Pass the Ball- slope

Ray Weier

In my precalculus class, the first unit in the textbook is entitled prerequisites and it covers many of the formulas and theorems from previous math classes which they have taken.  Since two of the topics to be reviewed were slopes and linear equations, I decided to try the “Pass the Ball” activity with them.

I had intended to take them outside for this activity but since the weather was lousy that day decided to try it right in the classroom.  We just moved the desks from the center of the room and had them stand in a circle.  We used a basketball and decided to each bounce the ball once and then “hand it” to the person next in line.  There were 19 students in this class.  We recorded times for 3, then 7, then 10, then 15, and finally 19 students.  We also took a time for 50 students by looping around several times, but did not announce to the class what that time was.

One of the students made a table for us on the white board for the number of students and the time for each group.  Using that table, each student did each of the following steps.

1.  Enter the data points into list L1 and L2  of a TI-83 Plus calculator.
2.  Stat plot the data points using an appropriate window.
3.  Take a line on a small piece of overhead transparency film and place it on their calculator
     screen to visually position a best fit line.
4.  Using two points from their line, calculate the slope and then use the point-slope formula to
     find a linear best-fit line.
5.  Enter their calculated equation into ‘y1 = ‘ and graph their line to see how well their line fit the
     data points.
6.  Use the Table feature of the calculator in Ask mode to calculate what the time for 50 students
     should have been.

After each of the students had completed these 6 steps, we discussed what kind of estimates they came up with.  We also discussed what a slope of 1.04 would mean in the context of this problem and what the y-intercept should be.

As a group activity with each of them following along on their calculators, I went through with them on the overhead screen the procedure for using STAT-CALC to find a linear regression equation.  We entered this equation into ‘y2 =’ and graphed both equations at the same time.  We also went back to the table on the calculators and compared the two equations evaluated for 50 students.

As a final activity, I showed them the actual experimental time for 50 students.  I had them add this additional data point into their lists and re-plot to see how closely the actual point came to falling on their lines.

Summary:  I really like this activity and it seems that the students do as well.  I was amazed at how linear the data points turned out to be.  The fact that they could make the connection between the slope and the time it took for each student to hand-off the ball was a great teaching moment for me.  I also did this activity a second time in my other precalculus class (7 students) with similar results.