Compensation is an addition strategy in which you adjust one of the addends to make it a friendly number by taking an amount from the other other addend. This strategy works because of the Associative Property of Addition, which allows us to group addends in any way way we want. In the SmartBoard grab below, you will see how we used compensation to take .1 from 3.14 and group it with 2.9 to make 3 wholes. Our new expression was 3.04 (this was the previous 3.14) + 3 (the previous 2.9). 3.04 + 3 can easily be solved using mental math. Also, to the right, you can see how you could use compensation to adjust 16.18 + 5.94 to 16.12 + 6 = 22.12.
Our next two strategies are for subtraction. The first is using finding the difference by building up, and we can use an open number line to model this. Here we started by placing the subtrahend and minuend on the number line. Then we began at the subtrahend, and took jumps to get to to the minuend. Every times we took a jump, we record the distance traveled on top of the jump. We went from 1.83 to 2 (+.17), from 2 to 4 (+2), and from 4 to 4.67 (+.67). Then we added up the total distance traveled between the minuend and subtrahend and that was the difference.
The last strategy is called constant difference, and it is useful when the subtrahend is close to, but slight less than, a friendly number. In constant difference, we adjust both the minuend and the subtrahend by adding the same amount to both (however much you need to make make the subtrahend friendly will determine this amount) in order to make a friendly expression. See below how we added .09 to the minuend and subtrahend of 5.03-2.91 to change it to 5.12-3= 2.12. Underlying this strategy is the concept that if the minuend and subtrahend both increase by the same amount, the difference between them will not change.
