Ratio Word Problems — Age 14 — Sailor Moon Style Printable (Frequencies, Intervals & Rhythms)

Student-facing printable worksheet in a playful Sailor Moon cadence that practises ratio problems using sound frequencies and rhythms. Includes teacher notes mapped to Australian Curriculum v9, step-by-step solutions, 100-word Sailor Moon–style teacher comments for each task, and extended rubrics with exemplary and proficient outcomes.

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In the name of the Moon — Ratio Word Problems

Drawing upon what you learned in the lesson, complete the following word problems. Write your working and answers in the spaces provided.

  1. Musical Interval — Frequencies
    A musician is playing notes with the frequencies 264.94 Hz and 529.88 Hz together. Will you like how these notes sound together? Justify your answer with mathematics then explain in words.
    Working and answer: ________________________________________________________________________
    _______________________________________________________________________________________
  2. Find a pleasing note
    A composer knows they find the sound of notes with the frequencies 220 Hz and 330 Hz pleasing to their ear. Find another note that, when paired with 330 Hz, the composer will find equally pleasing. Show your reasoning.
    Working and answer: ________________________________________________________________________
    _______________________________________________________________________________________
  3. Rhythm — Evenly spaced notes
    Tamya is playing a song on the piano that has 32 evenly spaced notes in a measure. How many evenly spaced notes would Luis need to play on the drums in order to make a 4:3 rhythm with Tamya? Show your working.
    Working and answer: ________________________________________________________________________
    _______________________________________________________________________________________
  4. Quick example — Clapping ratio
    Amorell and Erik are clapping two different beats at the same time. Amorell claps five times in the measure while Erik claps three times. What is the ratio of beats Amorell claps to beats Erik claps?
    Working and answer: _________________________________________________________________

Teacher Notes — Sailor Moon cadence (with solutions, ACARA v9 mapping, rubrics, and comments)

ACARA v9 mapping (suggested)

Year level: 8–9 (age 14). Mathematics — Number and Algebra: work with ratio, rate and proportion; apply ratios to solve practical problems. General capability: Numeracy. This set addresses recognising and working with ratios and proportional reasoning in real contexts (sound frequencies and rhythmic subdivisions).

Solutions and step-by-step explanations

  1. 264.94 Hz and 529.88 Hz

    Step 1 — Compute the ratio of the higher frequency to the lower: 529.88 ÷ 264.94 = 2. The ratio is 2:1 (or 1:2 depending on ordering).

    Step 2 — Interpret musically: a 2:1 frequency ratio is an octave, one of the most consonant (pleasing) intervals in Western music. So yes — mathematically these are an octave apart and usually sound pleasing together.

  2. 220 Hz and 330 Hz — find another note to pair with 330 Hz

    Step 1 — Find the ratio 330 ÷ 220 = 1.5 = 3/2. This is a perfect fifth interval (3:2).

    Step 2 — To find another note that pairs equally pleasing with 330 Hz, keep the same 3:2 proportion. An equally pleasing note above 330 is 330 × 3/2 = 495 Hz (a perfect fifth above 330). A pleasing note below is 330 × 2/3 = 220 Hz (the original).

    Answer: 495 Hz (or 220 Hz if asking for the lower partner).

  3. 32 notes and a 4:3 rhythm

    Step 1 — Interpret 4:3 as Tamya:Luis = 4:3. Tamya plays 32 notes which represent 4 equal parts. Each part = 32 ÷ 4 = 8 notes.

    Step 2 — Luis must play 3 parts so Luis plays 3 × 8 = 24 evenly spaced notes.

    Answer: 24 notes.

  4. Clapping example

    Amorell claps 5 times and Erik claps 3 times: ratio Amorell:Erik = 5:3. (Given example)

Extended rubrics (per task)

Each task is assessed along three criteria: (1) Correct calculation, (2) Use of proportional reasoning and simplification, (3) Clear explanation in words linked to the context. Two achievement levels shown below.

Exemplary: Correct numerical answer with fully simplified ratio or exact fraction; shows each step with clear arithmetic; includes an accurate interpretation tied to the musical or rhythmic context (mentions octave, perfect fifth, or how the subdivision forms the 4:3 relationship); uses correct units (Hz or note counts) and explains why the interval or rhythm is musically meaningful. Work is neat and complete.
Proficient: Correct answer and method shown; ratio simplified or correct fraction given; explanation present and mostly clear (may be brief), linking answer to context (e.g. says "octave" or "perfect fifth" or shows calculation for 4:3). Minor omissions in wording or small arithmetic rounding tolerated but reasoning is sound.

Teacher comments (Sailor Moon cadence) — 100-word guidance, one per task

Task 1 (264.94 Hz & 529.88 Hz) — Teacher comment (~100 words)

In the name of the Moon, I see your careful pairing of frequencies! You found the ratio 529.88 ÷ 264.94 = 2, and that is the magical 2:1 ratio called an octave. For full marks, show that calculation, name the interval (octave), and explain in words why a 2:1 frequency relationship sounds consonant — the wave cycles line up every second cycle, giving a steady blended tone. If you rounded during division, note the exact multiplication (264.94 × 2 = 529.88). Keep neat steps and always write units (Hz). Sailor clarity shines!

Task 2 (220 Hz & 330 Hz) — Teacher comment (~100 words)

In moonlit melody, you noticed 330 ÷ 220 = 3/2 — the perfect fifth. To show mastery, state the fraction 3/2, name the interval (perfect fifth), and then find another frequency that keeps that same ratio when paired with 330 Hz. Explain both directions: above 330 multiply by 3/2 to get 495 Hz, and below 330 multiply by 2/3 to get 220 Hz. Writing both options demonstrates understanding of proportional relationships and musical inversion. Be explicit with each arithmetic step and label your answer with Hz. Beautiful, harmonic reasoning!

Task 3 (32 notes and 4:3 rhythm) — Teacher comment (~100 words)

By moonbeam rhythm, you can divide 32 notes into 4 equal parts because Tamya represents the 4 in the 4:3 ratio. Show that each part is 32 ÷ 4 = 8 notes, then multiply by 3 to find Luis’s 3 parts: 3 × 8 = 24. Explain why this gives a 4:3 relationship — Tamya’s pulses happen at intervals of 8; Luis plays every one of 8 three times across the same measure. If the student misinterprets the ratio order, remind them to decide which musician corresponds to which number first. Clear labels win the day!

Task 4 (Clapping example 5:3) — Teacher comment (~100 words)

In the name of the Moon, this example is a simple check: Amorell claps 5 times, Erik claps 3 times, so the ratio is 5:3. Encourage students to write the ratio in simplest form (5:3 is already simplified) and to explain what it means: for every 5 claps by Amorell, Erik gives 3 claps in the same measure. Ask them to sketch or mark the beats to show alignment and to think about where the beats coincide — that visual link deepens proportional understanding. Praise correct work and ask for the alignment sketch if missing.

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