This lesson, as well as the remaining three lessons in this unit, make significant use of the
Distance, Speed and Time Simulation from NCTM's
E-Examples.
Before attempting this or any of the following lessons, use the applet on your own to ensure that you are familiar with all of its buttons and features.
Begin this lesson by having students take out the individual Fact Mastery Record that they began in the last lesson.
Have them choose two facts that they will learn next. Ask them to draw a number line model of each fact on a file card and describe to a partner how each product was obtained. On the back of each file card, they should write the corresponding equation. Tell students to review these facts several times during the day, and encourage them to take the cards home and practice with their family. (The next day, test each student privately on the two facts. If the answers are given rapidly and correctly, direct the student to blacken in these facts on their Fact Mastery Record. Continue this strategy until all the facts have been mastered.)
Project the Distance, Speed and Time Simulation, one of the NCTM E‑Examples, using an overhead projector, or allow students to bring up this simulation on computers, if Internet connections are available. Call on a volunteer to choose whether the boy or the girl will be used to model a multiplication fact. If the girl was chosen, click on the picture of the boy just above the "starting position" box; this will remove him from the simulation. (If the boy was chosen, then click on the pitcure of the girl instead.)
Establish the girl’s step size (i.e., stride length) using the arrows at the bottom of the applet. The step size can be any number from 1 to 15. Hit the PLAY button, and let students watch the demonstration.
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Play
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Step Forward
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Then ask, "How many strides do you think she took to get to the tree?" Allow students enough time to make a prediction; then, hit the STOP button, and run the simulation again, this time using the STEP FORWARD button. Each time you click on the STEP FORWARD button, the runner will move ahead one stride; students should count aloud each time the girl takes a step forward. (Note that for some stride lengths, you will not want to continue all the way to the end. For stride lengths of 2, 4, and 5, the runner will end exactly at 100. For other stride lengths, the runner will move all the way to 100, but the last stride will not be a full stride; however, this is not reflected in the applet. For instance, if a runner moves with stride length 6, she will move to 6, 12, 18, ..., 90, 96; on her next step, however, she will move to 100, which is only a stride of length 4. From the applet, however, there is no way to know that this last step was shorter than the others, and a student may get the false impression that 100 is a multiple of 6.)
At some point in the middle, pause the runner, and ask students to generate an equation that represents the situation. The number of steps will be the first factor, and the runner’s stride length will be the second factor. (Note that the applet records the number of strides as "time." For instructional purposes, the unit of time in lessons 2-4 will be defined as "strides." The designation will switch to "seconds" in lesson 5.) For instance, if the runner took 7 steps of length 6, the applet will show the total distance as 42. The corresponding equation would be 7 × 6 = 42.
Reset the runner to the start, and run the simulation again, setting a different length stride and using a different number of strides. Continue making changes, and allow students to predict the results. Ask questions like, "How far will she go if she takes three strides of length 8?" [24] Or, "How many strides of length 6 will she need to take to get to 36?" [6] Call students’ attention to the graph after each run of the simulation.
Now pair the students and distribute two dice to each pair. Also give them two copies of the Number Lines activity sheet.
Ask them to take turns rolling the dice, using the two numbers as factors in a multiplication number sentence. They should model the multiplication sentence on the number line, and then say the fact aloud. For instance, if a student rolled a 2 and a 6, he would draw, write and say the following:
| 2 × 6 = 12 |
| "Two hops of 6 equals 12." |
As some students work on this task, assign other pairs to use the applet to model and then record multiplication facts.
