How do schools teach subtraction now?

[Runoutofideas]

DD (yr1) came home from school yesterday saying that they'd been doing "hard takeways" and could I write some down for her to do some more. Wanting to encourage this sudden keenness I wrote a couple of calculations such as

76-23 which she could answer correctly by first taking the 3 from the 6 and getting the units answer then taking the 2 from the 7 and getting the 10's answer.

We then both came unstuck with sums such as 76-27 as clearly you can't take the 7 from the 6. I tried to get her to explain to me how she had been told in school and she got a bit confused. I didn't want to confuse the issue further by suggesting "borrowing" or "carrying a ten across" which is how I would do it. Any ideas on how the teacher would have explained it to them?

I know I should ask the teacher but I'm not picking her up from school today and I think she may be keen to try again tonight..... Thanks

I'm guessing that she used number lines or worked out 76-20-7

I doubt she would be doing column methods yet. I expect she has either been taught using a number line, jumping back from 76 in tens, then 7, ie 66, 56, 55, 54, 53, 52, 51, 50, 49. Or even by adding, starting on a number line at 27, adding in tens to 67, then adding in ones to 76, ie 37, 47, 57, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76. You count up all the 'jumps.'

No she kind of did it in a row - hard to explain but more like

76- 23 = (units 6-3 = 3 so answer is ? 3) then (tens 7-2 = 5 so put that in front of the 3). I was helping in class yesterday and saw them do that bit on the whiteboard.

I was of the generation (!) that was taught to take a ten over from the 70 in your sum, to make it 16-7, then leaving the tens column as 6-2, giving the answer of 49. Subsequently a friend told me she was supposed to teach the pupils in her primary class to add 10 to the 2 to make 12 and put 10 onto the 6. You get the same answer but I don't think it is logical! One could get seriously unstuck if you then had to do 1427 - 689, for example. Or if you had to do 12712 - 3544 - 699. Of course, you can use other methods to get around the sums and still get the right answer, but it would lose you valuable time in exams.....

I don't see any reason why you can't teach her your method and also let her learn the teacher's method if different. There are probably 5 different methods to approach it which will give her the right answer.

Children's brains are uncluttered enough to handle learning different methods, just like learning painting with different utensils from brushes to fingers to sponges. Practice with different methods will improve her arithmetic ability.

As long as she's getting the hang of how to tackle numbers and being able to get the answers, and is happy and confident doing it :-)

I believe they are suppose to count on from the smaller number rather than back from the larger.

So 76 - 27

Add 3 to 30 then add 40 to 70 then finally add 6 to 76. My dc were expected to write the numbers in a line with lines between to show the jumps over which they wrote the numbers they were adding:

....3....40.....6
27 - 30 - 70 - 76

then add up numbers on top row. (sorry about dots - line up issue!)

So she partitioned the numbers into tens and units, took tens away from tens and units away from units, then put them back together. That's the first stage before moving on to columns, but doesn't work for when the units in the smaller number are too big. That'll be a trickier thing to teach, so they would probably be encouraged to use a number line in that case, at this age.

Proper column subtraction, with passing tens over to the units etc, will probably be left for later on (depending on ability and school policy as well as NC.)

There are lots of ways of using a number line, but for subtraction children usually prefer to count on from the smaller number because they find it easier to count forwards than backwards. Either kiggy's method above up to the nearest 10, then on on tens, then the last few units, or up in tens if they are happy to do so, and just adding the extra units at the end.

At my DD's old school, they initially learned to say:
76-27:

step 1: 76-20=56
step 2: 56-7=49 (they were told to first take away the 6 to get to 50 and then to take away one more so they are actually taking away 7)
step 3: 76-27=49

I believe now they've moved on to column subtraction with old fashioned borrowing. My DD much prefers this.

Thanks everyone - I hadn't really appreciated that there were so many ways of doing the same thing. DD hasn't mentioned it so far this afternoon so hopefully I can ask the teacher tomorrow how they do it in her class.