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Understanding equals

As adults, we generally understand equals. It's easy to think most of the children understand it too. They know that when they see 246 + 7 = then they need to work out what 246 + 7 is. They know that when they see 327 - 5 = they need to work out what 327 - 5 is. And so on.

We see this in our lessons, in their books, on their whiteboards. All over the place really. If I said to you right now, prove to me that your class understand equals, no doubt (even this early in the year), you'd be able to find lots of bits of evidence to show me that they do.


So, what's the issue? They get it don't they?

Probably not. Unless it's been taught really well lower down and backed up since, they probably don't understand it. Next time you teach a maths lesson, show your class three statements:

346 = 300 + 40 + 6

300 + 40 + 6 = 346

300 + 40 + 6 = 300 + 46

Ask them if they are all correct and if not, which one is wrong and why. If they say that they are all correct then you're good to go. There's a high chance they really do understand equality (which is fantastic and you should definitely go and thank their previous teachers for saving you a job).

If they don't (and my experience suggests that they won't), they will probably tell you that the 300 + 40 + 6 = 300 + 46 is wrong because there needs to be an answer. These children don't understand equality. They think our beloved equals sign means 'work out this calculation and then write the answer'. It doesn't. It means it is equal. However, you can't just tell them that they are wrong and not explain why because they'll just continue with this massive (and very common) misconception.

If you have access to balance scales and Numicon then this is your chance to crack it out (Year 6 teachers, this includes you). Stick an equals sign in the middle of the balance scales and tell the class that equals means it balances. Pop a ten piece into one side and another ten into the other. Wait for the scales to settle and ask the class if they balance. They do because they are equal. Repeat with a different piece. When the class seem confident in this, we can introduce the idea that when we put 10 into one side and 6 and 4 into the other, they will also balance because they are equal and then do the same with maybe a 6 and 4 in one side and a 3 and 7 in the other. Numicon is great for this because it is weighted but if you don't have access to any (first convince the person with control over the purse strings to get you some) then you can use anything else with equal weights (including weights with numbers stuck onto them).

If you're feeling really adventurous, you could take your class to wherever your local see-saw is and balance some of them on it (just remember to properly risk assess it and fill in all that delightful paperwork that comes with taking children off school grounds).


Understanding equals is really important for children as it helps them with a lot of their maths - including setting them up better for learning algebra - if you don't understand what that little symbol means, how do you stand a chance of understanding what is being expected of you when you see 'a + 7 = 6 + 5. What is a?'


Just be aware that equals doesn't mean it's the same - 6 and 4 are equal to 10 but they definitely aren't the same. And for lots of the children we teach, that ten piece we used might look the same as the other ten piece we balanced it against, but it isn't the same. It is equal. Equal is not the same, it is the balance. If this doesn't make sense, think of it in terms of money - 5 pound coins are equal to a £5 note but they're not the same thing.


TLDR: your class probably don't understand equals. Teach it as balance to help them understand. Remember, equals does not mean the same or the answer, it means that both sides are balanced.

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