Representing even numbers

In the past few weeks I have been exploring times tables. We roll them off parrot fashion:

1 x 4 = 4
2 x 4 = 8
3 x 4 = 12

and so on, but these black symbols are hard to learn. After exploring the Slavonic abacus I wondered if there was another way of experiencing them; actually viewing them as tangible, physical products rather than marks on the page.

My explorations started with the four times table and my attempt to express it pictorially resulted in a trip to Foyles where I bought a copy of the 'Geometrix Colouring Book' by Jennifer Lynn Bishop - a bit of a gem. I  was immediately drawn to the Mandala design on the front cover which shows a series of squares, growing ever larger and overlaid on top of each other. To me a square perfectly represents 4 (it has 4 corners) and therefore two squares, one inside the other represent 8, and so on. My rather crude attempt to represent the 4 times table is shown below (sorry the pencils weren't up to it). In a corner of each of the squares I've shown the  number of times 4 has been multiplied and in the opposite corner I've shown the product. In fact I could probably have got away without showing the product as the square grows by one 'layer' each time, for example 2 x 4 is represented by a square with two layers, 3 x 4 with three layers, and so on. Each square is coloured in shades of red which to me captures what 4 looks like to me (synaesthetically).

A second bit of colouring took me on another journey though I'm not sure what to make of this picture or really whether this line of enquiry is worth following, but I thought I'd share it anyway. This time I arranged the products of the 2, 4, 6 and 8 times tables in a grid. Each coloured square represents 'one', for example '10' is shown as 10 yellow squares split into two lots of five, arranged in a right angle. Alongside the 2 x table square, the products of the 4, 6 and 8 times tables are shown where they overlap with the 2 times table. Naturally, each band shows at wider intervals, the bigger the number. Each number has been coloured the way I see it synaesthetically. I don't think this really worked - it looks confusing close up but somehow it's strangely pleasing at a distance!

And finally a bit of fun... Part of the four times table crudely drawn by me in paintbox. The products of 4, along with the colours they represent, are shown in the bottom left hand corner.