**Christine Watson, AC for Worcestershire, Herefordshire and North Gloucestershire**

Tom Button has created a set of travel graphs in GeoGebra, which are free for teachers to explore.

There are 10 of each set: distance-time graphs (under Velocity) and velocity-time graphs (under Acceleration).

So, how can you use them in the classroom?

Here are some suggestions for use in Key Stage 3 and 4.

**For pupils new to travel graphs. **Use Velocity 1 and show the car journey using Road. Discuss distances and speeds. Reset then show the Photos and play again, and discuss what pupils know now that they didn’t before. Then show the markers, and remove the photos. (You may wish to show photos and markers alternately to reinforce this.) Then reset, select Road and Markers, and play again. Discuss what difference this makes to clarity of understanding. Then show the graph and discuss what this adds to understanding. Then reset and play with Road, Markers and Graph.

**Road: Play in full, then play and pause**. Ask pupils to describe the velocity at each point. Where there is more than one vehicle, ask which is fastest, and which is slowest. This can be supported with appropriate vocabulary: steady speed, getting faster (increasing speed), getting slower (decreasing speed), stopped/paused/parked (at rest).

**Road: Play in full, then drag the slider 1 second at a time**. Ask pupils to make a table for the distance each vehicle has travelled at each stage. Use this to discuss the comparative speeds. Use the table to plot the journeys of each vehicle. This could be done in pairs or threes, with each pupil focusing on a different vehicle.

Alternatively, ask pupils to mark on the graph where they think the vehicle is, to create a set of points.

For support, show the photos so the pupils can check their distances.

**Road: Show the starting position, then drag the slider to the end as quickly as possible**. Ask pupils to identify the start and end points for each vehicle, then to discuss what may have happened in-between. Discuss their suggestions as a class, possibly with graphical versions. Then show the mid-point, 5 seconds, and ask pupils to identify which of their suggestions are still possible.

**What happens next?** Play and pause with any combination showing, asking pupils what has happened so far, what will happens next.

**Pupil Modelling.** Show Markers or Graph but not Road. As the animation plays, pupils walk to simulate the motion of the vehicles. Then show Road and repeat for a check. This can be a development of some of the activities above. (This can be developed further using Dataloggers – there may be one in the science labs. See Nuffield Foundation for suggestions.)

**Pupil generation.** Pupils create a graph. They then generate the road journey to match their graph. Pupils could be given sections of graph to combine: for a single vehicle, for 2, for 2 in opposite directions etc.

**Velocity-time.** Use one animation to generate a table of distance-time values. Use this to work out the speed at each second. Then create a velocity-time graph for the same data.

Compare the distance-time graph and the velocity-time graph. Discuss what the gradient on the velocity-time graph represents, and what the area under the curve represents. (Then, what does the area under the curve represent on the distance-time graph represent, if anything?)

**Key questions**

What happens to the (motion / position / markers / graph) when:

- the vehicle stops?
- the vehicle changes direction?
- the vehicle has a different starting point?
- the vehicle travels half as fast?
- the vehicle travels twice as fast?

Create a journey so that:

- the car starts at 0, and is at 200m after 5 seconds
- the vehicle returns to its starting position
- the car starts at 0 and the motorbike at 200, and they pass at halfway / 60
- there is a safe overtaking
- the average speed is 25 metres per second
- the acceleration is 0
- the acceleration is constant

What do the units of each element of the graph represent?

What does the gradient of the graph represent?

What does the area under the graph represent?

**You may wish to provide pupils with a laminated blank graph and/or table to complete (see below).**