Horizontal addition...I'm confused!

[tigermeow]

The other day DD saw a friend's son completing his maths homework. He had a set of maths problems to work through involving 3 digits e.g 234+532= He drew out his very neat columns, labelled the columns H T U (hundreds, tens and units) and then added up his sum. This is how I remember it from school. My friend said 'ooo, you'd best check with DD's school to see if they do it the same way'.
DD comes home and proceeds to write her own sums on her white board and do them correctly (not carry the ten over though).

I spoke to DD maths teacher today and mentioned that she had enjoyed adding last night and should I let her continue as i heard schools do addition in different ways. The teacher explained that they do 'horizontal' addition and they wont do the HTU colums way until the Juniors. OK, I am very confused...anyone want to give me a lesson in how to add 234+532 in a horizontal way! Also, now that DD is keen, should I just say 'no more sums' or show her the other way?
Many thanks.

bump

I'll have a go - it involves a number line (well just a line, you write numbers under it as required) - you would put 234 at the left end, then depending on confidence you jump to the nearest nice round number. My dd is in year one so goes to the next '10', if more confident you could jump to the next '100' which would be adding 66 to get to 300. You draw an arc showing the jump, write 300 under the number line and 66 over the arc. You then add 200 to get to 500 (another arc, note the 200 above it, enter 500 under the number line). Then 32 to reach 532. Add the jumps together - the numbers are generally easier to deal with than the original whole numbers and the idea is that this help with mental strategies for addition.

That may not help!! It's easier to show than explain!

No, that's for subtraction, forget that!

Right!

234+532=

Add the hundreds up = 700
Add the tens up = 60
Add the units up = 6

Add 700+60+6 = 766

My dc's did this. It apparently helps with mental maths! Makes it easier for them to see the maths problem, by breaking it down into easier blocks of numbers.

As soon as they go to secondary school (or into juniors sometimes) then they are taught "our" way. The good old fashioned way.

Personally, I taught both my dc's "my" way, and they preferred it!!!

Ok, 234 at the left, add the hundreds first and draw the jump to 734. Then add the tens with another jump and finally the units with a last jump.

Sorry, it should then look like this -

234+532= 700+60+6= 766

All in one line!

Yep! I've seen them do it ZoeC's way as well!

The number line thingy blew my mind!

Eeek! LOL!

What about if you need to carry over the tens e.g 666+ 555 ?

DD was able to add sums like 34+23 in her head by using the columns method- she claims to see the columns in her head.

I'm prefering the old fashioned way!

Do they do subraction horizontally too?

Poor DD, she was so excited about adding big numbers!

This is the problem I have with ds.

He is a whizz at maths, and can do it without writing it down. But he HAS to show his working out. He says "but I don't need to write it down to know the answer". Aaaahhhhh, big battles at school with teacher.

He much prefers mummy's way of doing sums.

666+555= 1100+110+11 = 1000+200+20+1 = 1221

Makes you wince doesn't it!

Subtration is what I was originally describing. You put the number you want subtracting on the left, then the number you are starting with on the right and you find the difference by splitting it into convenient jumps to the nearest round number, blocks of the round number then whatever the small bit is to reach the higher number.

You don't 'carry' with number lines, that's what they are trying to avoid really as it can confuse some (not all). With your example, you would start at 666, add 5 lots of 100 to reach 1166, add 5 lots of 10 to 1216 then the remaining 5. They teach counting in 10s and 100s from different numbers so get used to it.

If your dd can 'see' the columns then I would say that is fine - she has a mental strategy which is what the methods are trying to instil.

One point about writing method, this becomes MUCH more important the further through school you reach. Partly so the teacher can see where a mistake has been made and can therefore see if it was a simple error or a mistake with method. Also, at GCSE and A Level, there are a lot of points based on the working out - the final answer is only a relatively small part of the marks available. So it is a good habit to get into.

If you need to carry the tens....

666+555= 600+500+60+50+6+5
=1100+110+11
=1210+11
=1221

Whoops...didn't refresh

666+555= 1100+110+11 = 1000+200+20+1 = 1221

Makes you wince doesn't it!

Oh yes! lol!

I think I'll leave this method to the school to explain! I'll let her keep doing her method first and then she can learn a new method when she has to cover it in school.

Our school offered a "learn how to do our way of maths" evening to parents!

Couldn't go, I was at work. So the dc's had to try and explain it to me.

There was much confusion with the parents at the school gates the next day!

Although it makes us wince, it really seems to help with mental maths...by Y4 ish a good proportion of a class could do this without need for pencil/paper.

The way they do it first is they actually get them to write out the partitioning of the numbers before they recombine them:

So 666 + 555 = 600 + 500 = 1100
60 + 50 = 110
6 + 5 = 11
1100 + 110 + 11 = 1000
100 + 100 = 200
10 + 11 = 21
1000 + 200 + 21 = 1221

This does really help children understand what they're doing, but there are so many opportunities for errors along the way and it takes ages!

The method does now make sense- I've been practising! I need a few more attempts before showing DD. Right now though, she is just so happy to be able to add big numbers with the old fashioned method.

At what age do they start on the 'old fashioned' method? Or do they just not teach it any more?

Yes..vertical addition anywhere between end of Y3 to somewhere in Y4 depending on attainment.

And...vertical addition initially taugh as an extension of horizontal.

256
+175

11
120
300

etc...hope the layout works and doesn't come out all scrambled!

As I thought...scrambled. hundreds, tens and units should all be lined up in correct columns. Won't work on here!

I see what you mean, thank you for your help. Off to practise now!

DS1, who was in the extension group for maths, didn't learn column addition and subtraction till Y5. So Y3 is not the case in our school.

In the OLD QCA numeracy strategy the extended vertical method was a Y4 (hence able Y3) objective and the classic method a Y5 objective. Not quite sure where it appears in the new numeracy strategy (from Sept 2007).

Children were still encouraged to use the method they found the quickest and easiest for any given calculation.