Problems about Fractional Measurement Data

10 min

Narrative

This Warm-up prompts students to make sense of data and quantities before using them to solve problems, by familiarizing themselves with a context and the mathematics that might be involved. Students may be familiar with shoe sizes but may not recognize that each size is associated with a particular measurement.

Launch

  • Display the shoe-size chart and diagram of insoles.
  • “What do you notice? What do you wonder?”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 1 minute: partner discussion
  • Share and record responses.

Student Task

U.S. youth shoe size insole length (inches)
1 7687\frac{6}{8}
1.5 8
2 8188\frac{1}{8}
2.5 8288\frac{2}{8}
3 8488\frac{4}{8}
3.5
4 8688\frac{6}{8}
4.5 9
5 9189\frac{1}{8}
5.5
6 9489\frac{4}{8}
6.5 9589\frac{5}{8}
7 9689\frac{6}{8}

image of shoe size chart, 7 insole lengths. smallest insole length, 7 and 5 eighths.

Sample Response

Students may notice:

  • There is a chart with sizes in whole numbers and numbers with a point followed by a 5.
  • There are measurements in whole numbers and mixed numbers, measured in inches.
  • The diagram shows a length of 7687\frac{6}{8} for size 1 and how other sizes compare.
  • The fractions are all eighths.
  • The lengths for sizes 3.5 and 5.5 are missing.

Students may wonder:

  • What are the numbers with a point and a 5?
  • Why are most of the lengths fractions?
  • What does “insole” mean?
  • Why is the shortest length 7687\frac{6}{8} inches? What about shoes for toddlers?
  • What are the lengths for sizes 3.5 and 5.5?
Activity Synthesis (Teacher Notes)
  • Explain that an “insole” is the inside part of a shoe, underneath the foot. Its length is approximately the length of the foot.
  • Check students’ interpretation of the data and the diagram:
    • “What information do the table and the diagram show?”
    • “If someone's shoe size is 5, what’s the length of the insole?”
    • “What shoe size do you wear? What's the length of the insole?”
  • “What do you think the missing lengths might be for sizes 3.5 and 5.5?” (For 3.5, the missing length would be 8588\frac{5}{8}, as there are no other fractions in eighths between 8488\frac{4}{8} and 8688\frac{6}{8}. For size 5.5, it could be 9289\frac{2}{8} or 9389\frac{3}{8}.)
  • “Today we'll look at data and solve problems related to shoe lengths. The sizing chart here gives us an idea of where the numbers come from and what they mean.”
Standards
Building Toward
  • 4.MD.4·Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. <em>For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.</em>
  • 4.MD.B.4·Make a line plot to display a data set of measurements in fractions of a unit <span class="math">\((1/2, 1/4, 1/8)\)</span>. Solve problems involving addition and subtraction of fractions by using information presented in line plots. <span>For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.</span>

20 min

15 min