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In size 6, a pair of Nike Free Runs costs $100. In Size 8? $100. Size 11? $100, again. Is this fair? After all, people with small feet are paying the same as people with big feet, but they're getting less shoe!

In this lesson students will calculate unit rates to determine how much different sized shoes cost per ounce. They'll then use the unit rate to solve proportions to find out how much shoes would cost if Nike decided to charge by weight, and will discuss whether they should!

Students will

  • Given size and price of a shoe, graph price vs. size on a coordinate plane
  • Given size and weight of a shoe, graph weight vs. size on a coordinate plane
  • Calculate unit rate ($/oz) for different sizes of shoes, and describe how unit rate changes as size changes
  • For a given cost per ounce (e.g. $5.75/oz), calculate how much each size would cost if Nike charged by weight
  • Discuss advantages and disadvantages of this alternate pricing scheme

Before you begin

It may be helpful if students know how to calculate a unit rate, e.g. use the price and weight to calculate the cost per ounce ($/oz), though this is not necessary. In fact, you can easily use this lesson to introduce unit rates: both how to calculate them and why they're useful. Students should also be familiar with how to plot points on the coordinate plane.

Common Core Standards

Content Standards
Mathematical Practices

Shoutouts

Nike, Zappos