I wrote a while ago about teaching basic algebra to children and taking away their fear. But what do you do when it becomes a little more complicated?

When working with a pupil recently we came across this problem:

and the child was unsure how to start. I reminded her of when we had looked at ordering fractions and asked how she did that.

“I can’t do ^{3}/_{5}, ^{8}/_{10} and ^{12}/_{15},” she said “because they are all different, so I have to make them the same. I know 10÷2 is 5 so I can do 8÷2 and turn ^{8}/_{10} into ^{4}/_{5}, and I know that 15÷3 is 5, so I can 12÷3 and turn ^{12}/_{15} into ^{4}/_{5}. Then I put them into order – ^{3}/_{5, }^{4}/_{5},^{ 4}/_{5} – and then I turn them back so ^{3}/_{5} is the smallest and ^{8}/_{10} and ^{12}/_{15} are the same.”

I praised her for remembering so well and then told her this problem was just the same. It looked hard because k, m and n were all different, but maybe she could make them the same.

As soon as she started to think of the problem in that way she was able to see that m could be changed into 3n and k could be changed into 2n, so the problem was 2n + 3n + n = 1500 or 6n = 1500. Once she had worked out that this meant that n must be 250 she had no problem at all in converting 2n back to k and 3n back to m, giving the solution k=500, m=750 and n=250.

Algebra – it’s not too hard. It’s just like ordering fractions!

If you live in north Birmingham and would like to book my services as a private maths tutor, please get in touch.