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Online manipulatives bring all of the learning and fun without the mess. Our math virtual manipulatives help students grasp abstract concepts through modeling. Literacy virtual manipulatives create a fun space for practicing spelling, rhyming, and more!

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Virtual Manipulatives | Mathematical Modelling | Toy Theater

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Original teaching tools aimed at supporting teachers in the elementary school classroom. Two color counters, 3D dice, probability spinners, graph builders, fraction bars, base ten blocks, and more!

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Virtual manipulatives are an essential component in guiding students through the three phases of learning: concrete, representational, and abstract. ...

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The beginning of our introductory math journey is Logic. Through these challenging problem solving exercises, you’ll construct the critical thinking skills that are the basis for mathematical reasoning. You’ll use limited information to make predictions – eliminating the impossible to uncover the…

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Common Core State Standards Content Inventory | Virtual Nerd

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Virtual Nerd’s patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. In this non-linear system, users are free to take whatever path through the material best serves their needs. These unique feat…

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What is Geometry?

Geometry is a branch of mathematics that studies the sizes, shapes, positions angles and dimensions of things.

Flat shapes like squares, circles, and triangles are a part of flat geometry and are called 2D shapes. These shapes have only 2 dimensions, the length and the width.

Examples of 2D shapes in flat geometry

Solid objects are also known as 3D objects having the third dimension of height or depth.

Examples of 3D shapes in solid geometry

Angle:

The vertex of a shape where two edges meet form an angle. Different shapes in geometry have different angle measures.

For example:

A triangle is a 3 sided shape, and the measure of its 3 interior angles is 180˚

A square, rectangle or quadrilateral are 4 sided shapes, and the measure of their interior angles is 360˚

Other polygons like the pentagon, hexagon, heptagon, octagon have 5, 6, 7, 8 sides respectively and varying angles.

Examples of different Polygons with their angles and sides

We learn various aspects of shapes, like the measurement of angles, length of sides, area, volume, etc in geometry.

Similarity and congruence are two important aspects of geometry.

Similarity: Similarity is when two shapes are the same but their sizes may vary.

Congruence: Congruence is when two shapes are exactly the same in shape and size.

Coordinate Plane:

A coordinate plane is a 2D surface formed by using two number lines that intersect each other at the right angle.

The horizontal number line is the x-axis, and the vertical number line is the y-axis.

The intersection of the two axes is the (0,0) coordinate.

Using the coordinate plane, we plot points, lines, etc. By joining various points on the coordinate plane, we can create shapes.

We use Formula and Theorems to solve the geometry problems.

A formula is a mathematical equation to solve a geometry problem while a theorem is a statement that is proved using previously known facts.

For example, the " Pythagoras Theorem" proved that a2 + b2 = c2 for a right-angled triangle, where a and b are the sides of the right-angled triangle, and c is the hypotenuse.

However, a2 + b2 = c2 is the formula for finding the hypotenuse of a right-angled triangle.

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SplashLearn - Fun Math Practice Games for Kindergarten to 5th Grade

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Geometry is a branch of mathematics that studies the sizes, shapes, positions angles and dimensions of things. Flat shapes like squares, circles, and triangles are a part of flat geometry and are called 2D shapes. These shapes have only 2 dimensions, the length and the width.

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Puzzles, Activities and Lesson Plans - Mathigon

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Explore our free library of tasks, lesson ideas and puzzles using Polypad and virtual manipulatives.

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These websites, apps and magazines showcase the incredible breadth and beauty of mathematics.

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Polypad - Virtual Manipulatives - Mathigon

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Virtual manipulatives, dynamic geometry, graph plotting, data science and more: explore the ultimate mathematical playground!

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There are a TON of books about math on Epic! Some even connected to sports...

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There are a TON of books about math on Epic! Some even connected to sports...

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Built on a collection of 40,000+ popular, high-quality books from 250+ of the world's best publishers, Epic safely fuels curiosity and reading confidence for kids 12 and under.

Get Started

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online access fun thousands children great kids ebooks books

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Discover new children's books on Epic. With thousands of books and audiobooks there is no limit to what children can learn and explore.

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IXL is here to help you grow, with immersive learning, insights into progress, and targeted recommendations for next steps. Practice thousands of math and language arts skills at school, at home, and on the go!

Remember to bookmark this page so you can easily return.

To get started:

1. Sign in with your username and password on this page. Please ask your teacher if you don't know this information.

2. Take the Diagnostic and visit the Recommendations page for skills that are picked just for you! Or, explore skills by grade or topic.

3. Choose a skill and let the learning begin!

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Sign in to IXL for Independence Schools! Students will love earning awards and prizes while improving their skills in math and language arts.

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Math Game Time - Free Math Games & Worksheets for Kids & Teachers

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Math Game Time offers free math games, worksheets, homework help & videos for teachers, parents & children. Start enjoying cool, fun math games online today!

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Math Worksheets | Dynamically Created Math Worksheets

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Dynamically Created Math Worksheets for Addition, Subtraction, Multiplication, Division, Time, Fractions, Kindergarten and more Math Topics.

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Math explained in easy language, plus puzzles, games, worksheets and an illustrated dictionary. For K-12 kids, teachers and parents.

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Being Curious - Upper Primary is part of our Being a Good Thinker - Upper Primary collection.

Good thinkers are curious and ask good questions. They are excited by new ideas and are keen to explore and investigate them.

How can you become a more curious mathematician?

These problems will exploit your natural curiosity and encourage you to ask good mathematical questions.

You can browse through the Number, Measures, Geometry or Statistics collections, or scroll down to see the full set of problems below.

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Being Curious - Upper Primary is part of our Being a Good Thinker - Upper Primary collection. Good thinkers are curious and ask good questions. They are excited by new ideas and are keen to explore and investigate them. How can you become a more curious mathematician?

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Practice addition, multiplication, fractions and algebraic reasoning with our popular math games. Discover fun learning games kids love to play.

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A required part of this site couldn’t load. This may be due to a browser extension, network issues, or browser settings. Please check your connection, disable any ad blockers, or try using a different browser.

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To get four squares in a row-vertically, horizontally, or diagonally.

How to Play

1. To begin the game, Player 1 moves a marker (green square) to a number in the factor list of numbers 1-9 along the bottom of the game screen.

2. Player 2 then moves the other marker (green square) to any number in the factor list (including the number marked by Player 1). The product of the two marked numbers is determined, and that product is colored red for Player 2.

3. Player 1 moves either marker to another number, and the new product is colored blue for Player 1.

4. Players take turns moving a marker, and each product is marked red or blue, depending on which player made the product. However, if a product is already colored, the player does not get a square for that turn.

5. Play continues until one player wins, or until all squares have been colored.

Credit

This Product Game Investigation was adapted with permission and guidance from Prime Time: Factors and Multiples, Connected Mathematics Project, G. Lappan, J. Fey, W Fitzgerald, S. Friel and E. Phillips, Dale Seymour Publications (1996), pp. 17‑25.

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This applet is the Product Game: a fun, interactive game that exercises your skill with factors and multiples.

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Classroom Resources - National Council of Teachers of Mathematics

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Cool Math - free online cool math lessons, cool math games & apps, fun math activities, pre-algebra, algebra, precalculus

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Cool Math has free online cool math lessons, cool math games and fun math activities. Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too.

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How to Tessellate

In what follows I hope to explain how each of several methods can be applied to create tesselations, starting with pencil and paper and ending with computer software.

A. FUNDAMENTAL POLYGONS

It is not too difficult to find pages with squares, equilateral triangles, or hexagons tesselating the page. One good source is Graph Paper Masters from Dale Seymour Publications . The book is a source of black-line masters and comes with permission to copy for classroom use. Students can be invited to create their own schemes for coloring the figures. Before the four-color map theorem has been learned a challenge might be made to used the fewest number of colors to color all the regions.

B. SIMPLE TRANSFORMATIONS

Now a few simple tesselation patterns will be shown that can be done with paper, pencil, and scissors.

To tesselate a field of rectangles, start with a rectangle drawn on a page. Replace one side with some simple design.

Rectangle with one PAIR OF NEW SIDES.

This figure can be reproduced to fill the whole plane.

When doing this by hand, it is handy to start with a rectangle, draw your pattern down the middle, then cut slong that pattern, and join the parallel end segments.

Using the same method, a slightly more advanced SLIDE tesselation can be made using the three pairs of opposite sides in a regular hexagon

A regular hexagon.

Regular hexagon with sides transformed

Regular hexagon decorated

Regular hexagon decorated, tessellated, and with grid lines showing

This production took just a few minutes, once I spent an hour carefully reading the instructions and playing with the program.

ROTATION is another technique. It is shown here using an equilateral triangle.

Equilateral Triangle--plain

Equilateral Triangle transforming by rotation on Tessel Mania

Equilateral Triangle part 3

Equilateral Triangle- part 4

C. WORKING WITHIN TESSELMANIA
Tessel Mania must be on your computer for this to work.

Furthermore it must be configured to be able to upload the software. The fundamental figure I chose is one that can transform by Slide (top-to-bottom) and by Rotation about the midpoints of sides.

This is what the TM commands can do.

EDIT TILE (1) will work with or view a single tile.

TESSELATE is (2)

MAGNIFIED VIEWS is (3)

TILE MAGIC (4) shows how a tile was created

TESSELATION MAGIC (5) Shows how a tile moves to create the tessellation.

METAMORPHIC MAGIC (6) shows the entire tessellation transformed from the original tile to the final product.

When (4) or (5) or (6) are chosen a sub-menu appears which controls speed and the direction of morphing.

Tessel Mania--You can do it.

To begin transforming click on the thumbtack. Observe that the midpoints (of rotation) appear.

Next, move the TACK to any edge and click on it anywhere to create a point. While holding down, the TACK will transform the side as it is dragged around. Do this a few times and then get ready to Tesselate.

To TESSELATE click on COMMAND 2.

To STUDY the process of transformation click onCOMMANDS 4, 5, or 6.to STOP the action, click on the picture.

GET BACK to the single polygon by clicking on COMMAND 1.

DECORATE by clicking on the STAMP. A menu of objects will appear at the bottom. Select on by clicking, then move the arrow to the interior of the figure. The selected decoration will now be in the figure. Click if you want it to be applied there.

APPLY COLOR by clicking on the PAINT BUCKET. Then select a color by clicking . A texture, from below the colors, can also be selected. Then move to the region of the figure to be colored and click. If there is a second region it should be colored differently.

FINALLY TESSELATE. Click on COMMAND 2. The computer will select a second set of colors for decorating alternating figures.

Next are links to come Sample Tessellations from the supply within Tessel Mania. Be sure to close the screen when finished.

Web Sites, just a few, with Tesselations.
These are four web sites of hundreds that deal with TESSELATION.

Finally, when you get bored,....
.

A Tesselation I did on KALI. The triangle is 30-60-90 and can be printed with or without the lines. See any Reflections?

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How to Tessellate In what follows I hope to explain how each of several methods can be applied to create tesselations, starting with pencil and paper and ending with computer software. A. FUNDAMENTAL POLYGONS It is not too difficult to find pages with squares, equilateral triangles, or hexagons tesselating the page.

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This site deals with tessellations from the graphic artistry point of view.

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Problem of the Week - Math Olympiads for Elementary and Middle Schools

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Math Olympiads for Elementary and Middle Schools

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A+Click Thinking Outside The Box Questions

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AplusClick free funny math problems, questions, logic puzzles, and math games on numbers, geometry, algebra. Thinking Outside The Box.

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(Challenge #) Challenge Title

Algebra

Equations, linear

(8)Stamps, (30)Smiles,(58)Gone Fishin',(74)The Race

Modeling problems

(1)Line Up!, (29)Salaries,(42)Rose Bowl,(44)Table for 19,(77)Movie Money, (80)Gifts Galore

Patterns, representing

(6)Which Way?, (8)Stamps,(11)Play Ball!,(41)Radar Bills, (80)Gifts Galore

Problem Solving using Symbols

(21)Body Mass,(30)Smiles, (58)Gone Fishin',(60)Number Tricks

Representations, comparing

(7)Double or Not,(11)Play Ball!,(21)Body Mass,(29)Salaries, (60)Number Tricks

Geometry

2-D and 3-D figures, properties

(3)Popcorn, (4)Don't Fall In,(15)Big Trees,(35)Fire Hydrant,(54)Cut the Cake,(55)Decorating Boxes,(76)Visualizing

2-D representations of 3-D figures

(9)Mirror Mirror,(40)Putt-Putt, (54)Cut the Cake,(55)Decorating Boxes,(57)Envelopes

Connections to other disciplines

(3)Popcorn, (4)Don't Fall In,(5)Upside Down?,(37)Map Colors,(43)Seeing Stars,(51)Bar Codes,(56)Drip Drops, (62)Keeping Cool

Geometric models of algebraic concepts

(45)Three Squares,(46)Time Zones,(54)Cut the Cake

Networks

(6)Which Way?

Scale Drawing
(61)Statue of Liberty

Similarity/Congruence

(59)Japanese Floors, (61)Statue of Liberty

Transformations

(5)Upside Down?,(9)Mirror Mirror,(40)Putt-Putt, (41)Radar Bills, (49)Angolan Designs,(73)A Shard or Two,(79)Morphing

Measurement

Angles and Length

(9)Mirror Mirror,(10)What's My Angle,(39)Patios, (40)Putt-Putt,(44)Table for 19,(66)Airport Runways

Area and Circumference

(15)Big Trees,(23)Fractals,(32)Windshield Wipers,(39)Patios, (54)Cut the Cake

Estimation

(1)Line Up, (2)Beating Heart,(3)Popcorn, (10)What's My Angle,(15)Big Trees,(47)VCR

Metric and customary units

(34)Faster, (67)When in Rome

Rates and velocity

(1)Line Up, (2)Beating Heart,(16)Beanie Babies,(18)Tern Turn

Units, appropriate

(3)Popcorn, (15)Big Trees,(34)Faster, (74)The Race

Number

Compare and order decimals, fractions, percents

(14)Battling Averages,(17)Perplexing Percentages,(25)Grape Juice Jungle,(36)Majority Vote

Large numbers and notation

(2)Beating Heart,(7)Double or Not,(11)Play Ball!,(28)Pigeonholes, (56)Drip Drops

Ratio and proportions

(14)Battling Averages,(24)Gasoline Tanks,(25)Grape Juice Jungle,(47)VCR

Solve problems with decimals, fractions, percents

(3)Popcorn, (8)Stamps, (14)Battling Averages,(15)Big Trees,(47)VCR, (71)Archeology

Statistics & Probability

Collecting Data

(26)I Win!, (29)Salaries,(64)Wheel of Fortune

Graphical represenations of data

(20)Basketball Picks,(48)Working Hours,(53)Census,(64)Wheel of Fortune,(70)Soda

Make conjectures about differences

(27)Life Expectancy,(29)Salaries, (71)Archeology,(72)TV Ratings

Make conjectures about relationships

(27)Life Expectancy,(29)Salaries, (68)Bones,(72)TV Ratings

Probability, Apply

(19)Two Points, (26)I Win!, (52)Capture-Recapture,(63)Matching Birthdays, (69)Misaddressed

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Figure This! Math Challenges for Families - Challenge Index

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(Challenge #) Challenge Title Algebra Equations, linear (8)Stamps, (30)Smiles,(58)Gone Fishin',(74) The Race Modeling problems (1)Line Up!, (29)Salaries,(42)Rose Bowl,(44) Table for 19,(77) Movie Money, (80) Gifts Galore Patterns, representing (6)Which Way?, (8)Stamps,(11)Play Ball!,(41) Radar Bills, (80) Gifts Galore Problem Solving using Symbols (21)Body Mass,(30)Smiles, (58)Gone Fishin',(60) Number Tricks Representations, comparing (7)Double

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Math lessons, Interactive Games, Brain Teasers

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Math lessons, Interactive Games, Brain Teasers

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Illuminations Home - National Council of Teachers of Mathematics