To 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.
Scenario 3 Two students face each other from opposite walls and they travel to opposing points with equal strides and pace. Each student takes one step per second. During the activity, have students indicate the
point where they pass each other (intersect) using a piece of masking tape on the floor. Discuss the results.
Place
students into teams of two and distribute the Runners, Take Your Mark! (Two Runners) activity sheet to each group.
Students should visit the 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.
Note: 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 student sets both runners at zero by dragging their icons along the tracks and click once on their icons so they are facing the same direction.
- The students should take out their Runners, Take Your Mark! (Two Runners) activity sheet, record the step size of "1" for both runners, 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) records results on the graph.
- The students then select the Play Button
to run the simulation. After the
runners are completely done, the stop button resets the simulation.
- Next, the students set both of the runners at the zero position and choose different step sizes for each runner.
- The students then select the Slow Run Button and with each "click" (at least 10 times) records results on the graph.
- The students then select the Play Button to run the simulation. After the
runners are completely done, the stop button resets the simulation.
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 consider the 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.
