Mental math methods, with a reason to use each one.
“Speed math” is not one system. Sometimes the best move is to round a number and compensate; sometimes it is to split a product, recall a fact, follow a digit rule, or picture place value. Seeing when each method helps is more useful than memorising a list of tricks.
Compensate when a number is almost round
To add 398 + 57, move 2 from 57 to 398. The new calculation is 400 + 55 = 455. You have changed the shape of the calculation without changing its value. The same idea works for multiplication near 10 or 100, provided you keep track of what was added or removed.
398 + 57 = 400 + 55 = 455
Decompose when a factor has easy parts
For 24 × 13, write 13 as 10 + 3. Then 24 × 10 = 240 and 24 × 3 = 72. Add them for 312. This approach scales to larger numbers because the steps are ordinary multiplication and addition. Our mental multiplication guideshows a larger example and a near-100 method.
24 × 13 = 240 + 72 = 312
Rebuild a forgotten multiplication fact
If 7 × 8 does not come to mind, use 5 × 8 + 2 × 8 = 40 + 16 = 56. A derived answer is more trustworthy than a guess, and repeated derivation can help the fact become familiar. The multiplication-table tricks guidecovers 6, 7, 8 and 9 with checkable patterns.
Use a named method when its representation helps
The Trachtenberg methodgives digit-by-digit rules for operations such as multiplication. Its ×11 rule makes 43 × 11 into 4, then 4 + 3, then 3: 473. Soroban, the Japanese abacus, represents values with beads and rods; mental abacus calculation draws on that learnt representation. Our abacus guide explains the first steps.
Vedic mathematics includes other taught patterns, such as vertically-and-crosswise multiplication. See our worked Trachtenberg–Vedic comparisonbefore deciding which to practise. A name alone does not make a method suitable for every problem.
A short speed-math lesson plan
For a 15-minute lesson, use one objective: explain 9 × n as 10 × n − n. Spend three minutes asking learners how to find 10 × 7; four minutes demonstrating 9 × 7 = 70 − 7; five minutes practising 9 × 6, 9 × 8 and 9 × 14; then three minutes having learners explain and check one result. Accuracy and reasoning come before timing. This plan works for a class, a family practice session, or an adult studying alone.