Divide, Using Partial Quotients

10 min

Narrative

The purpose of this Number Talk is for students to demonstrate the strategies and understandings they have for dividing a three-digit number by a two-digit number. These understandings help students develop fluency and will be helpful later in this lesson when students use a partial-quotients algorithm to divide greater three-digit numbers by two-digit numbers.

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

Student Task

Find the value of each expression mentally.

  • 110÷10110 \div 10
  • 121÷11121 \div 11
  • 132÷12132 \div 12
  • 154÷14154 \div 14

Sample Response

  • 11: I just knew it.
  • 11: I know 10×11=11010 \times 11 = 110,  1×11=111 \times 11 = 11, and 10+1=1110 + 1 = 11.
  • 11: I know 10×12=12010 \times 12 = 120,  1×12=121 \times 12 = 12, and 10+1=1110 + 1 = 11.
  • 11: I know 10×14=14010 \times 14 = 140, 1×14=141 \times 14 = 14, and 10+1=1110 + 1 = 11.
Activity Synthesis (Teacher Notes)
  • “What stays the same with each problem? What changes?” (The quotient is always 11. There are always 11 groups of the divisor. The dividend and the divisor change.)
Standards
Addressing
  • 5.NBT.6·Find whole-number quotients of whole numbers with up to four-digit dividends and two-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.
  • 5.NBT.B.6·Find whole-number quotients of whole numbers with up to four-digit dividends and two-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