The best way to teach solving equations?
I think this is one of the things that maths teachers argue over the most.
There's the "move it to the other side" method, the "do it to both sides method" and (one I'd not heard of until recently) the "cover up method".
Method 1 is what I was taught and what I use myself. I knew that it was not a very good method as it does not explain why you're doing that and how it works. I defended this method forcefully, sure that my way of thinking must be the best way (I'm arrogant like that). But since teaching both methods at my placement school, and teaching different methods to my one-to-one tutees, I've come to realise that the second method is much less confusing, more intuitive, and more memorable.
Here is how I would write a model solution:
3x + 5 = 10
- 5 -5
3x = 5
3x/3 = 5/3 (written as fractions)
And then I'd cross out the two threes in the fraction on the left because they cancel each other out.
Writing the -5 underneath makes it really easy for pupils to see what they're doing and it's really hard to make a mistake.
Doing the dividing bit as fractions is good because it encourages pupils to leave things as fractions, it makes division easier (instead of actually dividing, just cancel down the fraction as far as you can in easy steps), and it means that the whole side will be divided and not just the last term.
That is the method I would recommend for higher-tier pupils.
The cover-up method is one I cam across recently and I think it's really good because it's the way a pupil would intuitively try to work out the answer.
In equations like 10 - x =7, most pupils can just "see" that the answer is 3. In equations like 3x + 4 = 10, it's harder to just seei it, but using the cover up method you can. Cover up the 3x, and say "what add 4 gives you 10?" They'll say 6. Then you uncover the 3x and say, "well then 3x must be 6. So what's one x?" And they'll say 2 (after painstakingly counting on their fingers, if they're anything like my pupils!)
I wouldn't teach higher tier pupils this because it's hard to apply it to more complicated equations (although it obviously still works). But for lower ability pupils it seems to be less confusing.
I'm glad I'm starting to realise what methods I'm going to be teaching because I want to be consistent, so that pupils don't get confused with lots of different methods.