Divide Unit Fractions by Whole Numbers

10 min

Narrative

The purpose of this Number Talk is for students to demonstrate strategies and understandings they have for dividing whole numbers. These understandings help students develop fluency and will be helpful later in this lesson when students divide a fraction by a whole number.

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.

  • 72÷472 \div 4
  • 36÷436 \div 4
  • 4÷44 \div 4
  • 2÷42\div 4

Sample Response

  • 18: I know 72÷2=3672 \div 2 = 36 and 36÷2=1836 \div 2 = 18.
  • 9: I just knew it.
  • 1: There is only 1 group of 4.
  • 12\frac {1}{2}: 2 split into 4 equal pieces is 12\frac {1}{2}.
Activity Synthesis (Teacher Notes)
  • “What patterns do you notice in the quotients?” (When the dividend is split in half, the quotient is also split in half.)
  • “Why does that happen?” (There are half as many to start with, so there will be half as many in each group.)
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.
Building Toward
  • 5.NF.7.a·Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. <em>For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.</em>
  • 5.NF.B.7.a·Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. <span>For example, create a story context for <span class="math">\((1/3) \div 4\)</span>, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that <span class="math">\((1/3) \div 4 = 1/12~\)</span> because <span class="math">\((1/12) \times 4 = 1/3\)</span>.</span>

15 min

20 min