In this unit, students extend their work with ratios and proportional reasoning as they formalize their understanding of what it means for quantities to be in a proportional relationship. They formalize these relationships by writing equations to represent them, and later connecting the constant change to a straight line on a graph.
By the time they reach this unit, students can determine whether quantities in a table form a proportional relationship. They use these knowledge and skills throughout this unit as they learn that proportional relationships can be described using a constant of proportionality (unit rate) that appears in their equations. In later grades, this idea is connected to the concept of slope.
Key Concepts:
 The relationship of quantities that vary together in a constant multiplicative way can be represented with an equation (Introduced in Lesson 1).
 Data pairs can be shown on a coordinate plane, and the relationship of quantities that vary together in a constant way is displayed as a straight line through the origin (Introduced in Lesson 3).
 The constant of proportionality describes how one quantity changes when the other quantity changes by 1 (Introduced in Lesson 6).
Prior Knowledge Needed:
 A unit rate answers the question "How much for 1?" (Grade 6, Unit 2; 6.RP.A.2)
 Relationships between two quantities that change together can be represented using an equation. (Grade 6, Unit 5; 6.EE.C.9)
Units on the Horizon:
 Proportional reasoning with percents (Grade 7, Unit 3)
 Scale drawings (Grade 7, Unit 13)
 Functions (Grade 8, Unit 6)
Lessons

Lesson Objective: Understand that an equation showing the proportional relationship between two quantities includes two variables and a constant. Students will choose an equation that represents the relationship between and independent and dependent var...

Lesson Objective: Practice verifying that a proportional relationship between quantities exists and writing equations that represent those relationships. This lesson builds on students’ work with unit rate and equations. Students are presented with a ta...

Lesson Objective: Understand that equations and graphs present the same information about a relationship. Students write equations and draw graphs to represent the proportional relationship between distance and time when given a constant speed. This les...

Lesson Objective: Practice writing equations and making graphs using equivalent measurements given in inches or feet. Practicing with known measurement equivalencies helps students to check that the equations and graphs their drawing make sense. They ca...

Lesson Objective: Apply knowledge of representing proportional relationships with equations and graphs. Students will apply their knowledge of proportional relationships, equations, tables, and graphs to create a pitch to potential investors, their pare...

Lesson objective: Understand that the constant of proportionality is a number that describes how one quantity changes when the other quantity changes by one. Students bring prior knowledge of using equations to express the relationship between two quant...

Lesson objective: Determine the constant of proportionality using division and write equations for a real life situation. This lesson helps to build procedural skill with determining the constant of proportionality. Equations are used here because it sh...

Lesson objective: Understand that the graph of a proportional relationship passes through the origin and increases linearly. Students bring prior knowledge of graphing proportional relationships from 6.RP.A.3A. This prior knowledge is extended to findin...

Objective: Display data pairs to see if they vary together in a constant way. This optional activity can be used instead of or in support of Unit 2 Lesson 8. Math concept addressed: In this Guided Collaborative Task, students will use their knowledge an...

Lesson objective: Fluently identify and interpret the constant of proportionality from tables and graphs. This lesson helps to build fluency with identifying the constant of proportionality from tables and graphs. Graphs and tables are used here because...