After several months of working together, ISA math coach Julie Arcement is ready to observe a teacher she has coached deliver an inquiry-based math lesson on linear regression centered around the following three activities.  The students are engaged with each other as they work collaboratively in groups.

Activity 1

Shaquille O’Neal is 7’1” tall and has a 15” foot.  What size shoe do you think he wears?  How did you come up with your conjecture?

Activity 2

The shoe size a person needs varies linearly with the length of his or her foot.  Use this relationship to determine a way to predict the shoe size of any man.

  • First, gather data (shoe size and the foot length of at least four young men in the class.}
  • Next, graph the data.
  • What do you observe?

Based on the points you graphed, do you agree that there is a linear relationship between shoe size and foot length?  How do you think you can use this graph to determine Shaquille O’Neal’s shoe size?  Explain.

Activity 3

We already know that the graph should be linear.  On your own, plot the points and create the line of best fit (the straight line that best models the data in your graph}.

  • Describe how you did it.
  • Compare the line with the lines of other students in your group. Your task here is to have a group discussion as to why your line better fits the data than the others in your group.  You will come to a consensus for your group’s line of best fit.  Be prepared to share your group’s graph with the class and how you determined it was the best from your group.
  • Write the equation of the line of best fit that you created.
  • Explain what the different parts of your equation represent.