maths partitioning

[crypticbow08]

DS, 5, is in reception and doing well. He likes maths, but doesn't like using number lines/100 squares, he'd rather do it in his head which has been fine except hes now doing double and triple number adding and taking away. I originally showed him the table method (37

+28)
Now, hes come home from school today doing partitioning, he says it is, and it looks so long winded and extra work. Is this the new way they teach them? Seems so much more complicated to me :s

Anyway, just wondering if this is common now, and if their is any reason they're doing this now?

Damn! Tried to get the 28 under the 37. Hopefully you'll get what I mean!

It is one of the ways.

They don't tend to teach column addition and subtraction till year 3 or 4 these days. I think partitioning is supposed to help them understand what they are actually doing when they add and subtract 2 or more numbers, and what place value really means (e.g. in your example, if you write 28 the 2 actually menas 20). Also, partitioning helps with mental arithmetic, and there is a lot of emphsis on mental arithmetic (they have a mental arithmitic test in their Year 6 SATs). I expect the teachers would prefer you to help him use the partitioning method at this stage, rather than teaching him column addition.

btw it might look long-winded to you (it is long-winded to write down in fact) but it's actually a very quick method once you are used to it.

Reception is very early to be partitioning! Well done him!

Thanks all. I never looked at it for helping towards mental arithmetic jellycat, he'll probably like that as he likes doing it in his head. I'll stop doing the column method for now than and get him to show me the partitioning properly! I only remember learning the column method. Thanks Chigley1, he does go into year 1 for his maths.

crypticbow08:

Well first off WOW! DD1 had no actual numbers save counting out loud (but nothing written) in Year R and although DD2 had numeric work - adding 2 digit numbers + 2 digit numbers was more Year 1. So you're school clearly has got him off to a very fast start!

Partitioning (with 2 digit numbers as in this example) is about thinking about the tens digits and the units digits separately.

DD1 turned out to be a highly visual learner and we had better success doing this with objects:

Tens digits were grapes and units were raisins (10 raisins = 1 grape)

Tens digits were duplo blocks and units were little lego blocks/ play mobile blocks (ten lego blocks = 1 duplo block)

Tens digits were squares of chocolate and units were smarties (ten smarties = 1 square of chocolate)

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So get out three small plates.

In your example 28 + 37 - you'd have 2 grapes & 8 raisins on one plate and 3 grapes and 7 raisins on another plate.

Put all the tens digits together on one plate (so move the 3 grapes from 37 and the 2 grapes from 28 onto one plate and you should have 5 grapes or 5 tens digits or 50). Set that aside for a bit.

Now move all the units digits onto one plate - move the 7 raisins to the plate of 8 raisins. Count them up - wow there are 15 raisins. We can cash in 10 raisins for one grape (count of 10 raisins and replace with a grape) so we've got 1 grape and 5 raisins on the plate.

we can then move the grape to join the 5 grapes from earlier = 6 grapes = 60 and if we move the 5 raisins onto the plate we've got 60 + 5 or 65.

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The issue for your DC will be understanding what to do when his numbers get >9, once you have two digits 10, 11, 12, 13,.... you can't put them into the units/ tens/ hundreds columns - there is only room for one digit per column - so they have to learn that you write the unit digit down and carry the tens digit.

I do agree that partitioning helps with mental arithmetic and that is a brilliant thing - but not everybody visualises numbers of things in the same way. DD2 can think about numbers and literally see what needs to be done in her head. DD1 needed grapes & raisins to make sense of what she was doing.

Partitioning can also be really confusing if place value (the meaning of each number in 138 - so that a child understands this stands for 1 one hundred, 3 tens and 8 units) - Woodlands Junior school has some nice place value games here: http://resources.woodlands-junior.kent.sch.uk/maths/interactive/numbers.htm#Place

And there are some good early addition number skills games here: resources.woodlands-junior.kent.sch.uk/maths/numberskills.html

Math champs also has some good practice with this kind of early addition skills here for ages 5 - 7: www.mathschamps.co.uk/games5-7?

Oxford Owl has some math games as well - but for the OP I'd suggest not just looking at 5 - 7 age range, but also look at resources in 7 - 9: www.oxfordowl.co.uk/welcome/for-home/maths-owl/fun-activities

HTH

My son in yr2 is only just being shown the column method by his teachers... I tried showing him in Yr1 (when they were using partitioning) but the teacher asked him NOT to use the column method yet (in yr1). When I asked about this at parents eve, I was told that being able to competently use the partitioning method is very important, and the column method doesn't get you to think in terms of hundreds / tens / units etc, whereas the partitioning method does (sorry, if I explained that badly!).

It sounds to me like your son is already beyond the need for partitioning and number lines.

Partitioning has two functions, one for building written math skill, one to aid mental skills.

Partitioning is a step towards vertical written methods for most children, just like grid method is a step towards vertical multiplication, both are taught in years 2 3 (for addition and subtraction) Y4 (vertical multiplication) and then drop off for those who can progress to vertical addition, subtraction and multiplication and "bus-stop" division during Y5 and would be methods only being used by the most struggling students by Y6.

It IS perfectly possible to have a child of age 5 who fully understands place value and vertical methods and uses this in class and for home learning. Some children simply do not need years of partitioning to understand a decimal based number system.

I have taught 2 such children, both of whom were in the top 2% in Gurthri assessments.

The important thing is to be totally sure that the child understands and can read the numbers written, ask your child ;

What does the 6 in 7689 represent ?
Which is the smallest value in the number 49 ?

Once place value is established then just refer to numbers by there value rather than digit name when using all vertical methods.

School will catch-up with your child around Y4/5.

For mental methods SOME people mentally partition, most UK adults do not because those born before 1972 were not taught partitioning OR grid method as neither were recognised teaching strategies until 1987.

Again whilst some people really have benefited from these methods and swear by them, there are multiple alternative techniques for mental arithmatic and typically children use a combination (their efficiency center).

For example today 18 children in my Y4 class had to mentally calculate 65.5% of 280.

Some partitioned the % into 50, 10, 5 and .5
Some ignored partitioning and divided by 10, using 10% to find 5%, mentally dividing by 2, or halving), used the 10 % to find 1% and division to find half of 1%.
Some divided by 100 then visualised vertical multiplication.
Some divided by 100 then used partition on 280.

No one method is superior to another, the child will ultimately selected a method that suits them best, fits most comfortably with the speed of their mind.

Thanks all. I only learnt the column method at school which is why I showed it him, although I did show him with tens/units above the columns, which he understood.

I think I am going to trust the school, and encourage him to partition if he is happy to do it as the school have been brilliant so far in recognising he was being slightly disruptive before xmas due to boredom and have completely changed the activities they do witj him to challenge and push him (now he behaves perfectly at school). Although if he doesn't take to partitioning, I'll let him do however he feels most comfortable.

RosemaryandThyme I think he does understand place value, if he had 426 he can tell me the 4 is the highest cause its 400 and that 6 is the lowest because 'its just 6'

Thanks for the advice everyone, I didn't want to confuse him with different methods, and I'd never seen partitioning before having only used column method or just done it in my head.