### Why do this problem?

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.

### Possible approach

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.

### Key questions

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?

### Possible extension

Learners could try

On the Road straight away without having the
example graphs first.

### Possible support

A worksheet with examples of graphs is available

here. Learners
can then identify which graph correctly represents each
statement.