Ratios, Unit Rate, and Percentages
Students will build on their knowledge of fractions as they use ratios and rates to describe relationships. Students will be able to describe ratios, unit rates, and percentages. Students will use tables and graphs to represent these relationships.
Essential Outcomes
Ratios and Proportional Relationships
Ratio
- 6.RP.1 – Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received three votes.”
- 6.RP.3 – Use ratio and rate reasoning to solve real-world and mathematical problems. Note: Strategies may include but are not limited to the following: tables of equivalent ratios, tape diagrams, double number lines, and equations.
- 6.RP.3a – 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.
- 6.RP.3d – Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Note: Conversion of units occur within a given measurement system, not across different measurement systems.
Unit Rate
- 6.RP.2 – Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal to zero), and use rate language in the context of a ratio relationship. e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there are 3⁄4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Note: Expectations for unit rates in this grade are limited to non-complex fractions.
- 6.RP.3 – Use ratio and rate reasoning to solve real-world and mathematical problems. Note: Strategies may include but are not limited to the following: tables of equivalent ratios, tape diagrams, double number lines, and equations.
- 6.RP.3b – Solve unit rate problems. e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? What is the unit rate? Note: Problems may include unit pricing and constant speed.
Proportional Reasoning with Percentages
- 6.RP.3 – Use ratio and rate reasoning to solve real-world and mathematical problems. Note: Strategies may include but are not limited to the following: tables of equivalent ratios, tape diagrams, double number lines, and equations.
- 6.RP.3c – Find a percent of a quantity as a rate per 100. Solve problems that involve finding the whole given a part and the percent, and finding a part of a whole given the percent. e.g., 30% of a quantity means 30/100 times the quantity.
Other Standards Addressed in this Unit
Expressions, Equations and Inequalities
- 6.EE.9- build base knowledge – Use variables to represent two quantities in a real-world problem that change in relationship to one another. Given a verbal context and an equation, identify the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
- e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times.
- e.g., Given the equation d = 65t to represent the relationship between distance and time, identify t as the independent variable and d as the dependent variable.
Essential Questions and Big Ideas
- What is a ratio?
- A ratio is a numerical relationship that represents how many times a number fits within another.
- What is a rate?
- A rate is a special type of ratio that shows the relationship between two different units.
- What is a unit rate?
- A unit rate represents the amount of a unit per one unit of another.
- How are percentages related to ratios?
- A percentage represents a ratio where you’re considering how much of an amount within 100.
- A percentage represents a part: whole ratio, not a part: part ratio.
- How do I solve problems with ratios, rates, or percentages?
- Tables and graphs can be used to solve problems with ratios, rates, or percentages.
- Fractions can be used to relate to ratios, rates, or percentages.
Download the complete Grade 6 Math Unit 1 framework to customize for your own planning.