These problems are ones that are made much clearer by drawing a rectangle to represent the “whole” and then deciding how to divide it into equal parts. The numbers are not too tricky but interpreting the question might be:

These are not intended to be fraction of an amount questions. An approach could be to decide upon an amount, but the intention is to direct students to drawing a representation of each question.

So much so that it becomes an obstacle in some cases. That may be because they need to spend more time on making a rectangle, or it may be because the rectangle isn’t actually the best approach. I have found, the more I try representations, that some make sense only if you already know the maths (I.e. The image follows the numbers, rather than the other way round).

I’ve found that, for some students, drawing a useful rectangle in the first place is quite an issue!

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So much so that it becomes an obstacle in some cases. That may be because they need to spend more time on making a rectangle, or it may be because the rectangle isn’t actually the best approach. I have found, the more I try representations, that some make sense only if you already know the maths (I.e. The image follows the numbers, rather than the other way round).

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