Math Background

Lesson: Fact Families
Developing the Concept

In this lesson, students explore fact families that use two numbers.

Materials: transparency of multiplication table (use the table from Learning Tool 14 or 15 in 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 what a fact family is and how to use a multiplication table to multiply and divide.

  • Say: Some fact families have only two numbers.
  • Write 6 x 6 = n on the board.
  • Say:Use your multiplication table to find the product of 6 and 6.
  • Ask:What is the product? (36)
  • Replace nin the multiplication sentence with 36.
  • Say:Shade the factors and the product for 6x 6 = 36 on your multiplication table.
  • Ask: Do the shaded squares show any related multiplication sentences?
    Students should realize that because the factors are the same number, there are no related multiplication sentences.
  • Ask:What related division sentences do the shaded squares show?
    (36 ÷ 6 = 6)
  • Write 36 ÷ 6 = 6 below 6 x 6 = 36 on the board.
  • Ask: Why is there only one related division sentence?
    Students should recognize that the quotient and the divisor are the same number.
  • Ask:What numbers are in this fact family? (6 and 36)
  • Ask:What other fact families can you find on your multiplication table that use only two numbers?
    Students should discover that fact families with the same factors (or the same divisor and quotient) use only two numbers. Some examples are: 2 x 2 = 4, 4 ÷ 2 = 2 and 3 x 3 = 9, 9 ÷ 3 = 3.

Wrap-Up and Assessment Hints
Give students a set of two or three numbers and have them use a multiplication table to find the fact family. When they are finished, have them explain the relationships between the number sentences.


Houghton Mifflin Math Grade 3