Lesson 11 Area and the Multiplication Table

    • Let’s explore area and the multiplication table.

Warm-up How Many Do You See: Arrays that Grow

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

  1. Array. 2 rows of 4 dots.
  2. A group of dots.
  3. Groups of dots.

Activity 1 Area and the Multiplication Table

Problem 1

What do you notice? What do you wonder?

Multiplication table showing 3 times 1.
A multiplication table showing 2 times 3.
Multiplication table showing 3 times 3.
Multiplication table with a rectangular outline.

Problem 2

Use the blank table to create your own rectangle.

Start from the top left corner. Record the product that the rectangle represents. Be prepared to explain your reasoning.

5-by-5 multiplication table.

Problem 3

Use the following table to create a rectangle with an area of 24 square units. Start from the top left corner. Record the product that the rectangle represents. Be prepared to explain your reasoning.

A multiplication table.

Activity 2 Products in the Multiplication Table

A multiplication table with the column and row for 2 partially filled in.

Problem 1

What do you notice? What do you wonder?

Problem 2

Find as many other products in the table as you can. You may want to start with rows and columns that show products of 2, 5, and 10.

A multiplication table with the column and row for 2 partially filled in.

Problem 3

What patterns do you see in the row and column that show products of 5?

Problem 4

Write some equations that show one of the patterns that you see in the multiplication table. Explain or show your reasoning.

Practice Problem

Problem 1

Multiplication table with numbers in the 3 column, the 6 column, and the 9 column.

  1. Describe some patterns that you see for the numbers in the table.

  2. Describe one of the patterns you saw using an equation.