Daft question - how are our dc taught to do subtraction?!

[IwishIwasmoreorganised]

I can obviously do it, but have poor skills at explaining my way to ds!

He's come home with his first subtraction homework - numbers up to 100 and also a number square to use (10 rows of 10).

I'm sure that he's done some at school but tonight's quick look and ask resulted in a stroppy, "how am I supposed to know?!"

Please can some kindly soul explain how I should explain this to him. I'd be very grateful.

We're teaching 'counting on' using a number line... it's like working out change by counting up to the next sensible round number.

Draw 27_63

Then draw a 'jump' from 27 to 30... writing (+3) above the jump.

Then jump 30 to 40... writing (+10) above
40 to 50 .... (+10)
50 to 60 (+10)
60 to 63 (+3)

Then add up all the jumps. As they get confident, they do 30 to 60 in one jump of (+30).

Children seem to find this easier to start with than jumping backwards.

Hi Iwish...

I'm just a Mum - so please take this as a simmering down of the method I have arrived at after taking my two DDs through this stage in maths:

Can I start by asking does your DS have good number bonds to 10 and to 20?

Also very important that place value is somewhat understood - so 46 = 4 tens and 6 units. Does he grasp place values units, tens, hundreds?

Now if you were to ask him what + 15 = 20? - would he instantly say 5?

Basically once those number bond skills (& place value) are embedded (that he knows all ways to make 2 to 20 by adding) you can work with him to explain that he has the subtraction facts as well - so 20 - ? = 15 - it's 5.

This can be supported visually with sweets or dried fruit - and subtraction is ideal for snacking. So he eats 5 raisins to work out 20 - 5 = ?

Now the number square is important beause it helps to demonstrate the patterning:

20 - 5 = 15
30 - 5 = 25
40 - 5 = 35
50 - 5 = 40
etc...

So basically it's about extending the pattern.

It really is worth spending some time exploring the patterns on the number square - 13 - 12, 23 - 12, 33 - 12, etc. - so he can really understanding what happens and changes.

Let him count back on the square and work this out as well - patience here can be a struggle, but better he discovers the patterning than you point it out. Direct his thinking with discussion and questions - and use visual examples if he's getting stuck or help counting back on the number square or number line (ruler will do).

Some schools (ours included) like to teach subtraction over 2 digits by splitting the tens from the units (decomposition).

So for example if you have 45 - 23 (and I'm intentionally starting with problems that don't involve borrowing/ carrying):

the school would encourage thinking of it in two steps:

40 - 20 = 20
and
5 - 3 = 2

then add 20 + 2 = 22 for the answer.

Column subtraction/ addition are actually introduced after this 'decomposition' stage. (at our school at least)

I'm very fond of column subtraction, because basically you never work with numbers >19, so if you know your number bonds to 20 it's a doddle - but I can understand that the benefits of appreciating number patterns and strong metnal maths skills might outweigh speed/ simplicity of calculation.

The final step is to then teach about borrowing in subtracting (ideally carrying in addition should have been taught first).

But basically it's about explaining that if you have

43 - 29 - you have a problem, because you can't take 9 from 3 (well you can't if you want a postive answer).

So it's about borrowing 10 units from the 10s column and adding them to the units you already have.

so splitting 43 into 30 + 13

Then you can tackle the problem in two steps:

43 = (30 + 13) and - 29

split as before

30 - 20 = 10
and
13 - 9 = 4

10 + 4 = 14

This can be shown visually by using two types of sweets/ dried fruits/ buttons, etc... But basically teach him to cash in the single 10 he's borrowing for 10 units.

Finally - and this is a stage often skipped - I think it is important to close the circle of learning subtraction by teaching your DS to check his answer.

So in the case of 43 - 29 = 14 - it's important for him to know that he should add 14 + 29 and see if it = 43 (which it does). So the answer checks. This may not seem so useful now, but will be eventually.

HTH

Cor blimey! Thanks for all of that!

For "just a Mum", that's a great deal of information about the different stages of teaching subtraction!

I really cannot remember learning number bonds and place value at school, I must have done obviously!

He does have a very good grasp of those, and he doesn't seem to find addition a problem at all but I think spending more time playing with the number square might help him to grasp to patterns going on in subtraction more fully.

School could almost do with having a revision session for parents like me !

Cripes. I was a whizz at math in school back in Canada, but we do it a very different way. Well, obviously not that different, as you get the same correct answer, but the working out looks very different. The fun I shall have this year trying to help DD learn it "the right way" (but that's not what the teacher does!) is not something I'm looking forward to.

Tom Lehrer explains it brilliantly...

Ok, so it's not how they are learning it now but it is very good! And it's certainly how I do subtraction!

This is how I learnt to do subtraction. I think PastSellByDate identified it as column subtraction, but I never knew it had this name, I just called it subtraction!

Yes, that's the bit that I'm struggling with AndiMac.

I can subtract, but really am struggling to remember if we used number squares at school - that seems to be the method of choice at ds's school. I am aware that while he's doing we'll, I don't want to complicate things for him by using a different technique.