So far in this lesson, you have seen two models for solving equations: a balance scale and cups and counters. In this section, you will use and investigate a third model, algebra tiles.

For algebra tiles, a rectangle represents the variable, usually x, and squares are used to represent numbers.

Consider the equation 2x − 3 = 5. This equation can be modeled with algebra tiles using 2 green rectangles (positive x-tiles) and 3 red squares (negative unit tiles) on the left side of the equal sign and 5 yellow squares (positive unit tiles) on the right side.

Watch this equation being solved using the algebra tile model.

On your own, use the interactive linked to the image below to set up and solve equations with algebra tiles.

• Click the “New Equation” button, the piece of paper in the yellow panel, to generate a two-step equation of the form ax + b = c.
• Use the tools to set up the equation, and click the Check tool to check your model.
• Once you have the correct setup, use zero pairs and remove tiles as necessary to solve the equation.
• Type your solution into the text box, and click the Check tool to check your answer.

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Need additional directions?

Pause and Reflect

How does the algebra tile model allow you to better visualize the concept of zero pairs?

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Check Your Answer

Zero pairs are a combination of one positive and one negative tile that add to 0. The algebra tile model shows a yellow/green positive tile next to a red negative tile.

How does the algebra tile model compare to the cups and counter model or the balance scale model?

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Check Your Answer

Possible response: All equation models require that actions done to one side of the equation be done to both sides of the equation. The algebra tile model visualizes the relationship between negative and positive numbers that the balance scale model does not.

Practice

For questions 1 – 3, use the algebra tile model to determine the value of x.

1. 4x − 5 = 15
   
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   Need a hint?

   How many positive unit tiles need to be added to both sides of the equation in order to make enough zero pairs to move the 5 negative unit tiles on the left side of the equation?
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   Check Your Answer

   x = 5
2. 2x + 7 = 3
   
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   Need a hint?

   How many negative unit tiles need to be added to both sides of the equation in order to make enough zero pairs to move the 7 positive unit tiles on the left side of the equation?
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   Check Your Answer

   x = -2
3. 3x − 5 = 4
   
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   Need a hint?

   How many positive unit tiles need to be added to both sides of the equation in order to make enough zero pairs to move the 5 negative unit tiles on the left side of the equation?
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   Check Your Answer

   x = 3