Partitioning

[FamiliesShareGerms]

DS is in year 2. They are doing lots of work on adding and subtracting at the moment, and last week's homework involved creating their own number line to add the tens then the units of one number to another to get the answer. DS really didn't want to do the number line stuff, because "I don't need to partition, I can do those sums in my head".

Obviously I made him do the number line for the sake of completing the task the teacher had set, but he's right that he can just add (or subtract) sums in his head without going through the partitioning process. Eg he worked out how old his granny is in about 20 seconds by going from 1944 to 2012 while we talking over dinner.

My question is whether I need to get him to focus on the partitioning model, even though he doesn't "need" to at present, because it is useful for maths further up the school. Or whether if he can do the mental arithmetic he doesn't need to learn that method after all.

Thoughts from those with older children or who know how maths is taught these days very welcome please!

My DS1 is in Yr2 and is learning maths via the partitioning model and number line. I understand the table format of adding and subtracting that you and I know will come in in Yr3.
I suggest you talk to his teacher and explain your concerns. The fact that your DS is ahead from the mainstream should not stop the teacher from accommodating him.

To be honest most examples of chunking at our school didn't involve carrying (your example of 2012 - 1944 for example would be very advanced for my DDs in Y2) - so it suggests your son is well past this stage.

Best to establish he can work sums out by adding/ subtracting units - tens - hundreds and then recombining answers for total. So get him to explain steps - once or twice & do the rest of homework in head.

But great that he's past that stage. Good for you! Sounds like he's quite a little mathematician!

I talk to my class quite explicitly about learning 'tools' to put in our 'calculating toolboxes'.

The use of a blank (self-drawn) number line is one of those 'tools'. Often when we're 'learning a tool' I will ask children to try it out on calculations that they can already do via another method (like trying out a spanner on a loose screw first so that you know which way it needs to turn to undo).

Once they are secure in the use of a tool, I very rapidly accelerate the task to something that they NEED the tool for. For some children, that might be a tiny extra step forward (e.g. to bridge over a multiple of 100), while for others I miught need to set really quite complex calculations for them to have to use the new tool 'for real'.

So in your shoes, I might do a little exploring to find out where he might need to record his partitioning (e.g. 821 - 354, where there is the step up to 400, then on to 821 in 1 or 2 steps, or 8213 - 3547, or decimals e.g. 64.1 - 27.6) and add that as a note to his teacher ... a 'we used number lines for these although X can do them mentally. He needs to use number lines for calculations like.... etc. It would be useful information for the teacher. Be careful to observe what he is doing, though, rather than 'tell' him how to apply what he knws. What it is genuinely useful to know is the point at which a child's mental staregies 'run out'.

PastSell,

The 2012 - 1944 is easy to find by a mental 'finding the difference by counting up' model, bridging the 1000. 1944 - how many to 2000 (56), then add on the 12. If number lines to find the difference is what is being taught at school, the fact that the OP's son can do that calculation mentally shows a good grasp of the principles.

teacher (and others), thanks, the suggestion of exploring with him the limits of his mental strategy (which he describes to me as "just doing")sounds perfect. Extra homework for DS tomorrow!

The trouble is, when he does his SATS later in year 2 he will get extra marks if he can show his working out. DS struggled with this but his teacher spent a lot of time nagging encouraging him to show his workings out, even if they weren't the usual way of doing it

Numbum,

That isn't usually true

The way the mark scheme usually works is that
a) Full marks are awarded for a right answer, with or without the working.
b) A lower mark is available for complete workings if, for example, there has been a mistranscription of the final answer leadning to that being incorrect.

Oh my lord! The bloody show your workings! Absolute nightmare for my Ds last year in fact it wouldn't surprise me if that's why he just stopped doing any work at all. He too knew the answers but the teacher was just relentless with him "because weeniesag HAS to be able to show his workings, he has his Y2 SATS coming up.....did I mention the Y2 SATS are coming up your Ds HAS to be able to show his workings......weeniesag you really absolutly definatly MUST show your workings because your Y2 SATS are just around the corner!!".

Call me ignorant but my reaction was why? If the answer is correct what is the big deal?. but after reading what teacher has written I see now, because there is still the chance of a mark.

Teacher can you please tell me in what way Y2 SATS benefit our children? They caused my Ds so much upset last year it was the main focus, but I don't know why they are so important, please could you enlighten me? :)

Thanks for the reassurance on the "show your markings" point: DS just shrugs and says "but that's the right answer"....

Just out of interest if a child did addition/subtraction the traditional way (carrying/borrowing) would that be acceptable???

So, What method did he use to work out his grandmas age then?

Im intrigued now! It took me a lot longer than 20 seconds

Blue - no idea! He just frowns for a bit then tells me the answer, and when I ask how he worked it out, he says "I just did"!

Blueschool, I think the quickest way to work out from 1944 -2012 in your head would be, so need to be secure in number bonds e.g. that 4+6=10:

I need 6 to get from 44 to 50
I need 50 to get from 1950 to 2000
I need a further 12 to get from 2000 to 2012

Add the 6 and 12 together =18
Then add on the 50 = 68

Glad to read all this as dd was in tears last night over maths homework because she couldn't explain how she had worked additions and subtractions for problems out, having done it in her head. I did suggest a number line but she wouldn't use one as 'that isn't the way I did it' ended up writing a number sentence and verbal explanation of what she did in her head for each one, can't see that being much good in sats!

Twocakes, I have no idea about how much info they need for SATS, but I think that in general it is good skill to learn how to explain how you do maths, simply because I think it means you are secure in your learning.
If I was working out the above problem, in my head I would simply have said "6,18,68" but that isn't very helpful if I have made a small calculation mistake and someone else was checking my work.

Littlemiss, I completely agree. I think she adds the tens and then the units in her head, but doesn't have a clue how to express that on paper. So she'll struggle when the questions get harder if she has no method. Will talk to the teacher later if I get a chance.

The need to explain what they have done is something that we tell them about lower in the school, so that when they get to upper school they can explain what has happened when the answer to a more difficult question isn't correct. Otherwise, they are getting it wrong, because they're doing it straight in their head, but can't explain what went wrong, which means I can't fix the misconception for them.

I know it's a pain in the rear, but it still needs to be encouraged. I tend to get mine to draw a picture, or use a number line.

Hi Teacherwith2kids:

Re: PastSell,

The 2012 - 1944 is easy to find by a mental 'finding the difference by counting up' model, bridging the 1000. 1944 - how many to 2000 (56), then add on the 12. If number lines to find the difference is what is being taught at school, the fact that the OP's son can do that calculation mentally shows a good grasp of the principles.

Just to say my post to FSG which you replied to (quoted above) was to say that it was great her son could do that in his head and clearly is doing very well (i.e. well past the stage of having to break things down into hundreds, tens and units and recombine - which in my opinion is good going for Y2 pre-Christmas).

What I was suggesting to FSG was simply that she might want to double check that he can partition the problem (I think I used 'chunking' - a bit loose, so possibly confusing - partitioning would be correct here) into thousands/ hundreds/ tens/ units and do the problems that way once or twice to establish he understands what to do and then let him get on with just doing it in his head. [I say this only because DD2 actually really resisted doing work by partitioning and doggedly refused to 'get it' which meant she was held back at her school - she just prefered to do it in her head and not show work]

Hope that's clearer for you Teacherwith2kids . Perhaps it is just us - but here teacher's like to see the working out of the problem (maybe that's old fashion Teacherwith2kids these days? don't know really.).

PastSell,

I suppose what I was saying was that partitioning would be a very 'clunky' way of doing that problem
...

2000 0 10 2 - 1000 900 40 4 is a bit of a pig, actually. Lots of borrowing / alternative partitioning strategies.

The 'jumps up on the numberline to find the difference' method would be more efficient for this particular calculation.

(I'm a great believer in children having alternative 'tools' to use in solving mathematical problems, with partitioning and counting up on a number line being two alternative tools available for this subtraction, and the second one being a more efficient mental strategy in this case given the numbers involved)

Hi teacherwith2kids:

Absolutely agree - but perhaps it's just our school - they insist that this method of partitioning out thousands/ hundreds/ tens and units is demonstrated in class work, even if the child is beyond that point and can happily carry out more complex calculations:

So with 2012 I agree - you can solve this more easily by subtracting 1900 from both 2012 and 1944:

2012 - 1944 could be expressed different so 2012 (=1900 + 112) - 1944 (=1900 + 44) = 1900 - 1900 = 0 /
So that leaves 112 - 44 which can be split up into (100 - 40) + (12 - 4) = 60 + 8 = 68.

Sadly, and again this may just be our school, DD did something akin to the above in Y4 and had it marked wrong for not understanding fully how to partition thousands/ hundreds/ tens/ units. She was also balled out for not following directions.

Yes, it's that kind of school with those kinds of teachers - but rest assured OFSTED rates it 'GOOD' and the Head repeatedly informs us it's really 'OUTSTANDING'.

By the way teacherwith2kids:

Staff have repeatedly informed my DD that column addition can't be taught/ understood until late Y5.

Fortunately, most parents don't take the blindest bit of notice of this and basically teach it at home and tell the children just not to use it in school.

Isn't English education grand?