# Creating maths problems to solve!

September 12, 2017

#### Bernard Bagnall has been coming up with problem-solving activities for NRICH for twenty years, including the challenges that we use in our National Young Mathematicians’ Awards! Find out how he creates the maths problems to solve…

It’s been interesting reflecting on how just two of the activities for the National Young Mathematicians’ Awards came about. Much of it is about asking “I wonder what would happen if . . . ?” You too could find yourself doing something similar somewhere; it may involve shape, pattern or number.

#### Ribbon Squares

I was staying at a small hotel in Jersey that had a small swimming pool. I have never been one for sunbathing so as I basked in the shade by the side of the pool my mind wandered, as it always does, to the world of maths around me. The pool was paved around in slab, nothing really special in that. But my mind was swimming with mathematical ideas. What if two people stood on different tiles, and hold a ribbon or ribbons across the pool? What if there were more people and each can hold one or two ribbons at a time? What are the smallest and largest ribbon squares they can make?

It obviously depends on the number of tiles around the pool so I’ll fix that and explore further.

See the full problem here.

Writing this has helped me, and may help others to see some of the possible actions that can help to promote a creative mind. So next time you are on a family holiday, ask yourselves – where is the maths hiding?

#### Make Those Bracelets

I love sequences and patterns. Putting coloured cubes/beads etc. into a repeating or reflective pattern can be both enjoyable and visually pleasing. So I gave myself some time and did this in the usual straight line. I then asked myself “I wonder what would happen if the ends of the line were joined up to make a loop?”. I played with this idea for quite a long while, recording all the different arrangements. I stopped and examined the recordings and to my surprise, some were the same – it was to do with it being a loop and not just a line with two ends.

So these two could be different if treated as a line but when it comes to a loop they are the same!

This was quite a WOW moment. I wondered if I could draw the arrangements in straight lines that when put into a loop would be different? I tried. It took some perseverance and some time but there was no hurry.

See the full problem here.

These two activities are just an example of the hundreds that I’ve produced for NRICH. They nearly all involve problem-solving skills. Working on these kinds of activities means opening up your bag of knowledge and skills and try some of them on the challenge.

Some of the skills that are regularly used are working systematically, pattern spotting, reasoning logically, visualising and then generalising and proving.

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