## Monday, 16 November 2015

### Why can't you simplify a + b?

Here we go, Year 7 bottom set teaching simplifying algebra, what does it mean to add together letters, or subtract letters. Why can't we write a + b as ab? Why is -2d + d equal to -d and not -3d? All of these are more I am trying to tackle. So we spent last lesson learning to translate "maths language" i.e.:

and completing activities around decoding expressions. This lesson then I started with this:

and got pupils to re-draw the picture so that all of the a arrows were together, and then the b arrows; invariably getting this picture:

We then moved on to this picture:

The interesting part of this of course being that some of the d's now move in the opposite direction, which cancel out d's above. We re-drew this to show that we don't actually need 4 d's.

We finished then with this:

which became this:

which was used to illustrate that we although it looks like we only need to go backwards, we cannot because we don't know how far backwards to go, so we have to go forward 2e before going backwards 5f.

I really like this representation of using lengths to represent variables, as it then generalises nicely into area when multiplying for example:

and then into other relationships between area and algebra.

The kids seem to be getting there with understanding, I think it will take them two or three more lessons before they are secure with approaching algebra like this, but I am convinced it will be worthwhile to start this process now in Year 7.