Estimation and mental math
When does an answer only need to be close, and how do you get close in a few seconds?
Where you are 5 inside
What this area is about
Many questions need “about how many”, not an exact count. An estimate answers them quickly, and it also checks an exact answer: if a worked-out result is far from the estimate, one of the two is wrong. Mental math is the companion habit of turning a problem into an easier one with the same answer, so it can be done without paper.
How these fit together
Estimating by rounding. Estimating by rounding rounds the numbers first and then computes. Estimating sums and differences applies that move to totals and gaps, written with \approx.
Choosing easier numbers. Friendly numbers picks nearby numbers that work well together, such as a multiple of the divisor, and says whether the estimate is over or under.
Exact, in your head. Mental strategies reshape a sum or product into an easier one with the same value, such as 457 + 299 = 457 + 300 - 1.
Huge quantities. Fermi estimation chains small guesses into a rough answer to a question nobody has counted.
A path through it
Estimating by rounding comes before friendly numbers, and friendly numbers before Fermi estimation. Sums and differences and mental strategies can come at any point.
Afterward, mental strategies feed partial sums and counting mixed coins, and friendly numbers feed long division, where a two-digit divisor needs an estimate at each step.