Math Background

Lesson: Fact Families
Introducing the Concept

Knowing how to use a multiplication table to multiply and divide will help students explore fact families.

Materials: 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 and divide.

  • Write8 x 3 = n on the board.
  • Say: Use your multiplication table to find the product of 8 and 3.
  • Ask: What is the product? (24)
  • Replace n in 8 x 3 = n with 24.
  • Say: Shade the factors and product for 8x 3 = 24 on your multiplication table.
    Some students may shade 8 in the first column, 3 in the first row, and 24 in the square where the row and column meet. Other students may shade 3 in the first column, 8 in the first row, and 24 in the square where the row and column meet. Both answers are acceptable.
  • Say: Look at the numbers you shaded and think about the Commutative Property of Multiplication.
  • Ask: What does the Commutative Property of Multiplication tell us?
    Changing the order of the factors does not change the product.
  • Ask: What related multiplication sentence is shown by the shaded squares?
    3 x 8 = 24
  • Write 3 x 8 = 24 on the board below 8 x 3 = 24.
  • Say: Look again at the numbers you shaded and think about the inverse of multiplication.
    If students don't recognize the term inverse, explain that inverse means “opposite.”
  • Ask: What is the inverse of multiplication? (division)
  • Ask: What division sentences do the shaded squares show? (24 ÷ 3 = 8 and 24 ÷ 8 = 3)
  • Write 24 ÷ 3 = 8 and 24 ÷ 8 = 3 on the board below 3 x 8 = 24.
  • Ask: What three numbers are used in each of these number sentences? Students should identify 3, 8, and 24.
  • Say: Multiplication and division sentences that use the same numbers are called a fact family.
  • Point to the multiplication and division sentences on the board.
  • Say: This is the fact family for 3, 8, and 24.
  • Say: Use your multiplication table to find the fact family for 2, 9, and 18.
    Prompt students with questions like the ones used above. The fact family for 2, 9, and 18 is 2 x 9 = 18, 9 x 2 = 18, 18 ÷ 9 = 2, and 18 ÷ 2 = 9.
Houghton Mifflin Math Grade 3