55 Interactive teaching tools for Mathematics
The following interactive teaching tools have been produced by the National Numeracy Strategy for use within the DML.
Though contained on the discs which are accompanying the unit plans, their use extends far wider than within a particular year group or term.

You can run them from rupertcollins.com just by clicking on the link or you can download them onto your computer by right clicking (hold control then click on a mac) and selecting 'Save Target As...' - you will then be given the option to save it onto your computer.
If you run them from rupertcollins.com use the back button to get back to this page.

The year is divided into 2 parts - 8A and 8B. For each part there is a Pupils' Practice Book.
Book 8A covers Units 1 to 11. Book 8B covers Units 12 to 20.
Each Unit will have its own set of interactive tutorials - one for each section within that unit.

Students learn mathematics by DOING mathematics, and not by watching someone else do mathematics. In recent years there has been an explosion in the number of high quality digital resources available from the Net and elsewhere that allow students to investigate, explore or consolidate the topics they are learning in their maths class.
Over time, it is hoped that this website will become a one-stop shop for quality interactive digital resources for mathematics education.
Currently there are well over three hundred and seventy-five quality resources and links available from this website. Have a browse and take away what you wish.
Items available in a variety of formats!

Students learn mathematics by DOING mathematics, and not by watching someone else do mathematics. In recent years there has been an explosion in the number of high quality digital resources available from the Net and elsewhere that allow students to investigate, explore or consolidate the topics they are learning in their maths class.
Currently there are well over three hundred quality resources and links available from this website. Have a browse and take away what you wish.

Math Manipulatives, Part 2 of the Math Web Resources and Standardized Test Preparation series, contains resources that enable students to interact online.
We begin with a short essay on virtual manipulatives, which addresses the following:

Here is a collection of Maths teaching resources designed to be projected on to a white board and then written on as part of a whole class exposition. They'll even work with an Interactive White Board!

Math Warehouse
Welcome To the Math Warehouse--a web site dedicated to dynamic Math lessons, demonstrations and interactive activities. EXTENSION

K-12 Algebra Applets--Arlen Strader of the Texas A & M University has two algebra tiles applet pages to help middle and high school students explore factoring of quadratic equations by arranging given tiles into a rectangle: Algebra Tiles1 (easy version-coefficients positive) and Algebra Tiles2 (hard version-coefficients positive and negative). There are also applets for Cartesian coordinates, slope, parallel and perpendicular lines, and Pythagorean Theorem. Ambleweb Numeracy Hour of Ambleside C.E. Primary School (UK) contains excellent interactive online Tools for Teachers to use with elementary students for demonstrating concepts and helping students to master basic skills. There is a large buttoned online four function calculator for demonstrating how to use a calculator, an online resource for teaching about angles and how to use a protractor, a virtual tangram, counter squares of various sizes and purposes on which you can scribble using the left button on your mouse, applets for studying number sequences and patterns, a simple bar graph to introduce graphing data, teaching time on an analog clock, and interactive geometry. There is also a section for interactive skill building at three levels of difficulty, puzzles, and games.

Arcytech's Gif showing pictures related to Java programs

Arcytech's Educational Java Programs are primarily forelementary and middle school students. Award-winning applets help students learn to count money, tell time, use patterns to explore fractions and geometric shapes; use base-10 blocks to explore whole and decimal numbers, place value and algebra with blocks; use integer bars to explore basic math facts, fractions, and more; use fraction bars to explore equivalent fractions, ordering fractions, adding fractions, and more. Additional applets help students explore the Pythagorean theorem and the value of Pi, and fractals. Lesson plans are included. Site developed by J. Bulaevsky. 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. British and Metric Conversions from Annenberg Media's Learner.org. is an interactive Web site to learn how to convert measurements between the metric system and the English (sometimes called British) system, which is commonly used in the United States. Learn the symbols, more about length, mass, temperature, volume, and then test your knowledge. C.a.R. (Compass and Ruler) is a dynamic geometry program simulating compass and ruler constructions on a computer. It's by by Rene Grothmann, professor of mathematics at the University of EichstÃ¤tt (Germany). For school geometry in the plane, there are lots of geometric objects like points, lines, rays, line segments, circles, arcs, angles, polygons and conic sections. Ruler and compass constructions can be changed by dragging one of the basic construction points. Arithmetic computations, numerical solutions, curves and functions go beyond classical constructions. It is even possible to construct in 3D using advanced macros. Other geometries, hyperbolic or elliptic, can be explored. The software is free open-source and comes with documentation, tutorials, and demos. Java needs to be installed. Collaborative Whiteboard from GE allows individuals or groups to draw anything freehand or type text. You can display a graphing grid, select and then draw geometric shapes, save the work and share it with others via email. Erathothenes' Sieve--watch the primes up to 400 being generated with this Java display. Euclid's //Elements// Dr. Dave Joyce of Clark University in Massachusetts brings all13 books of the Elements alive using a Java geometry applet to illustrate definitions and postulates. ExploreLearning.com is a subscription based set of over 400 virtual manipulatives (simulations of math and science concepts), which the authors call "Gizmos." The math series addresses the five NCTM strands for grades 6-12 and college developmental math, college algebra, and pre-calculus. Gizmos for elementary math for grades 3-5 are also available. ExploreLearning Gizmos, with associated Exploration Guides, help students develop critical thinking skills and conceptual understanding. The series is also correlated with national and state standards and major textbooks, and includes assessment and real time reporting. A 30-day free trial is available for the teacher or home. Sample Gizmo at the site can be immediately activated. Geometry 3-D Shapes is one of the Interactives from Annenberg Media's Learner.org. Students can interactively learn about three-dimensional shapes, calculate surface area and volume, and discover some of the mathematical properties of shapes. It comes with tutorials and an interactive test. Geometry Gallery from Saltire Software contains some excellent Java applets, which are easy to use and suitable for illustrating several theorems presented in a high school or post-secondary geometry course. These relate to angles in parallel lines, circular configurations, Pythagorean triples and incircles. Students can drag points to explore concepts.Four triangle calculators are presented. By entering SSS, SAS, or ASA, students can see the unique triangle that is formed, but if SSA is entered the resulting triangle is not unique (two are possible) or no triangle is possibly formed with given information. Some advanced geometrical configurations are explored. There is a geometry atlas of algebraic formulas with associated visuals. Saltire's work has been assisted with a number of National Science Foundation grants. Harcourtschool.com E-Lab: Extensive collection of interactive applets for grades 3-6. Activities to accompany each are provided. You can download an E-Lab activity and use it without being connected to the internet. While working on internet, Microsoft Java VM is recommended. Later versions of Java will be supported soon for online activity. Illuminations Activities from the National Council of Teachers of Mathematics (NCTM) contain Java applets identified by grade band to investigate various concepts within NCTM identified strands. Interactivate, which is a project of The Shodor Education Foundation, Inc., includes a set of interactive JAVA-based tools to support courseware in science and math. Activities are divided by grade-band (3-5, 6-8, 9-12, and undergraduate). Some activities allow students to keep score to monitor their progress, and are listed under assessments. Activities that use the tools support NCTM standards. Browse by topic, audience, type (activity, lesson, discussion), or subject (number and operations, geometry, algebra, probability, statistics, modeling, discrete, and other). A math dictionary of terms used within the site is included. Interactivate has also aligned its activities to several textbook series (e.g., Connected Math, Math Thematics, Mathematics in Context, and MathScape). Interactive Mathematics promotes learning math while you play with it! Primarily for upper secondary and college level students; basic math includes algebra, complex numbers, statistics, logarithms, trigonometry, plane analytic geometry, and graphing. Calculus includes differentiation, integration, and higher topics in calculus. Lectures and full examples are provided. Site provides links to LiveMath plug-in, Scientific Notebook, and Flash. Interactive Resources from the UK has four math packs, each with a wide range of excellent interactives for classroom use with preK-6 students. Explore numerous concepts related to NCTM strands. Some include whiteboard (drawing on the figures) capabilities. There are rulers, protractors, geoboards, Venn diagrams, number lines, and so on. Don't miss these teaching tools. Key Curriculum Press JavaSketchpad has several applets for use with secondary math students and above. See the interactive manipulative on the Pythagorean Theorem and the JavaSketchpad DR4 Gallery. In the Gallery you will find demonstrations from geometry (e.g., centroid), trigonometry and algebraic geometry (e.g., sine waver and conic sections), calculus (e.g., box volume and falling ladder), mechanics, and an applet on least squares. The Learning Equation (TLE) is brought to you by R. Blond of Edmonton, Alberta, Canada. TLE features JAVA applets that help students to interactively explore complex mathematics concepts typically studied in depth from grades 9 through post-secondary. Among topics are triangle relations, slopes, circle geometry, conic sections, exponential and trig functions; translations, reflections, stretching; and more. Learning Objects from Brock University (Canada) Department of Mathematics are tools to help students explore mathematical concepts interactively.

The Great Balancing Act: explore the mean and median

Parabola games: explore parabola properties, transformations and their use

Leap Frog: explore number patterns

Fire, Fire!: explore trigonometric ratios

Transformations: an introduction to transformational symmetries

Markov chains: What happens after years of movement in cities and suburbs, an introduction to Markov chains

Manipula Math with JAVA by International Education Software contains a collection of over 280 applets suitable for teaching math concepts to middle school, high school, and college students. Applets address middle school geometry and the Pythagorean Theorem, trigonometry, calculus, vectors, complex numbers, conics, and miscellaneous topics. Math Doodles is by Daren Carstens, who is the developer of the award winning software Math Arena. He offers several interactive puzzles and games for elementary learners to have fun. But there is learning, too, as students practice addition, subtraction, money skills, and pattern matching (shape, number, color), for example. Among current games are Connect Sums, Number Jump, Polyomino Shift, Double Traits, Sum Stacker, Time Shuffle, and more. Older learners also benefit, as students really need to think as they do these. Math Playground: Animated characters created with Flash add to the appeal of this learning site for grades 1-6. Among resources are some virtual math manipulatives, such as a protractor, fraction bars, equivalent fractions, percents, a spinner for probability, function machine, pattern blocks, and a geoboard. Mathplotter allows teachers of mathematics to draw pictures of equations and functions and to put those images in a Word or Excel document. These documents can then be printed for distribution to students as tests, handouts, worksheets and so on. Mathplotter can also be used in the classroom to explore the behavior of mathematical equations. There are some excellent tools for pre-calculus and calculus. Mathematics Open Reference is a free plane geometry textbook for high school learners. Its focus is on using interactive materials and animations to develop concepts. There are numerous interactive applets with at least one accompanying nearly every concept. This is highly recommended for visual learners and reinforcement for all.

Math Tools Gif

MathTools from the Math Forum contains a number of interactive tools for understanding concepts related to K-12 mathematics and calculus. Help kindergarten students understand concepts. Introduce topics with pattern blocks, number lines, fraction bars and more. Algebra concepts include number systems, integers and integer operations, properties (commutative, associative, distributive), multiplying/dividing, using variables, equivalent equations, inverse operations, graphing, linear equations and systems, quadratic equations, factoring, and more. Geometry interactives for plane and solid topics are extensive. Trigonometry includes the Law of Sines and Law of Cosines. There is a range of calculus tools for differentiation and integration topics. Mathsnet.net is a highly interactive site for doing mathematics, featuring concepts in number, geometry, algebra, graphs, data handling. JAVA, Javascript, or plug-ins may be needed. The geometry is of particular interest. There are curriculum, articles, books, and a section for download, including free software to explore topics interactively. Don't miss this award winning site brought to you by B. Dye in England. Math Warehouse is "dedicated to dynamic Math lessons, demonstrations, and interactive activities." There are topics in algebra, geometry, trigonometry. Worksheets are available for download, too. MegaMaths, brought to you by the BBC, is a School Radio series for elementary students aged 7-9. Each 15 minute episode promotes a whole-class approach to mental maths activities through a series of lively and stimulating quizzes. National Library of Virtual Manipulatives for Interactive Mathematics contains manipulatives and associated online activities for each of the five strands identified in standards set forth by the NCTM. This is an ongoing project of Utah State University and a must see site for grades preK-12. Select a manipulative from the grade level you teach and an activity from one of the strands. Number Line Applet: Introduce addition and subtraction of integers with this number line. Students see the concept after clicking onto the integers (-35 to 35) for the problem. From MSTE at University of Illinois-Urbana_Champaign. PBS Teacherline Interactives --explore with cubes, floor tiles, frog in a well (number patterns and relations), geoboard, histograms, making a rule, mixing orange juice, number cruncher, the race, real-life data, space blocks, surface area, and tesselate. Principles and Standards for School Mathematics Electronic Examples--interactive applets for investigating concepts from NCTM. Examples are divided into grade bands.

preK-2: Investigate patterns, triangles and properties of polygons, geometry and measurement; develop spatial skills by using tanagrams, learn estimation strategies

3-5: Communicate about math using games, use simulation software to investigate distance, rate, and time; investigate data

6-8: Visualize the concept of multiplication, investigate rate of change, length, perimeter, area, volume, congruence, similarity, and symmetry, and the Pythagorean Theorem

9-12: Explore vectors; use graphs, equations, and tables to investigate elimination of medicine from the body; explore inscribed figures, linear regression, and linear functions.

Seeing Math by the Concord Consortium has eight free secondary math interactives written in Java to assist algebra learners in the study of functions. "Each interactive provides a real-time connection between representations of the mathematics (symbolic, graphical, etc.), so that changes in one representation instantly cause changes in the other." Interactives include a qualitative grapher, piecewise linear grapher, linear transformer, quadratic transformer, function analyzer, system solver, plop it and proportioner. A user's guide, warm up exercise, frequently asked questions, and sample activity are provided.

Statistics represented by Deviation graph

Statistics: Are you teaching your students about statistics and survey research? Read Statistics Every Writer Should Know by Robert Niles. Learn about mean, median, percent, per capita, standard deviation, margin of error, data analysis, and more. Link to sites for data sources and interactive help to select the right statistical test.

Chi-Square by Amar Patel. The material in this lesson, which is correlated to NCTM standards for grades 9-12, will help students to understand statistical terms such as fairness, expectation, significance, and chi-square. Excel spreadsheet is needed. Content could be used with grade 8 and above, however. Cartoon characters add humor to the discussion.

Tools: Generate random numbers, sample sizes, charts and graphs, and perform statistical calculations using these tools:

Create a Graph, brought to you by the National Center for Education Statistics,is an interactive site that helps students understand how to create area, line, and bar graphs, and pie charts. You might point out to students the 10 Common Mistakes Found on Graphs, noted by CanTeach in Canada.

If you are looking for data to use when creating graphs, see the work of Robert Niles on finding data on the Internet.

If you have developed a bar graph using Microsoft Excel, show students how to Create a Pictograph from that data.

Tangoes. "Based on the ancient Chinese Tangram puzzle, Tangoes is a learning tool that combines artistic and mathematical elements to enhance visual perception ability; develop problem solving skills; creative thinking capacity and teamwork. Tangoes can be played by one, two or in teams. From ages four to one hundred and four, all ages are delighted by the challenge of forming the puzzle presented with the seven dynamic pieces." There is an online version that can be played for free. Tangrams from Channel4.com has three levels, then the challenge level.

Thinking Blocks Logo

Thinking Blocks teaches children how to visualize and solve math word problems. Using interactive blocks and cubes, children create models that illustrate the underlying math concepts within the problems. Thinking Blocks combines guided instruction, video explanations, and independent practice to help young students in grades 3-5 develop strong problem solving skills. Using Virtual Manipulatives on the Web to Develop Number Sense by Margo Mankus and hosted by the Graduate School of Education at George Mason University contains three interactive applets and a host of activities to develop concepts of number, operations, and geometry. Applets, developed by J. Bulaevsky, include pattern blocks, base ten blocks, and integer rods. These are great tools to demonstrate concepts in the classroom and to give students practice in class or at home.

Virtual Polyhedra Gif

Virtual Polyhedra, by G. Hart, is a collection of thousands of polyhedra that you not only can look at, but move and spin. Hart also provides extensive research on the topic and information on how to construct paper models.

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, P. Deubel highly recommends this site.

Visual Fractions Logo Gif

Visual Fractions, by Richard Rand, is an online tutorial with instruction and interactive practice in identifying, renaming, comparing, and operating on fractions, including mixed numbers (add, subtract, multiply, and divide). All examples are modeled with number lines or circles. This site helps students, primarily in grades 3-8, to picture fractions and operations on them. Visual Math: Functions contains JAVA applets for exploring linear and quadratic functions. Linear explorations include representations of linear functions, functions defined on intervals, equivalent expressions for functions, addition/subtraction, transformations, rate of change. Quadratic explorations equivalent quadratic expressions, comparisons and operations, solving equations, graph transformations (vertex form), add functions (polynomial form), products of linear functions, quadratic growth, graphic design, motion at changing speed, and economic decisions. Visual Math Learning is a free educational web site developed by W. Bateman, who indicates that the site features "an interactive on-line tutorial for teaching elementary mathematics and basic arithmetic for grades K-12 at the pre-algebra level. It is an instructional aid for parents, teachers, and educators of primary, elementary, and middle school students, as well as a resource for lesson plans, homework help, and home schooling math lessons. The tutorial includes games, puzzles, interactive diagrams, and computer animated virtual manipulatives that emphasize active learning concepts by visualization." Visualization of Elementary Math, by E. Kluk, M. Frank, and M. Mangru of Dickinson State University in North Dakota, contains several applets to help students with understanding meanings of elementary math operations. Applets include a visual multiplication table, visual addition (single and double digit), and visual fractions (making and comparing, adding and subtracting). Instructional examples are included. Waldo's Interactive Maths Pages contains over 50 Java applets for teaching math concepts. These are grouped within age ranges (11-14, 14-16, and 16-19) and then by topics usually studied within those ranges. Topics are extensive from angles and intersecting and parallel lines, exploring triangles, solving equations, sequences, graphing linear and quadratic equations, trigonometry, calculus, and much more. Waldo is a teacher in England who developed these. Don't miss this work, which links theory to the visual. Walter Fendt's Java Applets on Mathematics address arithmetic, elementary algebra, geometry (e.g., transformations, triangles, Pythagorean theorem, area and circumference of circles, and platonic solids), trigonometry (visual demonstration of graphs of sine, cosine and tangent of an angle), vector analysis, analysis (e.g., first and second derivatives), and complex numbers (arithmetic operations). These are very engaging and illustrative of concepts.

## Geometry 3D Shapes

## Numeracy Strategy teaching tools

55 Interactive teaching tools for MathematicsThe following interactive teaching tools have been produced by the National Numeracy Strategy for use within the DML.

Though contained on the discs which are accompanying the unit plans, their use extends far wider than within a particular year group or term.

You can run them from rupertcollins.com just by clicking on the link or you can download them onto your computer by right clicking (hold control then click on a mac) and selecting 'Save Target As...' - you will then be given the option to save it onto your computer.

If you run them from rupertcollins.com use the back button to get back to this page.

## Free Mathsframe Interactives

Mainly number

The year is divided into 2 parts -Interactive Tutorials8Aand8B. For each part there is a Pupils' Practice Book.Book

8Acovers Units1to11.Book8Bcovers Units12to20.Each Unit will have its own set of interactive tutorials - one for each section within that unit.

## The Interactive Mathematics Classroom

Students learn mathematics byDOINGmathematics, and not by watching someone else do mathematics. In recent years there has been an explosion in the number of high quality digital resources available from the Net and elsewhere that allow students to investigate, explore or consolidate the topics they are learning in their maths class.Over time, it is hoped that this website will become a one-stop shop for quality interactive digital resources for mathematics education.

Currently there are well over

quality resources and links available from this website. Have a browse and take away what you wish.three hundred and seventy-fiveItems available in a variety of formats!

## Junior High Math Interactives

A Canadian site## Crickweb

The Maths Teachers Toolkit - Flash games## Virtual Manipulatives Grade 7

A Canadian wiki with links to other grades and Canadian Maths resources## The Interactive Mathematics Classroom

Students learn mathematics byDOINGmathematics, and not by watching someone else do mathematics. In recent years there has been an explosion in the number of high quality digital resources available from the Net and elsewhere that allow students to investigate, explore or consolidate the topics they are learning in their maths class.Currently there are well over

quality resources and links available from this website. Have a browse and take away what you wish.three hundred## Interactive Mathematics Activities

Heaps of activities here in topic lists## Mathematics Interactivities

This is a short list of 20 of the interactivities I have produced. I work on new interactivities every week.But this list no longer gets updated. If you want to see the latest collections of my work, visit my Mathematical Interactivities or join the Interactivities Forum to learn how to make your own interactive educational multimedia resources.## Interactivate

## Wow Maths

Dynamic and Interactive learning resources (UK)## Math 6 Spy Guys

Lessons, strategies, glossary, operations## I Love Maths Games & Puzzles

## Interactive Mathematics Miscellany and Puzzles

## Maths Games

## Illuminations

## Math Manipulatives

Math Manipulatives, Part 2 of the Math Web Resources and Standardized Test Preparation series, contains resources that enable students to interact online.We begin with a short essay on virtual manipulatives, which addresses the following:

- The definition of a virtual manipulative
- The role of virtual manipulatives in the classroom
- Cautionary statements about using and overusing manipulatives and calculators

Or, you may jump right to the resources:Racing Game with One Die

Interactive Mathematics

This site is perfect for...

Studentsof mathematics at secondary and undergraduate levelsmaths quizzes, tests and examsTeachersof mathematicsreadersSmartBoard Resources - Secondary Maths

Shine Write

## Here is a collection of Maths teaching resources designed to be projected on to a white board and then written on as part of a whole class exposition. They'll even work with an Interactive White Board!

7th Grade Skill Builders- Interactive Sites

Activities for all strands

Math Warehouse

Welcome To the Math Warehouse--a web site dedicated to dynamic Math lessons, demonstrations and interactive activities. EXTENSION

K-12 Algebra Applets--Arlen Strader of the Texas A & M University has two algebra tiles applet pages to help middle and high school students explore factoring of quadratic equations by arranging given tiles into a rectangle:

Algebra Tiles1(easy version-coefficients positive) andAlgebra Tiles2(hard version-coefficients positive and negative). There are also applets for Cartesian coordinates, slope, parallel and perpendicular lines, and Pythagorean Theorem.Ambleweb Numeracy Hour of Ambleside C.E. Primary School (UK) contains excellent interactive online Tools for Teachers to use with elementary students for demonstrating concepts and helping students to master basic skills. There is a large buttoned online four function calculator for demonstrating how to use a calculator, an online resource for teaching about angles and how to use a protractor, a virtual tangram, counter squares of various sizes and purposes on which you can scribble using the left button on your mouse, applets for studying number sequences and patterns, a simple bar graph to introduce graphing data, teaching time on an analog clock, and interactive geometry. There is also a section for interactive skill building at three levels of difficulty, puzzles, and games.

primarily forelementary and middle school students. Award-winning applets help students learn to count money, tell time, use patterns to explore fractions and geometric shapes; use base-10 blocks to explore whole and decimal numbers, place value and algebra with blocks; use integer bars to explore basic math facts, fractions, and more; use fraction bars to explore equivalent fractions, ordering fractions, adding fractions, and more. Additional applets help students explore the Pythagorean theorem and the value of Pi, and fractals. Lesson plans are included. Site developed by J. Bulaevsky.Argyll Centreof 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.British and Metric Conversions from Annenberg Media's Learner.org. is an interactive Web site to learn how to convert measurements between the metric system and the English (sometimes called British) system, which is commonly used in the United States. Learn the symbols, more about length, mass, temperature, volume, and then test your knowledge.

C.a.R. (Compass and Ruler) is a dynamic geometry program simulating compass and ruler constructions on a computer. It's by by Rene Grothmann, professor of mathematics at the University of EichstÃ¤tt (Germany). For

school geometryin the plane, there are lots of geometric objects like points, lines, rays, line segments, circles, arcs, angles, polygons and conic sections. Ruler and compass constructions can be changed by dragging one of the basic construction points. Arithmetic computations, numerical solutions, curves and functions go beyond classical constructions. It is even possible to construct in 3D using advanced macros. Other geometries, hyperbolic or elliptic, can be explored. The software is free open-source and comes with documentation, tutorials, and demos. Java needs to be installed.Collaborative Whiteboard from GE allows individuals or groups to draw anything freehand or type text. You can display a graphing grid, select and then draw geometric shapes, save the work and share it with others via email.

Erathothenes' Sieve--watch the primes up to 400 being generated with this Java display.

Euclid's //Elements// Dr. Dave Joyce of Clark University in Massachusetts brings all13 books of the

Elementsalive using a Java geometry applet to illustrate definitions and postulates.ExploreLearning.com is a subscription based set of over 400 virtual manipulatives (simulations of math and science concepts), which the authors call "Gizmos." The math series addresses the five NCTM strands for grades 6-12 and college developmental math, college algebra, and pre-calculus. Gizmos for elementary math for grades 3-5 are also available. ExploreLearning Gizmos, with associated Exploration Guides, help students develop critical thinking skills and conceptual understanding. The series is also correlated with national and state standards and major textbooks, and includes assessment and real time reporting. A 30-day free trial is available for the teacher or home. Sample Gizmo at the site can be immediately activated.

Geometry 3-D Shapes is one of the

Interactivesfrom Annenberg Media's Learner.org. Students can interactively learn about three-dimensional shapes, calculate surface area and volume, and discover some of the mathematical properties of shapes. It comes with tutorials and an interactive test.Geometry Gallery from Saltire Software contains some excellent Java applets, which are easy to use and suitable for illustrating several theorems presented in a high school or post-secondary geometry course. These relate to angles in parallel lines, circular configurations, Pythagorean triples and incircles. Students can drag points to explore concepts. Four triangle calculators are presented. By entering SSS, SAS, or ASA, students can see the unique triangle that is formed, but if SSA is entered the resulting triangle is not unique (two are possible) or no triangle is possibly formed with given information. Some advanced geometrical configurations are explored. There is a geometry atlas of algebraic formulas with associated visuals. Saltire's work has been assisted with a number of National Science Foundation grants.

Harcourtschool.com E-Lab: Extensive collection of interactive applets for grades 3-6. Activities to accompany each are provided. You can download an E-Lab activity and use it without being connected to the internet. While working on internet, Microsoft Java VM is recommended. Later versions of Java will be supported soon for online activity.

Illuminations Activities from the National Council of Teachers of Mathematics (NCTM) contain Java applets identified by grade band to investigate various concepts within NCTM identified strands.

Interactivate, which is a project of The Shodor Education Foundation, Inc., includes a set of interactive JAVA-based tools to support courseware in science and math. Activities are divided by grade-band (3-5, 6-8, 9-12, and undergraduate). Some activities allow students to keep score to monitor their progress, and are listed under assessments. Activities that use the tools support NCTM standards. Browse by topic, audience, type (activity, lesson, discussion), or subject (number and operations, geometry, algebra, probability, statistics, modeling, discrete, and other). A math dictionary of terms used within the site is included. Interactivate has also aligned its activities to several textbook series (e.g., Connected Math, Math Thematics, Mathematics in Context, and MathScape).

Interactive Mathematics promotes learning math while you play with it!

Primarily for upper secondary and college levelstudents; basic math includes algebra, complex numbers, statistics, logarithms, trigonometry, plane analytic geometry, and graphing. Calculus includes differentiation, integration, and higher topics in calculus. Lectures and full examples are provided. Site provides links to LiveMath plug-in, Scientific Notebook, and Flash.Interactive Resources from the UK has four math packs, each with a wide range of excellent interactives for classroom use with preK-6 students. Explore numerous concepts related to NCTM strands. Some include whiteboard (drawing on the figures) capabilities. There are rulers, protractors, geoboards, Venn diagrams, number lines, and so on. Don't miss these teaching tools.

Key Curriculum Press JavaSketchpad has several applets for use with secondary math students and above. See the interactive manipulative on the Pythagorean Theorem and the JavaSketchpad DR4 Gallery. In the Gallery you will find demonstrations from geometry (e.g., centroid), trigonometry and algebraic geometry (e.g., sine waver and conic sections), calculus (e.g., box volume and falling ladder), mechanics, and an applet on least squares.

The Learning Equation (TLE) is brought to you by R. Blond of Edmonton, Alberta, Canada. TLE features JAVA applets that help students to interactively explore complex mathematics concepts typically studied in depth from grades 9 through post-secondary. Among topics are triangle relations, slopes, circle geometry, conic sections, exponential and trig functions; translations, reflections, stretching; and more.

Learning Objects from Brock University (Canada) Department of Mathematics are tools to help students explore mathematical concepts interactively.

- The Great Balancing Act: explore the mean and median
- Parabola games: explore parabola properties, transformations and their use
- Leap Frog: explore number patterns
- Fire, Fire!: explore trigonometric ratios
- Transformations: an introduction to transformational symmetries
- Markov chains: What happens after years of movement in cities and suburbs, an introduction to Markov chains

Manipula Math with JAVA by International Education Software contains a collection of over 280 applets suitable for teaching math concepts tomiddle school, high school, and college students.Applets address middle school geometry and the Pythagorean Theorem, trigonometry, calculus, vectors, complex numbers, conics, and miscellaneous topics.Math Doodles is by Daren Carstens, who is the developer of the award winning software Math Arena. He offers several interactive puzzles and games for elementary learners to have fun. But there is learning, too, as students practice addition, subtraction, money skills, and pattern matching (shape, number, color), for example. Among current games are Connect Sums, Number Jump, Polyomino Shift, Double Traits, Sum Stacker, Time Shuffle, and more. Older learners also benefit, as students really need to think as they do these.

Math Playground: Animated characters created with Flash add to the appeal of this learning site for grades 1-6. Among resources are some virtual math manipulatives, such as a protractor, fraction bars, equivalent fractions, percents, a spinner for probability, function machine, pattern blocks, and a geoboard.

Mathplotter allows teachers of mathematics to draw pictures of equations and functions and to put those images in a Word or Excel document. These documents can then be printed for distribution to students as tests, handouts, worksheets and so on. Mathplotter can also be used in the classroom to explore the behavior of mathematical equations. There are some excellent tools for pre-calculus and calculus.

Mathematics Open Reference is a free plane geometry textbook for high school learners. Its focus is on using interactive materials and animations to develop concepts. There are numerous interactive applets with at least one accompanying nearly every concept. This is highly recommended for visual learners and reinforcement for all.

K-12 mathematics and calculus. Help kindergarten students understand concepts. Introduce topics with pattern blocks, number lines, fraction bars and more. Algebra concepts include number systems, integers and integer operations, properties (commutative, associative, distributive), multiplying/dividing, using variables, equivalent equations, inverse operations, graphing, linear equations and systems, quadratic equations, factoring, and more. Geometry interactives for plane and solid topics are extensive. Trigonometry includes the Law of Sines and Law of Cosines. There is a range of calculus tools for differentiation and integration topics.Mathsnet.net is a

highly interactive site for doing mathematics, featuring concepts in number, geometry, algebra, graphs, data handling. JAVA, Javascript, or plug-ins may be needed. The geometry is of particular interest. There are curriculum, articles, books, and a section for download, including free software to explore topics interactively. Don't miss this award winning site brought to you by B. Dye in England.Math Warehouse is "dedicated to dynamic Math lessons, demonstrations, and interactive activities." There are topics in algebra, geometry, trigonometry. Worksheets are available for download, too.

MegaMaths, brought to you by the BBC, is a School Radio series for elementary students aged 7-9. Each 15 minute episode promotes a whole-class approach to mental maths activities through a series of lively and stimulating quizzes.

National Library of Virtual Manipulatives for Interactive Mathematics contains manipulatives and associated online activities for each of the five strands identified in standards set forth by the NCTM. This is an ongoing project of Utah State University and a must see site

for grades preK-12. Select a manipulative from the grade level you teach and an activity from one of the strands.Number Line Applet: Introduce addition and subtraction of integers with this number line. Students see the concept after clicking onto the integers (-35 to 35) for the problem. From MSTE at University of Illinois-Urbana_Champaign.

PBS Teacherline Interactives --explore with cubes, floor tiles, frog in a well (number patterns and relations), geoboard, histograms, making a rule, mixing orange juice, number cruncher, the race, real-life data, space blocks, surface area, and tesselate.

Principles and Standards for School Mathematics Electronic Examples--interactive applets for investigating concepts from NCTM. Examples are divided into grade bands.

Seeing Math by the Concord Consortium has eight free secondary math interactives written in Java to assist algebra learners in the study of functions. "Each interactive provides a real-time connection between representations of the mathematics (symbolic, graphical, etc.), so that changes in one representation instantly cause changes in the other." Interactives include a qualitative grapher, piecewise linear grapher, linear transformer, quadratic transformer, function analyzer, system solver, plop it and proportioner. A user's guide, warm up exercise, frequently asked questions, and sample activity are provided.preK-2: Investigate patterns, triangles and properties of polygons, geometry and measurement; develop spatial skills by using tanagrams, learn estimation strategies3-5:Communicate about math using games, use simulation software to investigate distance, rate, and time; investigate data6-8:Visualize the concept of multiplication, investigate rate of change, length, perimeter, area, volume, congruence, similarity, and symmetry, and the Pythagorean Theorem9-12:Explore vectors; use graphs, equations, and tables to investigate elimination of medicine from the body; explore inscribed figures, linear regression, and linear functions.Statistics:Are you teaching your students about statistics and survey research? Read Statistics Every Writer Should Know by Robert Niles. Learn about mean, median, percent, per capita, standard deviation, margin of error, data analysis, and more. Link to sites for data sources and interactive help to select the right statistical test.Tools:Generate random numbers, sample sizes, charts and graphs, and perform statistical calculations using these tools:Tangoes. "Based on the ancient Chinese Tangram puzzle, Tangoes is a learning tool that combines artistic and mathematical elements to enhance visual perception ability; develop problem solving skills; creative thinking capacity and teamwork. Tangoes can be played by one, two or in teams. From ages four to one hundred and four, all ages are delighted by the challenge of forming the puzzle presented with the seven dynamic pieces." There is an online version that can be played for free.

Tangrams from Channel4.com has three levels, then the challenge level.

Using Virtual Manipulatives on the Web to Develop Number Sense by Margo Mankus and hosted by the Graduate School of Education at George Mason University contains three interactive applets and a host of activities to develop concepts of number, operations, and geometry. Applets, developed by J. Bulaevsky, include pattern blocks, base ten blocks, and integer rods. These are great tools to demonstrate concepts in the classroom and to give students practice in class or at home.

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, P. Deubel highly recommends this site.

Visual Math: Functions contains JAVA applets for exploring linear and quadratic functions. Linear explorations include representations of linear functions, functions defined on intervals, equivalent expressions for functions, addition/subtraction, transformations, rate of change. Quadratic explorations equivalent quadratic expressions, comparisons and operations, solving equations, graph transformations (vertex form), add functions (polynomial form), products of linear functions, quadratic growth, graphic design, motion at changing speed, and economic decisions.

Visual Math Learning is a free educational web site developed by W. Bateman, who indicates that the site features "an interactive on-line tutorial for teaching elementary mathematics and basic arithmetic for grades K-12 at the pre-algebra level. It is an instructional aid for parents, teachers, and educators of primary, elementary, and middle school students, as well as a resource for lesson plans, homework help, and home schooling math lessons. The tutorial includes games, puzzles, interactive diagrams, and computer animated virtual manipulatives that emphasize active learning concepts by visualization."

Visualization of Elementary Math, by E. Kluk, M. Frank, and M. Mangru of Dickinson State University in North Dakota, contains several applets to help students with understanding meanings of elementary math operations. Applets include a visual multiplication table, visual addition (single and double digit), and visual fractions (making and comparing, adding and subtracting). Instructional examples are included.

Waldo's Interactive Maths Pages contains over 50 Java applets for teaching math concepts. These are grouped within age ranges (11-14, 14-16, and 16-19) and then by topics usually studied within those ranges. Topics are extensive from angles and intersecting and parallel lines, exploring triangles, solving equations, sequences, graphing linear and quadratic equations, trigonometry, calculus, and much more. Waldo is a teacher in England who developed these. Don't miss this work, which links theory to the visual.

Walter Fendt's Java Applets on Mathematics address arithmetic, elementary algebra, geometry (e.g., transformations, triangles, Pythagorean theorem, area and circumference of circles, and platonic solids), trigonometry (visual demonstration of graphs of sine, cosine and tangent of an angle), vector analysis, analysis (e.g., first and second derivatives), and complex numbers (arithmetic operations). These are very engaging and illustrative of concepts.