---
name: "speed_math_mental"
description: "Mental math fluency: teaches the verified mental-math tricks that actually work (Trachtenberg, Vedic, left-to-right arithmetic), an estimate-before-you-calculate protocol, and a five-minute daily drill generator. Use when someone wants faster mental arithmetic, better number sense, daily practice sets, or Fermi-style estimation help."
metadata: { "includeInPrompt": true }
---

# Speed Math: Mental

## Purpose
Make mental arithmetic fast and reliable. The skill covers three things: the small set of mental-math tricks that are genuinely verified, an estimate-first habit that catches wrong answers before they cost you, and a five-minute daily drill routine that builds automaticity. Everything here was checked against primary sources; see `references/trick-catalog.md` for the full catalog and the sources file for citations.

## Workflow

### 1. Teach the tricks (a few per session, never all at once)
Pick from `references/trick-catalog.md` based on what the person struggles with. Always work each example live, narrating each step, then give them one fresh problem to try. The highest-value five:
- Square numbers ending in 5: N(N+1), append 25. 35^2 = 1225.
- Multiply by 11: add each digit to its neighbor. 352 x 11 = 3872.
- Multiply by 5: halve, then append 0 (even) or 5 (odd). 2464 x 5 = 12320.
- Left-to-right addition/subtraction: break by place value, no carrying backwards. 476 + 385: 700, then 150, then 11, total 861.
- Near-base multiplication: (a-b)(a+b) = a^2 - b^2. 48 x 52 = 2500 - 4 = 2496.

### 2. Estimate before you calculate
This is the habit, not a trick. Before doing any exact calculation:
1. Round the numbers to something friendly and get a ballpark. (487 + 512: about 500 + 500 = 1000. Exact: 999.)
2. Run the exact method.
3. Compare. If the exact answer is far from the ballpark, redo it. Most mental-math errors are off-by-a-digit mistakes, and this catches them.
For questions with missing data, use the Fermi breakdown: split the big unknown into small sub-estimates you can guess (e.g. "how many piano tuners in Chicago" becomes people per tuner, households per tuner, tuners per shop). Multiply the sub-estimates; round numbers make the mental math trivial.

### 3. Run the daily drill
Generate a set with the bundled CLI:

```
python3 ~/workspace/skills/speed-math-mental/bin/drill.py --trick multiply-11 --count 10
```

Protocol: five minutes, one trick per day. Set a timer. Score yourself, then try to beat your own score next time you drill that trick (this "beat your score" framing is the timed-activity design the U.S. Dept of Education's What Works Clearinghouse rates as strong evidence). Rotate tricks across the week so each one gets hit every few days; the research case for short, frequent, spaced sessions over one long weekly cram is in the sources file.

## Output Contract
- When teaching: name the trick, show one worked example with every step visible, give one practice problem, then the answer with the working.
- When drilling: a printed problem set, a timer prompt, and an answer key where every answer was recomputed programmatically, never hand-typed.
- When estimating: the ballpark, the exact answer, and the comparison, in that order.

## Operating Rules
1. Every number in a worked example must be verified by actual computation before you show it. Recompute every answer yourself or run it through the drill CLI's checker; a wrong example teaches a wrong method.
2. Teach at most three new tricks in one session. Fluency comes from repetition, not coverage.
3. Never claim a trick "always works" beyond its documented domain. Squaring numbers ending in 5 works only for numbers ending in 5; say so.
4. Skip Vedic/Trachtenberg history as lesson content unless asked; the story is background, the method is the lesson. (Brief origin notes live in the references file.)
5. The drill CLI's `verify` mode recomputes all answers from scratch: run it after any change to the trick catalog.