Larger + Smaller

Remember that it's easier to add a smaller number to a larger e.g. 55+2 is easier to think about than 2+55

Group the same number

When you have a list of numbers to add, you can make a shortcut by spotting a list of numbers that are the same (receipts have lots of nines, for example)
8+9+2+8+7+8
Or re-arranging (to be clearer):
9+2+7+8+8+8
And thinking “3×8=24” so you have:
9+2+7+24

So on a receipt, you can cross off all the nines of the last column, counting how many nines there are.

Another little tip for adding a list of numbers e.g. on a receipt,  is to spot numbers that add up to 10 and cross them off with a pencil:
2+8=10, 7+3=10 etc.
So when adding these on paper:
1+2+7+8+9 there are two 10s here, the 2+8
1+2+7+8+9 that’s one 10
1+2+7+8+9 and there's the other one
So think 10+10+7=27

Another example:
5  8  2  7  5  6  3
8  2  7  5  6  3  think “10”
5  8  2  7  5  6  3  think “20”
5  8  2  7  5  6  3  think “30”
5  8  2  7  5  6  3  think “36”

A receipt example:
£3.45
£6.21
£8.86
12
£3.45
£6.21
£8.86
Adding the 10 pence column and insert a zero (to make adding easier)
 1 2 1 4
£3.45
£6.21
£8.86
 1 2 1 4 0 1 7 0 0 1 8 5 2 Adding them up

which is £18.52

Group in to 2 digits (starting from the right)

When thinking about a phone number, you naturally break it up:
01234123456 becomes 01234 12 34 56
So why not do that with maths? This makes remembering the numbers easier as well as calculating easier.
When I`m calculating large numbers in my head I think of 1475 as 14  75  (think fourteen, seventy-five) so

 1428 + 2231

 14 28 + 22 31 36 59

So it's easier to think about 28+31=59 then do the 14+22=36 rather than think of 1428+2231. Break the problem up in to smaller, manageable ones.
Carries still apply though:
2958+262

 29 58 + 2 62 32 20 58+62=120 so it's 20, carry one 1

Another little tip to do with the carry, I think in my head 29+1=30, 30+2=32 because it's easier to add 30+2 than 29+2+1. I add the carry to whatever number makes the calculation that bit easier.

Transfer from one pile to the other

Adding two numbers is like heaping two piles of things together so if you just took some from one pile and put it on the other, there's still the same amount of stuff:
So if I have to add in my head 61 + 29, I think “take 1 and put it on the other pile:
61 – 1 =60
29 + 1 = 30

60 + 30 = 90

Or 28 + 35, here I would take 2 from 35 and put it on 28
28 + 35 →  30 + 33
Which is 63

Another trick is when you're in a shop and there's lots of prices like £3.99, £9.99 etc. then you can round up, then take that one off:
£7.50 + £9.99 → £7.50 + £10 which is £17.50, then subtract the penny to obtain £17.49 exactly

A slightly harder implementation:
5.99+9.99
5.99 is one penny off 6 and 9.99 is one penny off 10 so
6 + 10 = 16 and subtract the 2 pence:
15.98
Then you see another price of 14.98 and you want to add this on, well 14.98 is two pence off of 15 so
15.98 + 14.98 becomes:
15.98 + 15 = 30.98
Take off the 2 pence: 30.96

This works for any number, especially numbers ending in 7, 8 or 9 which can be a bit tricky
44+18, since18 = 20 - 2
44 + 18 =
44 + 20 - 2
so add 20 to 44 making 64, then subtract the 2, making 62.
So this should make adding easier. Another example - when adding 19 to something, add 20, then subtract 1.

Align the decimal point and do the same

If you have 6.3 + 11.28, just align the decimal point, and do the same maths (add trailing zeros to make it look easier):

 6 • 30 + 22 • 31 28 • 61