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First/Multiplication

Associative Property: Efficient Grouping

Efficient regrouping of three factors to leverage friendly partial products (100, 50, 32, 60, 150, 250).
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Study Guide

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Associative Property: Efficient Grouping preview

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Practice Questions

  1. 18 × (25 × 4) vs (18 × 25) × 4
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    1800

  2. (32 × 5) × 20 vs 32 × (5 × 20)
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    3200

  3. (48 × 25) × 2 vs 48 × (25 × 2)
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    2400

  4. (14 × 50) × 2 vs 14 × (50 × 2)
    Show answer

    1400

  5. (16 × 12) × 5 vs 16 × (12 × 5)
    Show answer

    960

Teacher Resources
Teaching Notes

Emphasize how strategic grouping simplifies complex multiplication. Focus on creating friendly numbers for mental calculation.

Vocabulary
Grouping: How numbers are combined in an expression.
Efficient: Achieving maximum productivity with minimum wasted effort.
Common Mistakes
  • Choosing larger numbers without benefit
  • Not recognizing friendly pairs
  • Calculation errors
  • Ignoring associative property
  • Misapplying factors
Differentiation
SupportUse multiplication charts; provide pre-circled pairs.
ChallengeIntroduce four factors; estimate products first.
Discussion Questions
  • How does grouping change the problem's difficulty?
  • Can we always rearrange factors easily?
  • When is the associative property most useful?
  • How does this help with mental math?
Extension Activities
  • Use larger numbers.
  • Compare different groupings.
  • Create multiplication puzzles.
Parent Tip

Ask your child to find the easiest way to multiply 2 x 5 x 3.

Learning Path
Skill Cluster

Number Sense & Operations

Estimated Time

12 minutes

Skills Practiced
Strategy groupingAssociative property