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Mathematics · Grade 7

Proportional Relationships and Graphs

Learners compute unit rates from ratios of fractions (half a mile in a quarter hour is 2 miles per hour), test whether two quantities are proportional using tables and graphs, find the constant of proportionality in every representation and write equations of the form y = kx. The course ends by interpreting points on a proportional graph, especially (0, 0) and the unit-rate point (1, r).

  • 4 lessons
  • About 90 minutes
  • Proportional relationships check: 10 questions
  • Ways to answer: choose an answer, type a fraction, draw a graph, plot points, match pairs and type a number
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What learners will discover

  • Compute unit rates from ratios of fractions, including lengths, areas and other quantities in like or different units.
  • Decide whether two quantities are proportional by testing for equivalent ratios in a table or for a straight-line graph through the origin.
  • Identify the constant of proportionality in tables, graphs, equations and descriptions, and write proportional relationships as y = kx.
  • Explain what a point (x, y) on the graph of a proportional relationship means in context, including (0, 0) and the unit-rate point (1, r).

Lessons

  1. Unit rates with fractions 9 steps5 practiceabout 22 min
  2. Is it proportional? Tables and graphs 9 steps4 practiceabout 22 min
  3. The constant of proportionality and y = kx 9 steps5 practiceabout 23 min
  4. What the points on the graph mean 9 steps6 practiceabout 23 min
  5. Proportional relationships check 10 questions at the end

Keep exploring

Games to practice with

  • Number-Line HopHelp the frog hop to the right number — from counting to negative fractions.
  • Ratio KitchenScale recipes, fill ratio tables and find the better buy.
  • Coordinate CourierDrive the parcel van to the right address on the coordinate grid.

More 7th grade math

Guide for grown-ups