# Lambda Math

> Field skill for teaching MATHEMATICS in λambda. Loads lambda-core (the learning-science foundation) and adds math-specific conventions — chief among them that every answer and every worked step is presented in SIMPLEST form (reduced fractions, simplified surds, rationalised denominators, exact forms, canonical expressions). Use whenever a session's course or topic is mathematics (stage5-math, yr10-maths, MATH courses, or any quantitative teaching).

- Skill: `abaj8494/lambda-math` (Agent Skill)
- Install (CLI): `npx skillmds@latest add abaj8494/lambda-math`
- Raw SKILL.md: https://api.skillmd.com/api/skills/abaj8494/lambda-math/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: abaj8494 (https://skillmd.com/u/abaj8494)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/abaj8494/lambda-math

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# λambda math — subject conventions

**Load `lambda-core` and `lambda-notation` first.** Its principles (retrieval, generation, spacing,
elaborative encoding, calibration, evidence provenance) govern every math
session. This skill adds only what is specific to mathematics.

## Simplify — always, and it is not optional

A student shown `6/8` instead of `3/4`, or `√12` instead of `2√3`, is handed a
second puzzle on top of the first — and often reads the answer as *wrong*
because it doesn't match the form they were taught. Present every answer AND
every worked step in simplest form:

- **Fractions → lowest terms.** `3/4`, not `6/8`. Improper vs mixed by level
  and context; state which convention the course uses.
- **Surds simplified, denominators rationalised.** `2√3`, not `√12`;
  `(√2)/2`, not `1/√2`.
- **Expressions canonical.** Collect like terms, cancel common factors, factor
  or expand to the form the question wants, write polynomials in standard
  order.
- **Answers reduced.** `x = 2`, never `x = 4/2`; a decimal only if one was
  asked for.
- **Exact by default.** Keep `√`, `π`, and fractions exact; give a decimal
  ONLY to a stated precision when the question asks or it is a measurement —
  and say which you are giving.
- **Units** on every applied answer.

**Run a simplify-pass before posting.** A math answer is not finished until it
is in simplest form and sanity-checked (magnitude and units plausible). This
is the math equivalent of the trace-every-point check for a chart: a
half-simplified answer is a wrong answer to a student.

## When simplification IS the miss

If the learner's error is *failing to simplify* — left it as `6/8`, didn't
rationalise — that is the teach step: show the reduction once, then have them
simplify the next one themselves (the generation effect from lambda-core).
Don't silently present the simplified form and move on; teach the move.

## Notation & level

- Plain school notation for the learner's level; expand every symbol they have
  not met; introduce no shorthand without naming it.
- Pitch to the *level*, not the topic: a Year-9-level student on Year-10
  content gets smaller steps and heavier simplification — not less rigour.
- One idea per line of working; a line the student cannot reproduce cold is a
  line taught too fast.

## MCQ distractors

Unsimplified forms make excellent distractors — the student who doesn't reduce
picks `6/8`, the one who mis-rationalises picks `1/√2`. But the CORRECT option
is always fully simplified; never make "simplest form" itself the trick.