Addition
Before we move on to written addition calculations it is useful to look at some basic methods of mental addition that you probably use all the time but have never thought about.
Number Bonds (pairs that make up a number)
It is important for your child to know the number bonds that can be made by using the numbers 0 to 10. Begin with a target number of 10 and find all the pairs of numbers that make up 10. Say a number (0 to 10) and ask for the matching number to make 10. you say '4'  they say '6 '  when they can do this easily, change the target number to 20  you say '12'  they say '8' and so on. Then work on all the numbers up to 20. Knowing all the number bonds to 20 will really help when your child progresses to written addition and subtraction.
Number bonds for 100 are particularly useful  start with tens  you say '10' they say '90', then work in the 5's  you say '25' they say '75' and so on.
Practice number bonds with this online Number Bond Machine.
Or practice your mental addition with Math Trainer.
Partitioning (splitting up numbers)
More difficult numbers can be broken up into smaller numbers which are easier to manage. 73 is the same as 70 and 3  19 is the same as 10 and 9.
So if you need to add 73 + 19, split the numbers into 70+10+3+9, add the tens up and then the units. Do the same with larger numbers  147 becomes 100+40+7.
Rounding
Say you needed to add 37 and 9  Round the 9 up to a 10 and add it to 37 to give 37+10=47, as 10 is 1 more than 9 you then need to subtract 1 from the total, 471=46. So 37+9=46.
To add 8 – first add 10 then take away 2 To add 7 – first add 10 then take away 3
To add 11 – add 10 then add another 1 To add 12 – add 10 then add another 2
To add 13 – add 10 then add another 3 To add 14 – add 10 then add another 4
To add 15 – either add 10 then add 5 or add 20 and then take away 5
To add 16 – add 20 then take away 4
Doubling and Halving
Practice doubling numbers up to 50 and halving numbers up to 100  use partitioning to make the numbers easier (double the tens first and then double the units) eg. for 27  20x2=40 7x2=14 40+14=54
If you need to add two similar numbers, say 33+35, you can double one of the numbers and then add or subtract the difference  33x2=66 then 66+2=68 or 35x2=70 then 702=68
Number Lines  counting on
To calculate 37+17  Draw a blank number line  mark the starting number, 37
partition the number that you wish to add in easy chunks  17 is 10 and 7
37+10=47 47+7=54
or 37+10=47 47+10=57 573=54
For a printable page of blank number lines
or various number lines
