St Thomas of Canterbury, 18 October 2019

We did some perplexing things with paperclips and rubber bands this week. I showed the children how to bend a long strip of paper into an ‘s’ shape, then squash it together and add two paperclips at the two places where the paper touches. When I pulled on each end of the paper the children were surprised to see the two paperclips land on the table linked together.

The children then followed a set of drawings I had made, each one getting progressively harder and involving adding in one rubber band, then two rubber bands, then changing the positions of the bands along the strip of paper. The results were a combination of the paperclips and rubber bands being linked together in lots of different ways, some falling off the paper and some staying on. Some children made it to drawing 10, which results in an amazing Borromean link!

If you want to see how the paperclips become linked together, here is a slow motion video:

This is what the table looked like at the end! Lots of mess and lots of fun.

Table after Perplexing Paperclips 18 October 2019

St Thomas of Canterbury, 11 October 2019

An investigation of that classic problem in topology, the Three Utilities Problem. The children made their first attempt in flat, two-dimensional space i.e. on a mini whiteboard, so they could rub out their attempts and keep trying. After a few minutes I explained that the problem cannot be solved in two-dimensional space as there is not enough space! I asked the children what we could do in this case, and one boy was very quick to suggest trying it in three-dimensional space.

I produced four big tori, in the form of an inflated swim ring which I had wrapped in white duck tape and labelled, so that the dry wipe markers could be used and rubbed off as needed. After a few attempts, and some hints from me that they needed to use the whole length and circumference of the torus, we had some correct solutions.

three utilities

I then reminded the children that a torus is topologically equivalent to a coffee mug, and that if they could solve this problem on a torus they could also solve it on a mug. I then produced four white mugs which I had labelled. The dry wipe markers rub off very easily on a mug. The children spent the rest of the session exploring how to solve the problem. They needed a few hints about using the handle and the base, and going under the handle, but most of them got there in the end. The children seemed to really enjoying solving the problem using such unusual materials.

three utilities mug

St Thomas of Canterbury, 4 October 2019

We explored the Mobius loop in this week’s Curious Minds Club. The children made a straight loop and drew lines around the centre of the paper strip on the inside and the outside to prove the loop has two faces. They did the same along the edges to prove the loop has two edges. I showed they how to introduce a half twist, and how this changes the property of the new Mobius loop to only having one face and one edge.

The children cut the Mobius loop along its centre line to show that it does not fall into two pieces as expected, but becomes a loop with four half twists. I asked the children to predict what would happen if they cut a Mobius loop one third of the way in: some predicted two loops, and some predicted one twisted loop. They made the cut and were surprised to make two connected loops, one Mobius and one non-Mobius.

The next experiment was to connect together two straight Mobius loops. No one predicted that the result would be a square. Our final experiment was to connect together two Mobius loops of opposite chirality, one with a right half twist and one with a left half twist. The delightful result was two interconnected hearts!

St Thomas of Canterbury, 27 September 2019

Another activity to demonstrate that topology includes changing an object’s shape without changing its size. I challenged the children to see if they could fit their body through a piece of A4 card. They looked baffled. I asked them what tools they could use. They correctly offered cutting and folding. I showed them this method, which uses one fold and lots of alternate cuts. There were a few false starts but all the children did manage to complete the task, much to their satisfaction. I then challenged them to fit their body through a postcard, using the same method but this time making narrower cuts. Despite their scepticism the children were able to complete this task (with a bit of help at times). The ultimate challenge was to fit their body through the paper equivalent of a bank card. This was really tricky as the cuts have to be so narrow they are prone to snapping. We did have several successes, all showing a lot of persistence. We all had lots of fun exploring the topology of a piece of card.

St Thomas of Canterbury, 20 September 2019

A continuation of our exploration of topology. An explanation of the rules of deformation (no new holes, no filling in holes, no gluing, no tearing), followed by getting out the modelling clay and deforming a torus (or doughnut) into a coffee mug. An extension of this by deforming a two-hole torus into a pair of pants, and a three-hole torus into a vest (after explaining why a vest has three holes).

A new activity to demonstrate that topology includes changing an object’s shape without changing its size. Cutting a hole the size of a 5p in a piece of paper, trying to pass a 2p through this hole, finding this is impossible in 2D space, switching to 3D space by lifting up the piece of paper and introducing height, and finding that the 2p will pass through the hole once the paper is twisted and manipulated.

St Thomas of Canterbury, 13 September 2019

The first week of my brand new Curious Minds Club!

An explanation that maths is about more then numbers and sums: it is also about shapes and space. A demonstration of the difference between the two and three dimensions of space. An introduction to topology. An exercise with a piece of rubber (cut out of a balloon) with a circle drawn on it, stretching it into different polygons. An exercise with the upper case letters of the alphabet, categorising them by their number of holes. An explanation of the difference between a hole and an opening, using a pipe cleaner, with the objects being those classical to topology – a doughnut and a coffee mug. An exercise with a bag of objects, with the children categorising them by their number of holes, either 0, 1, 2 or >2.

St Thomas of Canterbury, 12 July 2019

This was our final week at Bletchley Juniors Codebreaking Club!

After our mammoth attempt at some frequency analysis last week we took it easier this week by playing some board and card games requiring the solving of secret clues: Mastermind and Cat Crimes. We played Ghost Blitz, as it is one child’s favourite game. We played Zeus on the Loose as it features the Ancient Greek Gods and Goddesses!

I think it is important to mark the endings of things, so I invited the parents to come at the end for a short ceremony. I said thanks to: Mrs Sanderson for letting us run the club; Anna for helping me to run the club every week; the parents for their support; and the children for helping to make it so much fun. I gave out certificates of achievement to all the children, along with a spy pen, a personalised pencil and a small gift of a book to suit their interests. As I am a qualified librarian I could not help but give a recommendation for a book to build on our learning about Ancient Greece: Greek Myths by Marcia Williams.

This is the last blog post about Bletchley Juniors Codebreaking Club. What an amazing journey we went on!

Certificate of Achievement