Counting on is adding foward using fingers when the number is added is under ten. Counting back is subtracting using fingers, when the number subtracted is under ten.
Rounding and compensating is rounding the added or subtracted number to the nearest tidy number, then compensating for the rounding. Compensating is done by splitting the new number into the old number and the leftover.
Counting on/back and rounding and compensating are easy strategies for addition and subtraction, when numbers get to big to be solved with basic facts.
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