Represent Division of Whole Numbers by Unit Fractions

10 min

Narrative

The purpose of this Number Talk is for students to demonstrate strategies and understandings they have for dividing a whole number by a unit fraction. These understandings will be helpful later in this lesson when students match situations to equations and solve the equations.

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.

  • 6÷16 \div 1
  • 6÷126 \div \frac {1}{2}
  • 6÷136 \div \frac {1}{3}
  • 6÷166 \div \frac {1}{6}

Sample Response

  • 6: I just know it.
  • 12: There are 2 halves in one whole and there are 6 so 6×2=126 \times 2 = 12.
  • 18: There are 3 pieces of 13\frac {1}{3} in 1 whole, so there will be 6 times as many pieces in 6 wholes.
  • 36: The pieces are half as big as in the previous expression, so there will be twice as many groups.

Synthesis

  • “Why is the quotient getting larger with each problem?” (We are dividing the same number into smaller sized groups, so there are going to be more groups.)
Standards
Addressing
  • 5.NF.7.b·Interpret division of a whole number by a unit fraction, and compute such quotients. <em>For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.</em>
  • 5.NF.B.7.b·Interpret division of a whole number by a unit fraction, and compute such quotients. <span>For example, create a story context for <span class="math">\(4 \div (1/5)\)</span>, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that <span class="math">\(4 \div (1/5) = 20~\)</span> because <span class="math">\(20 \times (1/5) = 4\)</span>.</span>

20 min

15 min