Ratios & Proportional
Relationships

Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates.

• 6.RP.A Understand ratio concepts and use ratio reasoning to solve problems.

  • 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

    • Write a ratio (6-R.1)

    • Write a ratio: word problems (6-R.3)

    • Which model represents the ratio? (6-R.4)

  • 6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b is not equal to 0, and use rate language in the context of a ratio relationship.

    • Unit rates (6-R.9)

  • 6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

    • 6.RP.3.a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

      • Identify equivalent ratios (6-R.5)

      • Write an equivalent ratio (6-R.6)

      • Ratio tables (6-R.7)

      • Equivalent ratios: word problems (6-R.8)

      • Ratios and rates: complete a table and make a graph (6-R.11)

    • 6.RP.3.b Solve unit rate problems including those involving unit pricing and constant speed.

      • Compare rates: word problems (6-R.14)

      • Ratios and rates: word problems (6-R.15)

      • Unit prices (6-V.2)

    • 6.RP.3.c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

      • What percentage is illustrated? (6-S.1)

      • Understanding percents: strip models (6-S.2)

      • Convert fractions to percents using grid models (6-S.3)

      • Convert between percents, fractions, and decimals (6-S.4)

      • Convert between percents, fractions, and decimals: word problems (6-S.5)

      • Solve percent problems using grid models (6-S.8)

      • Solve percent problems using strip models (6-S.9)

      • Percents of numbers and money amounts (6-S.10)

      • Percents of numbers: word problems (6-S.11)

      • Percents of numbers: fractional and decimal percents (6-S.12)

      • Find what percent one number is of another (6-S.13)

      • Find what percent one number is of another: word problems (6-S.14)

      • Find the total given a part and a percent (6-S.15)

      • Solve percent problems (6-S.16)

      • Solve percent word problems (6-S.17)

    • 6.RP.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

      • Convert and compare customary units (6-T.3)

      • Convert, compare, add, and subtract mixed customary units (6-T.4)

      • Customary unit conversions involving fractions and mixed numbers (6-T.6)

      • Convert and compare metric units (6-T.7)

      • Convert between customary and metric systems (6-T.8)