Houghton Mifflin Mathematics Grade 3: Chapter 9: Multiplication Tables and Fact Families: Developing the Concept

Using a Multiplication
Table to Divide

Introducing the Concept

Developing the Concept

     Fact Families
  Introducing the Concept
  Developing the Concept

Using a Multiplication Table to Divide

In this lesson, students use a multiplication table to explore the relationship between missing factors in multiplication and quotients in division.

Materials: transparency of multiplication table (use the table from the Overhead Teaching Activity for lesson 9-1) and overhead projector for demonstration; multiplication table for each student

Preparation: Students can use the multiplication tables they made in chapter 6 or make new tables. See page 256 in the student book for instructions or use Teaching Tool 3 in the Teacher Resource Book.

Prerequisite Skills and Background: Students should know how to use a multiplication table to multiply.

Display a multiplication table on the overhead projector.

Write 4 $times$ n = 28 on the board. Have a volunteer label the factors and the product.

Ask: How could you use a multiplication table to find a missing factor in a multiplication sentence?
Lead student discussion to find the row for the first factor, follow it across to the product, and then move up to the square at the top of the column. You could also find the column for the first factor, follow it down to the product, and then move left to the square at the end of the row. Have students follow these steps on their multiplication tables as you demonstrate on the overhead.

Ask: What is the missing factor in this multiplication sentence? (7)

Say: Finding a missing factor in multiplication is the same as finding a quotient in division.

Write 28 ÷ 4 = n on the board. Have a volunteer label the dividend, divisor, and quotient.

Ask: What is the divisor in 28 ÷ 4? (4)

Say: Locate 4 on the left side of your multiplication table.

Ask: What is the product in the multiplication sentence called in the division sentence? (the dividend)

Ask: What is the dividend in 28 ÷ 4? (28)

Say: Move across the row from 4 to 28.

Ask: What number is in the square at the top of that column? (7)

Ask: What is the quotient of 28 divided by 4? (7)

Ask: Is there another way to divide 28 by 4 on the multiplication table?
Elicit from students that you could find the column for the divisor, follow it down to the dividend, and then move left to the square at the end of the row.

Replace n in 4 $times$ n = 28 and 28 ÷ 4 = n with 7. Have a student read the number sentences aloud. (Four times seven equals twenty-eight, and twenty-eight divided by four equals seven.)

Have students solve more examples of finding the missing factor in a multiplication sentence and the quotient in a related division sentence. This will help students better understand the relationship between multiplication and division. Wrap-Up and Assessment Hints
You can determine whether students understand how to use a multiplication table to multiply and divide by having them use their own words to explain the procedure they follow. Show students a variety of multiplication sentences with missing factors and have them tell you the related division sentences.