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Algebra 1

Understanding an Area Model

Algebra 1Understanding an Area Model

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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 - 8, use the following instructions.

Use the simulation screen labeled “Explore”. Note you can switch between simulation screens using the toolbar located below the area model.
  1. Explain what the red and blue sliders do to the outside of the rectangle.
  2. Explain what the red and blue sliders do to the inside of the rectangle.
  3. Describe what changes and what doesn’t change when the red and blue sliders are moved. 💬
  4. Multiply 10✕15 using an area model. Find two different ways to partition the 10x15 rectangle. Use the sim to support you in filling out this table. 💬
    Problem Labeled Area Model with Partial Products List partial products and write as a sum Total area of rectangle

    10✕15

    A blank graph with a grid, a thick black line marking the top and left axes, and no labels or data points. The graph has a light gray background with evenly spaced horizontal and vertical lines.

    10✕15

    A blank graph with a grid, a thick black line marking the top and left axes, and no labels or data points. The graph has a light gray background with evenly spaced horizontal and vertical lines.

  5. Use the sim to model 6✕18. What is the total area of this rectangle? Represent the total area in multiple ways. A rectangle measures 18 units wide and 6 units tall. The width is divided into segments of 10 and 8 units. Shapes include a blue triangle, a red triangle, a green circle, and an eraser icon.
  6. In an area model, how do the partial products (interior numbers) get calculated?
  7. In an area model, what are two different ways the total area could get calculated?
  8. How do the partial products relate to the total area of the area model?
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