Teacher report (Ally McBeal cadence):
Oh! The courtroom of music and maths, where you, dear student, made a fine opening statement. You correctly identified the 1:2 ratio and that halving the string doubles frequency — C (261.63 Hz) to C' (523.26 Hz) — bravo. Your 2/3 work (G ≈ 392.45 Hz) and the cascading fifths to produce the Pythagorean C scale are essentially correct; rounding differences (±0.1–0.3 Hz) are acceptable at this level. Now — the twist! The interval table needs tidy-up. Example: C:D = 261.63/294.33 = 0.8888… which is 8/9 (not 4/5). C:G = 261.63/392.45 = 2/3; C:B ≈ 0.5267 → rounded to 0.53 → 53/100. Next steps: re-calculate each decimal ratio, apply the given rounding rule, then convert that decimal into a fraction. Clear method: divide, round as instructed, then express as fraction and simplify.
Parent comments (Ally McBeal cadence):
My! What a performance. We applauded the clever halving, the doubling of pitch, and the tidy scale. We stumbled on fraction conversion — easily fixed, together. Celebrate the correct scale-building method; practise the rounding-to-fraction step with two or three notes at a time. Encourage written steps: (1) divide, (2) round per rule, (3) convert to fraction, (4) simplify. Nudge toward using a calculator for the decimal and a small fraction table for conversion.
Overall alignment to ACARA v9 (Years 8–10):
These activities explicitly develop multiplicative reasoning and ratio proficiency (Number & Algebra: ratio and rates), apply measurement concepts to waves and sound (Measurement), and require problem solving and communicating mathematical reasoning. They meet — and in promoting real-world application and clear method use, exceed — expectations for middle to early senior secondary years.