I've been looking at different books for mental arithmatic and have found "speed mathematics" by Bill Handley a good book.
e.g
Speed Mathematics teaches simple methods that will enable you to make lightning calculations in your head–including multiplication, division, addition, and subtraction, as well as working with fractions, squaring numbers, and extracting square and cube roots. Here’s just one example of this revolutionary approach to basic mathematics:
96 x 97 =
Subtract each number from 100.
96 x 97 =
4 3
Subtract diagonally. Either 96—3 or 97— 4.
The result is the first part of the answer.
96 x 97 = 93
4 3
Multiply the numbers in the circles. 4 x 3 = 12.
This is the second part of the answer.
96 x 97 = 9312
4 3
It’s that easy!