Hi Bunzle:
absolutely hit this problem with DD1 who failed to subtract even 1 from 10 by May of Y2.
Like ScoobyBlue suggests - using objects (fingers are fine - but sometimes easier if not fingers) - can really help.
So I went the food route - and subtraction is perfect for this.
7 - 4. Try it with smarties, biscuits, grapes, raisins, whatever....
Give your DC 7. Ask them to eat 4. How many are left - count up - 3.
Now have them do it on paper.
Write it horizontally or vertically as you prefer (but beware that at school these problems are initially presented/ taught horizontally).
7 - 4 = 3
now draw 7 dots/ squares/ triangles. Cross out 4. how many left without crossing out - 3.
Now this is where 'place value' becomes really important. At some stage - and schools can gloss over this - it is important to understand that numbers we work with are 'base 10' - we use 0 - 9 and when we want to indicate more than 9 we start a new column.
-0
-1
-2
-3
-4
-5
-6
-7
-8
-9
10
11
12
...and so on
So you need to understand units/ tens/ hundreds (at least).
So working on your child identifying that in the number 349 - 3 = 3 hundreds, 4 = 4 tends and 9 = 9 units - really helps to decifer numbers.
Schools often teach DECONSTRUCTING methods - so working with numbers in terms of units, tens, hundreds, etc...
So adding 24 + 28 would be handled in several steps:
4 + 8 = 12
20 + 20 = 40
12 is actually 10 + 2
so add 10 to 40 = 50 and then add the 2 = 52
for 24 + 28 = 52.
It's very different from traditional vertical methods and some schools are very strict about when they want children to use this method - so my advice is if your child gets this deconstructing method GREAT. But if not, then try introducing traditional vertical method on the sly.
DD1 was very resistant at first - 'that's not the way Mrs. X does it' kind of thing - but eventually it made more sense.
When it comes to carrying (in either addition or subtraction) - it helps to use similar but differently sized objects - so grapes and raisins, duplo and lego bricks, small buttons and big buttons.
So with the 24 + 28 example using grapes & raisins
I would tell DD1 a grape = 10 and 1 raisin = 1 and ask her to show me 24 in grapes and raisins (2 grapes/ 4 raisins). Then show me 28 in grapes and raisins (2 grapes/ 8 raisins). now let's make a pile of grapes and a pile of raisins.
4 grapes and 12 raisins. Well we have more than 9 raisins here - so we're going to have to cash some in for a grape - so we need 10 raisins. Do we have it - yes, no problem - so that makes 1 grape and 2 raisins. We can add our new grape to the four grape plate and that gives us 5 grapes and 2 raisins which translates into 50 + 2 or 52.
This was the only way I could explain carrying to DD1 and it really seemed to turn that 'light bulb' on.
Some helpful place value games on Woodlands Junior Maths Zone: resources.woodlands-junior.kent.sch.uk/maths/interactive/numbers.htm#Place - really found the bead number game useful for helping make sense of place value/ carrying. The ghost counting interval games are excellent as well.
HTH