# Take your Dog for a Walk

Each day Pat takes the dog for a walk.

You can see them on the interactivity below.

Try moving Pat and the dog using the purple arrow keys. The graph shows how far Pat is walking from the gate after a certain amount of time.

What happens to the graph once Pat gets back to the gate?

Try to reproduce these graphs:

Can you tell a story that would result in each of the graphs above?

Use the interactivity to try out different ways of making Pat walk.

A few children got in touch to tell us that they had managed to reproduce these two graphs. Beth from Pierrepont Gamston Primary School summed up what she had noticed:

The first of the graphs would show the dog walking away from the gate and stopping but the second one shows the dog walking away from the gate and then going back to it.

That's right Beth - how do we know that the dog stops walking in the first graph?

Will and Saif, also from Pierrepont Gamston Primary School, had some ideas about why these situations might happen in real life:

The first one is simple: just stay still! We came up with a story for this one... Pat was walking the dog when the sky turned grey. She decided to stop for a minute when she bumped into a good friend and had a nice chat.

For the second one, walk down and then up again. Our explanation for this is that she was having a good dog walk when it began to rain. Unluckily, she had forgotten an umbrella and headed back home.

Good ideas! Hongqi from Copthorne Prep School in the UK had some different explanations for these situations:

For the first graph: One day Pat took his dog on a walk, he walked for a while and took a rest with his dog, the distance of them between the place they are resting and the gate won't change any more, so we can see a straight line.

For the second graph: One day Pat took his dog on a walk, Pat walked for a while and remembered he forgot something so he went back to the gate, the difference between Pat and the gate at first increased gradually and then decreased, so we can see a peak in the graph.

This is very clearly explained, Hongqi - well done! Thank you to everyone who sent in their ideas about this activity.

### Why do this problem?

The idea of this problem is to introduce learners to interpreting distance/time graphs. It lends itself to a trial and improvement approach, which can be an undervalued way of approaching a challenge.

### Possible approach

(If possible, it would be great to introduce the class to these ideas using a sensor, which gives an output on a distance/time graph by recording how far an object is from the sensor. However, this is not necessary.)

It is important to allow the class plenty of time to explore what the interactivity does, ideally using a laptop or tablet shared one between two.

After some open exploration time, bring everyone back together. Invite pairs to share any discoveries they have made so far, or anything they have noticed, or any questions they have.

If it has not already come up, you can ask what happens to the graph once Mike gets back to his house after the walk. Why is that the case? You could then display the graphs and ask the class to try to reproduce them. It may be appropriate to invite pupils to try and replicate the first graph on the interactive whiteboard so that everyone can see. Discussing the properties of this first
graph all together will help the children to continue the problem for themselves.

### Key questions

How would you describe the shape of the graph?

### Possible support

Being able to use the interactivity will mean that pupils can try out their ideas without worrying about getting it 'right' first time.

### Possible extension

Can Pat create the same graph with different walks? Can learners describe what they can change and what has to stay the same?