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Primary education

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Original poster

embarrassingly basic subtraction question

38 replies

Vicky2011 · 30/04/2011 18:21

Right, this is where I put my hands up and admit to being an utter thicko with maths :(

Am helping DS with his KS1 maths homework and can't figure out how do to subtraction that involves carrying, when there is a zero in the bigger number. So, on one example we've been given, we need to subtract 97 from 205. So far I've been adding a "10" to the units column and then taking one away from from the tens column, but when the tens or hundreds column is a zero I don't understand how you take one away from it. So on this example I've been getting as far as taking 7 from 15 but then getting stuck at the tens column.

I know that in this example DS could do this with a bit of work in his head by rounding 97 up to 100 and then adding the 3 back at the end but he tends to find that kind of mental arithmetic harder than having a written method so I was left feeling a bit of a buffoon when I got stuck trying to teach him the written method.

Any explanations - the simpler the better - would be greatly appreciated!

Many thanks

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lovecheese · 30/04/2011 18:23

Can he do blank number lines? My DD would use this method.

maxpower · 30/04/2011 18:26

ok, I'll try

205

Can't do 5-7 so take 1 from the 20

19(1)5

so do 15-7=8
and 9-9=0
and 1-0=1

205

=108

does that help?

thatsenough · 30/04/2011 18:29

You need to borrow from the hundreds column first (making the 2 a 1 and the 0 a 10), then borrow from the tens column which is now 10 and not 0 - This makes the units column 15 and the tens column 9.

Does that help at all?

lovecheese · 30/04/2011 18:31

Vicky - just a thought, is your DS even being taught the column method at school? I'm guessing he's in year 2?

HauntedLittleLunatic · 30/04/2011 18:31

At KS1 they "shouldn't" be doing column subtraction. I almost certainly won't be doing it at school and I wouldn't try and introfuce it. My DTDs are just being introduced in Yr5.

He should (I think..sure to be correct shortly) using a number line.

indifferent · 30/04/2011 18:35

I think you need to do it in order: yes you were right to try to borrow a whole TEN from the 10's column, but when you looked there weren't any there to borrow. So move to the next column on the left which luckily has some numbers in it so you can start there: first borrow a whole "100" from the 100's column. So change the 2 to a 1 in the 100's column. You now have a 100 to do what you like with. So what you do is put it into the 10's column, where it must itself be a ten (as ten tens is a 100). You can then borrow one of those tens for the units column, leaving you with 1 in the 100's column, 9 in the 10's column and the 15 that you need in the units.

You can now do the sum in each column

The units column is 15-7 which gives you 8
The tens column is 9 (remember we borrowed 10 tens from the hundreds then gave one of them to the units) minus 9 which gives you 0
The hundreds column is 1 - 0 which gives you 1

so the answer is 108

thatsenough · 30/04/2011 18:36

DS1, year 1 is being taught the comumn method - Should he not be?

Cathycat · 30/04/2011 18:40

Too early for all that palaver. Draw a horizontal line. Mark out 97 then after that 100 then after that 200 then after that 205. Count on from 97: 3 add 100 add 5 (write that down). Now it is easier to add using the biggest number first. So 100 add 5 add 3. So you have worked out subtraction by the method of counting on using a number line. HTH.

HauntedLittleLunatic · 30/04/2011 18:41

Should he or not....is a whole different debate.

I am not 100% sure exactly how the curriculum is structured and how much freedom there is. At the very least it is not common to be doing column addition subtraction until late KS2.

Original poster

Vicky2011 · 30/04/2011 18:42

Thanks everyone - to answer the questions about column subtraction first, no, you are right, he isn't being taught it as the main method but they have been taught it as an alternative method (I think he's being encouraged to go for a level 3 at KS1 if poss) but he generally finds columns easier, for both subtraction and addition, than number lines and when faced with a sum which he can't easily do in his head I tend to tell him to do whichever method works for him. (I have had this conversation with his teacher who said as long as he is getting the right answer it is fine).

So in this case I sent him away to do this sum on paper and he came back to me saying he didn't know how to make the zero one less and, to my embarrassment, neither did I! I will give all your methods a go and see what works best for him - the borrowing from the hundreds column seems the most logical as it's just a continuation of what we've already been doing but I will try them all. Many thanks again for your help!

OP posts:

Original poster

Vicky2011 · 30/04/2011 18:46

And Cathycat I agree, the number line does look a lot easier in this instance, he just seems to hate them for some reason but I will show him this as an example where it's a lot more straightforward!

OP posts:

FreudianSlipOnACrown · 30/04/2011 18:47

I'd be so tempted to say 205-100 and then add 3 back on. No idea if that's the wrong thing to do though...

caughtinanet · 30/04/2011 18:48

I agree that children who are confident in maths will be able to use different methods to subtract but in the example you've given I would have thought a number line solution is always going to be the quickest. I wonder if your son understands this as well as he thinks.

I was taught many moons ago but I can see the merits of a range of options and in this case I'd suggest that the solution of a full hundred and the 3 and 5 at either side jumps off the page as being the quickest and easiest to understand.

HauntedLittleLunatic · 30/04/2011 18:49

My personal choice (and I know I am not your DS) would be the add back method, which is easier to adapt to mental maths strategies which is what KS1 maths is about.

97 + 3 = 100
100+ 100 = 200
200 + 5 = 205

So we have added on 3+100+5=108

caughtinanet · 30/04/2011 18:50

Just seen that I've x posted with you and Freudianslip - I'd definitely suggest trying to run through number line method.

Original poster

Vicky2011 · 30/04/2011 18:59

This is a hugely helpful thread - thank you. I do find working with him on his maths really tricky. Bizarrely my mental arithmetic is pretty good (hothoused several decades ago for selection at 11) but the massive negative of that is that, while I'm generally able to get the answer for his sums fairly quickly I often have no clue how I have got there which is of zero use to DS. It's a bit like trying to teach someone to drive when it's become so automatic you can no longer remember the process.

Thanks again all!

OP posts:

blackeyedsusan · 01/05/2011 00:33

they may be trying to find the difference between the two numbers by using a number line. (suspect so as one number is just above 200 and one just below 100. ) how many numbers do you have to count to get from the small number to the big number.... 3 to get to 100, 100 to get from 100 to 200, 5 to get from 200 to 205 add together 3, 100 and 5

ChippingInLovesEasterEggs · 01/05/2011 01:10

It doesn't need to be any more complicated than this....

FreudianSlipOnACrown Sat 30-Apr-11 18:47:27
I'd be so tempted to say 205-100 and then add 3 back on. No idea if that's the wrong thing to do though...

I wish they taught math the 'old' way.

cupofteaplease · 01/05/2011 01:26

I'm a year 2 teacher and we don't go anywhere near column addition, even for level 3 children. We hold a maths evening for parents where we demonstrate the methods we teach in school and we discourage parents from teaching the column method at home...yet!

For subtraction, I tell children to draw an empty number line, place the largest number at the end of the line and jump bacowards. A capable child can choose to jump in any amount that they can cope with, so in your example, jump of 100 would be encouraged.

RoadArt · 01/05/2011 04:04

From what I have seen at schools, column addition is introduced around year 3/4. Is that right?

ll.

thatsenough · 01/05/2011 07:45

I think i'll have a chat with the teacher next week - we have been doing column addition since the start of year 1, introduced "borrowing" after Christmas and started subtraction not long after that. I know they will start long division at the start of year 2, but we do have a lesson to show us how it's done!

Number lines are still used as a reminder for simple number bonds, but i'd no idea they could be used for bigger subtractions as shown above - seems obvious now!

thatsenough · 01/05/2011 07:47

Sorry that should have been carrying for addition not borrowing.

Panzee · 01/05/2011 07:51

If they've been given numbers so close to the 100 mark it's to encourage them to round up/down.

cupofteaplease · 01/05/2011 08:37

"I think i'll have a chat with the teacher next week - we have been doing column addition since the start of year 1, introduced "borrowing" after Christmas and started subtraction not long after that. I know they will start long division at the start of year 2"

Is this a state school following the national curriculum? In Year 2, we introduce division as grouping and sharing. We'd be looking at multiples of 2, 5, 10, 3 and perhaps 4 for more capable pupils. I'm baffled at column addition in year 1 and long division in Year 2. Maths at KS1 should broadly be visual and practical so children understand why they are doing things, as well as how. I'm surprised a 6 year old could handle borrowing, carrying, grid methods for division etc.

I'm not criticising, I'm genuinely curious and surprised!

thatsenough · 01/05/2011 09:09

It's an independent prep, not a known for being a particuarly academic one, but lovely all the same, although having said that many children go on to very good schools for secondary education.Class sizes are small (only 12 in DS1s year, but likely to be 16 or so in DS2s when he joins reception next year).

They do seem to follow the national curriculum (but no SATs thankfully). His teacher did mention that DS picks up maths concepts quickly, but I'm sure that the rest of the class are at a similar level - I wish I could say the same for English as that is a definite weak point.

They have started grouping and sharing, but we haven't really got involved yet.

I had no idea that this wasn't the norm and will now be looking at different ways if DS seems to be struggling with any areas.

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