Ways to Solve Problems and Show Solutions

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for dividing by 8. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to divide when solving problems.

When students use multiplication facts they know to divide and then add or remove groups of 8 for facts they are less familiar with, 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.

  • 80÷880 \div 8
  • 72÷872 \div 8
  • 96÷896 \div 8
  • 96÷496 \div 4

Sample Response

  • 10: I just know it.
  • 9: 72 is 8 less than 80, so it’s 1 less group of 8.
  • 12: 96 is 16 more than 80, which is 2 more groups of 8.
  • 24: Since there are 12 groups of 8 in 96, I know there are twice as many groups of 4 in 96.
Activity Synthesis (Teacher Notes)
  • “How did knowing 80÷880 \div 8 help you find the other values?”
  • Consider asking:
    • “Who can restate _____’s reasoning in a different way?”
    • ““Did anyone use 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.

25 min

10 min