Grade 7 · Proportional & Applied Math
Constant of Proportionality
Learn to compare quantities multiplicatively and reason with rates through clear explanations, worked examples, an interactive model, and guided practice.
Lesson coverage
Learn the whole topic, not just one problem type.
This lesson and its practice bank deliberately rotate across these core facets so students build a connected understanding of the subject.
Interpret multiplicative comparisons.
Scale both terms by the same factor.
Compare quantities per one unit.
Recognize proportional patterns in representations.
Solve rate, scale, and proportional reasoning problems.
Build the idea
Constant of Proportionality is part of the use proportional reasoning, rational-number operations, equations, geometry, probability, and statistics. Start by identifying what each quantity, symbol, diagram, or graph represents before calculating.
Ratio meaning
Interpret multiplicative comparisons. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Equivalent ratios
Scale both terms by the same factor. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Unit rates
Compare quantities per one unit. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Tables & graphs
Recognize proportional patterns in representations. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Applications
Solve rate, scale, and proportional reasoning problems. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Use a reliable strategy
Write the relationship in a consistent form, identify what stays equivalent, then scale or simplify while preserving that relationship.
Check and explain
A correct answer is only part of mathematical understanding. Check units, signs, scale, and whether the result makes sense. Then explain the relationship in words so you can recognize the same structure when the numbers or context change.
Key terms
Words to know
- Constant of Proportionality
- The central skill or relationship explored in this lesson.
- Ratio
- A comparison of two quantities by division.
- Rate
- A ratio comparing quantities with different units.
- Unit rate
- A rate expressed per one unit.
Interactive math lab
Change it. See it. Understand it.
Adjust the values and watch the relationship respond.
| Quantity A | 6 |
|---|---|
| Quantity B | 3 |
| Rate / ratio | 2 |
Worked examples
See the idea in action.
Scale both terms by the same factor.
Unit rate = total cost ÷ number of items = 5.
Guided practice
20 questions drawn from a 150-question lesson bank.
Each practice session mixes the major skills in this lesson so you practice the whole topic, not just one repeated problem type.
A group has 2 red objects for every 3 blue objects. Which ratio compares red to blue?
Curriculum reference
Built as a continuous K–12 progression.
The sequence follows widely used K–12 mathematics progressions and references the Common Core mathematics framework. Explanations, examples, interactive models, and practice questions are original FreeLearnHub material.