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Algebra 1

Applying an Area Model to Polynomials

Algebra 1Applying an Area Model to Polynomials
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Access the interactive simulator to begin this project.

In this activity, whenever you see 💬, stop and share your responses with your partner. If you have different responses, try to come to a consensus.

For 1 - 3, use the instructions below.

Use the simulation screen labeled “Variables”. Note you can switch between simulation screens using the toolbar located below the area model.

Use the Variables Screen to answer the following questions.

1. Play around with entering your own variable expressions, then answer the following.

a. In an area model, how do the partial products (interior numbers) get calculated?

b. In an area model, how does the total area get calculated?

c. How do the partial products relate to the total area of the area model?

2. Use the sim to model 6(x+8). What is the total area of this rectangle? Represent the total area in multiple ways. 💬

A diagram with five rectangles: one at the top center, two below it side by side, one to the left, and a large rectangle split in half at the bottom. A green horizontal line spans the top rectangles.

3. Use the sim to model ( x + 3 ) ( x − 5 ) ( x + 3 ) ( x − 5 ) . What is the total area of this rectangle? Represent the total area in multiple ways. 💬

A diagram with a large rectangle divided into four sections, two small rectangles above and to the left, one small slightly larger rectagle above the two small ones above and to the left. Lines seperate the single box from the smaller boxes on the top and to the left. The top line is green. The left line is blue.

4. Challenge yourself to work through levels 1 - 4 of the Area Model Algebra Game!

5. How is multiplying variable expressions using an area model similar to multiplying numbers using an area model?

Extension

Challenge yourself to work backwards and factor an algebraic expression!

A rectangle is divided into two vertical sections labeled 4x and 12. There are three smaller squares: one above each section and one to the left of the rectangle.

The Area Model sim is playing tricks on you! It gives you the partial products, but not the side lengths. What numbers and/or variables must be on the outside of this rectangle?

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© May 21, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.