Tablecloths, Triangle Numbers and Transformations

Gingham Table Cloth

On Tuesday I had a day out. The sun was shinning and Cardiff looked beautiful on a clear June day as I arrived at the University to attend a one day seminar “Enriching Mathematical Thinking” delivered by the UK Mathematics Trust

It was a day dedicated to maths, and thinking mathematically. It was great fun. We were introduced to Charlie, a man who loves tablecloths. He loves them so much, he makes them. A colourful chap, he likes to use as many different colours as he can when making his tablecloths. But he also loves symmetry – and his tablecloths must be symmetrical.

We soon dived in and began exploring the maximum number of colours he could use for each tablecloth, depending on its symmetry.  From simple beginnings (counting!) we were soon developing complex algebraic formulas to describe his tablecloths. Fortunately, those really helpful people at NRich Maths have produced a handy resource to explain Charlie’s rules and an online tool to help visualise what’s going on.

This would be a great classroom activity – its accessible to all, at its most basic its a counting exercise but extends into algebra, it involves symmetry, triangle numbers and connects them to the algebra and, as an added bonus, is a colourful task that lends itself to classroom display. You can find out more about this activity **Here**

We also had an insight into the mind of a question setter and examiner of the UK Maths Challenge. I’ll admit I have occasionally wondered how to solve some of their more fiendish problems – at least now I’ll have some idea about how to start!

The graveyard shift – after lunch on a warm day when eyelids begin to feel heavy – fell to Vinay Kathotia. No-one drifted off for a moment. In his brilliant lecture on using stories in mathematics he entertained, amused and educated throughout. We, the audience, were hanging on his every word, engaged, involved and inspired to pinch his ideas and take them back to our classrooms. I don’t think I can do him justice by summarising his presentation here, so all I shall say is remember his name and if you get the opportunity to see him, grab it.

In the years that I’ve been teaching, I’ve been on a fair few INSETs and CPD courses, some good, some less so. This was the second time I’ve attended a UKMT Teacher Meeting and I can’t recommend them highly enough. Teachers: You’ve now missed this year’s series of meetings, but keep your eyes peeled and book a place on one of next year’s UKMT Teachers Meetings, probably the best CPD you can do. <Addendum> I’m told there might still be places on some meetings this summer – see the comment below or go here:

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One Comment

  1. Posted 27/06/2013 at 11:44 am | Permalink

    There are still a few UKMT Teachers Meetings that teachers may be able to catch this summer, in Warwick, Cambridge and Liverpool. Details at

    Glad you liked Attractive Tablecloths – it is one of our favourites.

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