Algebra Tiles

• ## Algebra Tiles

Grade: 6th to 8th, High School

Use tiles to represent variables and constants, learn how to represent and solve algebra problem. Solve equations, substitute in variable expressions, and expand and factor. Flip tiles, remove zero pairs, copy and arrange, and make your way toward a better understanding of algebra.

This interactive is optimized for your desktop and tablet.

Note: in Factor mode, all factors must be entered in parentheses. x(x + 1) will be marked wrong. (x)(x + 1) will be accepted.

### Modes

There are 4 modes: Solve, Substitute, Expand, or Factor.

• In Solve and Substitute, vertical lines indicate "is equal to" (=).
• In Expand and Factor, the large area is the product of the top and left areas, as in a standard multiplication table.

Add tiles to the workspace from the bottom left bank. The value of each tile is indicated. When moved to the workspace, the value will be erased.

• Flip turns tiles over, giving the inverse value. For example when a green x is flipped, it becomes a red –x tile. Flipping the red –x tile, gives the inverse green x tile. You can click the button to flip all tiles in the bank or move tiles to the workspace, and then click to flip those tiles over.
• Turn rotates the green x and red –x tiles 90°. This is most useful in the Expand and Factor activities.

### Other Tools

Tools may be used on single tiles by select them or a group of tiles by selecting several or dragging a rectangle around a group of tiles. The tool may be selected before the tile for a single action or after to allow for a repeated action.

• Pointer selects and moves tiles. This is the default tool. When the empty workspace or a tile from the bank is selected, this tool is automatically selected. Note: Depending on the activity, some tiles may not be removed.
• Eraser removes tiles from the workspace. Note: Depending on the activity, some tiles may not be removed.
• Remove Zero Pairs allows only zero pairs to be removed from the workspace. This is most helpful in solving Solve and Expand problems or anytime in Factor problems to ensure tiles are properly removed. A zero pair is a pair of tiles that sums to 0, such as a yellow 1 tile and a red –1 tile.
• Copy copies the currently selected tile(s). Move the tile(s) to see the copy. This is most helpful when a large number of tiles must be placed in the workspace, such as for x2 – 16.

### Completing a Problem

All problems must be completed in two steps:

1. Build the model

Place the correct pieces in the workspace. After you build the model of the given problem, Check your answer to move on to the next step. Only tile type, tile quantity, and workspace area are checked, not the way in which tiles are arranged.

If you want to start again, Reset to empty your workspace.

2. Solve the problem

After you solve the problem, Check your answer. Where applicable, answers must be given in simplified form. Both the entered answer and workspace must be correct. If one or both is incorrect, the incorrect portion will be indicated. Note: in Factor mode, all factors must be entered in parentheses. x(x + 1) will be marked wrong. (x)(x + 1) will be accepted.

If you want to start again, Reset to go back to your original model.

3. When you complete your problem or at any other point, you may start a New problem.

### Exploration

Solve an Equation

Place tiles equal to the expression to the left of the = in the left workspace. Place tiles equal to the expression to the right of the = in the right workspace. For example, if the expression is 3x– 2, place 3 green x tiles and 2 red 1 tiles in one half of the workspace. You will need to flip the tiles to get the red inverse tiles. Check your model to move on to the next step.

To solve the problem, arrange tiles so only a single green tile remains in one half of the workspace. Remember only equal values can be removed from both sides, such as a yellow tile from the left and a yellow tile from the right. To "move" a tile, first add the inverse value to both sides. If you want to move a red rectangle, add a yellow rectangle to both sides. Then you can remove the zero pair from one side.

Try solving several problems in this manner.

### Objectives and Standards

NCTM Standards and Expectations
• Algebra
• 6-8
• High School (9-12)
• Algebra