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Math Resources

Middle, Secondary, Post-Secondary:
Subject Specific Resources

Math Resources (Page 2 of 5): Middle, Secondary, Post-Secondary Subject Specific Resources

 

Algebra

Are your students ready for algebra?  Your students can find out by taking David Arnold's (Math Department of The College of the Redwoods) Algebra Readiness Test.  While most schools provide such a test, this is a good online test with 50 multiple choice questions, answers, and detailed solutions.  Don't be concerned that it is a 2003 version.

See the slide show from the Doing What Works Web site on the 11 benchmarks that students should have mastered prior to algebra.

In Foundations for Success, the National Mathematics Advisory Panel (2008) set an expectation for school algebra that "students to be able to proceed successfully at least through the content of Algebra II" (p. xvii).  Major topics recommended for school algebra include:

1. Symbols and Expressions: polynomial and rational expressions, arithmetic and finite geometric series.
2. Linear Equations, including linear inequalities
3. Quadratic Equations
4. Functions: linear, quadratic, polynomial, simple non-linear, exponential, logarithmic, trigonometric, and fitting simple mathematical models to data
5. Algebra of Polynomials.  This study would also extend to include complex numbers and operations, and mathematical induction.
6. Combinations and permutations, as applications of the binomial theorem and Pascal’s Triangle, and Finite Probability. (p. 16).

 

The following algebra resources should help to achieve those recommendations.

Algebra 1A (units 1-4) and Algebra 1B (units 5-7) combine for a complete course in Introductory Algebra.  The multimedia lessons, interactivity, immediate feedback, and practice lessons are excellent.  Materials include activities and labs, assessments, homework, simulations, and video lectures.  Brought to you by the National Repository of Online Courses at Monterey Institute for Technology and Education.  A single course designed similarly in Elementary Algebra (7 chapters) is also available, which begins with a review of pre-algebra concepts in chapter 1.

Algebasics.com contains 16 sections of step-by-step worked out problems on algebraic concepts.  Use this site with middle school students and above to introduce concepts or for test review, including SAT review. Macromedia Flash is used accompanied with audio explanations from a math teacher.  Select from hundreds of problems beginning with order of operations, rules for working with signed numbers, equations, ratio/proportion, inequalities, absolute value, exponents, polynomials, factoring, rational expressions/equations, linear equations and their systems, functions, radicals, quadratics, and applications.

AlgebraLab.org focuses on topics and skills from high school mathematics that students need for introductory science courses.  You'll find topics in algebra I and II, geometry, trigonometry, statistics.  There are lessons, hands-on activities, an interactive glossary, study aids with interactive practice problems, technical reading passages, word problems, connections between math and science to various careers, and more. The project was developed in conjunction with a Florida Department of Education Enhancing Education Through Technology Competitive Grant, a National Council of Teachers of Mathematics' Edward G. Begle Grant for classroom-based research in precollege mathematics, and Florida's Volusia County Schools.

Elementary Algebra with Applications (3rd edition) is a free online text from GetMath.com and Bernard Klein Publishing for students who have not had a formal course in algebra.  The entire document can be downloaded.  Quizzes, tests, and answers are included.  Written by experienced math teachers.

Learning Algebra Fundamentals for grades 7-12 was developed by Marlon Coates with funding from the Curriculum Foundation and RBC Foundation.  It contains 12 essential algebra components with Flash tutorials for visual presentation, alternate worked solutions, and practice material with solutions.

1. Exponent Laws
2. Polynomials: Like Terms
3. Distributive Law
4. Common Factoring
5. Solving Simple Equations
6. Solving Equations with Variables on Both Sides and Brackets
7. Solving Equations with Fractions
8. Determining the Equation of a Line Given Point and Y-Intercept
9. Determining the Equation of a Line Given Two Points
10. Graphing Equations Using a Table of Values
11. Graphing Equations Using Slope and Y-Intercept
12. Graphing Equations Using the X and Y Intercepts

Lure of the Labyrinth is a free online adventure game for pre-algebra learners, also suitable for middle school. Math is embedded in a story line--it' in an eerie world where monsters want world domination at any cost. The only way students can prevent that from happening is by solving the puzzles. Students progress through three sections, or "wings." Each is related to a different math strand: proportions (including fractions and ratios), variables and equations, number and operations (including geometry, order of operations and modular arithmetic). Each wing includes three puzzles, and each of the puzzles has three levels, from easy to hard. There are resources for teachers to help implement the game and also a section for families. This game is a product of the Learning Games to Go project, funded by a Star Schools grant from the U.S. Department of Education, spearheaded by Maryland Public Television.

The Math Dude,, available from Montgomery Public Schools (MD), is an award winning video series for helping middle and high school learners of Algebra I.  Shows can be viewed on the Web, via podcasts through iTunes or RSS feeds, or downloaded to your computer.  These are a must see!

Purplemath is a "not to miss" Algebra resource with lessons on preliminary, beginning, intermediate, advanced topics, and word problems.  An extensive list of Internet resources related to Algebra is also provided, including a link to online calculators.  This site, developed by E. Stapel of Western International University, is award winning.

Virtual Math Lab from West Texas A&M University concentrates on Beginning Algebra, Intermediate Algebra, and College Algebra.  Each course has complete tutorials (many with video explanations), practice problems with answers, and resources for extra help.

 

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Geometry

Are your students ready for a formal course in geometry?  While they may be in your geometry class, consider that their levels of geometric thinking might not be sufficient to engage in formal proofs.  View the Mind Map of the van Hiele Model of Geometric Thought at GoGeometry.com.  The Van Hiele model asserts that learners develop geometric thought sequentially through five levels of understanding.  Numbered as levels 0-4, they are visualization, analysis, informal deduction, deduction, and rigor.  Hopefully, students have progressed to the level of informal deduction by the end of grade 8.  Read more on The van Hiele Levels of Geometric Understanding by Marquerite Mason for further implications for teaching.

Geometry.net is a comprehensive math search engine for middle school math and above.  Additional topics include computers and the Internet, technology, physics, biology, biographers, and sports.  There is a math help desk with 28 sub-categories, and resources for standardized test preparation.

GoGeometry from the Land of the Incas, by Antonio Gutierrez, is an award-winning site that provides an eclectic mix of sound, science, and Incan history intended to interest students in Euclidean geometry. The site includes geometry problems, proofs, quizzes, puzzles, quotations, scientific speculation, and more.  Best used with high school students and above.

Math Open Reference is a free geometry textbook for high school learners by John Page.  There are topics in plane geometry, coordinate geometry, and solid geometry (e.g., cylinders, cubes). Its focus is on using interactive materials and animations to develop concepts.  Sections on constructions are excellent.

Poly is a shareware program for exploring and constructing polyhedra.  You can manipulate solids on the computer and also print out the net of the polyhedra so that you can create the physical 3-D model.  Poly is downloaded from Pedagoguery Software.

 

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Trigonometry and Pre-Calculus

Algebra and Trigonometry (2nd edition), a Prentice Hall book by Robert Blitzer, contains 12 chapters of useful quizzes and tests in multiple choice format, which can be taken online.  There are also graphing calculator tutorials and manuals for the TI-83/84 and TI-86 calculators.  Learners can create profiles to email quiz/test results to the instructor.

Dave's Short Trig Course, by Dave Joyce of Clark University in Massachusetts, contains explanations, practice problems and answers.  Best of all is that images are virtual manipulatives developed in Java so that learners can explore the properties presented.  A brief background of the Pythagorean Theorem and similar triangles is included.  See also Dave's Short Course on Complex Numbers

Demos with Positive Impact connects instructors of pre-calculus, calculus, and post-calculus courses with effective teaching tools to help them get important ideas across to students during their lectures. This project focuses on demonstrations that use some form of instructional technology (e.g., physical equipment or examples, graphical displays, simulations, computations, interactive modules, calculators, computers and computer software, the Web).  Really first-rate!

Exploring Precalculus, by Dr. William Mueller, provides an introduction to precalculus using Mathcad or StudyWorks as a calculation and visualization tool. Many interactive examples let you explore the concepts and practice the skills necessary for understanding calculus.  Central themes (functions, rates of change, and accumulation) are developed intuitively, from several perspectives (algebraic, numeric, and graphic).  Materials suitable for use in grades 9-12, and post-secondary.

FlashyTrig.com uses Flash accompanied by audio to provide an introduction to trigonometry based on the unit circle and the geometry of the right triangle.  The flash animations for illustrating the development of the six trig graphs are particularly useful for classroom demonstration.

 

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Calculus

Are your students ready for calculus?  The University of New Brunswick (Fredericton, Canada) has posted a Calculus Readiness Test with answers.   Many of the problems are challenging, but don't give up.

Calc101 provides automatic solutions, powered by webMathematica, to derivative and integral problems found in beginning calculus. The site's goal is to help you to raise your grade by 10%. Get all the steps including the final answer. Step-by-step matrix operations and determinants are coming soon; linear equations will come later. Derivatives and polynomial multiplication and division are free. There is a small fee for integral solutions and linear algebra, but you can always see the first and last step.

Calculus by International Education Software helps students to learn about limits, derivatives, and integrals visually through precise definitions and a series of interactive applets.

Calculus is among math projects at the secondary education level posted at Curriki and the Global Education and Learning Community.  Java is used for complete courses in AP Calculus at both the AB (Introductory Calculus 1 and 2) and BC (General Calculus 1 and 2) levels.  Audio explanations accompany text equivalent and multimedia demonstrations of concepts are presented.  Interactive practice problems are presented to test understanding.  Feedback shows how answers are derived.  This is truly worth using.  Note Java modules might take a while to download.

Calculus: Graphics for the Calculus Classroom by Douglas Arnold of the University of Minnesota.  This site contains a series of graphical demonstrations suitable for first year calculus: a differentials and differences animation, computing the volume of water in a tipped glass, Archimedes' calculation of pi, animation of a bouncing ball, secants and tangents, zooming in on a tangent line, a trig limit, graphs for a discussion on limits, a nowhere differentiable function, introduction to the number e, and computing the volume of the region formed by two intersecting cylinders. 

Calculus on the Web is partially supported by the National Science Foundation and is a project of G. Mendoza and D. Reich at Temple University.  This site has interactive exercises with feedback and help sections that explain concepts.  There are seven books online: Precalculus; Calculus 1, 2, and 3; Linear Algebra, Number Theory, and Abstract Algebra. 

Calculus-help.com by M. Kelley has been recognized by The National Council of Teachers of Mathematics and The College Board.  Don't miss Tutorials for the Calculus Phobe, an ongoing project to present topics from this subject in an easily understood audio-visual format.  Flash animation is incorporated.  Topics include limits, continuity, differentiation, with more to come.

Calculus: The Integrator from Wolfram Research is powered by webMathematica.  Enter any expression and the integration is performed for you.  Also read about the history and applications of integration.

Calculus Review by Linda Valdes of San José State University contains review sheets of key concepts followed by online quizzes for topics in limits, derivatives, and integration.  Well worth using these.

Calculus Tutor -- Karl's Calculus Tutor includes number systems, limits, continuity, derivatives and applications, exponentials and logs, trig functions, and sections on integration and applications.  Some interactive features are included.

Demos with Positive Impact connects instructors of pre-calculus, calculus, and post-calculus courses with effective teaching tools to help them get important ideas across to students during their lectures. This project focuses on demonstrations that use some form of instructional technology (e.g., physical equipment or examples, graphical displays, simulations, computations, interactive modules, calculators, computers and computer software, the Web).  Really first-rate!

Mathematics Visualization Toolkit (MVT) is a set of visual and computational tools designed to help students better visualize the concepts of Calculus. It contains:

• Scientific calculator
• Plotting tools
• Numerical tools
• Linear algebra tools
• Differential equations tools
• Content-specific applications
• Other Calculus visualization tools
• Tutorial-style help system (see section: History)

MVT was developed by the Department of Applied Mathematics at the University of Colorado at Boulder. Additional calculus resources are included, including game formats for review.

Visual Calculus from the University of Tennessee Math Department at Knoxville is an excellent resource that includes tutorials, drills and programs for pre-calculus and calculus.  Animations, interactive pages, step-by-step solutions and illustrations are included for topics ranging from functions, graphing with technology, solving equations, and conic sections to limits and continuity, derivatives and applications, integration and applications, sequences and series.  As a veteran calculus teacher, Patricia Deubel highly recommends this site.

 

 

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Statistics and Probability

DIG Stats is an excellent resource for integrating statistics and data visualization into mathematics and science courses in grades 9-14. Modules with student activities cover concepts from descriptive statistics, inferential statistics, two dimensional graphical analysis and three dimensional data visualization.  Using Microsoft Excel and graphing calculators, students analyze real world data sets from a variety of scientific disciplines.  Data were derived from WWW databases, university and government researchers, and student projects.  Guides, quizzes, and answers are provided.  This site is associated with the Central Virginia Governor's School for Science and Technology.

Exploring Data provides curriculum support materials for teachers of high school and up introductory statistics. These include activities, worksheets, overhead transparency masters, datasets and assessment to support data exploration, and a collection of articles to learn about statistics. Explore concepts like stem plots, dot plots, histograms, measures of location, box plots, normal plots, scatter plots, assessment, linear regression, probability, hypothesis testing, curve fitting, and much more. A resource list of additional support materials includes texts, web sites, datasets, java applets and mailing lists.  Most of the resources of the site are the property of Education Queensland in Australia.

Research Randomizer, part of the Social Psychology Network, is a free tool that can be used to introduce students to random sampling and random assignment.  Students in K-12 often conduct surveys, which is just one use of this tool.  It includes tutorials.

Statistics: Power from Data, a product of Statistics Canada,  is a complete online text with exercises, answers, and lesson plans.  Although intended for use with secondary students, the text could be used with middle school or post-secondary audiences.  Chapters address data collection, data processing, problems with using information, organizing data, graph types, analytical graphing, measures of central tendency and spread, sampling methods, and more.  There is a glossary.

What are the Odds? The Ins and Outs of Probability (by graduate students at University of Virginia) if primarily for secondary students.  It contains lesson plans, an interactive quiz, an extensive data bank of questions relating to probability concepts sorted by topic, history, and additional resources on probability.

 

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Multiple Subjects

Analyze Math by A. Dendane (United Arab Emirates University) contains math tutorials and problems (with applets) for a various topics in algebra, trig, geometry, calculus, and more.  Excellent explanations.

Argyll Centre of Edmonton Public Schools in Canada hosts Jim Reed's Math and Science Resources.  His resources address elementary and secondary topics in numbers/operations, patterns and relations, shape and space, probability and statistics, algebra, geometry, and trigonometry. Students can engage with interactive learning activities, see movies, and manipulate excellent Java math applets to study concepts.  The site is also an excellent resource for the home-schooled student.  Highly recommended.

GeoGebra is free, multiplatform, dynamic mathematics software for secondary schools that joins geometry, algebra and calculus. You can do constructions with points, vectors, segments, lines, conic sections as well as functions and change them dynamically afterwards.  You can enter equations and coordinates directly. GeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions and offers commands like Root or Extremum.  It received several international awards, including the European and German educational software awards. In Dynamic Mathematics with GeoGebra, authors Markus Hohenwarter, principle developer of the software, and Judith Preiner (2007) illustrate the basic ideas of the software and some of its versatile possibilities by discussing several interactive examples.

Henrico County Public Schools (VA) has developed a web site for its mathematics courses in middle and high school.  As a work in progress, their "goal is to create interactive, engaging, web pages that students will want to investigate and explore. Theses pages are different from a printed textbook in that they use java-based scripts, other web sites, software program files and browser plug-ins."  Middle school has courses 1, 2, and 3.  High school has integrated math 1, algebra 1 and 2, geometry, advanced algebra/trig, math analysis/trig, and statistics.  Within each course, multimedia use is extensive.   Do look at this site.

HippoCampus, a project of the Monterey Institute for Technology and Education, is a "free, public website for high school and college students that offers NROC multimedia correlated to most major textbooks." NROC is the National Repository of Online Courses for students and faculty in higher education, high school, and advanced placement.  Among the full math textbooks online are Algebra (IA, IB, and Elementary)  and Calculus (Introductory I and II, General I and II, AB and BC levels for advanced placement).  Multimedia includes audio explanations, visuals, interactivity.  Individual instructors can customize the Hippo website to better meet the needs for groups of students.   Highly recommended.

Khan Academy has 600 videos on YouTube covering multiple subjects from basic arithmetic, pre-algebra, algebra, geometry, trigonometry, pre-calculus, calculus, probability, SAT prep, to linear algebra, differential equations, physics, and finance, which have been recorded by Salman Khan.  There's also a section on Singapore Math at grade 3.

MathBits.com "is devoted to offering fun, yet challenging, lessons and activities in high school (and college level) mathematics and computer programming for students and teachers."  Subjects include algebra 1, geometry (including materials for using Geometer Sketchpad), and algebra 2, principally.

Math Expression has excellent tutorials, including animated videos with audio explanations and text equivalents.  Topics include graphing (e.g., using the coordinate plane, slope, writing equations of lines), basic algebra (e.g., variables, expressions, solving equations), exponents, fractions, symmetry, and volume.  Math study tips and practice questions help reinforce concept development.  There is also a Q&A Library.  The site is by Wei Chong, and is well-worth investigating.

Mathematics Across the Curriculum Electronic Bookshelf  developed at Dartmouth College features materials with an interdisciplinary approach to mathematics topics.  The bookshelf topics include algebra, calculus and differential equations, physical science, art, computer sciences, pre-algebra, history and geography, literature, biology/medicine/psychology, data analysis, statistics, business/economics, math and music, discrete math, and trigonometry.

National Curve Bank, maintained at the Department of Mathematics at California State University, Los Angeles, contains highly relevant visual content and explanations for upper level mathematics--calculus, pre-calculus, trigonometry, geometry, fractals, and so on.  JAVA applets are included.  Some content includes practice problems on various topics. The developers "strive to provide features - for example, animation and interaction - that a printed page cannot offer."   Geometrical, algebraic, and historical aspects of curves, "the kinds of attributes that make the mathematics special and enrich classroom learning" are included.  Participants are encouraged to submit your best web animation as a "deposit" in the National Curve Bank.  Highly recommended!

Science and Mathematics Initiative for Learning Enhancement (SMILE) at the Illinois Institute of Technology contains over 900 individual lessons in Biology, Chemistry, Mathematics, and Physics written by teachers and for teachers.  "The SMILE program is designed to enhance the elementary and high school learning of Science and Mathematics through the use of the phenomenological approach."  The section on mathematics contains almost 200 single concept lessons on geometry and measurement, patterns and logic, probability and statistics, recreational and creative math, practical and applied math, arithmetic, graphs and visuals, algebra and trigonometry, and miscellaneous. 

S.O.S. MATHematics by Math Medics, L.L.C., in Texas contains over 2500 pages of short and easily understood explanations from simplifying fractions to algebra, trigonometry, calculus, differential equations, complex variables, matrix algebra.  Tables are included and a link to CyberExams to practice for tests and quizzes.  Site is for high school, college, and adult learners.

The Math Page is by Lawrence Spector of the Borough of Manhattan Community College, The City University of New York.  This site has four major sections.  Practice problems illustrating concepts are presented throughout with answers.  

• Skills in Arithmetic is a complete course, which includes addition, subtraction, multiplication, division; mental arithmetic, powers of 10, regrouping, decimals, parts of natural numbers, fractions, and percents.
• Topics in Trigonometry addresses ratio and proportion, definitions of the trig functions, solving right triangles, the 30-60-90 degree right triangle, the law of sines, the law of cosines, the unit circle, radian measure, and arc length.
• Topics in Pre-calculus include formal rules of algebra, rational and irrational numbers, functions and graphs, logarithms, the binomial theorem, and mathematical induction.
• The Evolution of Real Numbers.

Things to Remember from Oswego City School District's Regentsprep.org in New York consists of four-pages of facts and formulas summarizing key concepts addressed in Algebra 2 (pp. 1-2), Trigonometry (p. 3), and Probability and Statistics (p. 4).  These are very useful for quick reference for test prep.

Zona Land's More Mathematics than Science is devoted to helping students understand algebra, geometry (including conic sections), trigonometry, and curve fitting.  Don't miss the interactive manipulatives and virtual reality demonstrations of concepts.

 

 

 

 

 

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The Amazon widget below shows books using the search phrase: math and high school.  You can also use the widget to search with other key words.  Suggestions include:

• math and middle school
• math and secondary
• math and algebra
• math and geometry
• math and trigonometry
• math and precalculus
• math and calculus
• math and statistics
• math and probability

 

References

 

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See related topics:  Math Manipulatives and Standardized Test Preparation.