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Are you confused by terms that educators use? The ASCD Lexicon of Learning might be what you need.

 

Start the new year with the 2012 Mathematics Game from the Math Forum.  Challenge your students in grades 3-12 to write expressions for the counting numbers 1 to 100 using the digits in the year 2012, standard operations, and grouping symbols.

 

Math Resources

Middle, Secondary, Post-Secondary:
Subject Specific Resources, including Apps for Mobile Devices

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

 

 

 

Algebra and Pre-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.

Watch the overviews from the Doing What Works Web site: National Math Panel: Critical Foundations for 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.

Algebra 2 Online from Henrico County Public Schools in Virginia is a full course described as follows: "This course contains both content that reviews or extends concepts and skills learned in previous grades and new, more abstract concepts in algebra. Students will gain proficiency in solving linear equations, inequalities, and systems of linear equations. New concepts include solving quadratic equations and inequalities, exploring conics, investigating polynomials, and applying and using matrices to organize and interpret data. Students will also investigate exponential and logarithmic functions."

Algebra: The Supplement is by Dan Meyer, a high school math teacher who also blogs about math.  This site is an entire year's worth of supplementary lessons in Algebra complete with handouts, PowerPoint demonstrations, pdf files, and keynotes.

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.

Advanced Algebra II: Conceptual Explanations by Kenny Felder is an entire book online.  Per the summary: "It is intended for students to read on their own to refresh or clarify what they learned in class. This text is designed for use with the "Advanced Algebra II: Homework and Activities" (http://cnx.org/content/col10686/latest/) and the "Advanced Algebra II: Teacher's Guide" (http://cnx.org/content/col10687/latest/) collections to make up the entire course."

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.

Get the Math is a multimedia project about algebra in the real world, which is for middle and high school learners.  Begin by viewing videos that show how professionals working in fashion, videogame design, and music production use algebraic thinking. They present challenges connected to their jobs to two teams of teens.  "At that point viewers are encouraged to try the challenges themselves using interactive tools provided on the GET THE MATH website, before returning to the video to see the teams’ solutions.  Students can further explore the same algebra concepts through additional interactive challenges on the website" (About section).  The project is made possible by the Moody's Foundation THIRTEEN in association with WNET New York Public Media.

Glencoe McGraw-Hill Pre-Algebra Personal Tutor contains a series of "personal tutor" videos aligned with this text, which assist learners to review concepts and the "how-to's" of problem solving.  These videos could also be used with any pre-algebra text/course.

Intermediate Algebra Quadratic Equations Word Problems Prof. Howard Sorkin of Broward College provided three sample problems involving rectangles, integers, and right triangles that use quadratic equations in their solutions.  He then has a set of 30 word problems for learners that use those strategies, followed by answers.

KarlFisch Algebra Videos are categorized by topic and deal with writing, solving, and graphing linear and quadratic equations and inequalities; systems of equations and inequalities, exponents and radicals, polynomials and factoring, rational expressions, and probability and statistics.  These can also be downloaded.

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.

Mathematics as a Second Language includes courses in Arithmetic, Algebra, and Calculus in Everyday Life, which students and teachers can use to review or learn concepts in a self-paced mode.  Materials are available in different formats: text, videos, and slide shows.  The site's mission is to "replace mathematical concepts that are difficult to understand with one or more simpler concepts that are easy to understand and hard to forget and to make all materials available free-of-charge to anyone who is interested in learning math." There are two algebra courses. Algebra By Example includes text and a study guide. The Game of Algebra "consists of animated Powerpoint and video presentations. Because different students will likely use different textbooks, the algebra videos are not linked to any one textbook but do match the slide show presentations" (Algebra Course Overview section).

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.

Schmoop Pre-Algebra is online and free.  Content is arranged in six learning guides: basic operations, fractions and decimals, ratios and percentages, basic geometry, basic statistics and probability, and basic algebra.  There are succinct explanations, diagrams, interactive examples, practice problems, and real-world applications.  This site is designed to make learning fun.  Content has been developed by educators and experts.  Many are from Ph.D. and Masters programs at Stanford, Harvard, UC Berkeley (and other top universities). The vast majority of Schmoop's writers have taught at the high school or college levels.

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

Virtual Nerd is an online, self-guided video tutorial site for math and science students (and teachers) in grades 7-12. The site has tutorials to help students work through concepts and problems in pre-Algebra, Algebra I, Algebra 2, and Physics.  A basic plan is free.  While the premium plan has a monthly fee, there are free accounts for educators that will enable their access to the entire library of tutorials.  They can use the tutorials to help students during class.

Wolfram Education Portal is a free website with math teaching tools and materials, organized by course.  You'll find a dynamic interactive textbook, lesson plans aligned to the Common Core Standards , widgets, interactive demonstrations, videos, and more.  Courses include algebra and calculus.

WOWmath.org features hundreds of videos developed by math teacher, Brad Robb, for algebra 1 and algebra 2.  They correlate with 2008 Holt - Algebra 1 California Edition; and 2008 Prentice Hall - Algebra 2 California Edition.

Algebra on your iPhone, iPod touch, or iPad

Algebra Pro for iPhone, iPod touch, or iPad has solvers, tutorials, and examples for topics found in algebra 1 and algebra 2.  It is available for about a dollar in iTunes.  Per its description, topics include: classifying numbers, points and lines, word problems, inequalities, direct and inverse variation, polynomials, zeros and end behavior, synthetic division, remainder theorem, factoring, domains and ranges, compositions of functions, inverse functions, piecewise functions, quadratic functions, quadratic formula, logarithms, logarithmic and exponential functions, rational functions, compound interest, graph symmetry, conic sections, arithmetic and geometric sequences, matrices, binomial expansion, complex numbers, rectangular and polar notation/conversions.

HMH Fuse contains Apple iPad technology.  Houghton Mifflin Harcourt has developed Common Core editions of algebra 1 and algebra 2 exclusively for a touchscreen mobile device.  According to HMH, the "mobile platform combines direct instruction, ongoing support, assessment, and intervention—enabling teachers to personalize instruction" (HMH Fuse Overview section).

Homeworkhelp.com has educational apps compatible with iPad, iPhone, and iPod Touch.  For example, for a few dollars each in iTunes, you'll find:

• Pre-Algebra Boosters: Part 1 and Part 2
• Algebra 2 Booster.

Wolfram Algebra Course Assistant can be used with your iPhone or iPad.  It is available in iTunes for a couple of dollars. Per the description in iTunes: "This app covers the following topics applicable to Algebra I, Algebra II, and College Algebra:

• Evaluate any numeric expression or substitute a value for a variable.
• Simplify fractions, square roots, or any other expression.
• Solve a simple equation or a system of equations for specific variables.
• Plot basic, parametric, or polar plots of the function(s) of your choice.
• Expand any polynomial. Factor numeric expressions, polynomials, and symbolic expressions.
• Divide any two expressions.
• Find the partial fraction decomposition of rational expressions."

Wolfram Pre-Algebra Course Assistant App assists with many topics covered in pre-algebra courses, including solving equations, simplifying expressions, and plotting equations on the coordinate plane. Powered by Wolfram|Alpha, the Pre-Algebra Course Assistant is optimized for iPhone, iPod touch, and iPad, and is available as a universal app in iTunes.

 

 

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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.

Floor Planner can be used with learners in grades 6-12 to interactively design floor plans in 2-D and 3-D using point-and-click, drag-and-drop tools, and then share them with others.  Consider scale drawings for studying geometric shapes, spatial relationships, and ratio/proportions, for example. Students can also show their creativity, and move elements of their design (e.g. furnishings) around as often as they like.  Its free for personal use.

Geometry: The Supplement is by Dan Meyer, a high school math teacher who also blogs about math.  This site is an entire year's worth of supplementary lessons in Geometry complete with handouts, PowerPoint demonstrations, pdf files, and keynotes.

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 with an introduction to trigonometry 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.

Geometry on your iPhone, iPod touch, and iPad

Easy Geometry for the iPad is available in iTunes for a couple of dollars.  With this app, developed by JMS Solutions, you can "explore the basic family of geometry shapes from the closed plane curves, quadrilaterals, triangles, polygons and geometric volumes. Learn the basic equations that describe each geometric shape as well as each shapes properties and interesting facts."  The "Interactive Geometry Calculator allows you to choose the parameters used to solve the basic geometric shape" and explore the boundaries of each (Description section).

Euclid-Geometric Constructions by Gaussian Distribution is compatible with iPhone, iPod touch, and iPad.  For just under a dollar, the app "introduces you to the world of geometric constructions in the form of a puzzle game. Starting from primitive tools, you'll learn to construct increasingly hard (and beautiful) patterns: bisectors, duplicators, regular polygons, lunes, etc. Solve puzzles to unlock more tools to aid in the construction of later puzzles. Free draw mode allows you to experiment with your own geometric patterns" (Description section).

Geometry Stash for iPad and iPhone is a quick reference guide for "commonly used theorems, postulates, and corollaries" with "descriptive, visual diagrams explaining each item" (Description section).  It's available for just under two dollars in iTunes.

HMH Fuse contains Apple iPad technology.  Houghton Mifflin Harcourt has developed a Common Core edition of geometry exclusively for a touchscreen mobile device.  According to HMH, the "mobile platform combines direct instruction, ongoing support, assessment, and intervention—enabling teachers to personalize instruction" (HMH Fuse Overview section).

 

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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.

Interactive Talking Math Book is "designed to be a complete pre-calculus preparatory supplement. It is not recommended as a substitute for other scholastic math books, but as an additional learning tool that can assist all math students. Audio, animation and interactivity using web based multimedia brings the math to life. Mathematical concepts are solidified with verbal reinforcement using interactive animated presentations and audio tutorials" (Book Preface section).  It was written by a technical mathematician, copyright is 2006, and published by Webovations Interactive Digital Media.  There are six chapters: number, sets, basic math, functions, geometry, and trigonometry.  A talking calculator is included, too.

Law of Sines and Law of Cosines are two applets that allow you to input sides and angles per each law and then each applet calculates the missing sides and angles in a triangle.  Some practical applications of each law are also included.  These are hosted by the Department of Physics and Astronomy at Georgia State University.

Trig and Pre-calculus on your iPhone, iPod touch, and iPad

Khan Academy PreCalculus is a series of free videos you can download from iTunes, which are compatible with iPhone, iPod touch, and iPad.  You'll begin with learning about limits, the Squeeze Theorem, sequences and series.  Videos are also available for other math content areas.

Trigonometry Pro HD by voi nguyen can be used on an iPad.  It is available in iTunes for a couple of dollars.  This "Interactive Trigonometry Calculator contains 13 Modules: Geometry, The Right Triangular Shapes, 30/60 Degrees Triangular Shapes, 45 Degrees Triangular Shapes, Oblique Triangular Shapes, Trigonometry/Geometry Equations, The Ultimate Units Converter, Animated Sin/Cos/Tan Graphs Functions, Interactive Central Angle, Interactive Unit Circle, Circle Functions, Lines, Point & Slopes Plot Functions and the bonus module is: The Arabic Numerals System."

 

 

 

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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.

Are your students ready for the AP Calculus exam?  See resources, including released questions from prior exams, at the College Board AP Central for both the AB and BC exam levels.

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 Revisited, posted at the MIT OpenCourseWare initiative, features a series of videos and related resources on topics covered in an introductory calculus course.

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!

Elementary Calculus: An Infinitesimal Approach, On-line Edition, copyright 2000 by H. Jerome Keisler, is a freely-available calculus text from the author.  You can download the whole book or selected chapters.  This is one of the books selected as part of the California Free Digital Textbook Initiative.

Mathematics as a Second Language includes courses in Arithmetic, Algebra, and Calculus in Everyday Life, which students and teachers can use to review or learn concepts in a self-paced mode.  Materials are available in different formats: text, videos, and slide shows.  The site's mission is to "replace mathematical concepts that are difficult to understand with one or more simpler concepts that are easy to understand and hard to forget and to make all materials available free-of-charge to anyone who is interested in learning math."  Calculus in Everyday Life relates "the basic concepts of Calculus to ideas we encounter in our lives every day. [The authors] especially invite teachers to read these "lessons" as they will, in turn, help you internalize how important a role basic arithmetic, algebra and geometry play in helping students be adequately prepared to take topics in higher mathematics of which calculus is one example. In addition, by the time you are finished you will have a deep understanding of limits, derivatives and integrals."  There is also a second calculus course for the more traditionalist. (Calculus Courses section)

Pre-Calculus and Calculus Online Tutorials from Harvey Mudd College in California are extensive and great for student review of concepts.

Video Calculus is a collection of over 50 lectures provided in two video formats that were developed by Selwyn Hollis of the Mathematics Department at the University of Houston.  Videos cover a full range of topics for calculus I and calculus II.

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.

Wolfram Education Portal is a free website with math teaching tools and materials, organized by course.  You'll find a dynamic interactive textbook, lesson plans aligned to the Common Core Standards , widgets, interactive demonstrations, videos, and more.  Courses include algebra and calculus.

WOWmath.org features hundreds of videos developed by math teacher, Brad Robb, for AP calculus (AB level).  They correlate with the 8th Edition Houghton Mifflin - Calculus of a Single Variable.

Calculus on your iPhone, iPod touch, and iPad

Calculus Pro by Larry Feldman is compatible with iPhone, iPod touch, and iPad.  Available in iTunes for about one dollar, it has examples, tutorials, and solvers for the following topics: Limits, continuity, differentiability; RDQ, LDQ, SDQ and NDQ, equations of tangent lines, partial derivatives, implicit differentiation; the chain, product, and quotient rules; related rates, optimization (min/max), derivatives of inverse functions, Taylor and Maclaurin series, derivative tables, derivatives of integrals, arc length, Riemann sums, fluid problems, double integrals, integration by parts, definite and indefinite integrals, volumes of solids of revolution, cross sectional volumes, integral tables; position, velocity and acceleration; and theorems.  See screen shots at http://www.lfeldman.com/calculuspro/screenshots  Feldman also has apps for other math content areas.

Wolfram Calculus Course Assistant is compatible with iPhone, iPod touch, and iPad and is available in iTunes for about three dollars.  It covers topics applicable to Calculus, AP Calculus AB, AP Calculus BC, Calculus I, and Calculus II.

 

 

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Statistics and Probability

ChartGizmo is free online software that can be used to create several kinds of graphs: Pie, Bar, Line, Ring, 3D Pie, 3D Bar, 3D Line, Candle, Scatterplot, TimeSeries.  A manual is available; chart settings can be customized. Several data sources are supported: static data, historical data, dynamic data from JavaScript code, dynamic data from html table on the page. Results can also be displayed on your own web pages.

Collaborative Statistics is an online textbook written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino, California. Per the Summary, "The textbook was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it."

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.

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.

Statistics and Probability on your iPhone, iPod touch, and iPad

Khan Academy Probability videos are free and compatible with iPhone, iPod touch, and iPad. Khan Academy also has videos for mobile devices for other content areas.

Wolfram Statistics Course Assistant is for iPhone or iPad.  It's available in iTunes for a couple of dollars.  This app enables you to create a bar chart, histogram, or scatter plot of any set of data; find the mean, median, mode, standard deviation, quartiles, and interquartile range of a dataset; calculate normal probabilities and find information about the normal distribution; calculate binomial probabilities and find information about the binomial distribution; compute probabilities based on dice rolls and coin flips; find the best-fit line of a set of data points; select random integers or random real numbers. (Description section)

 

 

 

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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.  Applets are found in the section called "Math Software."

Brightstorm.com has over 2000 online video lessons appropriate for middle and high school students.  The math lessons are free and developed by a group of math teachers for algebra 1, geometry, algebra 2, trigonometry, precalculus and calculus.   Additionally, the site offers a fee-based service to prepare for the SAT, ACT, and advanced placement courses.

GeoGebra is free, open-source, dynamic mathematics software 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) said, "You can use GeoGebra both as a teaching tool and to create interactive web pages for students from middle school up to college level. Specifically designed for educational purposes, GeoGebra can help you to foster experimental, problem-oriented and discovery learning of mathematics" (Abstract section).  They illustrate the basic ideas of the software and some of its versatile possibilities by discussing several interactive examples.  Educators can join the GeoGebraWiki to post their creations and view the work of others.  For example, see the main page in English of free teaching materials created with GeoGebra.

Google: Exploring Computational Thinking (CT) contains classroom-ready lessons, worksheets, and examples illustrating how educators can incorporate CT into the K-12 curriculum. You'll find everyday applications, too, such as pattern recognition, algorithm design, and other computational thinking skills.  Content was developed by teachers in collaboration with Google software engineers; math addresses pre-algebra, algebra, geometry, and calculus.  Additional features include a Getting Started Guide, web resources, and a discussion forum to connect with other CT educators.  Readers might be particularly interested in the conceptual frameworks and how-to papers listed in web resources for incorporating CT into every classroom.

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.

Higher Bitesize Maths from the BBC-Scotland contains Revisions (means study help with examples and illustrations) and Interactive Practice Tests on a variety of topics for algebra (functions, logarithms, polynomials, quadratic theory, and recurrence relations), geometry (circles, straight lines, vectors), trigonometry (compound and multiple angles, radians and equations, wave function), and calculus (differentiation and integration). [Note: Bitsize Maths, also from the BBC-Scotland, contains materials at a standard level for maths 1 and maths 2, also with study help (revisions) and interactive tests.  Maths 1 deals with number at the general level, Pythagorean theorem, trigonometry and angles; area and volume, algebra at the general level, and graphs. Maths 2 deals with trigonometry, algebra, and statistics.]

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.

Jim Reed's Math and Science Resources are hosted by the Argyll Centre of Edmonton Public Schools in Canada.  You will find 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.

Just Math Tutorials by math teacher PatrickJMT contains an extensive collection of his videos primarily for algebra, trigonometry, and calculus.  They are free to use and are suitable for high school and above.  There is also a section on miscellaneous topics such as probability and statistics, SAT test prep and the advanced placement AB and BC calculus test prep levels.

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.  Khan Academy also has videos available within iTunes for use on iPhone, iPod touch, and iPad.  See pre-algebra, for example, and you will see the list of other math apps.

MangaHigh is devoted to mathematics game-based learning for middle and high school learners.  Games are of a commercial quality, but are free.  You'll find interactivity, more than one level of difficulty, and topics such as transformations, estimation with basic number calculations, order of operations, equation solving (linear, quadratic, cubic, plotting coordinates), basic shapes to advanced geometry (some trig, too), ordering of decimals, fractions, percents.  Adaptive learning, which automatically adjusts difficulty level based on how students engage with the game, is featured in Prodigi where students work to master skills in number, algebra, data, and shape.  Games are endorsed by well-known UK mathematician Marcus du Sautoy.

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.

MathsIsFun.com provides supplementary content for K-12 in topics ranging from working with numbers and basic operations to money, algebra (with an introduction to trigonometry), geometry (including some interactives for constructions and using a protractor), data, measurement, worksheets, games, puzzles, and an illustrated math dictionary.  Tutorial information is provided within content.

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!

SAS Curriculum Pathways provides standards-based content in core subjects (English, Math, Science, History, and Spanish) for teachers and students in middle grades, high schools, and community colleges.  Math content addresses introductory algebra through advanced algebra, geometry, trigonometry, and data analysis and probability.  Activities include simulations, multimedia resources, innovative tools, and more; also included are web inquiries, additional web resources, and complete lessons. This award-winning content is free for U.S. educators.

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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