Students began their study of ratios and using proportional reasoning in grade 6. By grade 7, students also know how to perform multiplication and division with fractions and decimals. The lessons in this unit combine the use of fractions and decimals with more complex proportional situations using rates that are not restricted to whole numbers.
"Reasoning up and down" with ratios is emphasized throughout the unit, both through working toward a unit rate and through working with relationships within and between ratio pairs. When students use relationships between ratio pairs, they think about scaling both ratio components in the same way. This maintains the relationship between the quantities as they change together in the same way multiplicatively.
When students work with the relationship within a ratio, they use a multiplicative comparison. For instance, in the ratio of 3 practice balls for every 6 players, we think about always needing a number of practice balls that is 1/2 the number of players. This should remain true for any number of balls and players. The "within" relationship prepares students for learning about slope in later units. The unit provides a variety of ratio situations, including those with like and unlike units, modeled using tools such as tape diagrams and double number lines.
Key Concepts:
 Proportional relationships show two quantities that change together in a constant way, and are not limited to whole number quantities (Introduced in Lesson 1).
 The inverse relationship of multiplication and division is useful in solving problems about proportional relationships (Introduced in Lesson 2).
 Proportional relationships may exist between quantities with like units, as well as unlike units (Introduced in Lesson 4 and 7).
Prior Knowledge Needed:
 Compute unit rates (Grade 6, Unit 2; 6.RP.A.2)
 Compute with fractions and decimals (Grade 6, Unit 3; 6.NS.B.3; Grade 6, Unit 4, 6.NS.A.1)
 Dividing fractions by fractions (Grade 6, Unit 4; 6.NS.A.1)
 Writing and solving equations (Grade 6, Unit 9; 6.EE.B.7)
Units on the Horizon:
 Proportional Relationships (Grade 7, Unit 2; 7.RP.A.2)
 Proportional Reasoning with Percents (Grade 7, Unit 3; 7.RP.A.3)
Lessons

Lesson Objective: Understand that there are multiple ways to maintain a given proportional relationship. Some of these ways include: using multiplication or division to scale quantities up or down, finding a unit rate, or using other multiplicative reas...

Lesson Objective: Use understanding of the meaning of unit rate as “How much for one?” and use multiplication and division strategies to complete tables of related values. Students will reason with both the relationship between number of items, and with...

Lesson Objective: Apply understanding of both between and within relationships with like units. In this lesson, students adjust dimensions to create different sizes of bracelets. They may work with the between relationship as they adjust the lengths bas...

Lesson Objective: Understand that we can use the same multiplication ideas with fractions as we can with whole numbers to maintain proportional relationships. Students use their understanding of proportional relationships, as well as their understanding...

Lesson Objective: Practice changing quantities with like units to maintain a proportional relationship. Students work with money to maintain a savings plan. Tape diagrams are used to represent the relationship, and students work with varying values of m...

Lesson Objective: Apply understanding of proportional relationships and use tape diagrams to model relationships and solve problems. Students apply what they have learned about proportional relationships to decipher a cryptic recipe that describes the r...

Lesson Objective: Understand that the relationship between distance traveled and time elapsed may be proportional, and we can report that relationship with one number representing a speed. Students will work toward understanding that we can use unit rat...

Lesson Objective: Practice relating unlike units on double lines and reinforce understanding of intervals on the number lines. Students practice maintaining proportional relationships and finding missing values using double number lines. The parallel nu...

Lesson Objective: Apply knowledge of unit rates and use multiple number lines to compare the costs across three items. Students are typically asked to work with two rates. In this application problem, students compare three pairs of quantities that vary...