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!
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Algebra is a scary word. I know because it scared me when I was younger. I hated maths at school. I didn’t understand it, I didn’t want to understand it and I have no idea how I managed to get my maths O’level! It’s only since deciding, later in life, that I wanted to become a teacher that I have relearned maths and, thanks to family and this brilliant book by Derek Haylock, discovered that it doesn’t have to be hard.
I can remember sitting in lessons, struggling with numbers and then being horrified when suddenly we had letters thrown in as well. That didn’t make sense – letters belonged in English lessons, not maths.
Given all that, I can understand why children panic when it comes to algebra. The best way I have found to reassure them is to tell them it’s just a box.
5 + n = 7 looks impossible to some children, so we take the letter away and replace it with a box.
5 + □ = 7 is the sort of thing they’ve been used to since KS1.
Once they are happy with this it’s only a small step to coping with 5n = 20. They agree that writing 5 x n = 20 would be confusing because it looks like two letters, but it’s still algebra so it’s still just a box, so they just add in the x themselves. So now we have:
5 x □ = 20 . Simple!
I’ve had children go from tears and tantrums to smiles of delight in about 10 minutes, as they ask “Is that it?” From then on if you ask them if algebra is difficult they’ll smile at you and say, “No. It’s just a box.”