I’ve long been at pains to try and hammer into my Y13s the importance of diagrams (see this and this). The amount of times I’ve told them I won’t help them until they’ve sketched the problem is ridiculous. One thing they struggle a bit with is finding the range of a function from an equation. They can easily do it from diagrams and have not yet realised that they can sketch them themselves!
Today, however, two of them were working together and they were trying to find the range of f(x) = 2lxl + 3. They were talking about it and struggling to solve it. I pointed out that neither of them had sketched it yet. They sketched it. They got it.
Both of them saw instantly that the range was in fact f (x) is greater than or equal to 3. Then one of them said “these are really easy if you sketch them, but really hard when you just look at the equation.” It’s finally starting to sink in….
Cross-posted on Cavmaths here.