Reason about Quotients

10 min

Narrative

The purpose of this Estimation Exploration is for students to apply their understanding of dividing a whole number by a fraction from previous lessons. The dividend in this expression is much larger than those that students have previously worked with to encourage students to use multiplication to estimate.

Launch

  • Groups of 2
  • Display the expression.
  • “What is an estimate that’s too high? Too low? About right?”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 1 minute: partner discussion
  • Record responses.

Student Task

98÷1598 \div \frac{1}{5}

Record an estimate that is:

too low about right too high

Sample Response

Sample responses:

  • too low: 400 to 450
  • about right: 470 to 499
  • too high: 500 or more
Activity Synthesis (Teacher Notes)
  • “How do you know the value of 98÷1598 \div \frac{1}{5} is less than 500?" (It's less than 100÷15100 \div \frac{1}{5} and that's 500)
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