With compensating, a student adds a bigger or smaller round number to the original number then takes away or adds the difference. For example, if the addition sum is 63 + 99, the student can look at the numbers and see which one can round up easily. In this example, 99 can round up to 100. The student will then add 63 to 100, making a total of 163. The student must then subtract the difference between 99 and 100, so subtracts 1 from her answer; 163 - 1 = 162, therefore 63 + 99 = 162.
If the addition was 17 + 21, 21 can be rounded down to 20. 20 is then added to 17 which makes 37. However, a further 1 needs to be added to compensate for 21 being rounded down so 37 + 1 = 38 and therefore, 17 + 21 = 38.
When teaching addition using compensation, ensure that students remember to add or subtract the amount that was left after rounding up or down.
If the numbers in the addition are doubles or near doubles, students can use prior knowledge to work out the answer. For example, with the sum 48 + 40, a student may know that doubling 40 makes 80, or he may know that four doubled is eight so therefore double 40 is 80. He can then use this knowledge to arrive at 40 + 40 = 80. He then adds 8 to his answer; 80 + 8 = 88, therefore 48 + 40 = 88.
Partitioning works by breaking down the sum into simpler components, then using previous number fact knowledge to work out the answer. In two-digit addition, the numbers can be partitioned into tens and units. For example, in the addition 22 + 44, a student first adds the tens: 20 + 40 = 60. He then adds the units: 2 + 4 = 6. He then adds the tens to the units: 60 + 4 = 64. Alternatively, he may simplify the stages by partitioning only one of the numbers into tens and units. If he chooses to partition 22, the addition would work as follows: 44 + 20 = 64 then 64 + 2 (from the partitioning of 22) = 66.
Once you have provided students with a range of strategies, it is important to give plenty of opportunities for practicing these strategies. Allow your students to use the method that works best for them. Give your class word problems to solve and relate learning to real life, using puzzles and projects that will interest students. Allow students access to online games and math software in order to practice addition skills. Try Scholastic or Enchanted Learning as starting points.