To start, I gave the pupils a quadratic, all terms positive, and asked them to arrange the tiles into a square. Quickly they worked out that the quadratic wouldn't make a perfect square and there were tiles left over (I know that I should have started with some that were - improvement for next time). Next we looked at quadratics where they were short of tiles at the end. Pupils were happy with these types of questions after a few examples. At this point we were just playing with the tiles and we weren't writing anything down. I will do that in the next lesson.
Where we are going to have to spend more time is quadratics with a negative x term.
I'll work through an example and attempt to show you the process I went through with pupils.
I'll use the quadratic
Once pupils have the correct tiles in front of them, they should attempt to turn the tiles into a square.
At this point, my pupils told me that they didn't have enough tiles to complete the square and that the answer is
What they had failed to notice was that the empty space that's left should be filled with positive tiles.
This is the point at which they started to get confused so we did and will be doing a lot of practice here. Because I have added four positive tiles, I need to add four negative tiles so that I haven't changed the value of my quadratic. I had to explain with multiple examples here that the positive and negative tiles have been added but they make zero so have not changed the value of my quadratic overall. This is also why I've grouped them so that they look the same,
This means that my quadratic of
I'm still very early in my use of Algebra Tiles but so far the experience has been very positive and the pupils are coming round to them more. If anyone reading this is more confident with using the tiles and has a better method for using them for this purpose I'd love to hear about it. I'm very keen to use them better and more effectively.
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