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Fact Families: Multiplication and Division

Practice creating complete fact families from three given numbers. This exercise reinforces the connection between multiplication and division, developing fluency with inverse operations and deepening number sense.
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Preview

Fact Families: Multiplication and Division preview

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What to Do Next
Division: Fact Families Mixed Practice11 WS
6 × 8 = 48. Related fact: 48 ÷ 6 = ____

Practice Questions

  1. Numbers: 2, 7, 14 Write the fact family:
    Show answer

    2 × 7 = 14; 7 × 2 = 14; 14 ÷ 2 = 7; 14 ÷ 7 = 2

  2. Numbers: 3, 7, 21 Write the fact family:
    Show answer

    3 × 7 = 21; 7 × 3 = 21; 21 ÷ 3 = 7; 21 ÷ 7 = 3

  3. Numbers: 4, 7, 28 Write the fact family:
    Show answer

    4 × 7 = 28; 7 × 4 = 28; 28 ÷ 4 = 7; 28 ÷ 7 = 4

  4. Numbers: 5, 7, 35 Write the fact family:
    Show answer

    5 × 7 = 35; 7 × 5 = 35; 35 ÷ 5 = 7; 35 ÷ 7 = 5

  5. Numbers: 6, 7, 42 Write the fact family:
    Show answer

    6 × 7 = 42; 7 × 6 = 42; 42 ÷ 6 = 7; 42 ÷ 7 = 6

Teacher Resources
Lesson Plan

Inverse Operations: Multiplication and Division

Standards
3.OA.B.6
Printable Aids
Fact Family TriangleNumber Bonds
Teaching Notes

This activity reinforces the inverse relationship between multiplication and division, building a strong foundation for operations. It strengthens number sense by showing how numbers are interconnected within a family.

Vocabulary
Fact Family: Related addition/subtraction or multiplication/division facts.
Inverse Operations: Operations that undo each other.
Common Mistakes
  • Not including all four facts (two multiplication, two division).
  • Incorrectly identifying the product or quotient in the sentences.
  • Confusing the roles of the numbers (e.g., factors vs. product).
Differentiation
SupportUse concrete manipulatives or fact triangle visuals to build families.
ChallengeIntroduce larger numbers or include a missing number in a fact family.
Discussion Questions
  • What is a fact family, and why is it useful in mathematics?
  • How does understanding fact families help with solving division problems?
  • When might a fact family have only two facts instead of four?
  • How are multiplication and division considered inverse operations?
Extension Activities
  • Create fact family cards.
  • Play fact family matching games.
  • Write story problems.
Parent Tip

Ask your child to create fact families using different sets of three numbers.

Learning Path
Skill Cluster

Number Relationships & Operations

Grade Level

3-4

Skills Practiced
Fact familiesMultiplication factsDivision facts