Subtraction - major confusion

[Bitlost]

My Y2 DD is learning subtractions.

In the past, to calculate say 25-12, she'd write:
25-12=
20+5-10-2=
10+3=
13

I don't like it but at least it's correct.

Today the teacher corrected her homework and wrote:
25-12=
20+5-10+2

To me, the method given by the teacher today is wrong without the use of parenthesis, which I don't expect kids to know in y2 by the way. Using this new method, DD will rightly arrive to 17 as she will add 5 and 2 but it's of course the wrong answer to the initial question.

Which method do your kids use?

Thank you.

I don't understand your first version tbh! But the second looks similar to the partition-ing that my DD used to do, they learn the 2, 5 and 10 times tables first and are taught to split the numbers that way. Didn't make much sense to me and they did number lines rather than write them out that way, so possibly not much help!

I can't see how your dd gets to 10+3 in the first example if that's the way it's written, but I agree the second method looks plain wrong to me.

Have the school done a session/document on how maths is being taught at the school?

I don't know how she gets to 10+3 either but she consistently gets her subtractions right with this method. Guess it's become a bit of a black box method for her. It's not doing much for her feel of numbers though.

The school hasn't provided a model, sadly. I will have to go and ask for clarification.

Thank you.

I think the 10+3 is partitioning again - splitting the 10 from the 3. Splits the 25 into tens and fives (25) minus 10 (15) minus 2 (13).

DD's school had a maths evening. I was shocked how much it had changed!

It makes sense, you can rearrange the equation. Essentially they are teaching the addition/subtraction of the tens column and then the units column.
25 - 12 =
20 + 5 - 10 - 2 =
(20-10) + (5-2) =
10 + 3 = 13

Personally I disagree with these new 'teaching methods'. I have to reteach my DS so much nonsense he learns at school because it really holds him back. Looking back I wish I could have home schooled.

I understand both recording methods as 'ways of thinking'.

The first is 'I know 25 is 20+5, and I have written this down. To take away the 12 I am going to take the 10 away (and I do this from the tens), and I know that this will leave the 2 so I will subtract that next, and I do it from the units.' The partitioning of the 12 is implicit rather than explicit.

The second makes the partitioning of both numbers explicit 'I know that 25 is 20 + 5, and I know that 12 is 10 plus 2. So I partition both, and then implicitly subtract the tens and units separately.

The methods of recording differ in what is made explicit (written down) and what is implicit (assumed by the person calculating).

What you need to understand from the school is their calculation policy - this should be published, AFAIK, or certainly available from the school. There are assorted different ways of recording such a calculation - the last version you have given lends itself to a conversion to the expanded column method:

20 + 5

• 10 + 2

= 10 + 3 = 13 so that might be why they favour it. Depending on the school i have taught in, I might suggest that a child does this by a number line counting down (first the 10, then the 2, from an unpartitioned 25) or by counting up from the 12 to find the difference to get to 25. So it really does depend what the school has decided that their calculation progression should look like.

www.khanacademy.org/math/arithmetic/addition-subtraction

OMG I thought 'partitioning' and 'counting on' were cobblers... what are the poor kids supposed to make of yet another way of inventing the wheel?

So glad my dd has done with school now.

By the way Bitlost, I can see how your dd got to 10+3 in her original answer. She's tackled the Tens and Units separately. 20-10=10, and 5-2=3, therefore the answer is 10+3=13. Fairly logical, but rather long-winded, and the answer was right.

Wouldn't have worked so well if it had been 23-15 because she'd have done 20-10=10, and 3-5=.....er minus2??? Have they done negatives yet?

The teacher's so-called correction isn't really laid out in the right way. What they meant was (20+5) - (10+3) which would be technically correct but confusing for the children at this age, since they probably haven't started learning about brackets used in this way yet.

Dodo, just as a matter of interest -how do you mentally subtract, say 52 from 93 rapidly? And how do you calculate mentally when finding change for say £2.63 from £10?

As an adult, I use mental partitioning (90 - 50 = 40, 3 - 2 = 1, answer 41) to solve the first, and the classic 'counting up' method for change (£2.63 + 7 p = £2.70, add 30p, that's £3, add £7, that's £10, total change should be £7.37). Teaching young children to do this 'in writing' makes this process explicit, so they can then apply it mentally. It's not meant to be a 'long term written method', but a way of 'recording thinking' that will become mental arithmetic.

[I will confess to having a particular act I do in front of my classes for 'this is making my thinking visible to you because you can't read my mind, and you need to write your thinking down because I can't quite read all of your minds yet' when teaching this kind of thing]

Thank you all. I do understand the first method - I'm just surprised at how my daughter makes the jump from line 2 to 3. Maybe I underestimate her.

And, teacherwith2kids, I agree that it could be a first step towards the expanded column method which I've just discovered (thank you!) and do like. It's just that 25-12 is not equal to 20+5-10+2. It just isn't. It is equal to 20+5-(10+2) for example but not what the teacher suggests. Perhaps it's a necessary evil to get them to the expanded column method.

Anyhow, sounds like I need the maths policy!

Thank you all!

Buitlost, if I was your DD's teacher I'd have laid it out in the expanded column format, tbh - I agree that the horizontal layout is ambiguous and could lead to confusion. But I can sort of see where it's going IYSWIM?

How would your DD lay out 25 - 17, by the way?

(Interested!)

Hi there, very good point. She can't do subtractions if the units of the number you are taking away are bigger than the units of the number you're taking away from. Not yet.

And yes, I now see where this might be heading.

Thank you.

5+2=7 though so it doesn't make as much sense when set out like that

Year 6 son came home today and announced that his school will be reverting from number line subtraction to stacked with borrowing. They spent a whole math lesson on this. His teacher said with the 'new' SATs students need to perform their computations more quickly thus the reason for the change back to traditional arithmetic subtraction.

In my view, they've made some huge mistakes in my catchment using the new arithmetic methods, particularly with number line division, which is why if you go in into one of the higher Year 11 sets they are reteaching division to students who can solve quadratic equations.

t2k How would I take 52 from 93 quickly using mental arithmetic?

I'd round it up and make it 53, deduct from 93 = 40, add back 1 = 41

Spent £2.63 and change due from a tenner? As a customer I'd do:
£10.00 - 2.50 = 7.50 - 0.10 - 0.03 = £7.37
The shopkeeper would use the 'counting up' method as you did, or rely on the till to do it for them...

Mental arithmetic comes fairly easily to me now and I use some funny short-cuts, as I used to be a cashier in a bank in the days before chip-and-pin and computerised tills on the counters.

Must confess I am very cynical abut the way maths is now taught in schools; ever since I was told off by a teacher for showing my then Y2 dd vertical addition (which she understood straight away) instead of counting on a number line, because she kept losing her place on that, getting the answer wrong - not from lack of understanding the concept but at home we were working into the tens of thousands and a number line that long is a bloody pain!

Dodo, as the parent of a child who could add and subtract both 3 digit numbers and negative numbers mentally aged 4-5, i do feel your pain on that one.

We have always called it 'a tool box' and collect 'mthods' to put into it. Some are very specialist 'watchmaker's screwdrivers', others all-purpose sledgehammers that lack finesse. Having several of them and selecting them intelligently is, in my book both as a parent and a teacher, good. But the ultimate aim of efficient, rapid calculation mentally and on paper, based on the precise numbers in question, needs to be borne in mind throughout

That's it t2k - each one of us has a 'method' that suits us better than another, and the one thing that confused my dd was being shown several different methods to achieve the same result and then not being able to decide which method to use at any given time (then panicking in case she got the answer wrong).

This from a child who taught herself to tell the time aged 3 by constantly asking what time it was. One day she stopped asking and started telling me instead!

After the Y2 telling-off I had, we stopped playing with numbers at home, and I let them get on with it. One of the worst decisions I ever made.

But different methods are better suited to different calculations. And while some children will work out mental arithmetic methods for themselves others will have to be taught them. How are you going to know what method suits you best if you don't know what the methods are.

The second question doesn't work because either the teacher of the OP had a + where there should have been a - i.e it should be 20+5-10-2. Although personally 25-10-2 is better IMO.

Jotting it down is really just a stepping stone to being able to carry out the calculation mentally.

Being taught different methods is better for children because it increases their understanding overall and the new methods do improve mental maths. However, the decision by many schools to NOT teach stacked borrowing by year 5 is detrimental particularly to the students who are a little slower and messy.

The word problems are more complicated and have multiple steps by the end of KS2.

To add even more to the confusion, my dd was initially taught by counting up (is it called 'chunking') so she would say, to get from 12 to 20 you need 8, to get from 20 to 25 you need 5 so 8 + 5 = 13.

Now she's in Y4 they've started using columns but I think they're still encouraged to calculate mentally if possible.

Its so confusing, the partitioning makes it looks harder but on the other hand I dont know why and how I could do it and how/why my daughter could do it either. I have to admit that I didnt really pay any attention to her learning until nearly end of year 1. She although is very strong at mental maths, similar to teachers'kids she can do 3numbers add/subtract in her head from 4-5yrs old. Beg of this year we were tokd that she is losing her points because she couldnt explain her result or not following the teacher's way to solve the problems even sge always got all 100%. I now try to ask her to explain to me why she came up with the answer but its quite frustrating for her. We have a small game over the table during weekend's breakfast last Sunday among us(parents and her). I asked them what multiply to 29 equals to 1073 and she got the right answer faster than her dad. We asked her why she came to the answer but she couldnt explain it clearly. Its one of the area we need to work on this year for sure

That's interesting, Greenleave. My ds always had problem showing working out on the paper, but was able to tell me how he did it orally, although the way he did it was sometimes completely mystery to me.