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Using Polypad: Numbers

Number Tiles

Split and merge the Number Tiles to create new groups of tiles. Click and drag the black tab to create different arrangements of the tiles. Turn on the grid background to help see the number of tiles.

Number Bars

Use the settings menu to toggle between the color options for the Numbers Bars. Select "Hide Number Labels" to use Number Bars without numbers on them.

Number Cards

Place Numbers Cards on top of each other to create a new card with the sum of the two cards. Toggle this feature on and off in the settings menu.

Prime Factor Circles

Prime Factor Circles provide a visual for a number's prime factorization. Smaller prime numbers each have a different color, while the prime numbers above 7 are all the same color. You can pull apart and put back together the prime factor circles.

Dot Arrangements

Click Reorder to show the arrangement that results from moving the first factor in the list into the last spot in the list. Click Combine Factors to show the arrangement that results from multiplying the last two factors in the list.

Click Split Factors to create additional factor groups. The smallest possible factor will be placed first. Dot arrangements can be combined and pulled apart.

Here is an example of using the Number Tiles, Parallelograms, Prime Factor Circles and Dot Arrangements on one canvas.

Dot Arrangement 30 Visual - Polypad - Mathigon
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Number Grids

Addition, Multiplication, and Number Grids

Drag the black tabs to change the size of a number table. Double-click on a number to select that number. Using the transparency slider is helpful when placing one number table on top of another.

Multiplication Grids

Drag the black tabs to change the size of the Multiplication Grid. Dragging the black dot changes the base of the grid.

Additional Tools

Exploding Dots

Change the number boxes and the base of the Exploding Dots Machine in the panel that appears when clicking on the machine. Dragging dots from one box to the next creates explosions. Select the machine, and click on "Explode" to have the explosions happen automatically.

Blue dots have are positive. The red dots are opposite-dots or "anti-dots" and are negative. The "Annihilate" button at the bottom creates a zero for any dot and anti-dot pair in the same box.

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Bucket of Zero

The "1" and "-1" algebra tiles normally combine to make a gray "0." In the Bucket of Zero, they stay as a pair of "1" and "-1". The number at the top of the bucket shows the value of the sum of all "1"s and "-1"s in the bucket.

Visit to learn more about the Bucket of Zero.

Using Number Tiles on the Balance Scale

All Number Tiles work together on the Balance Scale.

Explore our Tasks and Learn More

Visit the Activities page to see lesson plans, student explorations, puzzles, and teaching ideas. Visit the Tutorial page to learn more about using Polypad.