## Topic A: Representing and

Reasoning About Ratios

**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.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.

**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: ____________________________***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.)