To begin, request that the students refer to their fact mastery records. Check to verify that they have memorized the two facts that they chose the day before. Have them cover the facts that they just learned, then list the facts that they have left to memorize. Ask them to make a plan for memorizing the remaining facts.
Show the students a table of values (with values filled in), and ask volunteers to graph the two lines on the chalkboard or overhead projector. Invite students to describe the race that was graphed. You might wish to use the table of values shown below.
On the overhead projector, place a blank graphing grid and table of values, and display the Distance, Speed, and Time Simulation. Call on volunteers to position the runner at a starting point other than 0, and call on other volunteers to set the stride lengths. Ask another volunteer to enter the starting points in the table of values. Now advance each runner one stride at a time, and record each distance in the table of values.
Call students’ attention to the graph in the right hand corner of the simulation after each stride. Ask volunteers to graph each path on the graphing grid and to describe what they graphed.
Distibute three copies of the Graphing Grid activity sheet and one copy of the Table of Values (Seconds) activity sheet to each student. Tell the students to assume that each stride takes one second, and invite students to set the parameters of a new simulation, including starting points which are not 0.
As one student runs the simulation, encourage other students to enter the distances in their table of values and graph the paths on their grids. Run the simulation once or twice more, setting different stride lengths, starting points, and number of strides. Call on different volunteers to graph the races on the overhead as the other students graph them on their own grids. For each race, discuss the entries in the table of values, the placement of each point, and the resulting line that models each runner’s path. When all students have finished, ask them to describe the race orally and then to write a description under the graph.
Now tell the students that the race will go all the way to the tree, and that they should watch the graph in the right hand corner of the simulation very carefully. Identify volunteers to position the runners at the starting point and to set the stride lengths. Run the simulation, this time choosing the PLAY button to start the race. (Clicking this button causes the entire race to happen at once, instead of step-by-step.) Invite discussion of the paths that show what the runners did. Repeat using other settings.
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Now pose the following challenges to the students, one at a time, and discussion student solutions for each one:
- Make a graph that shows a race in which the boy and the girl started from the same position, but the girl got to the tree first. [There are many solutions, but the stride length of the girl must be greater than the stride length of the boy.]
- Make a graph that shows a race in which the boy starts behind the girl, but the boy gets to the tree first. [There are many solutions, but the stride length of the boy must be significantly greater than the stride length of the girl.]
- Make a graph that shows a race in which the boy starts at the tree and the girl starts at the house, but the girl reaches the tree before the boy reaches the house. [There are many solutions, but the stride length of the girl must be greater than the stride length of the boy.]
- Make a graph that shows the girl running for 2 seconds with a stride length of 3, and then she runs for 5 seconds with a stride length of 3. [The graph will change directions after 2 seconds. It will become steeper, because the stride length increased.]
