Daft question - how are our dc taught to do subtraction?!(34 Posts)
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.
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.
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!
Column subtraction video
Tom Lehrer explains it brilliantly...http://www.youtube.com/watch?v=UIKGV2cTgqA
Ok, so it's not how they are learning it now but it is very good! And it's certainly how I do subtraction!
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.
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 !
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
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
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
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.
We're teaching 'counting on' using a number line... it's like working out change by counting up to the next sensible round number.
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.
Don't worry, I'm following what you mean. Thanks for your input.
I think we'll start off use the hundred square as that's what school sent home, but use these other techniques as well once he's happy with the first way.
Crap realised its add 3 to 30 and add 3 to 63 making answer 36 :-/ That'll teach me not to check my post :-/
63 - 27 = 36
27+3=30+30=60+3=63 but on a numberline
I would use counting on from the smaller number on a numberline.
27 at one end, 63 at other
+7 = 30, +30= 60, +7= 67. So answer is 44
Can use the hundred square to work how many units to next ten, how many tens to nearest 10 without going over, add rest of units
Chunking is division terminology really
Sorry can't draw to make it clearer
Not at all.
Not sure how i'd cope if i had a genius on my hands!
Sorry - I hope I didn't sound rude about the genius comment!
Thanks. He's not daft, but I wouldn't say he's a genius!
We'll go for the up the columns and along the rows of the number square first and see how we get on.
It's interesting and reassuring to see how many different ways are being used out there!
Or a backwards number line where you count on in chunks. E.g 67-23 put 23 at start of number line 67 at end then jump in whatever increments they are comfortable (if new to method 10's, 5's, 2's or 1's) if more confident maybe 23+7= 30 + 30 = 60 + 7 = 67 then count up all numbers + so 7 + 30 + 7 = 44
If he's year 1 and not genius level then it will be just going up the rows and back along the columns as I suggested. Our lower ability year 2s are consolidating this at the moment.
Yes. Lots of different ways to get your head around maths is good I agree and certainly helped me when I was younger.
Thanks for those suggestions, your way of explaining things is great and much clearer than I think I'd have come up with!
Off to google cuisinnaire rods!
If the question is 63-27, I would try with
1) 63-20 = 43
then split the 7 into 3 and 4
43 -3 = 40, but I still have to take away 4
40 - 4 = 36
2) "what if" method
what if instead of having 63-27 I had 63 -30, then the answer would be 33.
But I took away 3 too many (30 is bigger than 27 by 3), so I have to add 3 to 33, which gives me 36
3) "what if" method number 2
what if instead of having 63-27 I had 67 - 27, then the answer would be 40, but I started with 4 too many (67 is bigger than 63 by four), so I have to take 4 away from 40 = 36
However, I think this is a hard one to do in your head. Probably he has to do it looking at the 100 square, so he has to do "take away 10" to move vertically, take away one to move left.
Another thing you could do is having 63 beads, or pasta pieces, in 6 groups of 10 and then the three units, and then he can count 63 .... 53.... 43... while he takes away 10 at a time, and then counting 7 back from 43, to get to 36.
Show him in many different ways, I think the exposure to different ways is very important in Maths. Also, you could try the cuisinnaire rods.
How old is he? If he's KS1 and just been sent home with a 100 square then it could just be practise on how to use it. E.g. 54 - 23. Find 54, go up 2 rows (because that is 2 lots of 10) and then go 3 units to the left. The answer is under your finger!
Not to worry Brycie if it's not how they've been doing it. At least it gives me somewhere to start.
Thanks for your help.
Yes I could do with a creative accountant myself
Iwish - I might yet be wrong. Don't take that as gospel, I hate chunking with a passion!
Brycie, I see it as a very creative profession
It makes sense but is awfully long winded!
Happy to do it that way with him if he seems to recognise the technique.
I'm hoping that he's more receptive to having a go at it in the morning and just sits down and rattles them all off. That's how the additions have been going.
I think you end up with something that looks like this.
63 - 27
Am really happy to be told by a maths teacher I'm wrong, I won't mind at all. But at least we are keeping it alive unitil one comes along.
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