Adding up - how do they teach..?

[smee]

DS (just finished Yr1) is v.into maths and asking how do I, etc? DH was showing him how to add up bigger numbers, but something DS said made me think they teach them differently to how we were taught. Don't want to confuse him by showing him the wrong way, so how do they teach say adding 52 + 46 these days? I'd add 6+2, then 5+4, but are they taught to add the tens or hundreds first instead?

I teach units first

Thanks mrz; so I'm okay to show him how I'd naturally do it then?

At that stage, they should be using number lines. When they're adding tens and units numbers, they put the starting number on the line and then draw big jups for the tens.

e.g. draw a line, write on the number 52 and jump 4 10s, marking each one +10.

Then do a small jump for units, writing +6 above it.

Then annotate the line where the jumps 'land'.

e.g. starting at 52, next 10 lands at 62, next at 72, 82, 92, then the little jump for plus 6, makes 98.

We call our 10s jumps 'kangaroo jumps' and our units jumps 'bunny hops'.

Whenever you're adding tens and units numbers, you need to break down the number to its constituent parts. So 52+46 is 2+6 and 50+40.

The school may have a policy for progression in maths. Ours does - the number line being the Y1/2 method for starting to add larger numbers.

We use numberlines in reception and the beginning of Y1 but once we introduce column addition with those children who are ready we add units then tens

www.mathsisfun.com/numbers/addition-column.html

Blimey, thanks Rolla, sounds like a lot of work to add a simple sum, though I can see how it gets them there.

If I write the sum 52 + 46, he can do it in his head by looking at it, then mentally adding 2+6 and writing 8, then 5+4 = 9. He doesn't struggle with that at all, so he's doing what you suggest in his head rather than using a number line. So long as I'm not confusing him by letting him do that, am fine. Am only doing it because he's actively asking to. For me it's summer holidays.

cross posted mrz. THANK YOU! That's brilliantly helpful.

We introduce column addition in Y2 for the more able.

Smee, I'd really say 50+40 rather than 5+4, because it's not really 5+4 IYSWIM!

Otherwise, when you get into units adding over 10 you get into difficulty:

Your way
56+27
6+7=13
5+2=8

8+13 =22

Separating the tens and units:
56+27
6+7=13
50+20=70
70+13=83

It'll just make more sense, and make it easier later on!

This is a fine way of doing it. However, the only problem is that it can't be used in the same way with subtraction.
In the younger years, number lines are used primarily because you can add and subtract easily using the same method, and the children tend to get less confused. (Add to right, subtract to left)

Number lines also reinforce partitioning of tens/units etc, over and over and over again.

Your method is great for adding mentally.

Thanks Rolla; it's a minefield isn't it? He's just a boy who wants to know and as he's actively asking I don't want to block him. Still though, I don't want to teach him something that's going to annoy his teachers/ confuse him!

Does his school have a calculation policy?
If not perhaps he can tell you how he's taught in class.
We teach column addition in Y1 as it's easier for children to recognise the tens and units (hundreds - thousands) so don't have to use the method RollaCoaster describes although this is an earlier step.

That's the trouble mrz; holidays! I haven't a clue how they teach it at his school and he doesn't seem to have been taught it yet, but just wants to know. Seems a shame not to follow natural curiosity, but equally I can't find out from school as it's shut. Thanks for advice though.

Just illustrates how different schools work! Our calculation policy favours number lines through to Y3, although we do teach vertical addition in Y2 to about half the year group. (The most able in Y2 do Th,H,T,U on number lines - so we're not holding them back! They just jump in multiples of 10s and 100s!)

I actually find that number line + and - enables the children to do mental + and - of larger numbers more quickly, as they can visualise the number line.

Horses for courses!

I think you have to find a method that works for the child some of my children use 100 squares or base 10 rather than numberlines

We use number lines through to yr 4/5!

Yes, I like base 10 and smee's method for adding. We're not religiously tied to number lines! Fingers are quite useful too!

After years of sweating away with them, I gave up using 100 squares for adding and taking away. I find the children are confused by all the numbers written down in the wrong order (!), and don't really get the concept of adding tens from the patterns. I do use them for pattern in multiplication though, and sequences.

And in our school we do not call them units we call them ones.

OP - don't worry about teaching the 'wrong' method.

DD's school use a lot of approaches to maths so that the pupils can use the method that best fits the question or the one that they find easiest to use.

Much of what is taught is mental maths rather than written equations. After all when your in the queue at the post office how often do you work out the sum of what you need to buy on paper?

For 52 + 46 my dd would round to the nearest 10 and then sort out the differences.

i.e. 52 is nearly 50
46 is nearly 50

52 --50 take away 2
46 --50 add 4

50 + 50 = 100
4 - 2 = 2
100 - 2 = 98

when did "borrow one/pay it back and cary one to the doorstep" cease to be used in + - x and division?!!

(Why does someone not invent a proper division sign and put it on a standard keyboard...grrrr!)

When it became clear that a lot of children were just attempting to blindly follow the rule without having the faintest idea what they were actually doing (i.e. how a number breaks down into hundreds, tens, units, etc. and that each 1 in the tens column is equivalent to ten 1s in the units column).

(Professor, my post was slightly tongue in cheek rather than a genuine pop at the number of complex ways to reinvent the mathematical wheel )

So was mine, in theory, but it's late and that probably didn't come across well .

Can someone explain number lines to me? DS is a year off reception yet, but i'm very good at mental arithmetic etc, but crap at explaining it. eg:

'52 + 46 these days? I'd add 6+2, then 5+4, but are they taught to add the tens or hundreds first instead? '

My Dad taught me backwards maths, but I think it's the easiest way to do it.

52+46.

right, ignore the 2 and the 6. Add the 50 and the 40. That's easy, = 90.
Once yuou have that, treat teh 2 and the 6 like separate entities. This case is easy and it's 8. Answer is 98.

It's a very upsidedown way of doing it, but it works. I was the champion of mental arithmetic until I was 14.

can I just wade in and ask the teachers here, how much does it really matter, in your opinion(s), that children follow the methods they are taught in school? is it more important in the long run that they use methods they understand and can use successfully?

as someone said upthread, it's such a minefield, different methods every week it seems like.

OP, I have this book on my wishlist for the future as I've seen it recommended on MN countless times, I don't know if teachers approve though?

The whole point is teaching them a method that works AND they understand. There is a lot of time given to getting children to explain hpw they do it and trying different methods. There is no one correct way anymore!