Estimate and Measure Liquid Volume

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for dividing within 100 and to help students develop fluency.

When students use known multiplication and division facts to divide greater numbers, they look for and make 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.

  • 30÷330\div3
  • 60÷360\div3
  • 63÷363\div3
  • 54÷354\div3
Solution Steps (4)
  1. 1
    Calculate 30÷3
    →10 (known fact: 3×10=30)
  2. 2
    Calculate 60÷3
    →20 (double 30÷3=10, so 60÷3=20)
  3. 3
    Calculate 63÷3
    →21 (60÷3=20, add one more group of 3 gives 21)
  4. 4
    Calculate 54÷3
    →18 (60÷3=20, subtract 2 groups of 3 gives 18)

Sample Response

  • 10: I counted by 10. I knew that 3×103 \times 10 is 30.
  • 20: I knew that 10 groups of 3 makes 30, so I would need 10 more groups of 3 to make 60. That means the quotient is 20.
  • 21: I knew that 20 groups of 3 is 60. One more group of 3 would make 63, so it would be 21 groups.
  • 18: I knew that 20 groups of 3 is 60. So, 19 groups of 3 would be 57 and 18 groups of 3 would be 54.
Activity Synthesis (Teacher Notes)
  • “How did you use division facts that you already know to find some of the other quotients?” (I knew that 60÷360\div3 is double the answer of 30÷330\div3. Once I knew 60÷360\div3, I was able to find 63÷363\div3 by adding another group of 3 and 54÷354\div3 by taking away groups of 3.)
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