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Mathematics · Grade 6

Ratios and Equivalent Representations

Learners describe relationships with ratio language, build equivalent ratios in tables and on double number lines, and solve part-part-whole problems with tape diagrams. They then graph ratio pairs, see that they fall on a line through the origin, and compare mixtures such as paint and lemonade.

  • 4 lessons
  • About 85 minutes
  • Ratios check: 10 questions
  • Ways to answer: fill in the blanks, choose an answer, draw a graph, plot points, match pairs and type a number
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What learners will discover

  • Use ratio language and notation (a:b, a to b, for every) for part-to-part and part-to-whole relationships.
  • Generate equivalent ratios with tables and double number lines and use them to find missing values.
  • Solve part-part-whole ratio problems with tape diagrams.
  • Plot pairs of equivalent ratios on the coordinate plane and use equivalent ratios to compare two mixtures.

Lessons

  1. The language of ratios 7 steps4 practiceabout 18 min
  2. Equivalent ratios in tables and on double number lines 8 steps5 practiceabout 22 min
  3. Tape diagrams for part-part-whole problems 7 steps4 practiceabout 22 min
  4. Graph and compare ratios 8 steps4 practiceabout 23 min
  5. Ratios 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.
  • Fraction BridgesSaw planks into equal parts, paint fractions, build bridges that match and lay planks end to end to add.
  • Ratio KitchenScale recipes, fill ratio tables and find the better buy.

More 6th grade math

Guide for grown-ups