Request that students pull out their individual
Fact Mastery Record with which they have worked for the past three lessons. Ask students to prove that they have memorized the two facts that they chose the day before. Have them blacken all the facts they know so far, and then choose two facts that they will learn next. As in the previous lessons, request that they draw a number line model of each new target fact on one side of a file card and write the fact on the back. Remind them to review these facts several times during the day and to practice with their family.
Before class, make or find copies of overhead graphing grids. You can copy the Graphing Grid activity sheet onto a transparency.
Give each student several copies of the Graphing Grid activity sheet and one copy of the Table of Values (Strides) activity sheet.
Display the Distance, Speed, and Time Simulation. Call on a volunteer to choose whether the boy or the girl will be used to model a multiplication fact, position the runner at a starting point of 0, set the stride length, and move the runner one stride at a time. As the runner advances, ask the students to enter the value of the position of the appropriate runner in the table of values. Call students’ attention to the graph in the right hand corner of the simulation after each stride. Repeat with the other runner, and have students enter the position of the second runner in the table of values.
Demonstrate, using a graphing grid on the overhead projector, how to plot each point on a graphing grid. Ask the students to label the lower left hand corner (0, 0) and to number the horizontal and vertical lines on their individual grids. Then, ask for volunteers to graph the race on the overhead graphing grid. Assist the first student as he or she plots the path of one runner, and allow another student to plot the path of the other runner on the same transparency using a different color. Invite students to describe the similarities and differences they see in the paths.
Run the simulation once or twice more, setting different stride lengths and number of strides, and call on different volunteers to graph the races. For each race, discuss the entries in the table of values, the placement of each point, and the resulting line which models each runner's path.
To help students become competent and confident at this new skill, ask volunteers to suggest the number of strides and the stride lengths to be taken by each runner, and run the simulation several times. Each time, ask the students to enter the positions in the table of values and then to graph the race on a graphing grid. Finally, ask them to describe the race orally and then write a description under the grid on which they plotted the race.
To end the lesson, ask the class to predict how the graphs would look if a starting point other than 0 were used; that is, what would happen if one runner began the race at a point closer to the tree? Call on a volunteer to choose whether the boy or the girl will get the head start, and then position that runner at a starting point other than 0. Ask another volunteer to set the stride lengths. Finally, ask a third student to suggest the number of strides that each runner will take. Then, move the runners one stride at a time. As the runners advance, ask the students to enter their positions in the table of values. Call students’ attention to the graph in the right hand corner of the simulation after each stride. Now call on a volunteer to demonstrate on the overhead projector how to graph this race.
Repeat the simulation several times, each time varying which runner gets a head start, the amount of the head start, and the stride lengths. Be sure that students consider at least one race for each of the following three cases:
- The runner with the head start has a longer stride length. [The runner with the head start will win the race and, in fact, increase the amount of his or her lead.]
- The runner with the head start has a shorter stride length. [The lead of the runner with the head start will decrease as the race continues; depending on the length of the race, the other runner may catch or pass the runner with the head start.]
- The runner with the head start and the other runner have the same stride length. [The runner with the head start will maintain his or her lead for the duration of the race.]
To allow independent practice, you may want to make the computer and graphing grids available at other times during the day.
