Relate Quotients to Familiar Products

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for multiplying and dividing within 100. These understandings help students develop fluency and identify division facts that are related to known products.

When students use the relationship between multiplication and division to find the quotient in division facts they don’t know, they are looking for and making use of structure (MP7).

Launch

  • Display the first 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.

  • 4×104 \times 10
  • 40÷440 \div 4
  • 40÷1040 \div 10
  • 60÷660 \div 6
Solution Steps (4)
  1. 1
    Calculate 4×10
    →40 (skip count or place value)
  2. 2
    Calculate 40÷4
    →10 (use 4×10=40, so 40÷4=10)
  3. 3
    Calculate 40÷10
    →4 (use same fact: 4×10=40)
  4. 4
    Calculate 60÷6
    →10 (use 6×10=60, so 60÷6=10)

Sample Response

  • 40: I counted by 10, like 10, 20, 30, 40. I just knew it.
  • 10: Since I know that 4×10=404 \times 10 = 40, I know that 40 divided by 4 is 10, because 10 is the unknown factor.
  • 4: This is just like 40÷440 \div 4, but the other factor is unknown, so the quotient would be 4.
  • 10: Since I know that 6 times 10 is 60, I know that 60 divided by 6 would be 10, because 10 is the unknown factor.
Activity Synthesis (Teacher Notes)
  • “How do the first 3 expressions show that multiplication and division are related?” (The two division expressions both have one of the factors unknown. In the first expression, the 10 is unknown. In the second, the 4 is unknown.)
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.

20 min

15 min