Multiply a Unit Fraction by a Non-Unit Fraction

10 min

Narrative

The purpose of this Estimation Exploration is for students to estimate the area of a shaded region. In a previous Estimation Exploration, students looked at a shaded region where the length was represented by a unit fraction and the width could be estimated with a unit fraction. In the diagram, the length is a unit fraction. The width can not be a unit fraction since it is greater than 12\frac{1}{2}. This prepares students for the work of this lesson which is to consider products of a unit fraction and a non-unit fraction.

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 with length of about 1 half and width of about 3 fifths shaded.

Record an estimate that is:

too low about right too high

Sample Response

Sample responses:

  • too low: 18\frac{1}{8} to 14\frac{1}{4}
  • about right: 310\frac{3}{10} to 410\frac{4}{10}
  • too high: 12\frac{1}{2} or more

Synthesis

  • “Is the area of the shaded region more or less than 14\frac{1}{4} square unit? How do you know?” (It’s more because 12\frac{1}{2} of 12\frac{1}{2} is 14\frac{1}{4}, and more than that is shaded.)
Standards
Addressing
  • 5.NF.4.b·Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
  • 5.NF.B.4.b·Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

15 min

20 min