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Number Line helps students visualize number sequences and demonstrate strategies for counting, comparing, adding, subtracting, multiplying, and dividing.

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This tool allows you to create any geometric shape imaginable. Squares, triangles, rhombi, trapezoids and hexagons can be created, colored, enlarged, shrunk, rotated, reflected, sliced, and glued together.

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Money Pieces by The Math Learning Center

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Money Pieces help students visualize and understand money values and relationships.

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Cube Block Sculpture Activity | Art & Design Games for Kids | Toy Theater

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Use the 3D interactive cube builder to create anything you’d like! Perfect for improving spatial awareness and problem-solving skills, try it today!

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Number Rack facilitates the natural development of children’s number sense. Rows of moveable, colored beads encourage learners to think in groups of fives and tens, helping them to explore and discover a variety of addition and subtraction strategies.

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Bar, Picture, Line, or Scatter

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Pattern Shapes by The Math Learning Center

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Students use Pattern Shapes to explore geometry and fractions, create their own designs, or fill in outlines. As they work with shapes, students think about angles, investigate symmetry, and compose and decompose larger shapes.

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Modeled off of the original pattern blocks developed in the 1960s, our virtual pattern blocks include a yellow hexagon, red trapezoid, orange square, blue rhombus, beige narrow rhombus, and green equilateral triangle, offering a helpful complement to the concrete manipulatives found in classrooms. Designed using physics, these online pattern blocks can be rotated, moved around, and bumped into each other giving the feeling of real blocks. However, this virtual manipulative offers the added advantages of requiring no clean up and they're free!

Also check out our Tangram activity for another way to explore shapes and spatial rotation.

Visit classplayground.com for pattern block printables. We have also collected the pattern block printables into a book, available from Amazon.

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Pattern Blocks | Free Virtual Manipulatives | Toy Theater

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Modeled off of the original pattern blocks developed in the 1960s, our virtual pattern blocks include a yellow hexagon, red trapezoid, orange square, blue rhombus, beige narrow rhombus, and green equilateral triangle, offering a helpful complement to the concrete manipulatives found in classrooms. Designed using physics, these online pattern blocks can be rotated, moved around, and bumped into each other giving the feeling of real blocks.

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"We need to see that geometry is concerned with statements about space relations, space being at first the vague set of mental structures that make possible and organise our actions, but slowly gaining independence and becoming those same relations abstracted from experience and considered in themselves" ~ Caleb Gattegno (1971), inventor of the Geoboard

Geoboards have nearly infinite uses in the teacher's toolkit. Originally designed as wooden boards with nails on which students would manipulate rubber bands, our online geoboard provides greater versatility and no rubber bands for students to fling across the room!

Create and compose shapes with the 13 geoboard canvases, then analyze and compare them by rotating, expanding, shrinking, flipping, or mirroring them. Make your own virtual pattern blocks then remove the dots with a blank canvas to see what you created. Move the shapes around and make a whole new design! This virtual manipulative has an endless array of possibilities for teaching number sense, geometry, fractions, probability, data management, trigonometry, calculus, and even art and design. Explore the math behind art and the art of math!

Visit classplayground.com for more information about Geoboards, Printables and Videos.

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Geoboard | Free Virtual Manipulatives | Toy Theater

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"We need to see that geometry is concerned with statements about space relations, space being at first the vague set of mental structures that make possible and organise our actions, but slowly gaining independence and becoming those same relations abstracted from experience and considered in themselves" ~ Caleb Gattegno (1971), inventor of the Geoboard Geoboards have nearly infinite uses in the teacher's toolkit.

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Circles, Squares, Bears, Cubes, and Pennies

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Bear Counters | Free Virtual Manipulatives | Toy Theater

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Use these virtual bear counters for a wide range of math lessons ideal for whole-class, small group, and individual activities. They’ll never get lost!

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Shape Counters | Free Virtual Manipulatives | Toy Theater

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This shape counters manipulative is perfect for activities related to counting, addition, subtraction, graphing, patterns, and more!

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Array Display

Model multiplication and The Commutative Law in multiplication

Learning objectives:

Y1: solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher

Y2: recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers

Y2: show that multiplication of 2 numbers can be done in any order (commutative) and division of 1 number by another cannot

Y2: solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts

A whole-class teaching tool.

A great tool to demonstrate that multiplication can be done ina ny order and that division is the inverse of multiplication. Write a multiplication maths story, then press '=' to create an array.
Click on each column of the array and say'That's time number 1. That's time number 2... etc
Rotate the array to demonstrate that multiplication can be done in any order.

Have fun!

HAVING TROUBLE LOADING? Please try this version.

Homework suggestions:

This game is © copyright 1999-2020, J.Barrett, ictgames ltd. All Rights Reserved.

Made using the and libraries.

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Learning objectives: Y1: solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher Y2: recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers Y2: show that multiplication of 2 numbers can be done in any order (commutative) and division of 1 number by another cannot Y2: solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts A whole-class teaching tool.

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Two Color Counter Five Frame | Teaching Tools | Toy Theater

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Use two color counters to model equations in a five frame.

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Number Line helps students visualize number sequences and demonstrate strategies for counting, comparing, adding, subtracting, multiplying, and dividing.

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Interactive Hundreds Chart | Toy Theater

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Use this online hundreds chart to practice counting to one hundred, for modeling math problems, for skip counting, and more! Try it, it’s free!

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Adjust the number of dice & roll

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The best online dice roller and coin flipping app made for board games, drinking games, gambling, or as a random number generator.

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Number Frames by The Math Learning Center

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Number Frames help students structure numbers to five, ten, twenty, and one hundred. Students use the frames to count, represent, compare, and compute with numbers in a particular range.

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Students often struggle with the concept of fractions. This interactive fraction strips tool helps students visualize fractions. With these online fraction strips, students can model fractions, solve fraction problems, explore equivalent fractions, and observe the differences between denominators.

To use the interactive fraction strips tool, click and drag the strips onto the canvas. You can drag as many of each fraction as you'd like. To remove the strips, drag them off the canvas. Change the chart to accommodate two whole units by pressing the "Unit Double" button. Add annotations using the pencil tool and erase using the eraser. To clear the canvas, press the trash can button.

A few activities you can do with students while using the online fraction strip tool include:

Have students model a given fraction, mixed or not. For example 1 1/4 or 3/6.

Ask students to model addition, subtraction, multiplication, or division problems using the fraction strips.

Ask students to find equivalent fractions for a certain fraction. For example, how many sixths are equivalent to 1/3?

Ask students to use the pencil tool to divide one of the wholes on the chart into fourths. Then, students can check their work by dragging fourths onto the chart afterward.

Looking for more fraction manipulatives? Try our interactive fraction circles.

Visit classplayground.com for more resources and printables about fraction strips.

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Fraction Strips | Free Virtual Manipulatives | Toy Theater

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Use the interactive fraction strips tool to help students visualize, model, and explore fractions. Students can also solve problems using fraction strips.

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Arrays up to 50 x 50

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Those you share this with will see the current array and settings.

Make a new rectangle

Change the size of the rectangle by entering whole numbers (up to 50) in the boxes. Then press the MAKE button.

Add and move the sliders

Drag the slider handles from the left or top to divide the rectange into smaller parts. Include up to 4 sliders on each axis.

View partial products

Watch how the equation changes depending on the position of the sliders. Point at any region to see the corresponding piece of the equation.

Show or hide answers

Toggle these buttons to show or hide the results of the equation.

Partial Product Finder allows multiplication combinations to be represented as a rectangle, or array, with dimensions that match the combination. The sides of the rectangle can then be divided into parts to reveal partial products that make up the total product. This helps students develop the flexibility and conceptual understanding required to build fluency with basic facts and strategies for multiplication of larger numbers.

We Welcome Your Feedback

Help us guide the ongoing development of this app by sharing your reactions or suggestions.

Partial Product Finder is brought to you by The Math Learning Center, a nonprofit organization serving the education community since 1976. Visit us at www.mathlearningcenter.org, where you can learn more about our organization, the Bridges in Mathematics PK-5 curriculum we publish, and the many free math education resources we provide, including a robust suite of free virtual manipulatives for use online or as downloadable apps for a variety of operating systems, including Apple iOS and Google Chrome.

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Partial Product, by The Math Learning Center

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Partial Product Finder allows multiplication combinations to be represented as a rectangle, or array, with dimensions that match the combination.

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To create a BAR GRAPH, you must supply a value for (each) bar. It is also a good idea to provide: a name for each bar, title of graph (60 characters maximum), and title of x and y axis. Default options are set for (although you can change them): number of bars (1-31), min and max values, color of bars (gray scale choices available), 3D option, graph direction, graph size (TIP: more bars display best in larger graph sizes), background color, and image file type (if you are using an older browser or are having difficulty seeing the image select jpeg.)

First select the number of bars you would like to display, then complete the rest of the information below and, be sure to use no more than 7-digit values (between 1 and 9999999) for the best results (decimal points count as a digit).
Click here to fill in example using education data from NCES

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To create a BAR GRAPH, you must supply a value for (each) bar. It is also a good idea to provide: a name for each bar, title of graph (60 characters maximum), and title of x and y axis. Default options are set for (although you can change them): number of bars (1-31), min and max values, color of ba…

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Rekenrek | Free Virtual Manipulatives | Toy Theater

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Similar to a ten frame, the virtual rekenrek is a fun tool for building number sense, modeling operations, and improving motivation in math.

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Area Model for Multiplication of Fractions

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Area Model for Multiplication of Fractions

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Area Model for Multiplication of Fractions

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Modeling Products of Mixed Numbers - GeoGebra

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Modeling Products of Mixed Numbers - GeoGebra

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Modeling Products of Mixed Numbers - GeoGebra

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Multiply mixed numbers with an area model and an interactive solution.

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Used since ancient times, the abacus is making a comeback in education. This online abacus tool allows students to model all sorts of operations. In the early grades, students can simply use the abacus to represent quantities and numbers, building number sense. As they grow in their abilities, students can use the virtual abacus to represent addition, multiplication, or subtraction problems.

To use the online abacus, simply drag the beads across the rods from left to right or right to left. Students can represent larger numbers by assigning each rod a place value. For example, the dark purple beads represent the one's place, lavender the 10s place, the blue represents the hundreds place, sky blue represents the thousands place, etc. Students can represent numbers using the different place values and then perform operations. Alternatively, simply have students represent each addend with a different color.

Some activities you might try with the abacus include:

Represent multiplication problems as repeated addition. For example, 3 x 3 would be shown as 3 groups of 3 beads on the abacus, each group shown with a different color of beads.

Represent addition problems on the abacus

Represent large numbers on the abacus, using the place values mentioned above. For example, you might say 5,342, and students would have to show 5 sky blue beads, 3 blue beads, 4 lavender beads, and 2 dark purple beads.

Visit classplayground.com for more resources and printables related to addition and multiplication.

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Abacus | Free Virtual Manipulatives | Toy Theater

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This online abacus tool provides a fun, practical way for students to model math operations and build number sense. Try it today!

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Number Frames by The Math Learning Center

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Number Frames help students structure numbers to five, ten, twenty, and one hundred. Students use the frames to count, represent, compare, and compute with numbers in a particular range.

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Fractions lets students use a bar or circle to represent fractions.

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This tool allows you to manipulate various geometric solids and investigate their properties.

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Number Pieces by The Math Learning Center

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Number Pieces helps students develop a deeper understanding of place value while building their computation skills with multi-digit numbers. Students use the pieces to represent multi-digit numbers, regroup, add, subtract, multiply, and divide.

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Base Ten Blocks (also known as "Base 10 Blocks" and "Place Value Blocks") is an online mathematical manipulative that helps students learn addition, subtraction, number sense, place value and counting. It lets them investigate how to regroup and solve problems with whole numbers and eventually fractions and decimals.

Overall, Base Ten Blocks provides a visual foundation for the abstract algorithms we want students to use as they grow.

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Base Ten Blocks | Manipulatives | Coolmath4Kids

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Base Ten Blocks virtual manipulative - a free online tool for classrooms and homes

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Use this applet to determine the volume of a box by filling it with cubes, rows of cubes, or layers of cubes. Determine the surface area as well by using the box's net.

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About Smarter Balanced Calculators Scientific Calculator (Grade 7-8) Scientific, Graphing, & Regression Calculator (High School)

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Roll a Random Dice! Choose from 1 to 10 Dice - and let them roll! A random result every time!

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teacherled html5 interactive whiteboard ipad android teacher classroom resource math maths mathematics education hundred square

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Great Models for Counting Around the Class

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Explore different representations for fractions including improper fractions, mixed numbers, decimals, and percentages. Additionally, there are length, area, region, and set models.

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Fractions can be a complex concept for students to master. Our virtual fraction manipulatives offer concrete representations of fractions so that students achieve a deeper understanding of this important math concept. Use the online fraction manipulatives to model operations, compare fractions, percentages, and decimals, and much more!

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Fraction Manipulatives " Toy Theater | Learn * Create * Play

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Fractions can be a complex concept for students to master. Our virtual fraction manipulatives offer concrete representations of fractions so that students achieve a deeper understanding of this important math concept. Use the online fraction manipulatives to model operations, compare fractions, percentages, and decimals, and much more!

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Area Model for Multiplication of Fractions

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Area Model for Multiplication of Fractions

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Area Model for Multiplication of Fractions

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Non-Conventional Dice Roller

Use the following virtual dice roller to mimic dice that have a different number of faces from the conventional 6-faced die. The most common physical dice have 4, 6, 8, 10, 12, and 20 faces respectively, with 6-faced die comprising the majority of dice. This virtual dice roller can have any number of faces and can generate random numbers simulating a dice roll based on the number of faces and dice.

A dice is typically a small, throwable object that has multiple faces (most commonly six) and possible positions that indicate a number (or something else), used for generating random numbers and events. They are typically used for tabletop games, which include a wide variety of games, as well as for gambling. Examples of tabletop games that involve the use of dice include games like backgammon, Boggle, and Yahtzee, where dice are a central component of the game. Some other well-known tabletop games include Monopoly, Risk, Dungeons and Dragons, and Settlers of Catan. There are however, numerous others.

Dice shapes

The most commonly used dice shapes are shown in the image, and listed below.

Tetrahedron: 4 faces - the blue die

Cube: 6 faces - the orange, cubic die

Octahedron: 8 faces - the green die

Pentagonal trapezohedron: 10 faces - the orange, non-cubic die

Dodecahedron: 12 faces - the yellow die

Icosahedron: 20 faces - the purple die

Although the image shows some of the more common die shapes, there are many other polyhedral dice, or dice of other shapes. There are also non-numeric dice, dice that do not follow a counting sequence that begins at one, and spherical dice.

How random is a dice?

Based on probability, a die should have an equal probability of landing on each of its faces. However, this is not necessarily the case with mass produced dice as they cannot be truly random, since it is difficult to mass produce dice that are uniform, and there may be differences in the symmetry of the dice. Each dice, particularly d20 (20-sided polyhedral dice) and d8 (8-sided polyhedral dice) is often unbalanced, and more likely to roll certain numbers.
How to test how random your dice is:
Although it may not be the most accurate way to test how random your dice is, one relatively quick test you can do involves just a container, some water, and some salt:

1. Get a container that can fit the die you want to test

2. Fill the container with water, then add salt and the die to the water - if the die doesn't float, add more salt until the die floats

3. Flick the die and take note of which side faces upwards - repeatedly flick the dice and record the results

For a well-balanced die, you can expect a variety of numbers. If it is not well balanced, you will be more likely to notice certain numbers occurring more often. However, unless this test is performed numerous times, or the dice is heavily unbalanced, the user is not likely to notice a significant difference.

There are a number of companies that manufacture dice, and some more rigorous tests (than the one described above) have been performed on dice manufactured by different companies in an effort to determine how truly random the dice (mostly d20 dice) are. These studies confirmed that even dice manufactured within the same company under the same conditions could vary significantly from each other, and are not truly random. Some companies produced dice that were more random than others, but even then, they were not found to be truly random.

Virtual dice, like the one above, are almost always based on pseudo-random number generating algorithms, which are also not truly random. However, a virtual dice roll is likely more close to true randomness than most physical dice.

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Online virtual dice roller that is capable of simultaneously rolling up to 100 dice randomly. A virtual dice roller with any number of sides is also provided.

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Interactive Clock | Telling Time | Analog & Digital | Toy Theater

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Use the online teaching clock for a fun digital experience with your students. Students can learn to tell time with both analog and digital clocks!

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Math Clock helps students become fluent working with time. Learners use analog clocks with geared or free-moving hands to learn how to tell time, explore jumps with count by numbers, and visualize story problems involving intervals of time. By placing and shading fraction overlays, students use the clock to contextualize fractions with frequently used denominators.

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Teach multiplication with this versatile interactive times table grid. Find the product of two numbers from 1 through 12. Color in rows and columns and look for patterns throughout the chart. Practice multiplication by coloring the easiest rows or columns first, then build on that knowledge by moving up to harder multiples. This free virtual manipulative is sure to help your students visualize the full gamut of multiples from 1 to 12 to move them beyond memorization to deeper comprehension.

Visit classplayground.com for more information about Multiplication Charts and Printables and Worksheets.

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Multiplication Chart 1 to 12 | Virtual Manipulatives | Toy Theater

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Teach multiplication with this versatile interactive times table grid. Find the product of two numbers from 1 through 12. Color in rows and columns and look for patterns throughout the chart. Practice multiplication by coloring the easiest rows or columns first, then build on that knowledge by moving up to harder multiples.

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This tool allows you to practice multiplying single-digit numbers.

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KP Mathematics