Mental Math Blog
Full explanations of the shortcuts worth learning, one at a time — why each one works, worked examples, and an interactive demo you can try right in the post.
How to square numbers ending in 5
A number ending in 5 has a squaring shortcut that turns a multiplication into a lookup: take the leading digits, multiply by one more than themselves, and append 25. Here's why it works and how to make it automatic.
How to multiply numbers close to 100
Two numbers near 100 — like 97 and 103 — multiply much faster once you stop treating them as arbitrary numbers and start treating them as small deviations from 100.