Lesson 10 Explore Multiplication Strategies with Rectangles

    • Let’s use rectangles to explore multiplication strategies.

Warm-up How Many Do You See: Squares

How many do you see? How do you see them?

  1. Partially shaded area diagram.
  2. Diagram. Rectangle split into 2 parts. Both parts partitioned into 2 rows of 6 of the same size squares.
  3. Shaded area diagram.

Activity 1 From Diagrams to Expressions

Problem 1

Andre and Elena are finding the area of this rectangle.

Diagram. Rectangle partitioned into 3 rows of 6 of the same size squares. Rectangle length, 6. Rectangle width, 3.

Andre writes .

He marks the rectangle like this:

Area diagram. Rectangle split into two parts.

He then writes:


Elena writes  .

She marks the rectangle like this:

Diagram. Rectangle split into 2 parts. One part partitioned into 3 rows of 5 of the same size squares, the other partitioned into 3 rows of 1 of the same size squares.

She then writes:




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Discuss with a partner:

  1. How are Andre and Elena’s strategies alike? How are they different?

  2. How are the numbers in Andre’s expressions related to his diagram?

  3. How are the numbers in Elena’s expressions related to her diagram?

Problem 2

Here is another rectangle.

Its area can be found by finding .

  1. Mark or shade the rectangle in a way that would help you find its area.

    Diagram. Rectangle partitioned into 4 rows of 9 of the same size squares. Rectangle length, 9. Rectangle width, 4.

  2. Write one or more expressions that can represent your work on the diagram and show how you find the area.

Activity 2 From Expressions to Diagrams

Here are some rectangles and expressions that show how three students saw the area of the rectangles.

For each rectangle:

  1. Name the two factors that can be multiplied to find its area.

  2. Mark or shade each rectangle to show how each student saw the area. Be prepared to explain your reasoning.

  1. Noah:

    Diagram. Rectangle partitioned into 3 rows of 7 of the same size squares. Rectangle length, 7. Rectangle width, 3.

  2. Priya:

    Area diagram. Rectangle partitioned into 4 rows of 6 of the same size squares.

  3. Tyler:

    Diagram. A rectangle partitioned into 8 rows of 8 of the same size squares.

Practice Problem

Problem 1

  1. Highlight parts of the diagram to show the expression .

    Area diagram.

  2. Explain how you could use the diagram to calculate .