HUNTERTUTORING

Study Guide — 7.RP.A.2

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Recognize and represent proportional relationships between quantities

Ratios and proportional relationships connect quantities — use tables, tape diagrams, and unit rates.

What this standard means

  • Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
  • Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
  • Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
  • Apply recognize and represent proportional relationships between quantities with models and explanation

_See printable PDF for diagram._

How to use the 20 practice sets

| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |

Pacing: 10–15 minutes per session.

How to practice

1. Write ratios in three forms: a:b, a/b, and words 2. Use double number lines for equivalent ratios 3. Find unit rate before scaling up or down

_See printable PDF for diagram._

Common mistakes

  • Mixing up part-to-part and part-to-whole ratios
  • Adding ratios instead of scaling
  • Forgetting units in unit rate answers

Review and practice tests

1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for 7.RP.A.2.

  • [ ] Writes and simplifies ratios correctly
  • [ ] Finds equivalent ratios from a table or diagram
  • [ ] Solves unit rate and percent problems in context

Materials for this standard

  • Practice Problems — 20 printable sets (computational and word problems)
  • Word Problems — 20 word-only sets plus 10 difficulty-tier sets
  • Review — 10 difficulty levels
  • Practice Test — 10 difficulty levels
  • Answer key — for parents and tutors

For your personal study only. Copying, printing, screenshotting, or sharing this material is not permitted and may result in loss of access.

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