Tips for addition
The first tip for solving addition problems is to teach students to "count on." Counting on works by having the student count on from the biggest number or the largest addend in an addition problem. For example, in the problem 7+4= the student counts up from 7 (seven) aloud by saying 'seven,.... eight, nine, ten, eleven." The student can use his/her fingers, toes or other method.
The second tip is to look for doubles, like 4 + 4 or 6 + 6, and add them first in a long addition problem. This is done because most children learn their doubles before they learn random pairs of addends.
The third is to go to the 12 addition facts that are "one more than" the doubles: 1+2, 2+3, 3+4, etc, all the way up to 12+13. The answer is always one more than the doubles, which we definitely know. Example: 7+8: Since 7+7 = 14, then one more is 15.
The forth is to move on to the "doubles plus 2". 1+3, 2+4, 3+5, up to 11+13. There are 2 ways to look at this: First, the double plus 2 more (some kids like this). Notice that if you change the "piles" and borrow one from the larger pile and put it into the smaller, you have doubles - of the counting number that is "missing" between the two you are adding. We call this group the Missing Doubles. Example: 6+8: If you borrow one from 8, that leaves 7. Put the one you borrowed in the 6 pile and you have 7 again. So 6+8 is the same as 7+7 and that we know also. Notice that 7 is the counting number between 6 and 8.
The fifth is finger counting. When adding 6 + 4, students must ask themselves "Open or closed?" With addition it is open. They open their hands and raise up four fingers (the smallest number). The palm of their hand says "6" and then they continue counting on the four fingers to get the sum.
The last is to memorize the essential addition problems. For example: the zero plus rule and the Communicative Law of Addition (0+9=9 -or- 0+X=X and 9+0=9 -or- X+0=X).