Concepts of Division

10 min

Narrative

This Number Talk encourages students to think about the relationship between the size of the divisor and the size of the quotient and to rely on the structure of division expressions to mentally find quotients. 

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 strategy.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 120÷12120 \div 12
  • 120÷6120 \div 6
  • 120÷3120 \div 3
  • 120÷2120 \div 2

Sample Response

  • 10: I know it.
  • 20: There are twice as many groups as in the last problem, so there will be half as many in each group.
  • 40: 12 divided by 3 is 4. 12 tens divided by 3 is 4 tens.
  • 60: I know half of 120 is 60.

Synthesis

  • “Why did the quotient get bigger with each problem?” (You are making smaller groups so there are more in each of them.)
Standards
Building On
  • 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.

20 min

15 min