Solve Multiplicative Comparison Problems

10 min

Narrative

The purpose of this Number Talk is to elicit the strategies and understandings students have for finding an unknown factor and for relating multiplication and division. These understandings help students develop fluency and will be helpful later in this lesson when students represent and solve multiplicative comparison problems with unknown factors.

Launch

  • Display one expression.
  • “Give me a signal when you have an answer and can explain how you got it.”
  • 1 minute: quiet think time
Teacher Instructions
  • Record answers and strategies.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each unknown mentally.

  • 8×?=168 \times {?} = 16
  • 3×?=243 \times {?} = 24
  • ?×8=32{?} \times 8 = 32
  • 40÷8=?40 \div 8 = {?}

Sample Response

Sample responses:

  • 2: I know my facts. Two groups of 8 is 16.
  • 8: I know my facts. If 2 groups of 8 is 16, then 1 more group of 8 would make 24.
  • 4: I know my facts. To make 32, you would need 1 more group of 8.
  • 5: I know my facts. It’s like the other equations, ?×8{?} \times 8 is 40. 40 is 5 groups of 8. 
Activity Synthesis (Teacher Notes)
  • “Does 40÷840 \div 8 belong in this Number Talk? Why or why not?” (It does belong because division is like finding an unknown factor.)
Standards
Addressing
  • 4.OA.1·Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
  • 4.OA.A.1·Interpret a multiplication equation as a comparison, e.g., interpret <span class="math">\(35 = 5 \times 7\)</span> as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

20 min

15 min