This is a level 4 activity from the Figure It Out series.
A PDF of the student activity is included.
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FIO, Link, Algebra, Book One, Which Wheels Where? page 24
This activity asks the students to interpret line graphs illustrating a scooter race between Josh and Rewi. Where the line graph for one racer is steeper than the line graph for the second racer, we can conclude that the first racer is going faster than the second. We know this because the graph indicates that the first racer is covering more distance than the second racer during the same time period.
Some students incorrectly interpret such line graphs as “going up a hill”. They interpret the graph in terms of its physical features rather than in terms of the underlying mathematics relating to the concept of rate.
In figure 1, a vertical line through both graphs can help the students to see who is leading at a particular time. Similar vertical lines can be drawn at different times to help the students decide who is in front at that particular moment. Here, the vertical line shows that Josh has travelled further than Rewi for the same elapsed time.
Figure 2 shows how horizontal lines can also be used to work out who has taken the longer time to cover a particular distance. Here, the horizontal line shows that Rewi has taken longer than Josh to cover the same distance.
When they have completed question 6, the students might like to draw lines showing the progress of someone who walked the race route as well as someone who, for example, cycled the route. Possible lines of progress for the individuals are shown below.
Answers to Activity
1. a. Josh
b. Rewi
2. Rewi
3. Rewi overtakes Josh.
4. Answers will vary. Josh obviously stopped because time passes, but his distance from the start remains unchanged. He may have fallen off his scooter or stopped to fix a loose wheel.
5. His speed has increased.
6. The graph might look something like this.
A description might then be:
At the beginning of the race, I was behind Josh but ahead of Rewi. Then at time B, Rewi caught up with me and I passed Josh (who had stopped). Rewi got ahead of me until a bit later (at time C), when I sped up and overtook him and won the race.