introduce this activity, ask two student volunteers to stand in front
of the classroom to physically demonstrate and discuss the results of
each of the following scenarios:
Scenario 1. Two students start from the same
position at one end of the classroom. One student takes giant-steps
while the other takes baby-steps. Each student takes one step per second. Who gets to the other end of the classroom first? How many steps are taken? Discuss the results.
Scenario 2. One student starts behind the other at the same end of the classroom, both walking with equal stride and pace. Each student takes one step per second.
Who gets to the other end of the classroom first? How many steps does
each student take? Discuss the results. Ask students to predict the
effect of changing the length of stride.
Place students into teams of two and distribute a Runners, Take Your Mark! (Single Runner) Activity Sheet to each group.
Runners, Take Your Mark! (Single Runner) Activity Sheet
Students should open the Runner Simulation Tool.
Runner Simulation Tool
Working together, partners share the responsibility of "Mouse
Driver" and "Reader/Recorder". The "Reader/Recorder" will read the
directions from the activity sheet and record observations while
guiding the activity. The "Mouse Driver" controls the action of the
mouse and movement on the computer screen. Partners should switch roles
until all have moved the runner.
- Be sure to tell students about two key assumptions used in this activity.
(a) The runner always takes one step per second (no matter how big the step size is).
(b) We will measure time in seconds, even
though the actual movement in the simulation will probably be much faster.
- To begin, the students select either the male or female
runner. To do this the student "clicks" upon the male or female icon in
the box next to the graph of the runner they DON’T want to use. This
will cause that runner to temporarily vanish from the running line and
graph. Next the students set the runner to zero by dragging the icon
along the track and clicking until the runner is facing the direction
of running from left to right.
- The students should take out their Runners, Take Your Mark! (Single Runner) Activity Sheet, record the step size of "1", and set the step size on the interactive
applet to "1".
- The students then select the Slow Run Button and with each "click" (at least
10 times), results are recorded on the graph.
- The students then select the Play Buttonto run the simulation. After the
runner is completely done, the stop button resets the simulation.
- Next, the students set the runner’s step size to 2, select the Slow Run Button and record the results on the graph.
- Repeat this with the step sizes of 4 and 5 and record the
results. Students may vary the runner’s step size all the way up to 15.
In this race simulation software, the finish
time is rounded up to the nearest whole number. Thus, for example, if a
runner starts at 0 with step size 3, the finish time shown will be 34,
rather than 33 1/3. Students may notice this and comment that 34 × 3
does not equal 100. They may notice that with step size of 3, and one
step per second, the finish time should be 33 1/3 seconds. Please be
aware of this limitation of the software as you teach the lesson.
The closing should be structured so that students can review and
pull together what they have learned. Include questions or tasks that
encourage students to reflect on their work. For example, have students
Questions for Students (below). In so doing they will
consolidate what they have learned. Furthermore, this will provide an
opportunity for you and the students to assess what they have learned
and what they still want or need to understand. This will give you
ideas for further instruction.