Student: Ella McBeal (Age 13) — Units 1–2 Summary (ACARA v9 alignment)
Unit 1: Pythagorean Scale (Mathematics: Number & Algebra — Ratio and Proportion; Science: Waves & Sound)
Ella calculated the octave (1:2) from middle C (261.63 Hz), found the 2:3 derived pitches, adjusted values into the C octave and produced a complete Pythagorean C scale. Evidence: accurate frequency table and clear explanation of how halving the string raises pitch by an octave.
Unit 2: Interval Ratios (Mathematics: Real numbers, rounding, algebraic conversion)
Ella computed exact C:note ratios, applied four specified rounding rules, converted decimals (including repeating) back to simplified fractions and recorded final interval ratios. Work shows correct procedure for truncation, rounding and algebraic conversion of repeating decimals to fractions.
Progression of Standards Achieved
Unit 1 developed conceptual understanding of ratios and frequency. Unit 2 progressed to numerical precision, procedural fluency and algebraic reasoning — demonstrating growth from qualitative ratio construction to quantitative, rigorous ratio representation.
Outcome (Exemplary)
Work is accurate, all steps shown, notation clear and reasoning justified. Next steps: compare Pythagorean intervals with equal-tempered tuning and graph frequency deviations.