Model and solve equations using algebra tiles

What Are Algebra Tiles?

Algebra tiles are colored shapes that represent numbers and variables:

• Small yellow squares → represent +1 (unit tile)
• Small red squares → represent -1 (negative unit tile)
• Large green rectangles → represent +x (variable tile)
• Large red rectangles → represent -x (negative variable tile)
• Large blue squares → represent x² (used in advanced problems)

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Purpose of Algebra Tiles

• To visualize equations and expressions
• To model solving steps without guessing
• To understand balancing in equations

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Steps to Solve Equations with Algebra Tiles

Step 1: Represent the equation

Example: x + 3 = 5

• Use 1 green rectangle (x)
• Use 3 yellow squares (+3) on the left
• Use 5 yellow squares (+5) on the right

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Step 2: Keep the balance

• The two sides of the equation are like a balance scale.
• Whatever you do to one side, you must do to the other.

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Step 3: Remove equal tiles from both sides

• Remove 3 yellow squares from both sides.
• Now the left side has only x, and the right side has 2 yellow squares.

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Step 4: Find the value of x

• The green rectangle = 2 yellow squares
• So, x = 2

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Another Example with Negatives

Example: x – 2 = 3

Model it:

• 1 green rectangle (x)
• 2 red squares (-1 each) on the left
• 3 yellow squares on the right

Remove the -2 from the left by adding 2 yellow squares to both sides.

Left: x
Right: 3 yellow + 2 yellow = 5 yellow squares

• Answer: x = 5

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Key Rules

• Always keep the equation balanced.
• Remove or add tiles on both sides equally.
• Positive tiles and negative tiles cancel each other:
• (+1) + (-1) = 0
• (+x) + (-x) = 0

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Practice Problems

Use algebra tiles to solve:

1. x + 4 = 7
2. x – 3 = 2
3. x + 2 = –1
4. –x + 3 = 1
5. 2x + 1 = 5

Learn with an example

let’s practice!