Mental computation

Mental computation is doing addition, subtraction, multiplication, or division "in one's head" without using paper and pencil, or a calculator. There are many ways to do mental computation. A few of them include using basic facts, front-end estimation, and compatible numbers.

Example using basic facts:

If a 6-pack of candy bars costs $2.40, How much does each candy bar cost?

2.40 ÷ 6 = ?

One solution strategy is to think 24 ÷ 6 = 4 (using a basic fact)

Thus 2.40 ÷ 6 = 0.40

Therefore each candy bar costs $0.40.

Example using front-end estimation:
Bob and Joan traveled 313 miles on the first day of their trip and 178 miles on the second day. How many miles did they travel in total?
313 + 178 = ?
One solution strategy is to think:
300 + 100 = 400
10 + 70 = 80
3 + 8 = 11
400 + 80 + 11 = 491
Thus, Bob and Joan traveled 491 miles in total.
Example using compatible numbers:
The 32 students in Mr. Clark's class surveyed their favorite fast foods. Of these students, 13 listed pizza as their favorite. How many listed some other food?
32 - 13 = ?
One solution strategy is to think 32 is close to 33. 33 and 13 are compatible numbers. That is, 33 - 13 is easy to compute mentally:
33 - 13 = 20
33 is 1 more than 32, so I will need to subtract 1 from 20.
20 - 1 = 19
So, in Mr. Clark's class, 19 students listed some fast food other than pizza as their favorite.

Also called mental arithmetic, mental math, and mental mathematics.

See also compatible numbers, estimation strategies, front-end estimation.