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Today I sing like a monochord — proud, amused, a little theatrical. My thirteen-year-old began Unit 1 tuning into ratios: middle C at 261.63 Hz, halving strings to hear octaves, finding G by multiplying 2/3, and assembling a Pythagorean C scale. Skills: ratio sense, frequency computation, octave bounds. In Unit 2 we stepped into precise measurement and algebraic thinking: dividing frequencies, applying four rounding rules, converting terminating and repeating decimals back to fractions, and simplifying interval ratios. With gentle nudges and light support, my child moved from concrete ratio work to abstract decimal manipulation and fraction reconstruction, demonstrating procedural fluency, number sense, and justification. Standards progressed neatly: proportional reasoning → decimal operations and rounding → algebraic fraction derivation. Outcome: exemplary—confident calculations, clear work shown, and a grin when a repeating decimal finally became a tidy fraction. Encore? Parent note: poised for next study — temperament, critical listening, and independent application of math to music.


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