# Using Polypad: Numbers

## Introduction

This tutorial provides an overview of the Number Tiles. Below are the topics covered.

• Number Tiles
• Number Bars
• Number Frames
• Number Cards
• Number Lines
• Prime Factor Circles
• Dot Arrangements
• Number Grids
• Multiplication Grids
• Additional Tools, including Exploding Dots and the Bucket of Zero

## 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. Click on the gear for each number tile to turn on and off the labels and the handle.

## Number Bars

Click on the gear under a number bar for options to hide the number label on each bar. Select Alternate Tile Colors in the Customize UI menu to change colors of the bars in the tile panel.

## Number Frames

Use the black handles to change the size of the number frame. Use the Flip button or double-click on a counter to flip it over.

## 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 Customize UI menu.

## Number Line

Configure the Number Line using the settings menu that appears when clicking on a Number Line. More advanced settings can be found by clicking the gear in the action bar. Integer, decimals, fractions, percents and values of π all work as possible labels. The labels can appear above or below the number line.

Use the arrows to model jumps along the number line.

## 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.

## 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.

### 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.

### 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 natbanting.com to learn more about the Bucket of Zero.

## Using Numbers on the Balance Scale

All of these tile types work together on the Balance Scale.