I can certainly say you're right in your hypothesis about how syllabi work: there are quite a lot of pre-requisite relationships, but those certainly do not determine everything about the order in which things are presented. You might find it interesting to look at as many syllabi as you can find for examples of different orders, to get a feel for what's uaully done. Another thing to watch out for is that, even when concept X doesn't actually require concept Y, if you're looking at material where Y is taught before X, you may find that X is introduced making use of Y as part of an example, so if you're doing things out of order you have to be alert to that and ready to substitute. (I'm encountering a case of this with DS at the moment in fact; he's doing something which is traditionally considered advanced although it's easy, and I'm having to adjust the material I give him a bit.)

Percentages are just hundredths, yes, but the typical school percentage problem is conceptually harder than the typical school fraction problem because it includes difficulties about what should be done with the fractions. E.g. "after a discount of whatever% the price of the article is whatever - find the original price". The challenge there isn't the manipulation of the fractions, it's the understanding of the world to get to the sum. DS found that hard for a little while, mostly I think because of lack of shopping experience! He got there, but he certainly wouldn't have been ready when he first learned fractions. (I think if I had introduced such problems then, he'd have ended up learning how to do the problem types by rote, which I'm sure is what many children do, but it's surely less good for mathematical development than encountering them at a point where numeracy is ingrained enough that you can confidently solve from first principles.)

I don't think there's any harm (rather the reverse, actually) in meeting things you can't yet understand because you haven't got a prerequisite, but OTOH there probably is harm in having a frustrated parent trying to get you to understand! I tend to offer lots of choices and go on the basis that if it's his choice to work on something it must be OK for him. But I have an easy situation (in maths!); he's very mathy, I'm very mathy, it's easy to keep it fun. Not sure what you should do. Maybe stick to the standard syllabus order for "work" but make lots of recreational maths available, and be prepared to skip lightly over things you encounter in the syllabus if they've already been learned as recreation?


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