Represent Division of Unit Fractions by Whole Numbers
10 min
Narrative
The purpose of this Estimation Exploration is for students to think about dividing a unit fraction into smaller pieces. In the lesson, students will be given extra information so they can determine the exact size of shaded regions like the one presented here.
Launch
- Groups of 2
- Display the image.
- “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
How much is shaded?
Record an estimate that is:
| too low | about right | too high |
|---|---|---|
Sample Response
Sample responses:
- too low: 1001 to 401
- about right: 201 to 161
- too high: 81 to 121
Synthesis
- Draw and display the image:
- “How is this diagram the same as the diagram in the problem? How is it different?” (Both diagrams show 41 of the whole and then a piece of that 41 is shaded. The shaded piece in this diagram is cut horizontally. The other diagram is long and narrow and the shaded piece is an entire vertical slice.)
Standards
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>