Use an Algorithm with Partial Quotients

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for division using partial quotients. These understandings help students develop fluency and will be helpful later in this lesson when they interpret algorithm notation that shows partial 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.

  • 500÷5500 \div 5
  • 60÷560 \div 5
  • 5÷55 \div 5
  • 565÷5565 \div 5

Sample Response

  • 100: 5×100=5005 \times 100 = 500
  • 12: 5×12=605 \times 12 = 60
  • 1: 5×1=55 \times 1 = 5
  • 113: Since 500+60+5=565500+60+5=565, I can add all the partial quotients from the first 3 problems.

Synthesis

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

10 min

10 min