Module 1
Ratios and Unit Rates
Focus Standards
(6.RP.1) Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “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 nearly three votes.”
(6.RP.2) Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
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) 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.
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.
b. Solve unit rate problems including those involving unit pricing and constant speed. For example, 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?
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.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when
multiplying or dividing quantities.
(6.RP.1) Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “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 nearly three votes.”
(6.RP.2) Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
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) 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.
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.
b. Solve unit rate problems including those involving unit pricing and constant speed. For example, 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?
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.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when
multiplying or dividing quantities.
Topic A - Representing and reasoning about ratios
Lessons 1-1: Ratios (Math Notebook - A Ratio Is…)
Lessons 1-2: Ratios (Math Notebook - All About Ratios)
Lessons 3-4: Equivalent Ratios (Math Notebook - Equivalent Ratios)
Lessons 5-6: Solving Problems by Finding Equivalent Ratios
Lesson 7: Associated Ratios and the Value of a Ratio
Lesson 8: Equivalent Ratios Defined Through the Value of a Ratio
Assessment: 6.RP.1 and 6.RP.3 Date: ____________________________
Lessons 1-2: Ratios (Math Notebook - All About Ratios)
Lessons 3-4: Equivalent Ratios (Math Notebook - Equivalent Ratios)
Lessons 5-6: Solving Problems by Finding Equivalent Ratios
Lesson 7: Associated Ratios and the Value of a Ratio
Lesson 8: Equivalent Ratios Defined Through the Value of a Ratio
Assessment: 6.RP.1 and 6.RP.3 Date: ____________________________
topic b - collections of equivalent ratios
Lesson 9: Tables of Equivalent Ratios
Lesson 10: The Structure of Ratio Tables: Additive and Multiplicative
Lesson 11: Comparing Ratios Using Ratio Tables
Lesson 12: From Ratio Tables to Double Number Line Diagrams
Lesson 13: From Ratio Tables to Equations Using the Value of the Ratio
Lesson 14: From Ratio Tables, Equations, and Double Number Line Diagrams to Plots on the Coordinate Plane
Lesson 15: A Synthesis of Representations of Equivalent Ratio Collections
Assessment: Mid Module Assessment Date: _____________________________________
Lesson 10: The Structure of Ratio Tables: Additive and Multiplicative
Lesson 11: Comparing Ratios Using Ratio Tables
Lesson 12: From Ratio Tables to Double Number Line Diagrams
Lesson 13: From Ratio Tables to Equations Using the Value of the Ratio
Lesson 14: From Ratio Tables, Equations, and Double Number Line Diagrams to Plots on the Coordinate Plane
Lesson 15: A Synthesis of Representations of Equivalent Ratio Collections
Assessment: Mid Module Assessment Date: _____________________________________
topic C - unit rates
Lesson 16: From Ratios to Rates
Lesson 17: From Rates to Ratios
Lesson 18: Finding a Rate by Dividing Two Quantities
Lessons 19–20: Comparison Shopping—Unit Price and Related Measurement Conversions
Lessons 21–22: Getting the Job Done—Speed, Work, and Measurement Units
Lesson 23: Problem Solving Using Rates, Unit Rates, and Conversions
Assessment: 6.RP.2, 6.RP.3a and 6.RP.3b Date: ____________________________
Lesson 17: From Rates to Ratios
Lesson 18: Finding a Rate by Dividing Two Quantities
Lessons 19–20: Comparison Shopping—Unit Price and Related Measurement Conversions
Lessons 21–22: Getting the Job Done—Speed, Work, and Measurement Units
Lesson 23: Problem Solving Using Rates, Unit Rates, and Conversions
Assessment: 6.RP.2, 6.RP.3a and 6.RP.3b Date: ____________________________
topic D -
Lesson 24: Percent and Rates per 100
Lesson 25: A Fraction as a Percent
Lesson 26: Percent of a Quantity
Lessons 27–29: Solving Percent Problems
Assessment: End of Module Assessment Date: _____________________________________
Lesson 25: A Fraction as a Percent
Lesson 26: Percent of a Quantity
Lessons 27–29: Solving Percent Problems
Assessment: End of Module Assessment Date: _____________________________________
New or Recently Introduced Terms
Ratio (A pair of non-negative numbers, A:B, where both are not zero, and that are used to indicate that there is a relationship between two quantities such that when there are A units of one quantity, there are B units of the second quantity.)
Rate (A rate indicates, for a proportional relationship between two quantities, how many units of one quantity there are for every 1 unit of the second quantity. For a ratio of A:B between two quantities, the rate is A/B units of the first quantity per unit of the second quantity.)
Unit Rate (The numeric value of the rate, e.g., in the rate 2.5 mph, the unit rate is 2.5.)
Value of a Ratio (For the ratio A:B, the value of the ratio is the quotient A/B.)
Equivalent Ratios (Ratios that have the same value.)
Percent (Percent of a quantity is a rate per 100.)
Associated Ratios (e.g., if a popular shade of purple is made by mixing 2 cups of blue paint for every 3 cups of red paint, not only can we say that the ratio of blue paint to red paint in the mixture is 2:3, but we can discuss associated ratios such as the ratio of cups of red paint to cups of blue paint, the ratio of cups of blue paint to total cups of purple paint, the ratio of cups of red paint to total cups of purple paint, etc.)
Double Number Line (See example under Suggested Tools and Representations.)
Ratio Table (A table listing pairs of numbers that form equivalent ratios; see example under Suggested Tools and Representations.)
Rate (A rate indicates, for a proportional relationship between two quantities, how many units of one quantity there are for every 1 unit of the second quantity. For a ratio of A:B between two quantities, the rate is A/B units of the first quantity per unit of the second quantity.)
Unit Rate (The numeric value of the rate, e.g., in the rate 2.5 mph, the unit rate is 2.5.)
Value of a Ratio (For the ratio A:B, the value of the ratio is the quotient A/B.)
Equivalent Ratios (Ratios that have the same value.)
Percent (Percent of a quantity is a rate per 100.)
Associated Ratios (e.g., if a popular shade of purple is made by mixing 2 cups of blue paint for every 3 cups of red paint, not only can we say that the ratio of blue paint to red paint in the mixture is 2:3, but we can discuss associated ratios such as the ratio of cups of red paint to cups of blue paint, the ratio of cups of blue paint to total cups of purple paint, the ratio of cups of red paint to total cups of purple paint, etc.)
Double Number Line (See example under Suggested Tools and Representations.)
Ratio Table (A table listing pairs of numbers that form equivalent ratios; see example under Suggested Tools and Representations.)