Multiply Unit Fractions

10 min

Narrative

The purpose of this Estimation Exploration is for students to estimate the area of a shaded region. In the Activity Synthesis, students discuss whether the product is greater or less than the expression 12 ×16\frac{1}{2} \times \frac{1}{6}. This allows them to connect the shaded area to their previous work with multiplication expressions (MP7).

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

What is the area of the shaded region?

Diagram. Square, length and width, 1. Rectangle of length about 1 half and width about 1 fourth shaded.

Record an estimate that is:

too low about right too high

Sample Response

Sample responses:

  • too low: 116\frac{1}{16} to 120\frac{1}{20}
  • about right: 16\frac{1}{6} to 110\frac{1}{10}
  • too high: 14\frac{1}{4} to 12\frac{1}{2}
Activity Synthesis (Teacher Notes)
  • “Is the area of the shaded region more or less than 12 × 16\frac{1}{2}  \times  \frac{1}{6}? How do you know?” (More. It looks like it is 12\frac{1}{2} the length and more than 16\frac{1}{6} the width.)
  • “What is the value of 12×16\frac{1}{2} \times \frac{1}{6}?” (112\frac{1}{12})
Standards
Addressing
  • 5.NF.4.a·Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. <em>For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)</em>
  • 5.NF.B.4.a·Interpret the product <span class="math">\((a/b) \times q\)</span> as <span class="math">\(a\)</span> parts of a partition of <span class="math">\(q\)</span> into <span class="math">\(b\)</span> equal parts; equivalently, as the result of a sequence of operations <span class="math">\(a \times q \div b\)</span>. <span>For example, use a visual fraction model to show <span class="math">\((2/3) \times 4 = 8/3\)</span>, and create a story context for this equation. Do the same with <span class="math">\((2/3) \times (4/5) = 8/15\)</span>. (In general, <span class="math">\((a/b) \times (c/d) = ac/bd\)</span>.)</span>

20 min

15 min