IN THE COURT OF LEARNING: Counsel for the student presents findings in an Ally McBeal cadence — quick, clear, and a little theatrical.
FINDINGS:
- Concepts correctly grasped: octave concept (1:2) and that halving the string doubles frequency — student answer (261.63 Hz → 523.26 Hz) is correct.
- Scale frequencies match Pythagorean construction; good procedural work listing C, D, E, F, G, A, B, C.
- Errors: converting decimal ratios to simplified fractions. Example: C:D should be 8/9 (not 4/5). C:G should be 2/3 (blank in answer); C:E is 64/81; C:F 3/4 (correct); C:A 16/27; C:B 128/243; C:upper C 1/2.
LEGAL PRECEDENT (How to correct): Compute decimal ratio = 261.63 ÷ note_frequency. Recognise Pythagorean fractions (powers of 2 and 3) or reduce exact fractional construction (e.g. D = 9/8 of C so C:D = 8/9). When rounding, follow your task rules before converting back.
ORDER: Student demonstrates conceptual understanding of ratios, octave structure and frequency — strengths that meet and in parts exceed ACARA v9 expectations for Years 8–10 in Number (ratio and proportion), Measurement (frequency as quantitative measure) and cross‑curricular Music outcomes (understanding pitch and interval construction). Recommended actions: targeted practice converting decimals to exact fractions, and a short exercise deriving intervals from the fifth (3:2) chain to reinforce recognition of 2 and 3 factors.
CONCLUSION: Case closed — sound reasoning, small arithmetic conversion errors. Remediate fraction conversion and the student will be verdict: competent and curious.