Best method for subtraction (or how dc are taught now)

[AmazonGrace]

There's so many different ways and I think I've totally confused ds tonight by showing him my method.

I've consulted my Maths for Mums and Dads and I have my Carol worksheet books but there's different methods.

Which one do they use the most at school?

I will be asking at parents evening in a few wks but just wanted your thoughts in the meantime.

Ds has quite a good grasp with maths but it's me trying to explain when you 'borrow' from the tens column. I think his method was probably done on a number line? We had a quick go at sums just before bed which was a bad idea as he just couldn't keep still and wasn't focused at all (bad Mum decision) but he'd asked about something else so we progressed.

Anyway, the two other methods (one of which I 'think' he also has used before) are as follows:-

32-17 (build up from the lower figure)

32-17 ('borrow from the tens column)

Do they use either at school? Ds seemed a bit borrowing from the tens.

I hate this, I feel like I damage what he's learned so far, everytime I open my mouth!

And then to confuse it even more, Maths for Mums and Dads had as follows:-

32
-17
-5
20
=15

Depends what year he's in really

Starts off with visuals

If I have 10 beads and I take away 4 how many do I have left?

Number lines work for counting on from the smaller number to the bigger number so 17-32 you count up the line

Number lines also work backwards but generally in chunks so they might do 32-2=30, -10=20, -3=17 then you add the jumps so 2+10+3=15

They do do the formal written method but rather than borrowing they take a ten from the tens column then add it to the units

Exactly the same process but the terminology is different and less confusing -if you borrow something you have to give it back don't you?

Would expect formal written (columns) to be secure at end of yr 4 ish

He's in Y3 and changed schools in March. Not sure if they would have used different methods.

Thanks for the info. We should go through things like this in the mornings where he'd be more focussed and more able to do this.

He was just trying to extend going to bed for as long as he could get away with .

So in Y3 would they still be using the number lines?

Yes number lines at this stage of yr 3 definitely

DD is Y3 and using unstructured number lines. She has also just started column addition, and I guess that there is a subtraction version as 18years has explained. It's different from the way we did it. Eg for 321 -123 they would write it out as
300 + 20 + 1
on one line and the other number similarly on the next line. There is effectively borrowing but it is called stealing, and conceptually it's a bit different because it is more explicit that a 1 from one column is becoming a 10 in the next column. It's brilliant.

Sorry, probably not much help, I only know what DD has told me!

Number line works well. Explain that you are finding the difference between the two numbers.
32 - 17

Make a line and mark 17 on the left side, then you find the difference by counting on.
The first step is a jump from 17 to the next largest 10. In this case 20. Mark +3 on the jump.
The next step is a jump of 10s in this case a single jump to 30. Mark +10 on the jump
If still not at the required number, in this case 32 see what jumps you need to make, in this case an extra jump of 2 required. Mark +2
.......+3. . +10. ...,..... . +2
1720_3032

Then you add the "jumps"
3+10+2 = 15

This method relies on a knowledge of number bonds to 10.
Ability to count on in 10s.
The curriculum now has column addition as a statutory requirement, which is introduced once the children demonstrate a good grasp of the underlying concepts.

Personally I find when teaching my dd that using the difference approach to the subtraction problems makes it easier, as they are using the number line the same way they do in addition. So re emphasizes, instead of making subtraction require a different approach.

They will move on from number lines to column subtraction and borrowing from tens once your ds has a strong enough knowledge of the number system. The problem with teaching that first us they have no comprehension of why and so can't check. I used to play a game with base ten (cubes and rods which are 1s and 10s) where they collect 10 cubes and swap it for a ten-you then reverse it to subtract which explains the borrowing concept.

Apologies if this doesn't make sense up with ds every hour so far tonight!

another aspect of primary maths is learning when to use the most appropriate method.

So number lines are good when you are jumping from numbers that are reasonably close together (e.g., 32-26: either count by ones, when they're just starting, or jump from 26 to 30, and then 30 to 32).

If the two numbers end with the same (or near) digits, then counting up by tens/ones is easy (e.g., 57-37 or 58-37) without having to go to the nearest 10 and bridge through that - instead, they can add whole tens until they get near the target number.

If the number being taken away is relatively small, then counting backwards (or jumping backwards): so 32-4, easiest just to count back; 32-14, easiest to take away 10, then take away 4.

They also learn to look for patterns: so 32-2 is easy if they understand the tens/units system; so is 32-12, etc. Taking away 10 or 20 etc can also be done similarly, as can numbers near 10, 20, etc. (e.g., to take away 9, take 10 and add 1 back; to take 11, take away 10 and then 1 more).

All these sorts of methods should be reasonably automatic and used in appropriate places before column subtraction is started, because they show understanding of the underlying process. Being able to choose which is most suitable for a given question demonstrates an appreciation for the size of the numbers and a feel for what subtraction is actually doing and what kind of answer might be expected, which is more useful than a method where they just learn to 'do something' on paper.

After that, by all means a paper method of columns and borrowing is good. I find money often useful for starting with the concept of borrowing, as many children realise that 10p = 10 pennies, and can understand that if you wanted to give someone 17p and you had 32p made up of three ten-pence pieces and two pennies, that you'd have to change one of the ten-pence pieces into pennies in order to do it.

Thank you all

I'll come back to this later. Will go through the methods DSL uses.

DS not DSL!

Does you child's school have a calculation policy? If so, it should be laid out in that. If not maybe ask school how the methods progress.

Children are not taught just one way. We use physical objects, number tracks, number lines, hundred squares, bead strings, breaking into tens and units (e.g. 34 + 52 = 30+50, then 4+2, then 80+6), basic columns with numbers that don't cross a boundary (e.g. 26 + 41, or 89 - 36), then carefully teach how to do calculations that need the units changing. We expect children to sometimes do the same calculation in two methods to double check their answer.

If you child has just started column addition and subtraction I don't suggest crossing the tens boundary for a while, so no borrowing or decomposition.

I think the first thing I need to do is to ask his teacher at parents evening and go from there. I love that ds wants to learn but then feel like I let him down by not knowing how he's been taught and then probably totally confusing him in the process, which is counter productive.

But thank you all for your responses.

I think it would be helpful if schools used the convenience of their web pages to offer the formula which they use, surely they use the same methods to teach each year group, even though each child maybe at dfferent levels.

hijacks thread - does anybody know when they use the column method and "borrow" they do it by making the top number smaller rather than the bottom number bigger. Think of doing 1000-364

AmazonGrace:

Not sure if this is your situation - but counting back/ up & number lines never really worked for DD1 - so we worked with actual objects.

It's very old fashioned - but with DD1 who just didn't get subtraction at all - we used foodstuffs: grapes/ raisings/ baked beans/ peas/ smarties/ M&Ms/ chocolate buttons/ etc...

With numbers >10 - because of the skill involved in borrowing it helps to use similar objects: Duplo & lego bricks: Duplo = 10 / lego = 1 or Grapes = 10 and raisins = 1. (we tried to make the objects related - but the tens were bigger than the ones or 'units').

So then you can try something challenging like 15 - 7

So you have one plate with one grape and 5 raisins = 15

you want to take away 7

take away 5 raisins and set them on another plate - so that's 15 - 5 which gives you 10 (or one grape).

We're out of raisins and can't take all 7 so we'll need to cash in our grape for 10 raisins so we can take the last 2 raisins away:

10 raisins take away 2 raisins leaves you with - 8 raisins on the answer plate and 7 raisins on the 'take away plate' (showing you what you took away).

Again - we played with objects for a bit and then gradually introduced paper & pen/ pencil & did the sum on paper to reinforce the work with objects.

HTH

Thanks PSBD, that's a useful exercise to help ds to 'see' how it works. Will try this too

My dd is in y3 and I think the method she is taught is similar to mine but is actually better explained IYSWIM. So in y2 they were taught to partition numbers e.g. 379 would be broken down into 300 + 70 + 9. In y3 they are taught to subtract in a similar way i.e. your 32 - 17 becomes 32 - 10 (= 22) - 7 = 15. It makes you realise why learning the number bonds was so important. Dh's way of adding or subtracting numbers involves rounding numbers either up or down to the nearest ten and then subtracting or adding the difference e.g. 13 + 18 becomes 13 + 20 - 2 which completely confused dd! I think maybe children need to be a bit older before they understand that there is more than one way of getting the right answer.

There seems to be great emphasis at dd's school at the moment on mental arithmetic although according to the booklet we were given from school they will eventually move onto written calculations using columns etc. when the basics and understanding of the principles are rock solid.

I gather little information from ds once he leaves school, he has however told me that they are 'playing' regular games with regards to times tables, he's had symmetry work and he had to halve three digit numbers last week i.e. 570 but it's the methods in which he's taught where there's this barrier between the two of us, he's obviously been taught a completely different way to me (dinosaur - left school in '86).

I'm hoping we will be given lots of information at parents evening.

Some examples of calculations policies that you may find useful:
Southwark
Staffs

AsBright, thank you so much for the link, I've added it to my 'reading list' but had a quick look at Y3 subtraction and it makes much more sense.

I never answer your earlier question either re school calculation policy? Tbh I've never heard of this before so no idea if ds school has one or not. I wish they had a link to something sites such as the one you posted.

Excuse typos! Multi-tasking