Proportional Reasoning Vocabulary
Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts
Lesson
Set out your lesson
“Multiplicative reasoning vocabulary includes ratio, rate, unit rate, compound unit, and scale factor. In direct proportion both quantities change by the same factor; in inverse proportion one increases as the other decreases so their product stays constant.”
Bring to the table
- Paper
- Pencil
- 12 small objects
Extra for the adult
Worked example. Traveling 150 miles in 3 hours gives a unit rate of 50 miles per hour, a compound unit. Distance at constant speed is directly proportional to time; time for a fixed job can be inversely proportional to the number of equally productive workers.
Optional challenge. Write equations for one direct and one inverse proportion and explain how scale factor or constant product appears.
What to notice. Save a photo of the two tables and labeled vocabulary, or a short note quoting an accurate distinction between direct and inverse proportion.
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Teaching approaches
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1 approach
Multiplicative reasoning vocabulary includes ratio, rate, unit rate, compound unit, and scale factor. In direct proportion both quantities change by the same factor; in inverse proportion one increases as the other decreases so their product stays constant.
Spend 15–20 minutes matching ratio, rate, unit rate, compound unit, scale factor, direct proportion, and inverse proportion to examples.
Family records and proof options
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Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
PhET Interactive Simulations · Practice link — not the full lesson
Proportion Playground
Before you open · source notes
Proportion Playground supports hands-on exploration for Proportional Reasoning Vocabulary. Not every lab worksheet.
Free interactive page, no sign-in required for the tested path.
Before you openAsk the learner what they changed in the sim or page and what they observed.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
PhET Interactive Simulations. “Proportion Playground.” External page; Gakuva does not copy, host, embed, or redistribute materials.
Unknown — link only
Check understanding
- Distinguish between 'direct proportion' and 'inverse proportion' with real-world examples
- Use 'rate', 'speed', and 'density' correctly and explain what units they are measured in
- Calculate using compound measures — e.g. work out the speed of a car that travels 120 miles in 2 hours
“If your child is solving a problem about speed or density, can they explain what 'compound unit' means and tell the difference between direct proportion (more of one means more of the other) and inverse proportion (more of one means less of the other)?”
Curriculum record
- Type
- Language
- Subject
- Mathematics
- Domain
- Ratio & Proportion
- Age range
- Ages 11–14
Standards