The Price is Right (Part 1)

The Price is Right bidder’s row and games provide many opportunities for mathematical connections. I will describe activities integrated with the mathematics of probability and statistics. 

​Bidder's row

            First, students are shown an item and guess the price. Like the television show, the goal is to be the closest without going over. Students record their guesses for ten items that are shown to them. The students are then told the actual price and record this. Students use the guessed prices as the independent variable (x-axis) and the actual price as the dependent variable (y-axis) to produce a scatterplot. In doing this activity with middle years students, the following items were used: television, tablets, trampoline, men’s watch, women’s watch, moped, two video game consoles, basketball hoop, and a ping pong table. Any items that could be relevant to a teacher’s student population could be used and prices can be readily found on the internet.
         Next, students are given a piece of spaghetti and asked to show the line of a person that was a perfect guesser; where every guessed price matched the actual price. Spaghetti is used because it is thin, helps with visualization, and allows students to easily make adjustments to the line of best fit. Students then answer the following questions:

1. How many of your points fall on the spaghetti line? What does this mean?
2. Where do you see the points where your guess was too high? Too low?
3. Describe any patterns or trends to your scatterplot.
4. Draw in an “estimated” line of best fit that fits your data well. How does it compare to the line y = x?
5. Produce an equation for the line of best fit. Use your line of best fit equation to predict the actual price of an item if you guessed $350.
6. What does the slope of your line of best fit mean in this context?
7. What does your y-intercept mean in this context? 

              For question 1, the line y = x is the line that students’ spaghetti should be showing. For question 2, it may be counterintuitive to students that points that fall below the spaghetti line are over-bids and points above the spaghetti line are under-bids. Students can use a few of their points that they know were under-bids or over-bids to check this as they determine where the points appear. The y-intercept for the line of best fit for the students’ data would not have a sensible interpretation in this context as no contestant would bid zero dollars. 
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Temptation Game

Reference
Stohlmann, M. (2018). The math is right! The Australian Mathematics Teacher, 74(3), 9-14.