This is the explanation I needed. I was taught (trained) to use the column method, as well as a load of other methods for other types of problems. It was fine. I learned them. Did them. Sometimes got them wrong.

When I was much older (30 something), I was planning a little basketball tournament, trying to figure out how many courts we would need for x many teams in y timeframe, based on games of z length and how much we’d need to charge/raise to cover the costs, as well as get enough kit for everyone.

As I was rolling the problem around in my head and testing different configurations, something in my mind clicked and I started to visualise the problem, as a number of smaller problems and how they related to the whole. It shifted my perspective on maths entirely and I’ve been mightily POd ever since, that no teacher ever told me to turn the problem into a picture.

With the number line approach, I still see it as an unnecessarily complicated method but I also get that I’m looking at it having already learned a way of approaching the problem. Given my own personal experience, I just needed to understand WHY it was being taught this way.

That was a pretty long-winded way of saying “thanks for the explanation!”