Solve Problems with Multiplication and Division

10 min

Narrative

This Number Talk encourages students to think flexibly about numbers to divide. The understandings elicited here will be helpful throughout this unit as students divide whole numbers and build toward fluent multiplication and division.

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.

  • 848÷8848 \div 8
  • 4,848÷84,848 \div 8
  • 4,852÷84,852 \div 8
  • 5,848÷85,848 \div 8

Sample Response

  • 106: 800÷8800 \div 8 is 100 and 48÷8=648 \div 8 = 6, and then 100+6100 + 6 is 106.

  • 606:

    • 4,800÷8=6004,800 \div 8 = 600 and 48÷8=648 \div 8 = 6, and then 600+6600 + 6 is 606.
    • 4,000÷8=5004,000 \div 8 = 500 and 848÷8=106848 \div 8 = 106, and then 500+106500 + 106 is 606.
  • 606 with a remainder of 4: 4,852 is only 4 more than 4,848, so it’s not enough to make another group of 8.
  • 731: 5,848 is 1,000 more than 4,848 and 1,000÷8=1251,000 \div 8 = 125. (800÷8=100800 \div 8 = 100 and 200÷8=25200 \div 8 = 25.) 606+125=731606 + 125 = 731.

Synthesis

  • “How did you use the first few expressions to help you find the value of the last expression?”
  • “How might you use multiplication to find the value of each quotient?”
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