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First/Multiplication

Associative Property: Missing Factor

Use associative property to solve for unknown factor in regrouped products.
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Prerequisites
Associative Property: Efficient Grouping6 WS
18 × (25 × 4) vs (18 × 25) × 4 → Easier: ______ Product: ______
What to Do Next
Distributive Expansion: 1-digit × 2-digit6 WS
7 × 34 = ________

Practice Questions

  1. (3 × ?) × 5 = 3 × (4 × 5) ? = ? Product = ?
    Show answer

    (3 × 4) × 5 = 3 × (4 × 5) 4 = 4 Product = 60

  2. (6 × ?) × 2 = 6 × (3 × 2) ? = ? Product = ?
    Show answer

    (6 × 3) × 2 = 6 × (3 × 2) 3 = 3 Product = 36

  3. (? × 5) × 4 = 5 × (2 × 4) ? = ? Product = ?
    Show answer

    (2 × 5) × 4 = 5 × (2 × 4) 2 = 2 Product = 40

  4. (7 × ?) × 3 = 7 × (2 × 3) ? = ? Product = ?
    Show answer

    (7 × 2) × 3 = 7 × (2 × 3) 2 = 2 Product = 42

  5. (8 × ?) × 5 = 8 × (2 × 5) ? = ? Product = ?
    Show answer

    (8 × 2) × 5 = 8 × (2 × 5) 2 = 2 Product = 80

Teacher Resources
Teaching Notes

Explain the associative property to group factors for easier mental calculation. Emphasize that grouping changes, but the product remains the same.

Vocabulary
Associative Property: Changing grouping doesn't change the answer.
Factor: A number multiplied to get a product.
Common Mistakes
  • Adding factors instead
  • Confusing with commutative property
  • Incorrectly grouping factors
  • Calculation errors
  • Ignoring the unknown factor
Differentiation
SupportUse manipulatives or visual models to demonstrate grouping.
ChallengeIntroduce problems with larger numbers or multiple missing factors.
Discussion Questions
  • What is the associative property?
  • How does grouping factors help simplify multiplication?
  • When is the associative property most useful?
  • Can this property be applied to addition or subtraction?
Extension Activities
  • Use blocks to show grouping.
  • Draw parentheses.
  • Create your own problems.
Parent Tip

Ask your child to group toys in different ways to show the same total.

Learning Path
Skill Cluster

Number Sense and Operations

Estimated Time

12 minutes

Skills Practiced
Associative propertyEquation reasoning