For all the rich maths tasks and probing questions in this series, and for the pedagogy behind the concept, please visit the Probing Maths Questions Index page.

For my 3rd probing maths questions activity, I have decided to indulge my romantic side. Yes, as the November night’s draw in, and the temperatures start to drop, let’s try to warm all our insides with the tale of Romeo and Juliet in “Will they Meet?”…

I must confess, I am not entirely sure of the origins of this task. I have been using it for the last few years under a different guise, and only recently decided to put a romantic spin on it. Maybe it is because I recently got married!

Romeo and Juliet have had a row (probably Romeo’s fault), and as a result, Juliet has gone off in a huff. Romeo is desperate to catch-up to her to resolve the situation. But every time Romeo moves, Juliet moves in the same direction, but half as far (as she is only little). So, if Romeo moves 6 squares to the right, at the same time Juliet will move 3 squares to the right.

I have summarised the rules here:

So the first question is: can you help Romeo and Juliet get back together?

But, far more importantly, what other questions, suggestions, modifications can you think of to ask your students to investigate? Remember, they can be on absolutely anything. Work within the parameter of the original task, or change the rules completely. They can be questions that take 30 seconds to solve, or one which you do not know the answer to yourself.

Here are a couple to get you going:

• Can Romeo always catch up to Juliet? How do you know?
• Can they ever meet in more than one place?
• If you know where they meet and where Romeo starts, can you work out where Juliet starts?
• What if Romeo moved 3 times as far as Juliet? Will they always meet then?

And if you could help me spread the word about this, I would really appreciate it. I really want to help build a series of tasks with interesting, engaging, unusual questions that will engage and challenge students of all ages and abilities. Any help in my quest would be greatly appreciated 🙂