Teaching Speed-Time Graphs

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I am a former maths teacher and owner of DoingMaths. I love writing about maths, its applications, and fun mathematical facts.

An introduction to speed-time graphs

Speed-time graphs is one of those topics that you can really have some fun with when teaching. This is the outline of an outstanding lesson on speed-time graphs which covers many of the aspects of learning that Ofsted love to see. This is a lesson that also actually works well outside of a lesson observation sheet and greatly helps pupils’ understanding.

What you will need for this lesson

For this lesson you will need an electronic whiteboard or computer linked projector, stopwatches (one between two pupils) and the ready-to-fill-in speed time graph worksheet available from my website below. You will also need a clip of the motorbike chase from Terminator 2 (the one where John Connor starts on the dirt bike and the bad guy is chasing after him in the lorry). This can be found on YouTube under ‘Terminator 2 bike chase’. We are going to be drawing a speed-time graph of John Connor’s journey from the moment he sets off on the bike, to the moment the lorry explodes at the end of the clip.

Getting the lesson started

First of all, hand out the worksheets, one to each pupil. Explain that we are going to draw a speed time graph of a journey in a film (eagle-eyed pupils will already have spotted the word Terminator on the sheet), and we will be timing the journey at different points. Play the video through once, without stopwatches, so that the class can get an idea of what is happening, keeping an eye out for the incidents mentioned on the sheet. This will also give a good opportunity to get any Terminator related excitement out of their systems before the real work begins.

Now give out the stopwatches. The pupils will work in pairs; one will be timing, the other will be writing down the time. Explain that you are going to play the clip again and the pupils with stopwatches will need to start timing when John sets off on the bike. You will shout ‘now’ whenever one of the mentioned events takes place, just in case anybody is struggling to keep up, at which point the pupils with the stopwatches will call out the time to their partner who then writes it on their sheet). Emphasise that the stopwatch people mustn’t stop their watches at any point; just giving a reading to the nearest second for each event will be fine.

Get everybody ready with their equipment and then start the video. By the end, every pair should have times for every incident on the sheet and the stopwatch people can quickly copy the numbers down from their partners so that everybody has a completed sheet.

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Drawing the speed-time graph

The class now needs to draw these results onto a graph with time on the x axis and speed on the y axis. How much of a helping hand you give the class now depends upon how competent you feel they are at drawing graphs, but I find the most that is usually needed is to draw the axes on the board along with the axis titles and let the class go from there. Advise the class to join the dots with straight lines and label each change in motion A, B, C – I.

Once the class is just about done, draw your own version of the chart on the board. You can now lead the class through working out acceleration and distance using their graphs.

Lesson plenary

For a great plenary (and a way of ticking even more inspection boxes), I display the finished speed time graph on the board and move my finger or a pointer along the line, getting the class to do the sound effects of the journey as you go (accelerating sounds for positive gradients, squealing brake sounds for any sudden stops etc.). This is a really fun way to end a fantastic lesson and helps the pupils remember the basics of what the gradient of a speed time graph means.