maths - adding up in columns(29 Posts)
In which year are children taught to add up in columns?
My daughter is in yr 2 and has recently brought home some maths involving adding numbers in 100s and 10s. She tried to explain how she is being taught but I'm afraid it made absolutely no sense to me and didn't seem to make it that easy to add up.
Dh and I showed her how we were taught using columns and it seemed to make more sense to her and she enjoyed it.
I don't want to go against the school and confuse her by combining methods so was wondering how long I need to wait until she is taught in the way that I understand and can therefore help her?
During KS2 at some point. Probably year 3 or 4.
What method is she using? A lot of the written methods use in year 2 are stepping stones towards mental arithmetic rather than a formal written calculation. Eventually they should do it in their head rather than have to write the steps down. Obviously some of those methods will help with understanding written calculations later as well.
Whilst showing her the column addition is fine. You need to be careful that she doesn't end up relying on it at the expense of her mental arithmetic skills.
I think she brought home something like 432 + 125 say.
She started working it out by writing
400 + 100 equals
30 + 20 equals
2 + 5 equals
I get that they need to understand that in this eg the 4 is not a 4 but 400 but don't understand how writing things out sideways rather columns makes it any easier to understand the maths?
I think when they add in 10s they use a sort of number line with loops and +10. unless you know what happens to a number when you add 10 to it, I'm not sure how that helps? A number square makes more aense
DD has been doing it in yr 4. I got politely told off for doing it in columns in yr1 as they have to consolidate their knowledge of place value first.
My DD is in year 3 and has been doing column addition. The way you show your DD having been doing it is the way DD has been doing it. It especially helps for ie 478 + 369 when using column addition they would need to "carry" across.
Writing out a sum horizontally as you showed ensures that children can partition a large number into its parts. Column addition doesn't really need any understanding of place value so that's why it's left until yr 3 or 4.
My year 4 has just been taught addition and subtraction in columns.
My DD had a bit of column addition in Y1 and more in Y2. Frankly, I don't think it matters how you write it, as long as they understand what they are doing - that they add hudreds, tens and units separately.
Mine actually understood it back in Reception as she came from a Montessori nursery and was really friendly with 100,10 and 1s bead materials - using the beads she could add up quite large numbers without knowing that she was doing something difficult.
In Y1 some of her friends were confused with column addition, so I pulled out our beads and explained it - and within 5 min they were adding without problems!
I think our partitioning for additions at school in Y2 looked like this.
134+231 = 100+200=300
30+ 30 = 60
4+ 1 = 5
After that they were shown straight forward column addition.
The partitioning will help with understanding column addition and subtraction later, particularly in calculations that involve carrying or 'borrowing'.
But it will also be hugely useful for mental arithmetic. As an adult I'd never use a written calculation for something like 432+125 because I can easily do it in my head. 9 times out of 10 I would only partition the smaller number and do something like
532+20 = 552
552+5 = 557
Occasionally I would partition both numbers. I don't need to write that down and can do it quick enough that it takes seconds.
In year 2, most will have to write it down, especially with 3-digit numbers, but she may well get to a stage at some point where she no longer needs to write the steps down.
Number lines / partitioning as she showed you in y2.
Column addition only when really understand concept of numbers in y3/4.
If they don't know that 92+10 = 102 when counting out loud up in 10s etc then the y2 methods help them understand it. You shouldn't imo move to column addition until that kind of knowledge is really sound.
If they don't get the whole concept of numbers it makes it really hard later as they can't see whether answers are feasible/realistic etc. cutting corners now can make life much harder later.
(Disclaimer. Not a teacher, but a maths graduate with 2 (adopted) children, elder one who's early maths teaching was poor and who took ages catching up).
My DS3 is in Y2 and has recently started doing column addition. He is top set for maths and has up to this point been doing the adding hundreds tens and units separately method but likes the column method and finds it simpler now that he understands how addition works.
Y3 DC, has been doing column addition and subtraction since beginning of year and this evening homework was:
subtraction of three digit numbers with borrowing
DC did say top group was working from y5 book.
So probably y4/y5 with breaking barrier of ten (borrowing-, carrying+)
I would think all the methods involving partitioning will seize altogether by end of y4, mental calculus and column method will be used in preparation for senior school, that was the case with older DC.
No harm in showing column method to your DD, providing her understanding of place value is in place.
Thanks for all your replies. It's so long ago that I was taught maths that I can't remember what method was used. I do remember in juniors (so I guess yr3/4) we were taught Fletcher maths which I hated as to me it seemed such a long winded method of doing a sum. I think I was very comfortable with numbers and I remember being in yr 5 and in idle moments writing down huge lists of two and three digit numbers and adding them up for fun!
I also vaguely remember my mum despairing at how I was taught maths and teaching me the column method so I guess its history repeating itself.
I suppose I struggle with the idea of having to reconstruct numbers having broken them down into all their component parts. It seems overly complex.
DD did start to tell me this eve that her group were working on something like 536 - 109 but we both got distracted before I could find out how they did it. I'm sure I wouldn't have understood a word!
I think all I can do is be patient until the school methods start looking a bit more familiar. I'm too old and jaded to start learning a new way now!
Thanks again for taking the time to reply
The new national curriculum (starting from Sept 2014) will apply to your DD in Key Stage 2 (years 3 - 6 of primary school).
Page 19 of the programme of study for Maths from the new national curriculum says: "add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction" - link: https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/239129/PRIMARY_national_curriculum_-_Mathematics.pdf
So basically if your child's instinct is 'deconstructing' numbers and horizontal addition of numbers of values >20 is long winded - then if it makes sense to you and it works for her my advice is just teach it. Warn her the school may ask her to do it the other way - but at our school where column method is strictly FORBIDDEN in all calculations - parents have just gone ahead and taught it at home ignoring the school.
Dd in year3 and they have moved on from breaking down numbers horizontally as you've written and number line, to now doing addition and subtraction using columns. I'd do it in the same order as the school is teaching it or you will confuse for sure, dd hated me showing her different methods. Once they move to column, dd found it very easy to master even carrying the 10 because of the prep before hand. Plus when they are required to do it in school etc it'll be easier if they know one sure method rather than being confused between two or three.
I think if they are partitioning numbers to add, partitioning the number horizontally is more effective than vertically and segues nicely into column addition e.g.
437----> 400 30 7
+ 122 ---> 100 20 2
559 500 50 9 = 559
It also reinforces place value when laying out on HTU grids.
I would definitely avoid the 4 + 1 makes 5 for the hundreds column for example as place value is key to so many areas of maths learning!
Sorry if that's overlong (or doesn't align properly when posted lol)
Sheesh, DC school try to avoid it completely. I hope they aren't obliged to by whatever revamp of the NC. Until recently, it was only for Top set in yr 5, maybe. I strongly prefer modern maths methods instead.
There was a radio 4 programme on modern maths teaching recently that I think is still available on iplayer.
You could also ask the school if they hold maths workshops for parents, or even the teacher if s/he can run over the methods with you.
Blue, they had a workshop last term. I couldn't go as I work full time, but they gave me all the handouts. Trouble is, at that stage they were only dealing with 2 digit numbers and I could follow the logic.
Oh well, she must be picking it up whatever way they are teaching it as she came home yesterday with an achievement award for her progress in maths :-)
I think it depends when place value is rolled out.
Notably Mathsfactor starts with place value very early on (this is an on-line tutorial) - so DDs both got that 4 and 1 in the hundreds column were in fact representative of 4 one hundreds and 1 one hundred.
Place value in school (to be fair this is St. Mediocre where teaching long division will NEVER happen) was not taught until Year 4. It was taught so poorly and kids were so confused that DD1 secretly taught them Carol Vorderman's method in the playground - but using crayons to shade 3 columns (she asked the children to chose colours for units, tens and hundred) and then writing numbers in the column and discussing what they meant.
She also taught the illegal column method during play breaks as well.
I think the kids are voting with their feet.
However - at our school horizontal method is mental arithmetic only - they are not allowed to use white boards or writing paper.
So given that JumpingJetFlash - I hope you can see that most kids find horizontal method o.k. with numbers ending '0' but impossible once it's numbers like 453 - 278.
Not true past. Most kids are fine with horizontal methods and mental arithmetic not ending in 0. I don't think you can criticise the methods based on your DC's school's rubbish teaching of the maths curriculum.
Past To do 453-278 mentally you would use a totally different method anyway (at least I would).
Add 2 to get 280, 20 to get to 300, 100 to get to 400, add 53 gets you to 175. This works really well on a numberline too, which is why I like numberlines so much.
You shouldn't try to do column subtraction in your head.
Ah, now you see I always do column subtraction in my head. I would end up losing the plot if I tried to do something like you've described!
I think we're talking at cross purposes.
You're speaking as if decomposition/ horizontal addition/ subtraction is always written & assisted by a number line and have ?misunderstood (?willfully) that I was suggesting the traditional vertical method (aka column addition/ subtraction) was mental.
I very definitely mean that column addition/ subtraction is a written method (in this case with chalks on the playground/ on paper secretly at home with the curtains drawn as this is a deeply illicit method of doing maths that teachers disapprove of)
at our school (clearly not everywhere) - horizontal method (decomposition) is a mental method with no aids (NO NUMBER LINES). Bit tough in Y3. The kids hate it, get frustrated and most parents are just going their own way and teaching the method (largely column method) that works for them & that they were taught.
Your suggested method is 5 steps they have to do in their head. Now admittedly on paper this is much easier - not my preferred method mind you - but easier.
My preferred (but wrong as told to me by a teaching professional at St. Mediocre) is:
Take 453 and make it an easier number to deal with in relation to - 278.
So split 453 into 153 & 300 (because 300 is a nice easy number slightly bigger than 278).
300 - 278 = 22 (can be done by counting up to 300 or in steps - 278 + 2 = 280 and 280 + 20 = 300 - 20 +2 = 22)
And then adding 22 + the 153 - this can be deconstructed
to 100 + (50 + 20 = 70) + (2 + 3 = 5) = 175.
However, I was told immediately (when demonstrating something similar for DD1's teacher in Y4 parent/ teacher meeting): this was all wrong and entirely why parents helping with math is DAMAGING to children.
Got to love that 'working together with parents to achieve the best outcomes for our pupils' ethic.
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