Thoughts on why kids struggle to understand fractions and proportion


Division (mathematics)

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I’m at the very beginning of my teaching career. Amongst the day-to-day business of teaching, whilst on my PGCE I spent quite a lot of time thinking about how to break down mathematical ideas into key concepts that the kids could understand and thought about how best to communicate them. I found this time valuable and illuminating as it challenged my own deep understanding of concepts that I’d taken for granted. The area of maths that I have so far found most interesting to think through in this way has been proportion and the link with fractions.

Why do so many kids really struggle to understand the idea of proportion and also how you can represent it as a fraction? I’m not sure for certain but I think one explanation is that they don’t understand division. Read more of this post

Making 100


Pupils write out the digits 1 to 10 like this:

1   2   3   4   5   6   7   8   9   10

The aim is to create an expression that equals 100 by putting as many + – X and / signs between the digits as they like. You might like to demo one like this:

1    2   3 + 4   5   6  X 7 / 8 – 9 = 123 + 456 X 7 / 8 – 9 = 513

Obviously this one is too high but it does illustrate the method. You can decide whether the pupils must use BODMAS or not (I’d suggest they do!) and whether they are allowed to put brackets in as well.

There are many solutions and you might like to post them in the comments section below when you find them!

Thanks to Cat for this engaging little starter. It might make a brilliant homework too!

Have fun!

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