On Monday, a colleague of mine found an interesting problem (I don’t know where) and brought it over to me to take a look at. It was presented in the textbook in one of those “fake-real world type scenarios” so I thought I could do better with the context. Originally it was about finding the distance from the corner of a garden to a tap in the middle of the garden. Here it is now – it’s not exactly an “any questions?” type task because the question is obvious I think: “Will John get to the dodgeball before Sarah?”

After a brief discussion on the lack of information given within the problem, and the modelling assumptions about constant speed vs acceleration, present the students with more information to tackle the problem:

**Given that the court is a perfect rectangle, if John runs at 8 m/s and Sarah runs at 5 m/s, will John get to the dodgeball first? **

Happy Problem Solving!

Question/Extension Exploration: Can anyone solve this without the use of Pythagoras?

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Without Pythagoras (which is non-trivial to apply here), I’m wondering what you could get out of it just doing inequalities, analysis style. Sarah’s distance is less than Dan’s and more than Andrea’s…

This also makes me think about a problem with three pictures. Students in the corners, ready to run for the ball, a picture at the moment of getting the ball, then a picture of them back in the corners, ball in a new place. Who gets it this time? Is there a movie clip to use for this?

Fun context!

That’s interesting John – funnily enough I didn’t think about it that way. Indeed if Sarah’s distance is greater than 5 metres, she won’t be able to get to the ball first unless you decrease John’s speed. By changing the context, I’ve negated the need to actually calculate Sarah’s distance to the ball.

Like your idea of an animated aspect!