In this Warm-up, students compute absolute guessing errors using class data. The absolute errors they find here will be plotted in the next activity.

The absolute errors could be calculated and compiled in different ways, by hand or using technology, including a spreadsheet tool (MP5). For example, students could:

• Complete a table of values individually.
• Complete a table in groups of 2–4, with the calculations done by hand but divided among group members.
• Complete a table as a class, with each student calculating only one absolute guessing error and sharing it with the class.

If desired, display a completed table for all to see, or simply invite students to share some observations about the absolute guessing errors they found. If no one mentioned that all the values are positive, ask them about it and solicit some ideas about why this is the case.

Also ask students if they could tell from the data how good the guesses were. (Were the guesses close? Were there a lot of overestimates or underestimates?)

Tell students that they will plot the data next.

In this activity, students create a scatter plot of the data they compiled earlier and examine the scatter plot. Unless the data they collected consist mostly of overestimates or mostly of underestimates, students are likely to notice the data points forming a V shape. They then consider whether the relationship between the guesses and absolute guessing errors form a function.

This activity allows students to see how changing the target number in a guessing game changes the absolute guessing errors and changes the scatter plot of the data.

Here, students see that they are still finding the difference between the guesses and a number, that the absolute guessing errors are still all positive, and that the data points still seem to form a V above the horizontal axis. What is different is that the position of the V shape has now shifted horizontally and that the number of points forming the two pieces of the V may have changed.

The work here prepares students to later see the absolute value function in terms of finding the distance between input values and 0.

The activity is written so that students could perform the calculations and graphing individually and by hand. To make more time for reasoning and analysis, however, use of statistical and graphing technology for computation and plotting is recommended, as is splitting up the work among students.