What calculation shortcuts exist to help or speed-up mental (or paper) calculations?

To square a number ending in 5:

Remove the ending 5. Let the resulting number be n, and compute n(n+1). Append 25 to the end of n(n+1) and that's your answer.

Example: 85². Here, we drop the last digit to get 8, compute 8*9 = 72, so 85² = 7225. Similarly, we can compute 115². Here, we drop the last digit to get 11, compute 11*12 = 132, so 115² = 13225.

How does this work?: Note that (10n + 5)² = 100n² + 100n + 25 = 100 * n(n+1) + 25.

When squaring a number, break the calculation into three smaller calculations and add them using the FOIL method.

Example:

302^2 = 300^2 + 2*(300*2) + 2^2.