Shark Learning
Second/Multiplication

Associative Property: Equivalence

Associative/commutative reasoning with three factors to determine an unknown without brute force multiplication.
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Study Guide

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Practice Questions

  1. (9 × 14) × ? = (9 × 7) × 28
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    14

  2. (12 × ?) × 15 = (6 × 10) × 18
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    6

  3. (8 × 21) × ? = (16 × 7) × 21
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    14

  4. (25 × ?) × 4 = (50 × 10) × 2
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    10

  5. (? × 18) × 5 = (9 × 6) × 20
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    12

Teacher Resources
Teaching Notes

Emphasize understanding how number properties simplify calculations. Model using factor comparison.

Vocabulary
Associative Property: Changing the grouping of factors does not change the product.
Equivalent: Having the same value.
Common Mistakes
  • Confusing with commutative property
  • Full expansion (ignoring instructions)
  • Incorrect factor comparison/cancellation
  • Misapplying associative property
  • Basic multiplication errors
Differentiation
SupportUse visual models or arrays for smaller numbers.
ChallengeIntroduce variables to represent unknown factors.
Discussion Questions
  • What does 'associative' mean in math?
  • How does cancelling factors simplify the problem?
  • When is this property most useful?
  • Can we use this method for addition problems?
Extension Activities
  • Use addition or subtraction.
  • Find missing numbers.
  • Create own examples.
Parent Tip

Ask your child to show how (2x3)x4 is the same as 2x(3x4).

Learning Path
Skill Cluster

Number Properties & Operations

Estimated Time

10 minutes

Skills Practiced
Associative propertyFactor grouping