Round and Round Again

10 min

Narrative

The purpose of this Number Talk is to elicit the strategies and understandings students have for the products of 4 and 6 as they relate to the products of 5. These understandings help students develop fluency and will be helpful later when students consider solutions for and solve two-step word problems.

When students use products of 5 to determine products of 4 by thinking of them as one less group or one less object in each group, or work from products of 5 to determine products of 6 by thinking of them as one more group or one more object in each group, they look for and make use of structure (MP7).

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 expression mentally.

  • 5×75 \times 7
  • 4×74 \times 7
  • 6×76 \times 7
  • 4×84 \times 8
Solution Steps (4)
  1. 1
    Find 5×7 mentally
    →35 (skip count or known fact)
  2. 2
    Find 4×7 using 5×7
    →4×7 = 5×7 - 7 = 35-7 = 28 (one less group of 7)
  3. 3
    Find 6×7 using 5×7
    →6×7 = 5×7 + 7 = 35+7 = 42 (one more group of 7)
  4. 4
    Find 4×8 using 5×8
    →4×8 = 5×8 - 8 = 40-8 = 32 (one less group of 8)

Sample Response

  • 35: I counted by 5, like 5, 10, 15, 20, 25, 30, 35. I just knew it.
  • 28: There would be 4 groups of 7 instead of 5. So 35 minus 7 would be 28.
  • 42: There would be 1 more group of 7 than in the first problem. So, 35 plus 7 would be 42.
  • 32: There would be 1 less group of 8 than 5×85 \times 8. So 40 minus 8 would be 32.
Activity Synthesis (Teacher Notes)
  • “How does knowing 5×75\times7 help you find some of the other products?” (I can remove a group of 7 to find 4×74\times7 or add a group of 7 to find 6×76\times7.)
  • Consider asking:
    • “Who can restate _____’s reasoning in a different way?”
    • “Did anyone have the same strategy but would explain it differently?”
    • “Did anyone approach the problem in a different way?”
    • “Does anyone want to add on to _____’s strategy?”
Standards
Addressing
  • 3.OA.7·Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
  • 3.OA.C.7·Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that <span class="math">\(8 \times 5 = 40\)</span>, one knows <span class="math">\(40 \div 5 = 8\)</span>) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

15 min

20 min