In my previous entry concerning Dr. Arthur Benjamin, I mentioned that I'd like to find his Mathemagics lecture. It's now been posted over on YouTube!

The complete lecture itself teaches how to improve your mental calculation skills, and is very clearly taught. These videos also came with audio tapes and a workbook, which are referred to in the videos. It's not hard to make up your own sample problems, however.

The above video is only the first of 11 parts. Here's an index for the complete set of Mathemagic video clips:

Part 1: Introduction, Adding 2- and 3-digit numbers
Part 2: Adding 2- and 3-digit numbers, Calculating tips, Subtracting 2- and 3-digit numbers
Part 3: Subtracting 2- and 3-digit numbers
Part 4: Subtracting 2- and 3-digit numbers, Multiplying 2- and 3-digit numbers by 1-digit numbers
Part 5: Multiplying 3-digit numbers by 1-digit numbers, Percentages, Division of 2- and 3-digit numbers by 1-digit numbers
Part 6: Division of 3-digit numbers by 1-digit numbers
Part 7: Multiplying fractions
Part 8: Multiplying, Adding and subtracting fractions, Converting fractions to decimals
Part 9: Converting fractions to decimals, Estimation, Squaring
Part 10: Squaring, Algebra
Part 11: Algebra, Fibonacci addition trick

Towards the end, there are a few times you are referred to the workbook for a more detailed explanation. Here are some links on the web that can give you the required explanations:

Converting fractions to decimals
The 1089 trick
How did Dr. Benjamin predict the result of digit #11 divided by digit #10?

Video Format:
YouTube