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When you buy a pair of shoes, you probably double-check to make sure they’re both the same size, but should they be? Most people don’t have feet that are exactly the same length, so what does that say about how we should be buying our footwear?

In this lesson, students collect survey and measurement data, construct bar graphs, and discuss distributions and measures of central tendency in order to figure out whether shoe companies should necessarily be selling their products in same-size pairs.

Students will

  • Collect survey data about class shoe sizes and construct a bar graph from the results
  • Describe the shape of the resulting distribution and the relationship between shoe size and frequency
  • Estimate measures of central tendency from the distribution
  • Collect individual left- and right- foot measurements to appropriate accuracy and chart the paired results
  • Calculate the intrapersonal differences in foot size and create a distribution to display the results
  • Use the resulting data to construct an argument about the practice of selling shoes in matched-size pairs

Before you begin

Students should be able to construct a bar graph from a table of frequency data.

Common Core Standards

Content Standards
Mathematical Practices

Additional Materials

  • Rulers (with millimeters)


Peter Iroga