Lesson 2 Partial Products in Diagrams

    • Let’s interpret diagrams that can help us find products.

Warm-up Which One Doesn’t Belong: Diagrams to Find Products

Which one doesn’t belong?

  1. Diagram, rectangle partitioned horizontally into 2 rectangles.
  2. Diagram, rectangle partitioned vertically and horizontally into 4 rectangles.
  3. Diagram, rectangle partitioned vertically and horizontally into 4 rectangles.
  4. Diagram, rectangle partitioned vertically into 2 rectangles. 

Activity 1 Decompose in Many Ways

  1. Write the value of each product inside the rectangles.

    Diagram, rectangle partitioned vertically and horizontally into 4 rectangles.

  2. Find the value of .

  3. This diagram represents .

    Write the value of each product inside the rectangles.

    Diagram, rectangle partitioned vertically and horizontally into 6 rectangles.

  4. Find the value of .

Activity 2 Calculate in Many Ways

Here are some different diagrams that represent . For each diagram, write a multiplication expression inside each rectangle to represent the product.

  1. Diagram, rectangle partitioned vertically and horizontally into 6 rectangles.
  2. Diagram, rectangle partitioned horizontally into 2 rectangles.
  3. Diagram, rectangle partitioned vertically into 3 rectangles.

  4. Use one of the diagrams to find the value of .

  5. Explain why you chose that diagram to find the product.

Practice Problem

Problem 1

Complete the diagrams and use each of them to find .

  1. Diagram, rectangle partitioned vertically and horizontally into 6 rectangles. 
  2. Diagram, rectangle partitioned horizontally into 2 rectangles. Top rectangle, vertical side, 30, horizontal side, two hundred fifty three. Bottom rectangle, vertical side, 1.

  3. How are the strategies the same? How are they different?