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
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Teaching Table · Reviewed guide
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
Full guide and materials
- Paper
- Pencil
- 12 small objects
- Step 1. Build equivalent ratios and identify the scale factor.
- Step 2. Turn a rate into a unit rate and label its compound unit, such as miles per hour.
- Step 3. Use a direct-proportion table where doubling one quantity doubles the other.
- Step 4. Use an inverse-proportion table where more workers means fewer hours for a fixed task, and check that the product stays constant.
- Quick check. Present one ratio, one compound-unit rate, one direct proportion, and one inverse proportion. Success means your child names each relationship and explains the defining change.
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.
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Learning resources
Reviewed external links that reinforce this concept. They do not replace Gakuva’s teaching approach.
No reviewed resources for this concept yet.
The teaching approach above still stands. Curated practice links will appear here as the shelf fills.
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