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.