Mental strategies
Some sums and products look hard on paper but are easy in your head. What makes them easy, and how do you turn a hard one into an easy one?
Where you are 2 inside
What this area is about
Mental math is not a faster way to run the paper method. It is a habit of changing a problem into an easier one with the same answer before working it out. A number close to a round one can be rounded and then fixed. A product can be reshaped, one factor halved and the other doubled, until it is one you already know. The skill is spotting when such a change pays off.
How these fit together
The area has two strategies, one for each pair of operations.
Adding and subtracting. Compensation when adding and subtracting adds or subtracts a round number and then takes back the extra, so 457 + 299 becomes 457 + 300 - 1.
Multiplying. Doubling, halving and quick products reshapes a product into an easier one with the same value, so 18 \times 25 becomes 9 \times 50, and halves to divide by 2 or 4.
A path through it
The two strategies stand apart; compensation usually comes first, since it needs only addition and subtraction.
Both feed the written method of partial sums and counting a handful of mixed coins.