Four on the Road

This problem looks at the link between a situation described in words and the same situation described graphically. Learners interpret motion as shown on a distance time graph and then investigate the freedoms they have when drawing a graph based on given information. The freedom and constraints naturally provoke rich discussion when this task is approached in small groups.

Sketch one of the graphs on the board. Ask for suggestions for what the two axes could represent and encourage discussion about the story the graph would be telling.

Introduce the idea that the $x$ axis shows the time in minutes since noon, and the $y$ axis shows the distance travelled. Show the three graphs of the car and the scooter. In pairs, learners could discuss what the graphs tell them about the motion of the two vehicles. It is worth discussing the idea that "overtaking" means one vehicle passing another travelling in the same direction, whereas "meeting" usually means that the two vehicles are travelling in opposite directions. Another area for discussion could be to suggest a scale and units for the $y$ axis, based on learners' knowledge of cars and scooters.

For the five statements, learners could each sketch what they think the graph could look like, and then compare their answers in pairs or small groups. This can lead to fruitful discussion about the ways in which the statements constrain the appearance of the graph and what freedom they have.

After working on the last part of the problem to produce a graph showing all the statements, learners could try On the Road which investigates the meeting time of the bike and the scooter.

What is the same on all three graphs? What is different?

What is fixed by the information given in the statements? What can be changed?

Is there only one possible graph for each statement?