Of the two Scholarship days I have been to, the most useful bits were a handful of simple but practical and resourceful ideas to be used in maths lessons. These included a 'think of a domino' trick, folding an envelope into a tetrahedron and using old train tickets to investigate number and shape.

I tried out the domino trick on a top set year 9 class to whom the traditional 'think of a number' trick fell rather flatly. It goes as follows:

'Think of any domino, multiply one of the numbers on it by 5, add 7, multiply the result by 2 and add the other number from your domino.'

From the number they end up with, which you ask for, you can amaze your pupils by telling them, with a quick calculation, which domino they had originally thought of (I'll let you figure out how for yourselves). My class were keen to understand how it worked and it acted as a good introduction to the topic of algebra.

The second idea I tried was making a tetrahedron out of an envelope. If you join the diagonals of a normal envelope and cut out the top triangle, you can fold one half into the other...low and behold a tetrahedron! An unruly middle set year 8 class enjoyed this, and kept them busy for at least 20 minutes...

Another cool idea was to make a Level 1 Menger Sponge from old train tickets. A Menger Sponge is a 3D fractal that in its limit (Level infinite) has infinite surface area and zero volume. I have seen Menger Sponges being made before, in fact I helped to make the MegaMenger at the University of Leeds a couple of years ago. But I particularly liked the idea of handing out the old train tickets and asking the class to investigate the properties of the numbers on them (perhaps as a starter) before going on to build cubes and then join 20 of them together to form a Level 1 Sponge.

I look forward to sharing ideas and resources with fellow Scholars at future Scholarship events. If I go to enough hopefully I'll collect enough train tickets to build a Menger Sponge with one of my classes.

**Jack Wood**

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