Solve Problems with Equal Groups

10 min

Narrative

The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information. 

Launch

  • Groups of 2
  • Display the expression.
  • “What is an estimate that’s too high? Too low? About right?”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 1 minute: partner discussion
  • Record responses.

Student Task

4×184 \times 18

Record an estimate that is:

too low about right too high
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Solution Steps (3)
  1. 1
    Find a lower bound using known fact
    →4×10 = 40, so 4×18 > 40
  2. 2
    Find an upper bound using known fact
    →4×20 = 80, so 4×18 < 80
  3. 3
    Estimate 4×18
    →About right: between 40 and 80 (actual is 72)

Sample Response

Sample responses
  • Too low: 40 or less
  • About right: 40–79
  • Too high: 80 or more
Activity Synthesis (Teacher Notes)
  • Consider asking:
    • “Is anyone’s estimate less than ___? Is anyone’s estimate greater than ___?”
    • “Based on this discussion, does anyone want to revise their estimate?”
Standards
Addressing
  • 3.OA.5·Apply properties of operations as strategies to multiply and divide.
  • 3.OA.B.5·Apply properties of operations as strategies to multiply and divide.<span>Students need not use formal terms for these properties.</span> <span>Examples: If <span class="math">\(6 \times 4 = 24\)</span> is known, then <span class="math">\(4 \times 6 = 24\)</span> is also known. (Commutative property of multiplication.) <span class="math">\(3 \times 5 \times 2\)</span> can be found by <span class="math">\(3 \times 5 = 15\)</span>, then <span class="math">\(15 \times 2 = 30\)</span>, or by <span class="math">\(5 \times 2 = 10\)</span>, then <span class="math">\(3 \times 10 = 30\)</span>. (Associative property of multiplication.) Knowing that <span class="math">\(8 \times 5 = 40\)</span> and <span class="math">\(8 \times 2 = 16\)</span>, one can find <span class="math">\(8 \times 7\)</span> as <span class="math">\(8 \times (5 + 2) = (8 \times 5) + (8 \times 2) = 40 + 16 = 56\)</span>. (Distributive property.)</span>

20 min

15 min