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Why algebra tiles are the most amazing thing, like, ever

12/3/2015

 
I discovered algebra tiles last year when, in a fit of desperation, I took to the Internet to find a good way of teaching completing the square in a way that might actually get it to stick in the heads of my Year 11s. 
I'd previously completely failed and confused them all by doing it via "the formula", and was beginning to wonder if I'd ever manage to teach it properly, a problem compounded by the fact that (if I'm honest), I don't think I'd ever properly understood why it worked. 

Anyway, I found an absolute gem of a worksheet - I've just tried looking now and for the life of me I can't locate it anywhere on Google, especially as algebra tiles really seem to have taken off in the maths education world and there's a huge stack of resources out there now. Luckily I've got a copy saved - it looked like this:
Picture
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Picture
Off I trotted to the photocopier, and Year 11 spent a fairly happy hour solving completing the square problems by looking at units "left over" or "borrowed". At the end of the lesson, a quick straw poll revealed that over 3/4 of them now understood how to complete the square, and they evidenced it by completing two A* exam questions.

(As an aside to this, I had at least five or six pupils who continued to use diagrams to solve CTS all the way through the GCSE course. When a question came up on the exam paper, guess which pupils got it correct?)

Feeling quite pleased with myself, I popped back to the Internet for a bit more research and discovered that, although pretty scarce last year, algebra tiles were actually a "thing". They appeared to be more popular in America than over here. I then spent a happy evening or two laminating and cutting out to produce my own sets of algebra tiles:
Picture
A few algebra tiles from one of my sets.
In the spirit of a year of trying something new, I then decided to try and teach a load of algebra to my classes using the tiles. I taught all the algebra content up to grade B with my Year 7 top set, and for the first time I felt like the pupils really understood what they were doing, and also managed to finally convince a Year 9 that 3x wasn't the same as x³.

I then got some long-suffering TAs to make whole-class sets for our store cupboard, and although I've not got them out much this year (mastery curriculum with lower-attainers means a lot of fractions and multiplication and not much algebra - yet!), some of the rest of my department have used them and loved them.

The only thing I'm not entirely convinced on is using negative tiles. In a similar vein to the issues I had with bar modelling to solve equations with negatives, representing a negative quantity with a positive area can be a bit of a conceptual headache. For now, I'm sitting on the fence as to whether I'd continue to use the negative tiles with pupils, but the positive ones are absolutely essential for providing a concrete model for any algebra skills.

If you want to make your own, it's important to get the dimensions right. Start with a 1 x 1 tile. The x tile needs to have the same width as the 1 x 1 tile, but it's important that you can't fit an exact multiple of the 1 x 1 tile along its length - this is to stop pupils automatically assuming that x = 3 and avoid issues when factorising. The x² tile has the same length and width as the x tile (so x multiplied by x gives an area of x².
Picture
Matching up dimensions of square tile, x and unit tiles.
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Make sure that you can't fit an exact multiple of the unit tile along the x and the square!
Alternatively, if you want to grab yourself a copy of my templates and some guidance sheets, head to the Downloads section and have fun laminating! You can request a password here. For other ideas, you can check out the demonstration videos I've currently got on this YouTube playlist.

Related posts

Completing the square using algebra tiles
Solving linear equations using algebra tiles
Factorising linear expressions using algebra tiles
Bar Modelling - Reflections on Celebration of Maths 2015

Grant Gardner link
4/4/2016 19:40:46

Check out our algebra tiles, www.assessmentservices-edu.com/Algebra-tiles.aspx

spanish tiles link
14/6/2016 07:16:13

I'd continue to use the negative tiles with pupils, but the positive ones are absolutely essential for providing a concrete model for any algebra skills.


Comments are closed.

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