Equal addition as a method of subtraction

[Mackonadragos]

Is there any school in Britain that still teaches this method? I am incredibly frustrated with the so-called borrowing and decomposition method.

It gets very tedious and messy when it comes to large numbers including many zeros. Just checked Target your Maths Year 4 and 5 and both shies away from such numbers. (Try 5000 - 3786)

I am trying to teach my children (one is a very low ability when it comes to maths, one is average) and I am very frustrated that, although I know equal addition, good old reliable, mechanical tool, I am unable to teach them, as they refuse, as school never introduced it to them as viable alternative. (My average child would easily grasp it. He says he can do column subtraction unless it involves zeroes, which he cannot do.)

What is the bloody point of using a method which is not easy and simple when it comes to certain numbers (numbers with many zeroes in them).

Equal addition is simple and reliable. (Still used in my country.)

My son is in year 2 and he would either use column subtraction - which I think is the easiest algorithmic method of subtraction. So if it involved zeros he would go back to the largest non zero number borrow one give that to the neighbouring zero to make 10 then borrow one from that ten to give 9 and make the next zero 10 then repeat. from here he could quickly do the subtraction. I find students find this easiest as it's purely algorithmic. They just need to be taught how to proceed if you can't borrow from the next digit (because that digit is zero).

If he was doing it mentally he would either consider which number he'd need to add to 3786 to get 5000 (so he'd need to add 4 to make 3790 then 10 to make 3800 then 200 to get 4000 then 1000 to give 5000 giving 1214. Alternative he'd subtract a number close which was easier then add or subtract the remainder at the end. For example 5000-3800 = 1200 so 5000-3786 = 1200+14 = 1214. These methods are more likely to be useful in the long run as they can be done mentally and are quick but may not suit a student with less fluency with numbers which is why the former method might be better.

Interesting. I've never heard of it before, and google says it's used in Australia and Latin America today.

Watched the you tube, I am not sure it's simpler though, especially with big numbers. They do teach few different methods of calculation and let the children choose at my ds's school.

Here are two links, regarding the method.

www.atm.org.uk/write/MediaUploads/Journals/MT234/Non-Member/ATM-MT234-47-49.pdf

uk.sagepub.com/sites/default/files/upm-binaries/62657_Haylock.pdf

Well, I have been using it throughout my life (I'm from Eastern Europe), of course without knowing how this method is called in English.

I haven't check the sources, but they might be British teachers (or American perhaps).

I am all for number lines. I love them, I find it useful. However, the borrowing method involving many zeroes starts a long cascade of making tens and then taking away one making them nine (with loads of crossing, and ultimately making the mistake with it).

My husband, British educated, I believe, uses this method (he is not here, so I cannot test him now), but we are in our early 40s, so it might be that the younger generation is being thought the borrowing-decomposition method. I am not sure.

Perhaps someone, or many uses it without knowing the name of the method?

I meant - my husband, British, might use the equal addition method. So it might have been though in the past.

I don't think there's a huge amount of difference between equal addition and decomposition which is used more commonly - I definitely don't see an advantage of using it over decomposition. I would just brush up on decomposition yourself as it's going to be confusing for your children to be taught two different but similar methods.

It's regrouping or exchanging NOT borrowing. You never give anything back, so how can it be borrowing?
I love teaching subtraction with lots of zeroes when I do maths interventions. We use base-10 apparatus and it becomes immediately obvious to the children what they have to do as they keep exchanging through the columns.
5000 becomes (or is regrouped into) 4x1000 + 9x100 + 9x10+ 10x1
I'm 45 and the only time I've ever heard someone talk about your equal addition method was a few years ago when another Teaching Assistant mentioned it in the playground as how she did it when she was first a teacher in the late 1960s/early 1970s. She didn't call it that, though.

I really wouldn't go teaching different methods to school as you will likely confuse your children.

If you use coins and a 'bank' it is easy to teach the exchanging method.

So if you haven't go enough 10ps you take a £1 coin , go to the bank, exchange it for 10x10p and go from there. Teach it with coins and then introduce the written method alongside to show what is happening.

I don't think it helps to teach methods different from the primary. (Though in secondary it becomes more reasonable).

Yes, I know, it is not correctly named, but I was just using the most commonly used name (my children use this word, so I presume this is how they refer to it in school.) The teacher uses the name as decomposition or "borrowing and regrouping" in her hand-out.

Teacher should know better...
I second Teen's recommendation to use coins.

My less able daughter is quite good with column additions. She has no sense of numbers (it is apparent when I make her use number line, as it helps her to visualise bigger numbers). Column addition is a beautifully easy mechanical way of doing this, regardless of how big the number is.

However, when it comes to column subtraction, it involves this odd and complicated way of decomposing numbers when it comes to zeroes. (Without the zeroes it is not so bad.) In which case you have to turn it into 10 then doing the same with the previous zero only to take away 1 to turn it into 9 and so on and on.

Equal addition can even be explained easily (adding the same amount to both numbers, the difference will be the same.)

I am not a math teacher of course, and I find it very painful to try to explain it so differently from my ingrained ways.

I did that add 'ten to the top and 1 to the bottom' method at school but that was many years ago and not how my ds/Dd is being taught now

I agree that "borrowing" isn't a good word - I always use stealing. I think the suggestion upthread of using £1s, 10p, 1p coins is great. You could do £2 (200p - 27 etc). You could then do the column subtraction at the same time so when the 2 becomes a 1 you exchange one of the pounds for 10 10p coins, then exchange one 10p coin for 10 1ps - take three of them away etc.

One of the issues with algorithmic methods is that kids often have no idea why they're doing each step. I think a less numerate child is likely to find the equal subtraction method even more confusing as they have to not only understand one hundred = 10 tens but they have to understand that subtracting an extra hundred is the same as removing one hundred from the original number - it adds one more step of logic.

The way I do it:

Say you have 207 - 48
Give the child 2x£1 and 7x1p
Put them in piles in order, with space for 10ps

They have to give you 48p, and they have to give you the pennies first.
They haven't got 8 pennies to give you.
They ideally would change a 10p but haven't got any of those, so they take 1 of their £1 to the bank and ask for 10x10p.
They now only have 1x£1 but have 10x10p
Now they take a 10p to the bank and exchange it for 10x1p

So now they have 1x£1, 9x10p and now 17x1p
So they can give you 8x1p, and also are ready to give you the 4x10p
Then they can see what they have left: 9x1p, 5x10p and 1x£1
Answer = 159

Once they an do it with coins, with a running commentary out loud, model what they are doing on paper as they do it.
Then switch to on paper but checking' with the coins.
Then abandon the coins altogether.

(You can 'make' some fake £10 coins if needed too).

Yes yes yes to what Teen says, especially the running commentary bit.

Thank you for the suggestions. I will look into it more detail tmrrow, as it is getting late.

I must admit, that the way I was thought column subtraction was mechanical, and I never thought about it much. However, I can use it very reliably on paper and pencil, and I feel that my daughter will miss out on this easy mechanical way.

Figure 9.15 shows the steps involved in tackling 802 - 247 by decomposition.

An extract from the second article on page 128.
Figure 9.15(a) the person doing the calculation is faced with the problem of ‘2 subtract 7’. The decomposition method requires a ten to be exchanged for ten units, but in the 802 the zero indicates that there are no tens. This is the problem! However, it is not
difficult to see that the thing to do is to go across to the hundreds column and exchange one of these for 10 tens, as shown in Figure 9.15(b), then to take one of these tens and exchange it for ten units, as shown in Figure 9.15(c). The subtraction can then be completed, as in Figure 9.15(d). Of course, all this can be carried out and
understood easily in terms of base-ten blocks or coins, representing hundreds, tens and ones (units).

Figures on page 129, but i am unable to copy it across.

When just doing it mechanically, is it the case that you start from the left hand-side column, making 10s? (Unfortunately, the hand-out I use, just gives one example with zeroes, with the final sum, and I now realise I might not even start from the right end? As Permanent mentioned, it needs to start with "going back to the largest non zero number". Doing a bit of decomposition with the numbers before starting the actual subtraction? When all the the 10s are in place doing the "borrowing"? I think i need to talk to the teacher next week.

(One of the worst thing is when one does not even realise that she does not understand something. ohhh.)

Another example that might help (or not)

341 - 147

Start with 3x£1, 4x10p, 1x1p

First you need to give me 7x1p
You haven't got that, so take one of your 10ps to the bank and change it for 10x1p
Now you can give me the 7x1p (leaving you with 4)

next you need to give me 4x10p. You no longer have 4 of them as you exchanged one, so go to the bank change 1of your £1 to 10x10p

now you have 13x10p so you can give me 4 (leaving you with 9)

finally give me a £1 (leaving you with 1)

So (reading upwards in my explanation) you have answer 194

Thank you for everyone taking their time to answer my question.

I don't remember how I was thought and I have no recollection whether I had found it easy or difficult to learn. I always used it mechanically, and I have the suspicion that back in those days there was no explanation attached to it.

I had a look of your suggestion of using either coins or units of 100s etc. I will test my kids to see whether it makes sense to them at all, but nevertheless, I will keep it in my growing math explanation paraphernalia.