Counting on is adding foward using fingers, when the number 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. Compensatng is done by splitting the new number into the old number and the leftover.
Counting on/back and rounding and compensating are easy stratigies to use for addition and subtraction, when numbers get too big to be solved with basic facts.
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