Math Background

Lesson: Using a Multiplication Table to Divide
Developing the Concept

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 Learning Tool 14 or 15 in the Learning Tools Folder) and overhead projector for demonstration; multiplication table for each student

Preparation: Students can use the multiplication tables they made earlier, make new tables, or use Learning Tool 14 or 15 in the Learning Tools Folder.

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

  • Display a multiplication table on the overhead projector.
  • Write4 x n = 28 on the board. Have a volunteer label the factors and the product.
    Four times n equals twenty-eight
  • 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.
  • Write28 ÷ 4 = n on the board. Have a volunteer label the dividend, divisor, and quotient.
    Four times n equals twenty-eight; twenty-eight divided by four equals n.
  • 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 x 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.


Houghton Mifflin Math Grade 3