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.

In plain words: Students solve real-world ratio and rate problems with tables, tape diagrams, double number lines, or equations.

Quick picks

Example problem: At the market, 8 apples cost $4.
How much do 9 apples cost?
Assign problem on Goblins →
Teach it with: Who is the fastest runner on Earth?6th grade · Unit rates · 3 min
Common mistake: Adding the same amount to both parts instead of multiplying (2:3 → 4:5 instead of 4:6).
Builds on: 6.RP.A.1Ratio language 6.RP.A.2Unit rate
Leads to: 7.RP.A.1Unit rates with fractions 7.RP.A.2Proportional relationships 7.RP.A.3Ratio and percent problems

6.RP.A.3.aRatio tablesMake 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.6.RP.A.3.bUnit rate and speedSolve unit rate problems including those involving unit pricing and constant speed.6.RP.A.3.cPercent of a quantityFind 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.6.RP.A.3.dConverting unitsUse ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Khan Academy Resources

Ratio tables 6.RP.A.3.a

Ratio tables Ratio tables Ratios with tape diagrams Part-part-whole ratios Ratios on coordinate plane Equivalent ratio word problems Equivalent ratios: recipe Ratios with tape diagrams Ratios and double number lines Ratios on coordinate plane Equivalent ratios Comparing rates example Solving ratio problems with tables

Unit rate and speed 6.RP.A.3.b

Rate review Equivalent ratio word problems Rate problems Comparing rates Proportion word problem: cookies Proportion word problem: hot dogs Rate problems Part to whole ratio word problem using tables

Percent of a quantity 6.RP.A.3.c

Converting percents and fractions review Converting between percents, fractions, & decimals Converting decimals and percents review Convert decimals to percents Convert percents to decimals Percent word problems Intro to percents Equivalent representations of percent problems Relate fractions, decimals, and percents Benchmark percents Percents from fraction models Convert percents to fractions Finding percents Solving percent problems Percent word problem: 100 is what percent of 80?Percent word problem: 78 is 15% of what number?The meaning of percent Meaning of 109%Converting percents to decimals & fractions example Converting decimals to percents: 1.501 Converting decimals to percents: 0.601 Percent word problem: recycling cans Finding common percentages Fraction, decimal, and percent from visual model Finding the whole with a tape diagram Finding a percent Converting percents to decimals: 113.9%Percents from fraction models Percent of a whole number Percent word problem: penguins Finding percentages with a double number line Converting percents to decimals: 59.2%

Converting units 6.RP.A.3.d

Ratios and units of measurement Ratios and measurement

Ratio and rate problems 6.RP.A.3

Equivalent ratios Create double number lines Relate double number lines and ratio tables Equivalent ratios with equal groups Understand equivalent ratios in the real world Equivalent ratios in the real world Ratios with double number lines Simplify a ratio from a tape diagram Ratios with tape diagrams (part:whole)Understanding equivalent ratios Interpreting unequal ratios

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6.RP.A.3: Ratio and rate problems