Bouncing Tennis Balls
6th to 8th
Students form teams of four to bounce a tennis ball. Pose the problem problem:
A bounce is defined as dropping the ball from the student's
waist. One student keeps the time while the second student bounces and
catches the ball, the third student counts the bounces, and the fourth
student records the data in a table showing both the number of bounces
during each ten-second interval and the cumulative number of bounces.
Each trial consists of a two-minute experiment, with the number of
bounces recorded after every ten seconds (or twenty seconds for fewer
data points). The timekeeper calls out the time at ten-second
intervals. When the time is called, the counter calls out the number of
bounces that occurred during that ten-second interval. The recorder
records this count and keeps track of the cumulative number of bounces.
The same process is followed by each student, with the students
rotating roles, so that each student can collect a set of data. All the
students must bounce the ball on the same surface (e.g., tile, carpet,
concrete) because differences in the surface could affect the number of
Distribute the Bouncing Tennis Balls Recording Sheet to the students.
Bouncing Balls Recording Sheet
The data from one student's experiment are recorded in the table below.
Line of Best Fit Tool
Once the data have been collected, each student prepares a graph
showing the cumulative bounces over two minutes. This graph can be
constructed by using the Line of Best Fit
Alternatively, students may graph the data by hand, by using a
graphing calculator, or by using a spreadsheet, depending on the
students' experiences and on what information the teacher wants to
gather about what the students know and are able to do.
The image below shows the data plotted using the Line of Best Fit Tool.
Alternatively, students may use a graphing calculator to display their data. The figure below shows such a display.
Students present their results to classmates by showing their
graphs. The discussion can involve what the students found easy and
what they found difficult in completing this task. Students'
discussions can be revealing. During the discussion, think about these
Your observations related to these and other questions will yield
information about what your students appear to know and are able to do
that will guide you in making instructional decisions.
Initially students need to become aware of their own
understanding of time, change over time, and the use of new kinds of
measure (i.e., rates). Posing such questions as those listed below
focuses their attention on these ideas (adapted from Kleiman et al.
In this context, distance is how far the object or person moves
(travels). Speed is how fast the object or person is moving
(traveling). Both are described in terms of direction. Distance is
measured in such units as feet, miles, or kilometers. Speed is measured
in relation to time using units such as meters per second or miles per
Adapted from Friel, Susan, et al, Navigating Through Algebra in Grades 6 - 8, from the Navigations Series, NCTM (2001).
During the activity, it is important to observe the students. Note
which students made graphs correctly, paying attention to how they used
the idea of scale to set up the time and distance axes. Listen to
students' conversations about their graphs, attending to comments that
indicated the students realized that the number of bounces depends on
the length of time the ball is bounced and that patterns develop when
the ball is bounced in a consistent way.
[This activity has been adapted from Jones and Day (1998, pp. 18-19).]
Questions for Students
Refer to the lesson plan.