvidia and the Radeon from ATI Presents mathematical theory and subsequently provides examples using practical applications. [via]
Elementary Algebra 9780077224790 ISBN: 0077224795 Edition: 6 Pub Date: 2008 Publisher: McGraw-Hill Companies, The Summary: Mark Dugopolski was born and raised in Menominee, Michigan. He received a degree in mathematics education from Michigan State University and then taught high school mathematics in the Chicago area. While teaching high school, he received a master's degree in mathematics from Northern Illinois University. He then entered a doctoral program in mathematics at the University of Illinois in Champaign, where he earned his ...doctorate in topology in 1977. He was then appointed to the faculty at Southeastern Louisiana University, where he now holds the position of professor of mathematics. He has taught high school and college mathematics for over 30 years. He is a member of the MAA, the AMS, and the AMATYC. He has written many articles and mathematics textbooks. He has a wife and two daughters. When he is not working, he enjoys hiking, bicycling, jogging, tennis, fishing, and motorcycling. Dugopolski, Mark is the author of Elementary Algebra, published 2008 under ISBN 9780077224790 and 0077224795. Three hundred twelve Elementary Algebra textbooks are available for sale on ValoreBooks.com, one hundred ten used from the cheapest price of $72.66, or buy new starting at $103.93 new instructor edition same as student editon page by page it has the all the answer the mi... [more]ALTERNATE EDITION: Brand new instructor edition same as student editon page by page it has the all the answer the minor diference will ship immediately Hardback Instructors Edition, All text is same as student edition but may contain additional information or answers. In Stock, Based in Ohio. Ships SAME or NEXT busi [more] ALTERNATE EDITION:
The Geometry Practice Resource Book is the perfect tool for struggling students. The 128 page resource book covers the concepts of triangles, polygons, quadrilaterals, circles, congruence, similarity, symmetry, coordinate and non-coordinate geometry, angles, patterns, and reasoning. Clear instructions, examples, practice pages, definitions, and problem-solving strategies will be a big help for students. Teachers will appreciate the assessment section, answer keys, and references. Ideal for students in grades 7+. Resource Books Are Not Returnable.
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Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminatingThis book is a supplement to the text Teaching Fractions and Ratios for Understanding. It is not merely an answer key, but a resource that includes in-depth discussions of the problems in the text; develops and extends discussion of the issues, teaching problems, and other considerations raised in the chapters; and contains additional problems--with...Chance continues to govern our lives in the 21st Century. From the genes we inherit and the environment into which we are born, to the lottery ticket we buy at the local store, much of life is a gamble. In business, education, travel, health, and marriage, we take chances in the hope of obtaining something better. Chance colors our lives with uncertainty,... more...
College Algebra - 2nd edition Summary: The BPB team has created a book where the use of the graphing calculator is optional but visualizing the mathematics is not. By creating algebraic visual side-by-sides to solve various problems in the examples, the authors show students the relationship of the algebraic solution with the visual, often graphical, solution. In addition to helping students visualize the math with side-by-sides, the authors focus on helping students make the connection between x-intercep...show morets, zeros, and solutions, both visually and algebraically. Features Functions Early and Integrated--This is the only non-graphing-calculator-required book on the market that introduces functions in Chapter 1 and thus sets BPB apart. Algebraic Visual Side-by-Sides--Examples are worked out both algebraically and visually to increase student understanding of the concepts. 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New To This Edition Visualizing the Graph--This new feature asks students to match an equation with its graph. This focus on visualization and conceptual understanding appears in every chapter to help students see "the big picture." More Focus on Graphs--Throughout the text, there is an increased focus on graphs and graphing, again reminding students how helpful visualization can be in the discipline of mathematics. In particular, graphing of polynomial functions by hand has been added and emphasized in Section 3.1 at the request of reviewers. Reorganization of Material--Section 1.5 has been split into two sections, 1.5 and 1.6. Composition of functions has been moved from Section 4.1 to 1.6, where it appears with the material on the algebra of functions. Vocabulary Review--Appearing once in every chapter, in the Skill Maintenance portion of an exercise set, this feature checks and reviews students' understanding of the language of mathematics. Classify the Function--With a focus on conceptual understanding, students are asked one time per chapterOver 1000 New Exercises--The authors have worked hard to add additional exercises, where needed and often at the request of reviewers, on key topics throughout the text. Appendix Covering Basic Concepts from Geometry--New to this edition is an appendix covering basic concepts from geometry that students need to know in order to work with topics pertaining to angles and triangles. New Annotated Instructor's Edition --This special edition of the text provides answers to almost all text exercises in color on the page that the exercise appears. This provides the instructor with immediate access to answers without searching the back of the book.. Systems of Equations in Two Variables. Systems of Equations in Three Variables. Matrices and Systems of Equations. Matrix Operations. Inverses of Matrices. Determinants and Cramer's Rule. Systems of Inequalities and Linear Programming. Partial Fractions. 6. Conic Sections. The Parabola. The Circle and the Ellipse. The Hyperbola. Nonlinear Systems of Equations. Book is in good condition. Orders ship within 24-36 hours with free tracking. To help ensure your complete satisfaction we accept returns for five days after your order arrives. The interior is good a...show morend completely readable and may or may not contain marks/highlights/writing that will capture key points for you. The exterior is good or acceptable and shows some shelf wear around the edges possibly showing heavier wear in some areas. Book may or may not contain cd rom or accessory if applicable. Beyond Words Books is a green initiative supporting recycling efforts, local jobs, & other local organizations through spreading the gift of literacy. Your purchase, satisfaction, & positive feedback help fund this mission & are integral to our selling success on Amazon. 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The Panel will advise the President and the Secretary of Education on the best use of scientifically based research to advance the teaching and learning of mathematics, with a specific focus on preparation for and success in algebra. 10 11 Basis of the Panels work Review of 16,000 research studies and related documents. Public testimony gathered from 110 individuals. Review of written commentary from 160 organizations and individuals 12 public meetings held around the country Analysis of survey results from 743 Algebra I teachers 11 12 Two Major Themes First Things First - Positive results can be achieved in a reasonable time at accessible cost by addressing clearly important things now. - A consistent, wise, community-wide effort will be required. Learning as We Go Along - In some areas, adequate research does not exist. - The community will learn more later on the basis of carefully evaluated practice and research. - We should follow a disciplined model of continuous improvement. 12 13 Curricular Content Streamline the Mathematics Curriculum in Grades PreK-8 Follow a Coherent Progression, with Emphasis on Mastery of Key Topics Focus on the Critical Foundations for Algebra - Proficiency with Whole Numbers - Proficiency with Fractions Particular Aspects of Geometry and Measurement Avoid Any Approach that Continually Revisits Topics without Closure 13 14 Curricular Content An Authentic Algebra Course All school districts Should ensure that all prepared students have access to an authentic algebra course, and Should prepare more students than at present to enroll in such a course by Grade 8. 14 15 Curricular Content What Mathematics Do Teachers Need to Know For early childhood teachers Topics on whole numbers, fractions, and the appropriate geometry and measurement topics in the Critical Foundations of Algebra For elementary teachers All topics in the Critical Foundations of Algebra and those topics typically covered in an introductory Algebra course For middle school teachers - The Critical Foundations of Algebra - All of the Major Topics of School Algebra 15 16 Learning Processes Scientific Knowledge on Learning and Cognition Needs to be Applied to the Classroom to Improve Student Achievement Most children develop considerable knowledge of mathematics before they begin kindergarten. Children from families with low incomes, low levels of parental education, and single parents often have less mathematical knowledge when they begin school than do children from more advantaged backgrounds. This tends to hinder their learning for years to come. There are promising interventions to improve the mathematical knowledge of these young children before they enter kindergarten. 16 17 Learning Processes To prepare students for Algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, factual knowledge and problem solving skills. Limitations in the ability to keep many things in mind (working-memory) can hinder mathematics performance. Practice can offset this through automatic recall, which results in less information to keep in mind and frees attention for new aspects of material at hand. Learning is most effective when practice is combined with instruction on related concepts. Conceptual understanding promotes transfer of learning to new problems and better long-term retention. 17 18 Learning Processes Childrens goals and beliefs about learning are related to their mathematics performance. Childrens beliefs about the relative importance of effort and ability can be changed. Experiential studies have demonstrated that changing childrens beliefs from a focus on ability to a focus on effort increases their engagement in mathematics learning, which in turn improves mathematics outcomes. 18 19 Instructional Practices Instructional practice should be informed by high quality research, when available, and by the best professional judgment and experience of accomplished classroom teachers. All-encompassing recommendations that instruction should be student-centered or teacher-directed are not supported by research. 19 20 Instructional Practices Research on students who are low achievers, have difficulties in mathematics, or have learning disabilities related to mathematics tells us that the effective practice includes Explicit methods of instruction available on a regular basis Clear problem solving models Carefully orchestrated examples/ sequences of examples. Concrete objects to understand abstract representations and notation. Participatory thinking aloud by students and teachers. 20 21 For More Information Please visit us online at http// 21 22 Mathematical Proficiency Defined National Research Council (2002) defines proficiency as Understanding mathematics Computing Fluently Applying concepts to solve problems Reasoning logically Engaging and communicating with mathematics 23 Grous and Ceulla (2000) reported the following can increase student learning and have a positive effect on student achievement Increasing the extent of the students opportunity to learn (OTL) mathematics content. Focusing instruction on the meaningful development of important mathematical ideas. Providing learning opportunities for both concepts and skills by solving problems. Giving students both an opportunity to discover and invent new knowledge and an opportunity to practice what they have learned. Using small groups of students to work on activities, problems, and assignments (e.g., small groups, Davidson, 1985 cooperative learning, Slavin, 1990 peer assisted learning and tutoring, Baker, et al., 2002). Whole-class discussion following individual and group work. Teaching math with a focus on number sense that encourages students to become problem solvers in a wide variety of situations and to view math as important for thinking. Use of concrete materials on a long-term basis to increase achievement and improve attitudes toward math. 25 Lets turn to Alabama and Georgia 26 Alabama SBR Math SPDG-Supported Activities 27 GOAL 1 Through the implementation of SBR instructional strategies within the framework, there will be a 20 percent reduction in the achievement gap between students with and without disabilities in the area of math and age appropriate progress in pre-literacy/reading and math. 28 Alabama State Department MATH INITIATIVE 2008-2009 29 Overview 12 school districts participated in 2007-2008. An additional 4 school districts participated in 2008-2009 (16 total). On average, Eighth Grade students increased their Computational Fluency scores from 28.8 to 35.4. The percent of students needing intensive focus on computational fluency decreased from 20 to 14. 61 Eighth Grade ModulesSpecial Education Students 62 Transitional Math Four school improvement schools were selected during Year 2 for implementation of Transitional Math One high school in Butler County - Greenville One high school in Elmore County - Stanhope Two high schools in Montgomery County Jefferson Davis and Robert E. Lee The four participating schools received eight days of technical assistance a month from two consultants from SOPRIS West. 63 Transitional Mathematics is designed to help students understand operations on whole numbers conceptually and addresses the needs of struggling students who have scored at or below the 40th percentile on national math tests. Transitional Mathematics is based on three broad design principals Ensuring that students have relevant background knowledge. Using a balanced approach in computational practice. Addressing the need for careful time management. 64 I. Process Evaluation The Transitional Math program uses curriculum based student progress monitoring, which services as a fidelity tool. In August 2009, the TransMath Online Assessment System will be launched as Individualized student placement based on students mastery of foundational math skills. 71 of all students progressed from the Frustration to Instructional or Mastery Level 66 of SWD progressed from the Frustration to Instructional or Mastery Level CONCEPTS/ESTIMATION Of the targeted group of students 28 were SWD 56 of all students progressed from the Frustration to Instructional or Mastery Level 45 of SWD progressed from the Frustration to Instructional or Mastery Level 101 Formative Data Examples Coffee County Middle School Saturday school with math focus Math vocabulary and fluency AIMSWeb for progress monitoring 6th and 8th gr. Numeracy coaches Strategies from SPDG training Results for 24 sections of 6th grade math 79 of the sections had gt50 of students with matched scores from January to March improved 102 (No Transcript) 103 Coffee County Examining Teacher Practices Pilot Survey of 6th Grade Teachers Use of 12 targeted strategies from Riccominis training on differentiating in math Six teachers participated in the survey Twelve strategies/methods from the training were identified on the survey 104 Instruction Methods/Strategies on Survey Grouping Scaffolded Instruction General Learning Strategies (Ex. RIDE) Math Vocabulary Spaced Instructional Review (SIR) Interleave Worked Example Writing about Math Graphic Organizers for Math Mnemonic Strategy Fluency Explicit Methods of Instruction Memory Strategies Chunking Keyword 105 Survey Results 106 2009 Statewide CRCT Results 6th Grade All Students 75 met/exceeded the standard 6 percentage point increase from 2008 15 percentage point increase since 2006 Exceeded state target 7th Grade All Students 84 met/exceeded the standard 4 percentage point increase from 2008 14 percentage point increase since 2006 Exceeded state target 8th Grade All Students 70 met/exceeded the standard 8 percentage point increase from 2009 Exceeded target 107 Students with Disabilities CRCT Math Scores 08 to 09 More than a five percentage point increase in math scores for grades 6, 7, and 8 for SWD 108 Students with Disabilities Georgia High School Graduation Test Grade 11, first-time test takers 08 to 09 for SWD 63 met/exceeded standards 4 percentage point increase from 2008 109 Lessons Learned/Next Steps Review of requirements for data collection to better ensure uniformity Importance of continuing connection with general education statewide math initiatives Selection of new cohort of schools for Year 3 Continued follow-up for cohort 1 other 110 Open Discussion
Math 104: Calculus About this Course Math 104: Calculus is designed to prepare you to earn real college credit by passing the Calculus CLEP and Calculus Excelsior exams. This course covers topics that are included on the exams, such as polynomials, factoring, higher-order derivative and intermediate value theorem. Use it to help you learn what you need to know about calculus topics to help you succeed on the exams. The calculus instructors are experienced and knowledgeable educators who have put together comprehensive video lessons in categories ranging from breaking a complex concept down into its basic components to calculating velocity. Each category is broken down into smaller chapters that will cover topics more in-depth. These video lessons make learning fun and interesting. You get the aid of self-graded quizzes and practice tests to allow you to gauge how much you have learned. Category Objectives Applications of Derivatives Learn how to estimate function values using linearization and how to use Newton's method to find roots of equations. Also, study linearization of functions, optimization and differentiation, optimizing complex systems and optimizing simple systems. Area Under the Curve and Integrals Take a look at average value theorem, definite integrals, indefinite integrals as anti-derivatives, linear properties of definite integrals, the fundamental theorem of calculus, sum notation and the trapezoid rule. Learn how to find the arc length of a function, find the limits of Riemann sums, to identify and draw left, right and middle sums, use Riemann sums for functions and graphs and use Riemann sums to calculate integrals. Calculating Derivatives and Derivative Rules Discover how to apply the rules of differentiation to calculate derivatives, calculate derivatives of exponential equations and find derivatives of implicit functions. Additionally, take a look at derivatives of polynomial equations, derivatives of trigonometric functions, higher-order derivatives, derivatives of inverse trigonometric functions and linear properties of a derivative. Continuity Study continuity in a function, discontinuities in functions and graphs, intermediate value theorem and regions of continuity in a function. Differential Equations Find out about differential notation in physics, separation of variables to solve system differential equations and calculating rate and exponential growth. Geometry and Trigonometry in Calculus Learn to find distance with the Pythagorean theorem, calculate the volumes of basic shapes and solve visualizing geometry problems. Also study sine and cosine. Graphing and Functions Discover concepts that include compounding functions and graphing functions of functions, figuring the equation of a line using point-slope formula, graphing exponentials and logarithms and graphing basic functions. Additionally, study horizontal and vertical asymptotes, implicit functions, exponents, slopes and tangents. Graphing Derivatives and L'Hopital's Rule Learn to apply L'Hopital's Rule and about concavity and inflection points on graphs, function properties from derivatives, identifying functions from derivative graphs, graphing the derivative from any function, determining maximum and minimum values of a graph and non-differentiable graphs of derivatives. Integration and Integration Techniques Examine anti-derivatives, integrals of simple shapes, integrals of exponential functions, integrals of trigonometric functions and improper integrals. Also take a look at how to solve integrals using substitution, how to use trigonometric substitution to solve integrals and how to factorize fractions with quadratic denominators. Integration Applications Learn how to calculate volumes using single intervals, find area between functions with integration, find simple areas with root finding and integration and find volumes of revolution with integration. Limits Study concepts including asymptotes, infinity, limits, continuity and the squeeze theorem, Also learn to determine the limits of functions and use a graph to define limits. Rate of Change Examine derivatives, Rolle's theorem, velocity and the rate of change. Additionally, look at the definition of mean value theorem and 'differentiable.' Using Scientific Calculators for Calculus Discover how to use a scientific calculator, solve equations on a scientific calculator and understand radians and degrees on a scientific calculator. Also study trigonometry functions and exponentials on a calculator
Trigonometric Formulas There is a collection of facts, formulas and identities from this course that students should be expected to memorize because having them at ready recollection is essential for their success in Precalculus, Calculus and beyond. Instructors should design test items that require these formulas in order to assess whether they have been learned. Students must not be allowed to bring these to the test on a formula sheet.
tutorial CD-ROM provides algorithmically generated practice exercises that are correlated at the objective level to the exercises in the textbook. Every practice exercise is accompanied by an example and a guided solution designed to involve students in the solution process. Selected exercises may also include a video clip to help students visualize concepts. The software provides helpful feedback for incorrect answers and can generate printed summaries of studentsâ progress.
The following lessons were created as supplements for use with McDougal Littell's "Mathematics Concepts and Skills; Course 1" by Larson, Boswell, Kanold, and Stiff shown below. This text is one of the few on California's state list of approved textbooks for middle and high schools. Keep in mind that these previews are pictures of the actual PowerPoint slides and they show no animation. Please download this free PowerPoint lesson as a comparison: Lesson 1-9.(Click here to download free PowerPoint viewer.) Click on any highlighted lesson below to view its contents. Students may use this site, when they are absent.
Oftentimes, when it comes to math, some people struggle with the concepts, finding it too difficult. But follow these few steps and Math will be easy in every class. Ad Steps 1 Master Your Basics: The number one reason that people struggle in math class is because their basics and their fundamentals are not fully developed. Algebra and Geometry are the building blocks for the more advanced math later on (Calculus, Differential Equations, etc...). Ad 2 Get Ahead: Most schools give you a textbook for math and it's a pretty big book. What you can do is, study ahead. Whenever you have time, you can look a section ahead, and be prepared for tomorrow's material. 3 Self-Study: This is the most efficient way of studying math. I would recommend you to buy math textbooks from a local bookstore. You can also search on the internet for great math books.Don't get a book that is very short (100 pages) for a topic like Geometry. Get a textbook or a few workbooks on the topic. It's good to buy more than one book, since some books leave out certain things. 4 Studying: When you self-study, it's good to have the book and a notebook with you, college ruled preferably. Write down all the vocabulary and terms and the example problems. You don't have to do each and every single practice problem if you find it repetitive, just have an intuitive answer. (As long as you know the process of solving it) It's also good to get into a habit of working on more Word Problems, which can help you apply the concept into real-life situations. 5 Competition: If you do enough self-studying, and you look through your studying notes when you have free time, you should already have a very good basis in math. If you're a fast learner, then it would be even better since you can learn the higher level concepts quicker. If your school has a math club or team that you can join, go for it! Chances are, you'll meet individuals who are very talented in math and can help you expand your knowledge by attending competitions. 6 Loving Math: Once you do this part, math would be no challenge whatsoever. Once you get good in math, help others, it's okay to show off you knowledge, in a good way. Once you start to take interest in math and start studying it and attend math competitions and expand your knowledge on math, you will love it. Once you have a passion for math, you will want to learn more, achieve more, and become the mathematician you've never imagined.
REVIEW FOR MATH PLACEMENT TEST Students entering HolyCrossCollege are required to take a math placement test to help them determine where they should begin in our sequence of math classes. Some students find it helpful to review before taking the placement test.This is wise, especially if the student hasn't taken a math class recently. You should be able to do these problems without the use of a calculator but feel free to check your answers.The answers for the 100 practice problems appear after problem #100. Here are some definitions, concepts, objectives, and practice problems to help you review for the placement test. You should be able to: recognize operation symbols and the words representing those symbols. ·Additiona + bthe sum of a and b ·Subtractiona – bthe difference of a and b ·Multiplicationa·b,(a)(b),a(b),abthe product of a and b ·Divisiona/b, a χ bthe quotient of a and b recognize comparison symbols. ·Equality Symbols =is equal to "`is not equal to ·Inequality Symbols <is less than >is greater than <is less than or equal to >is greater than or equal to recognize grouping symbols. ()Parentheses []Brackets {}Braces are occasionally used for grouping also, but are usually reserved for set notation apply the rules for order of operations. When evaluating a math expression, perform the operations in the following order, ·beginning with the expression in the innermost parentheses or brackets first, and working out. ·Simplify all numbers with exponents, working from left to right if more than one of these expressions is present. ·Then do all multiplications and divisions left to right. ·Perform all additions and subtractions left to right. You should be able to: 5.add, subtract, multiply and divide whole numbers. 6.add, subtract, multiply and divide fractions. 7.add, subtract, multiply and divide decimals. 8.solve percent problems. 9. identify the opposite, reciprocal, and the absolute value of a number.
Pre Algebra Bridge the gap between basic math and algebra with Pre-Algebra Solved!™, the smart way to ace your homework and get better grades. Simply enter in your homework problems and Pre-Algebra Solved!™ does the rest, providing the solution with step-by-step explanations. Infinite Pre-Algebra create worksheets and tests with exactly the types of questions you want in just minutes. Infinite Pre-Algebra create worksheets and tests with exactly the types of questions you want in just minutes. No more writing questions by hand, searching through old books and worksheets, or wading through a database of prewritten... Algebra - One on One is an educational game for those wanting a fun way to learn Algebra. This program covers 21 functions. It has a practice and a game area. You can choose from calculate value, choose formula, or figure formula and calculate. It has a great help system that makes it easy for the beginner to do and understand algebra. It also has a "Einstein" level that even experts will find fun and challenging. Basic Algebra Shape-Up is interactive software that covers creating formulas; using ratios, proportions, and scale; working with integers, simple and multi-step equations. Students are able to track their individual progress. Student scores are kept in a management system that allows teachers and tutors to view and print reports. Ket is a minimalist, immersive algebra editor for the keyboard literate. Ket is a minimalist, immersive algebra editor for the keyboard literate.This software is provided for people who regularly perform not-too-specialized algebra at or around a computer. The software takes time to learn, but will, in time, provide a... Algebra Homework Help 1. Algebra Homework Help 1.0 is a useful software which helps you with your homework. How it works:Simply e-mail or fax your problems to us. We'll provide you with a free estimate in hours. It is very important that you include the following details... Innoexe Visual Algebra works in three modes. Work with others over the internet, network, or alone. Chat with others and solve problems at the same time. IVA is perfect for tutors teaching students over the internet or a network connection. Innoexe Visual Algebra will solve your problems step by step and explain as it goes. Innoexe Visual Algebra will change the way you look at algebra problems. All registered users will receive free up grades. Equator is a... Middle-School (grades 5 through 9) math program written to provide skills in context. Students write and solve simple algebra problems, then manipulate the vertices of an on-screen triangle so that it matches given information about its angles. Sample problem: "Make triangle ABC so that m OS: Mac Software Terms: Education, Elementary, High School, Junior High, K-12, Mathematics, Middle School, Pre-algebra Thinknowlogy is an innovative open source artificial language system, designed to be intelligent. Thinknowlogy is an innovative open source artificial language system, designed to be intelligent. Grammar is the foundation of natural language and contains logic. This logic is used to create intelligent behavior in Thinknowlogy. Therefore,... Is algebra showing up in your kid's homeworks? Is algebra showing up in your kid's homeworks? MULTIPLEjm will help your kids learn algebra ( + - x : ) a fun way. They will trying to beat their high score, have fun, and learn! It really helps my kids learn the tables, it will help yours. ......
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
Synopses & Reviews Publisher Comments: Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations
Speed Revision for Edexcel GCSE Maths Linear Foundation Colour-coded pages help students revise at the speed they need. This title is written by experienced examiners and authors. Copy of full "Heinemann ...Show synopsisColour-coded pages help students revise at the speed they need. This title is written by experienced examiners and authors. Copy of full "Heinemann Edexcel GCSE Maths Student" textbook is provided on CD-Rom, linked to the practice questions for extra consolidation. It highlights the sub-topics most likely to be tested in the exam. It decodes the maths language used in exam papers. Practice questions and tests indicate the grade students are working at. It features exam-style practice papers, written by examiners. It includes examples with step-by-step worked solutions, highlighting common errors and giving examiners' tips. It contains revision advice - when to start, planning a revision timetable, revision methods.Hide synopsis Edexcel GCSE Mathematics for 2006
9780130608444mediate Algebra 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. The Fourth Edition contains additional modeling and real-data coverage. A conceptual approach to functions is introduced early in the book and revisited in Ch. 5, 6, 7, 8, and 10 readers are exposed to a variety of realistic situations where functions are used to explain and record the changes we observe in the world. A discussion of solving linear equations in Chapter 2 now includes coverage of equations with no solution and equations with infinitely many solutions. The sections on determinants and Cramer's rule have been moved out of Chapter 4 into an appendix. This material can be covered with ease after Section 4.3
vision, the geometric laws that relate different views of a scene. Geometry, one of the oldest branches of ... multipleviews of a scene from the perspective of various types of geometries. A key feature is that it ... role incomputer communications. Producers and users of images, in particular three-dimensional images, ... numerous computervision algorithms included in the OpenCV library. You will learn how to read, write, ... a variety of computervision algorithms and be exposed to important concepts in image analysis that will ... mathematical morphology and image filtering. The detection and use of interest points incomputervision is ... filtering. The detection and use of interest points incomputervision is presented with applications for ... Exploit the image geometryin order to match different views of a pictured scene Calibrate the camera from ... programming. It can be used as a companion book in university-level computervision courses. It constitutes an ... image pairs and of multi-view image recordings. Scientists thus began to look at basic computervision ... last decade of the twentieth century, computervision made considerable progress towards the ... consolidation of its fundaments, in particular regarding the treatment of geometry for the evaluation of stereo ...
by Step Approach, 6thedition. This softcover edition includes all the features of the longer book, ... Browse A STEP BY STEP APPROACH is for general beginning statistics courses with a basic algebra prereq- Textbook: ElementaryStatistics: A Brief Version, 6thedition, by Allan G. Bluman. Supplies: Any scientific calculator (a graphing calculator is not necessary.) Calculators on cell phones, tablets, or other electronic devices will NOT be allowed during tests or in-class assignments. ... particularly for the Academic Support Classes that support the 6th, ... ElementaryStatistics: Picturing the World. Larson Statistical Reasoning for ... Smith ElementaryStatistics: A Step by Step Approach. Bluman Discrete Mathematics and its Applications. Textbook: ElementaryStatistics a Step by Step Approach, 6thEdition by Allan Bluman, McGraw/Hill, 2006. Available at Alsheqary bookstore ... Introductory statistics is a not an easy course and much of the material needs to be
Elementary Algebra For College Students Early Graphing 9780136134169 ISBN: 0136134165 Edition: 3 Pub Date: 2007 Publisher: Prentice Hall Algebra Early Graphing for College Students, An...gel continues to focus on the needs of the students taking this class and the instructors teaching them. Angel, Allen R. is the author of Elementary Algebra For College Students Early Graphing, published 2007 under ISBN 9780136134169 and 0136134165. Two hundred ninety seven Elementary Algebra For College Students Early Graphing textbooks are available for sale on ValoreBooks.com, twenty three used from the cheapest price of $30.91, or buy new starting at $93Dublin, OHShipping:Standard, ExpeditedComments:Brand New Hardback US Student Edition. In Stock, Based in Ohio. Ships SAME or NEXT business day. ... [more] [more
Hey all. Can anyone give me suggestions on great books that give tips on how to teach Algebra 1? I'm not really looking for a text book at this point (my new school will have that) but a source that guides me through coming at the subject at a conceptual level. For example, working with the distributive property: what activities would best help the students understand what that is all about? I'm going to be teaching Algebra 1 for the first time next year. I'm confident that I can do it, since I have a conceptual frame of mind in teaching math. I can look at what the text presents and develop more conceptually based lessons, but if anyone knows of good sources, please share them with me
I think the difficulty is that mathematics requires rigorous definitions and logic, especially as one advances in it. However, for ABE or GED students, it is usually enough to know that the equal sign is like a balance scale. In order for the sides to be in balance, the expressions on both sides must have the same value. If you add something to one side, you must add it to the other side as well to maintain the balance. If you subtract from one side, you must subtract it from the other side as well. When students get into algebra, they need to know that some transformations of an expression can change the character of the equality. For example (−/a/)^2 = /a/^2, but it does NOT follow by taking the square root of both sides that −/a/ = /a/. Likewise, /y//(/x/ − 1) = 3 needs to be qualified by /x/ ≠ 1, even though the equation can be transformed to /y/ = 3/x/ − 3, which has a solution for /x/ = 1 at /y/ = 0. For most purposes in ABE or GED classes, the balance analogy works well without getting into abstract discussions about various kinds of equivalence relations and the transformations that change the relation or leave it unchanged. If anyone has a better explanation of the equal sign for ABE and GED students, I would like to hear it. Chip Burkitt On 8/14/2010 1:04 AM, Michael Gyori wrote: > Greetings all, > After all this discussion about what the equal sign (or equality) > means, I find myself somewhat in a maze. A discussion of equality > takes us into a potentially esoteric realm from the perspective of our > students. > Might it be time to attempt to more clearly (and simply!) define terms
High School (Grades 9-12) Math September 8, 2010 at 3:16 PM Mathematics (Levels 3-7) at Journeys School follows a classic sequence of pre-algebra, algebra, geometry, advanced algebra, advanced math and calculus. The emphasis of this course is to promote the development of mathematical thinking and problem-solving capabilities. Each student is expected to master prerequisite concepts for the study of higher math at the college level. At the end of four years of math at Journeys School, students have developed a variety of tools to solve many "real-world" problems as well as master a fluency in the language of math and an appreciation of the underlying structure of mathematical systems. These systems of problem solving are critical in all other areas of academic study. Logical reasoning and problem solving for complex challenges are two basic ways in which mathematics can be utilized outside of the classroom. Clarity in communication through concise and logical thinking is fundamental to conveying a message or understanding a problem. These skills, along with pure mathematical skills, are an intimate part of the mathematics curriculum.
course offered by the Saylor Foundation.'... More This is a free online course offered by the Saylor Foundation. ' Algebra problem, like Y = 2X + 5, merely produces a pairing of two predetermined numbers, although an infinite set of pairs. Algebra is even useful in rate problems, such as calculating how the money in your savings account increases because of the interest rate R, such as Y = X0+Rt where t is elapsed time and X0 is the initial deposit. But with compounded interest, now things get complicated for algebra as the rate R is now itself a function of time with Y = X0+ R(t)t. Now we have a rate of change which itself is changing. Calculus "to the rescue," as Isaac Newton introduced the world to mathematics specifically designed to handle "those things that change." Calculus is among the most important and useful developments of human thought. Even though it is over 300 years old, it is still considered the beginning and cornerstone of modern mathematics. It is a wonderful, beautiful, and useful set of ideas and techniques. You will see the fundamental ideas of this course over and over again in future courses in mathematics as well as in all of the sciences, including physical, biological, social, economic, and engineering. However, calculus is an intellectual step up from your previous mathematics courses. Many of the ideas you will learn in this course are more carefully defined and have both a functional and a graphical meaning. Some of the algorithms are quite complicated, and in many cases, you will need to make a decision as to which appropriate algorithm to use. Calculus offers a huge variety of applications and many of them will be saved for future courses you might take. This course is divided into four learning sections, or units, plus a reference section, or Appendix. The course begins with a unit that provides a review of algebra specifically designed to help and prepare for the study of calculus. The second unit discusses functions, graphs, limits, and continuity. Understanding "limits" could not be more important as that topic really begins the study of calculus. The third unit will introduce and explain derivatives. With derivatives we are now ready to handle all those "things that change" mentioned above. The fourth unit makes "visual sense" of derivatives by discussing derivatives and graphs. Finally, the fifth unit provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over.'