In this unit, students extend their understanding of ratio and proportion. Ratio tables are the primary representation taught for scaling ratios up and down, although students are welcome to use other methods. Students learn to look for relationships “within” the components of a ratio and “between” components of ratios that are in a proportional relationship. They learn that every ratio can be associated with a unit rate and that there are two different ways to write a unit rate. Students are likely to struggle with the concept that a fraction bar, ratio bar, and division bar are the same. It is important to keep careful track of the units in ratios and rates in order to scale them up and down correctly. The final five lessons connect ratios to percents. Percent is a rate per 100. To find percent, the whole is divided equally into one hundred parts. Knowing the whole is divided into 100 parts, use of the given percentage can allow students to take a value (percent) of the 100. Three types of percent problem are: part unknown, percent (or fraction) unknown, and whole unknown.
Key Concepts:
 Every ratio can be associated with a unit rate; the ratio a:b is associated with the unit rate a/b:1.
 In a proportional relationship, as one quantity changes, the other quantity changes in a way that preserves the multiplicative relationship.
 The same ratio or unit rate can be represented in many different ways.
Prior Knowledge Needed:
 Understand the concept of a ratio and use ratio language to describe a ratio relationship between 2 quantities. (6.RP.A.1)
Units on the Horizon:
 Representing Relationships (Grade 6, Unit 5)
 Proportional Reasoning (Grade 7, Unit 1)
 Introduction to Linearity (Grade 8, Unit 7)
Lessons

Lesson objective: Understand that two ratios can be scaled up or down in order to make a comparison. Students bring prior knowledge of ratio concepts and language from 6.RP.A.1. This prior knowledge is extended to create proportions as students use mult...

Lesson objective: Create and use ratio tables to identify quantities in a proportional relationship. This lesson provides an opportunity for students to practice creating and using ratio tables. Ratio tables are used here because they support multiplica...

Lesson objective: Solve problems involving proportional relationships. This lesson provides an opportunity for students to apply their knowledge and understanding of proportional relationships to a reallife situation. Students are asked to resize photo...

Lesson objective: Understand that every ratio can be written as a unit rate. Students bring prior knowledge of using ratios to solve problems from 6.RP.3. This prior knowledge is extended to use unit rates to compare ratios that are not easily scaled up...

Lesson objective: Practice finding unit rates, and use unit rates to compare and write other ratios. This lesson provides an opportunity for students to practice finding unit rates. Ratio tables are used here because they support the ability to scale up...

Objective: Understand and solve unit rate problems by using double number lines, tape diagrams, a table or other method to decide if a pay rate is fair. This optional activity can be used after Unit 2 Lesson 5. Math concept addressed: In this Guided Col...

Lesson objective: Apply knowledge of unit rate to determine which sibling grew faster. This lesson provides an opportunity for students to apply their knowledge and understanding of unit rate to a realworld situation. Students are asked to determine wh...

Lesson objective: Understand that there are two unit rates associated with quantities a and b in a proportional relationship: "a per one b" and "b per one a." Students bring prior knowledge of unit rate from 6.RP.A.2. This prior knowledge is extended to...

Lesson objective: Practice writing two different unit rates for quantities in a proportional relationship. This lesson helps to build fluency with converting ratios into unit rates. Ratio tables are used here because it supports students in keeping trac...

Lesson objective: Apply knowledge for writing unit rates in two different ways to decide who completed events the fastest. This lesson provides an opportunity for students to apply their knowledge and understanding of unit rate to a reallife situation....

Lesson objective: Understand that percent means standardizing ratios as a comparison to 100. Students bring prior knowledge of ratios from 6.RP.1. This prior knowledge is extended to percent as students use a double number line to compare ratios by usin...

Lesson objective: Use a double number line to determine percent of a given number. Students practice determining percent of a number. Double number lines are used here because this model supports using benchmark percents to determine another percent of ...

Lesson objective: Practice using a double number line to determine a number when a percent of it is known. Related to finding a percent of a number, a double number can also be used to find a number when a percent of it is known. A double number line is...

Lesson objective: Use ratio tables to organize values and practice scaling the values up or down to calculate percent. Students practice calculating percent using values in a ratio table. Ratio tables are used here because a ratio table can support scal...

Lesson objective: Apply the use of a double number line to solving problems involving percent. This lesson provides an opportunity for students to apply their knowledge and understanding of percent to a reallife situation. Students are asked to calcula...