On-line Mathematics Manipulatives
and TETC 2001, 2002

Participants will learn about interactive Web sites that include on-line mathematics manipulatives for school or home use. Mathematics topics to be covered include pattern blocks, tangrams, flash cards, algebra tiles, pentominoes, etc. Mathematics standards that relate to these topics will be discussed.

Deborah A. McAllister, Peggy S. Moyer - Fall 2002
Shirley A. McDonald - Fall 2001

NCTM Principles and Standards for School Mathematics - Go to site - http://standards.nctm.org/

E-Examples - Go to site - http://standards.nctm.org/document/eexamples/index.htm

Illuminations - Go to site - http://illuminations.nctm.org/ or Go to site

Tennessee Curriculum Standards for Content Areas with State Assessment -

Go to site - http://www.state.tn.us/education/ci/cicurassessedstandards.htm

Google search engine - Go to site - http://www.google.com/ - Good search engine for finding mathematics manipulatives

A+ Math - Go to site - http://www.aplusmath.com/

A+ Games - Go to site - http://www.aplusmath.com/Games/index.html

A+ Flash Cards - Go to site - http://www.aplusmath.com/Flashcards/index.html

A+ Homework Helper - Go to site - http://www.aplusmath.com/Homework_Helper/index.html

The ArithmAttack - Go to site - http://www.dep.anl.gov/aattack.htm

Calculators and Online Math Tools - Go to site - http://www.useekufind.com/learningquest/tmcaltoo.htm

CleverMedia - Go to site - http://www.clevermedia.com

CleverMedia Pentominoes - Go to site - http://clevermedia.com/game.cgi?pentominoes

Education 4 Kids, Drill Games - Go to site - http://edu4kids.com/

Educational Java Programs, Arcytech - Go to site - http://ejad.best.vwh.net/java/

Enchanted Mind - Puzzles - Go to site - http://www.enchantedmind.com/html/puzzles/interactive_puzzles/creative_java_puzzles.html

Enchanted Mind - Tangrams - Go to site - http://www.enchantedmind.com/puzzles/tangram/tangram.html

Enchanted Mind - Pentominos - Go to site - http://www.enchantedmind.com/puzzles/pentamino/pentamino.html

Enchanted Mind - Master Mind - Go to site - http://www.enchantedmind.com/puzzles/mastermind/mastermind.html

Fractions - Go to site - http://www.aaamath.com/fra.html

Gamequarium - Go to site - http://www.gamequarium.com/

Gamequarium Jr. - Go to site - http://www.gamequarium.com/junior.html

The Monty Hall Problem - Let's Make a Puzzler (with Click and Clack, the Tappit Brothers) - Go to site - http://cartalk.cars.com/About/Monty/

E-lab/Harcourt School Publishers - Go to site - http://www.harcourtschool.com/elab/

Scott Kim, Inversions - Go to site - http://scottkim.com/

Math Baseball, funbrain.com - Go to site - http://www.funbrain.com/math/index.html

Math.com Puzzles, Games, and Contests - Go to site - http://www.math.com/students/puzzles/puzzleapps.html

National Library of Virtual Manipulatives for Interactive Mathematics - Go to site (Utah State University/NSF grant) - http://matti.usu.edu/nlvm/nav/vlibrary.html

Neufeld Learning Systems Inc. - Go to site - http://neufeldmath.com/

PrimaryGames.com - Math - Go to site - http://www.primarygames.com/math.htm

Quia Mathematics - Go to site - http://www.quia.com/dir/math/

Jim Reed's Home Page - Go to site - http://argyll.epsb.edmonton.ab.ca/jreed/

From Jim Reed's Sidebar, take the Math Online link -

Go to site - http://dev1.epsb.edmonton.ab.ca/math14_Jim/math9/

Also explore other grades. You will find algebra tiles, etc.

Resource Room.net - Math Times Tables Practice Page -

Go to site - http://www.resourceroom.net/math/1timestables.asp

Select 'low-frills, low-stress practice' link -

Go to site - http://www.resourceroom.net/math/1timestables.asp#facts/

Saxon Publishers - Go to site - http://www1.saxonpublishers.com/

Tower of Hanoi, Lawrence Hall of Science - Go to site - http://www.lhs.berkeley.edu/Java/Tower/towerhistory.html

Tower of Hanoi - Go to site - http://chemeng.p.lodz.pl/zylla/games/hanoi5e.html

Tower of Hanoi, Article 19 Group Inc. - Go to site - http://www.article19.com/shockwave/toh.htm

Visual Fractions - Go to site - http://www.visualfractions.com/

What Time Is It? PrimaryGames.com - Go to site - http://www.primarygames.com/time/start.htm

www.multiplication.com - Go to site - http://www.multiplication.com/ - Select Games

Applets for the Interactive Textbook on Physics, Mathematics, and Chemistry - Go to site - http://dept.physics.upenn.edu/courses/gladney/mathphys/java/java_collection.html

Physics Java Applets - Go to site - http://plabpc.csustan.edu/java/

4.1. Creating, Describing, and Analyzing Patterns to Recognize Relationships and Make Predictions (Algebra) -

Making Patterns - Go to site http://standards.nctm.org/document/eexamples/chap4/4.1/index.htm

Describing Patterns - Go to site - http://standards.nctm.org/document/eexamples/chap4/4.1/Part2.htm

Extending Pattern Understandings -

Go to site - http://standards.nctm.org/document/eexamples/chap4/4.1/Part3.htm

4.2 Investigating the Concept of Triangle and Properties of Polygons (Geometry) -

Go to site - http://standards.nctm.org/document/eexamples/chap4/4.2/index.htm

Go to site - http://standards.nctm.org/document/eexamples/chap4/4.2/part2.htm

4.3 Learning Geometry and Measurement Concepts by Creating Paths and Navigating Mazes (Geometry, Problem Solving) -

Hiding Ladybug - Go to site - http://standards.nctm.org/document/eexamples/chap4/4.3/index.htm

Making Rectangles - Go to site - http://standards.nctm.org/document/eexamples/chap4/4.3/Part2.htm

Ladybug Mazes - Go to site - http://standards.nctm.org/document/eexamples/chap4/4.3/Part3.htm

4.4 Developing Geometry Understandings and Spatial Skills through Puzzlelike Problems with Tangrams (Geometry, Problem Solving) -

Tangram Puzzles - Go to site - http://standards.nctm.org/document/eexamples/chap4/4.4/index.htm

Tangram Challenges - Go to site - http://standards.nctm.org/document/eexamples/chap4/4.4/part2.htm

4.5 Learning about Number Relationships and Properties of Numbers Using Calculators and Hundred Boards (Number and Operations, Reasoning and Proof, Communication) -

Displaying Number Patterns - Go to site - http://standards.nctm.org/document/eexamples/chap4/4.5/index.htm

Patterns to 100 and Beyond -

Go to site - http://standards.nctm.org/document/eexamples/chap4/4.5/calc_full/part2.htm

5.1 Communicating about Mathematics Using Games (Number and Operations, Communication) -

Playing Fraction Track - Go to site - http://standards.nctm.org/document/eexamples/chap5/5.1/index.htm

5.2 Understanding Distance, Speed, and Time Relationships Using Simulation Software (Algebra) - Go to site - http://standards.nctm.org/document/eexamples/chap5/5.2/index.htm

5.3 Exploring Properties of Rectangles and Parallelograms Using Dynamic Software (Geometry) -

Go to site - http://standards.nctm.org/document/eexamples/chap5/5.3/index.htm

5.5 Collecting, Representing, and Interpreting Data Using Spreadsheets and Graphing Software (Representation) -

Collecting and Examining Weather Data -

Go to site - http://standards.nctm.org/document/eexamples/chap5/5.5/index.htm

Representing and Interpreting Data -

Go to site - http://standards.nctm.org/document/eexamples/chap5/5.5/part2.htm

6.1 Learning about Multiplication Using Dynamic Sketches of an Area Model (Number and Operations) - Go to site - http://standards.nctm.org/document/eexamples/chap6/6.1/index.htm

6.2 Learning about Rate of Change in Linear Functions Using Interactive Graphs (Algebra) -

Constant Cost Per Minute - Go to site - http://standards.nctm.org/document/eexamples/chap6/6.2/index.htm

Changing Cost Per Minute - Go to site - http://standards.nctm.org/document/eexamples/chap6/6.2/part2.htm

6.3 Learning about Length, Perimeter, Area, and Volume of Similar Objects Using Interactive Figures (Geometry) -

Side Length and Area of Similar Figures -

Go to site - http://standards.nctm.org/document/eexamples/chap6/6.3/index.htm

Side Length, Volume, and Surface Area of Similar Solids -

Go to site - http://standards.nctm.org/document/eexamples/chap6/6.3/part2.htm

6.4 Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures (Geometry) -

Visualizing Transformations - Go to site - http://standards.nctm.org/document/eexamples/chap6/6.4/index.htm

Identifying Unknown Transformations -

Go to site - http://standards.nctm.org/document/eexamples/chap6/6.4/part2.htm

Composing Reflections - Go to site - http://standards.nctm.org/document/eexamples/chap6/6.4/part3.htm

Composing Transformations - Go to site - http://standards.nctm.org/document/eexamples/chap6/6.4/part4.htm

6.5 Understanding the Pythagorean Relationship Using Interactive Figures (Geometry) -

Go to site - http://standards.nctm.org/document/eexamples/chap6/6.5/index.htm

6.6 Comparing Properties of the Mean and the Median through the use of Technology (Data Analysis and Probability) - Go to site - http://standards.nctm.org/document/eexamples/chap6/6.6/index.htm

7.1 Learning about Properties of Vectors and Vector Sums Using Dynamic Software (Number and Operations) -

Components of a Vector - Go to site - http://standards.nctm.org/document/eexamples/chap7/7.1/index.htm

Sums of Vectors and Their Properties -

Go to site - http://standards.nctm.org/document/eexamples/chap7/7.1/part2.htm

7.2 Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body (Algebra) -

Modeling the Situation - Go to site - http://standards.nctm.org/document/eexamples/chap7/7.2/index.htm

Long-Term Effect - Go to site - http://standards.nctm.org/document/eexamples/chap7/7.2/part2.htm

Graphing the Situation - Go to site - http://standards.nctm.org/document/eexamples/chap7/7.2/part3.htm

7.3 Understanding Ratios of Areas of Inscribed Figures Using Interactive Diagrams (Connections, Geometry) - Go to site - http://standards.nctm.org/document/eexamples/chap7/7.3/index.htm

7.4 Understanding the Least Squares Regression Line with a Visual Model (Data Analysis and Probability) - Go to site - http://standards.nctm.org/document/eexamples/chap7/7.4/index.htm

7.5 Exploring Linear Functions: Representational Relationships (Problem Solving) -

Go to site - http://standards.nctm.org/document/eexamples/chap7/7.5/index.htm

From the NCTM Illuminations (in addition to E-Examples; see also Selected Web Resources and Lesson Plans)

Developing Geometry Concepts Using Computer Programming Environments (Geometry) -

Go to site - http://Illuminations.nctm.org/imath/prek2/GeometryConcepts/index.html

Exploring Geometric Solids and Their Properties (Geometry) -

Go to site - http://Illuminations.nctm.org/imath/3-5/GeometricSolids/index.html

Getting to Know the Shapes -

Go to site - http://Illuminations.nctm.org/imath/3-5/GeometricSolids/GeoSolids1.html

Study the Shapes - Go to site - http://Illuminations.nctm.org/imath/3-5/GeometricSolids/GeoSolids2.html

Construct a Solid - Go to site - http://Illuminations.nctm.org/imath/3-5/GeometricSolids/GeoSolids4.html

Analyzing Numeric and Geometric Patterns of Paper Pool (Number and Operations) -

Go to site - http://Illuminations.nctm.org/imath/6-8/pooltable/index.html

Paper Pool Game - Go to site - http://Illuminations.nctm.org/imath/6-8/pooltable/pool1.html

Explore More Tables - Go to site - http://Illuminations.nctm.org/imath/6-8/pooltable/pool2.html

Spatial Reasoning using Cubes and Isometric Drawings (Geometry) -

Go to site - http://illuminations.nctm.org/imath/6-8/isometric/index.html

1. Exploring the Isometric Drawing Tool/Building a Shape - Go to site - http://illuminations.nctm.org/imath/6-8/isometric/cube68i1.htm

Moving Cubes - Go to site - http://illuminations.nctm.org/imath/6-8/isometric/cube68i2.htm

2. Solid to Isometric -- One to Many/Another View - Go to site - http://illuminations.nctm.org/imath/6-8/isometric/cube68r1.htm

Solid to Isometric -- The Same Solid?/Do They Match? - Go to site - http://illuminations.nctm.org/imath/6-8/isometric/cube68r2.htm

Creating Solids from Isometric Drawings -- One to Many/When is a cube not a cube? - Go to site - http://illuminations.nctm.org/imath/6-8/isometric/cube68r3.htm

Isometric to Solid -- One to None??/Some "Escher" Drawings - Go to site - http://illuminations.nctm.org/imath/6-8/isometric/cube68r4.htm

3. Other 2D Representations -- Front-Right-Top - Go to site - http://illuminations.nctm.org/imath/6-8/isometric/cube68o1.htm

Other 2D Representations -- Building Plans - Go to site - http://illuminations.nctm.org/imath/6-8/isometric/cube68o2.htm

Other 2D Representations -- Mat Plans - Go to site - http://illuminations.nctm.org/imath/6-8/isometric/cube68o3.htm

4. Volume & Surface Area - Go to site - http://illuminations.nctm.org/imath/6-8/isometric/cube68m1.htm

The Factor Game (Number and Operations) -

Go to site - http://Illuminations.nctm.org/imath/6-8/FactorGame/index.html

Playing the Factor Game - Go to site - http://Illuminations.nctm.org/imath/6-8/FactorGame/factor1.html

Playing to Win - Go to site - http://Illuminations.nctm.org/imath/6-8/FactorGame/factor2.html

Making Connections - Go to site - http://Illuminations.nctm.org/imath/6-8/FactorGame/factor3.html

The Product Game (Number and Operations) -

Go to site - http://Illuminations.nctm.org/imath/6-8/ProductGame/index.html

Playing the Product Game - Go to site - http://Illuminations.nctm.org/imath/6-8/ProductGame/product1.html

Make Your Own Product Game -

Go to site - http://Illuminations.nctm.org/imath/6-8/ProductGame/product2.html

Classifying Numbers - Go to site - http://Illuminations.nctm.org/imath/6-8/ProductGame/product3.html

Connections and Extensions - Go to site - http://Illuminations.nctm.org/imath/6-8/ProductGame/product4.html

Simulating Probability Situations Using Box Models (Data Analysis and Probability) -

Go to site - http://Illuminations.nctm.org/imath/6-8/BoxModel/index.html

Exploring Histograms (Data Analysis and Probability) -

Go to site - http://Illuminations.nctm.org/imath/6-8/BarChart/index.html

Investigating Linear Relationships: The Regression Line and Correlation (Data Analysis and Probability) -

The Regression Line - Go to site - http://Illuminations.nctm.org/imath/912/LinearRelationships/index.html

The Effects of Outliers - Go to site - http://Illuminations.nctm.org/imath/912/LinearRelationships/part2.html

Correlation and the Regression Line -

Go to site - http://Illuminations.nctm.org/imath/912/LinearRelationships/part3.html

The Centroid and the Regression Line -

Go to site - http://Illuminations.nctm.org/imath/912/LinearRelationships/part4.html

Put the Heart into Mathematics: Cardiac Output, Rates of Change and Accumulation (Algebra, Connections) -

Cardiac Output, Rates of Change and Accumulation - Go to site - http://illuminations.nctm.org/imath/912/cardiac/index.html

Make a Conjecture - Go to site - http://illuminations.nctm.org/imath/912/cardiac/cardiac.html

Gather Data -

Go to site - http://illuminations.nctm.org/imath/912/cardiac/cardiac2.html

Analyze the Data -

Go to site - http://illuminations.nctm.org/imath/912/cardiac/cardiac3.html

Reflecting on Your Work -

Go to site - http://illuminations.nctm.org/imath/912/cardiac/cardiac4.html

Shedding Light on the Subject: Function Models of Light Decay (Algebra, Connections) -

Overview - Go to site - http://illuminations.nctm.org/imath/912/Light/index.html

Make a Conjecture - Go to site - http://illuminations.nctm.org/imath/912/Light/light.html

Gather Data -

Go to site - http://illuminations.nctm.org/imath/912/Light/light2.html

Analyzing the Data -

Go to site - http://illuminations.nctm.org/imath/912/Light/light3.html

Reflect on Your Work -

Go to site - http://illuminations.nctm.org/imath/912/Light/light4.html

Symmetries and Their Properties (Geometry) -

Overview of the Series - Go to site - http://illuminations.nctm.org/imath/912/sy_begin/index.html

1. Rotational Symmetry - Go to site - http://illuminations.nctm.org/imath/912/sy_rotations/index.html

Describing Rotations -

Go to site - http://illuminations.nctm.org/imath/912/sy_rotations/page1.html

Finding What Doesn't Change -

Go to site - http://illuminations.nctm.org/imath/912/sy_rotations/page2.html

Relating Rotations to Symmetry -

Go to site - http://illuminations.nctm.org/imath/912/sy_rotations/page3.html

Conclusions -

Go to site - http://illuminations.nctm.org/imath/912/sy_rotations/page4.html

2. Reflections - Go to site - http://illuminations.nctm.org/imath/912/sy_reflections/index.html

Describing Reflections -

Go to site - http://illuminations.nctm.org/imath/912/sy_reflections/page1.html

Relationships Between Reflections and Symmetry -

Go to site - http://illuminations.nctm.org/imath/912/sy_reflections/page2.html

Reflections Across Two Mirror Lines -

Go to site - http://illuminations.nctm.org/imath/912/sy_reflections/page3.html

Conclusions -

Go to site - http://illuminations.nctm.org/imath/912/sy_reflections/page4.html

3. Translations - Go to site - http://illuminations.nctm.org/imath/912/sy_translations/index.html

4. Glide Reflections -

Go to site - http://illuminations.nctm.org/imath/912/sy_glide/index.html

Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond (Algebra) - Go to site - http://Illuminations.nctm.org/imath/912/TroutPond/index.html

Numerical Analysis - Go to site - http://Illuminations.nctm.org/imath/912/TroutPond/Trout2.html

Graphical Analysis - Go to site - http://Illuminations.nctm.org/imath/912/TroutPond/Trout3.html

Whelk-Come to Mathematics: Using Rational Functions to Investigate the Behavior of Northwestern Crows (Algebra) - Go to site - http://Illuminations.nctm.org/imath/912/Whelk/index.html

Conduct an Experiment - Go to site - http://Illuminations.nctm.org/imath/912/Whelk/whelk2.html

Analyze the Data - Go to site - http://Illuminations.nctm.org/imath/912/Whelk/whelk3.html

Work to a Conclusion - Go to site - http://Illuminations.nctm.org/imath/912/Whelk/whelk4.html

Sound Wave: How do Computers Represent Sound? (Connections) - Go to site - http://illuminations.nctm.org/imath/912/soundwave/index.html

UTC - Go to site - http://www.utc.edu/

Teacher Preparation Academy - Go to site - http://oneweb.utc.edu/~tpa/index.html

Dr. Deborah A. McAllister - Go to site - http://oneweb.utc.edu/~deborah-mcallister/index.html

Conference expenses reimbursed through a grant from the Center of Excellence for Computer Applications, UTC, Dr. Clinton Smullen, III, Director - Go to site - http://www.utc.edu/~ceca/