I’m baffled by subtraction methods – help!
Every generation seems to have its way of working out subtraction (or taking away). You might want to help your child with their maths but be completely baffled by the subtraction method they’re trying to use. So, do you teach them how you were taught at school so that you understand what you’re teaching them, or do you learn the method they’re trying to use?
There’s no right answer. On the one hand, subtraction is subtraction, and the best strategy is usually the best way for whoever is attempting to solve it – so there are many useful methods. But, on the other hand, if your child is learning a standard practice at school, you might make life more confusing for them by mixing up different ways.
Why so many different methods?
So let’s take you through the structure of standard methods, link you to videos that will help you to learn/teach it at any stage, and make sure you’ve got some hair left after helping your child out!
First, you’ll be thinking about how many digits (0 – 9) you’re dealing with: 2, 3, or 4. Usually, it’s going to be easier to solve 2-digit subtractions. 38 – 24 is easier than 384 – 242, after all.
But what about 38 – 19? Is that easier or harder than 384 – 242? Well, it depends on which method you’re using. 38 – 19 might be seen as more difficult if you’re doing it as a column subtraction (old-skool way of doing it)
| 38 |
| -19 |
But it is a doddle if you’re using a number line (you might end up working it out by counting on it!).
That’s the thing about arithmetic methods – part of the skill is knowing which is the most efficient way of doing the calculation – working it out in your head, jotting down some notes or drawings, or using a more formal method. And that’s why it’s handy to know many different strategies, so you’ve got them in hand to choose the best one for your calculation.
Knowing many different methods also means you’ve much more fluency in handling numbers so that when you and your child are dealing with more complex numbers and problems, your fluency in basic arithmetic isn’t going to hold you back – you’ll know it by heart. It’s a bit like being able to remember a times-table fact instantly.
In the beginning, so many different methods might be confusing, and you might be tempted to stick with a couple. That’s understandable, but you’re probably making future learning more difficult in the long run. So ensuring you’ve got the methods solidly understood and practiced is a good idea.
They’re the same other than the words used – if your child’s school teaches that the 8 in 38 is a ‘unit,’ you’ll need the video ‘using digits’; if it teaches that the eight is in the ‘ones,’ column, you’ll need the video ‘using values. It’s handy for your child to know there are two ways of describing the column, but you don’t need to use both – pick one form of words and stick with it. Most English schools use ‘values.’
Number line methods are a brilliantly visual way of working out arithmetic problems. This is probably how you naturally work out issues in your head if you’re doing a measuring job at home. It’s tempting to think that number lines are the ‘easy’ way and you move onto column methods when you’re ‘good at it, but actually, it’s all about whichever is most appropriate for the numbers, like in the 38-19 problem earlier.
A number line can be ‘open’ – without any numbers written on it, or ‘marked’ with some or all of the numbers written on already. And children can put their marks on a number line to help them make sense of the jumps.
Using a number line in a subtraction like 43 – 38, you can count backward from 43. Or you can count forwards from 38. Either way, you’re finding the ‘difference’ between the two numbers; sometimes, one will be more efficient than the other.
Now have a nice cup of tea
Now you can have a cuppa before we get onto the next bit. Maybe a nice biscuit to get your sugar level back up. But come back again; this is where it gets really exciting!
The exciting bit – exchanging
So we’ve covered subtracting 2-, 3- and 4-digit numbers without exchanging (borrowing), but life’s never as easy as that. Let’s take a 3-digit example,
| HTU |
| 438 |
| – 169 |
