What’s the Quotient?

10 min

Narrative

This Number Talk encourages students to look for and use the structure of base-ten numbers and the properties of operations to mentally find the values of division expressions (MP7). The reasoning elicited here will be helpful later in the lesson when students find quotients of multi-digit numbers.

Launch

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

Student Task

Find the value of each expression mentally.

  • 48÷348 \div 3
  • 480÷3480 \div 3
  • 528÷3528 \div 3
  • 5,280÷35,280 \div 3

Sample Response

  • 16: 48 is 30+1830 + 18. Dividing 30 by 3 gives 10, and dividing 18 by 3 gives 6, and 10+6=1610 + 6 = 16.
  • 160: 480 is 10 times 48, so the result of 480÷3480 \div 3 is 10 times the result of 48÷348 \div 3.
  • 176: 528 is 480+48480 + 48, so 528÷3528 \div 3 is (480÷3)+(48÷3)(480 \div 3) + (48 \div 3) or 160+16160 + 16.
  • 1,760: 5,280 is 10 times 528, so the result of 5,280÷35,280 \div 3 is 10 times the result of 528÷3528 \div 3.

Synthesis

  • “How is each expression related to the expression before it?”
  • 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
  • 4.NBT.6·Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
  • 4.NBT.B.6·Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

15 min

20 min