## Module 1 - Ratios and

Proportional relationships

**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.

**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: ____________________________***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**à**Date: _____________________________________***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 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**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.)