Author note — to cover

Definitions and classification: rational as one integer over another, including integers, terminating and recurring decimals; pi and non-square roots as irrational; deciding for root(9/16) and root 0.25. Foundation needs the vocabulary and examples; Higher links to surds. Irrationality proofs are A level. (N8, N10)

• Fluency — direct questions on rational and irrational numbers, limited to this lesson's stated scope (4 questions).
• Application — use the same skill in unfamiliar or contextual questions without introducing a later method (4 questions).
• Check — single-choice classification where root(9/16) and root 0.25 catch the 'roots are irrational' reflex; fraction-valued answers appear only as choice options (4 questions).