Lambda Math

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.