In this unit, students will extend their understanding of proportional relationships and unit rates to write expressions and equations that model the relationship between proportional quantities. Students will identify the independent and dependent quantities, model the relationship in multiple ways, and find missing values in the relationship.
Key Concepts:
 Mathematical relationships can be represented with expressions, and we can use those expressions as we use numbers (Lesson 1)
 The relationship between two quantities that change together can be shown with an equation using variables to represent the two quantities. Because the value of one quantity depends on the value of the other, these variables are called independent and dependent variables. (Lesson 5)
 We can model the relationship between independent and dependent variables using equations. (Lesson 9)
Prior Knowledge Needed:
 Performing Operations with decimals (Grade 5, Unit 10; 5.NBT.B.7)
 Ratios; (Grade 6, Unit 1; 6.RP.A.1 & 6.RP.A.3)
 Rates, including percent; (Grade 6, Unit 2; 6.NS.B.3 & 6.RP.A.2)
 Dividing Fractions; (Grade 6, Unit 4; 6.NS.A.1)
 Understanding fraction equivalence and comparison; (Grade 4, Unit 5; 4.NF.A.1)
Units on the Horizon:
 Relationships in the coordinate plane (Grade 6, Unit 7)
 Algebraic expressions (Grade 6, Unit 8)
 Proportional relationships (Grade 7, Unit 2)
 Introduction to linearity (Grade 8, Unit 7)
Lessons

Lesson objective: Understand that numerical values can be represented as expressions using a ratio and multiplication. Students bring prior knowledge of ratios from 6.RP.A.3. This prior knowledge is extended to expressions as students use the ratio to w...

Lesson objective: Fluently multiply and divide within a table to find a ratio to help write an algebraic expression. This lesson helps to build fluency with writing expressions. A table is used here because it highlights the relationship within the rati...

Lesson objective: Fluently write expressions and use substitution to solve realworld mathematical problems. This lesson helps to build fluency with writing algebraic expressions. A table is used here because it supports the previous ratio and unit rate...

Lesson objective: Apply the understanding of writing expressions to represent recipe amounts. This lesson provides an opportunity for students to apply their knowledge and understanding of writing expressions to a reallife situation. Students are asked...

Lesson objective: Extend understanding that mathematical relationships can be written as expressions and we can show the relationship between the expressions with an equation using variables to represent quantities. Students bring prior knowledge of exp...

Lesson objective: Graph coordinate points from an equation using a table. This lesson helps to build fluency with graphing coordinate points from an equation. A table is used here because it shows the relationship between the equation and the graph. Thi...

Lesson objective: Fluently write equations from tables, graphs, situations, and patterns. This lesson helps to build fluency with writing equations. Tables, graphs, situaitons, and patterns are used here because each support the development of the indep...

Lesson objective: Apply the knowledge of how equations, graphs, and tables relate. This lesson provides an opportunity for students to apply their knowledge and understanding of equations to a reallife situation. Students are asked to write three equat...

Lesson objective: Understand that we can model the relationship between independent and dependent variables using equations. Students bring prior knowledge of expressions from 6.EE.B.6. This prior knowledge is extended to independent and dependent varia...

Lesson objective: Fluently match equations with tables, graphs, situations, or patterns with the same relationship while playing a game. This lesson helps to build fluency with independent and dependent variables. Tables, graphs, scenarios, and patterns...

Lesson objective: Extend understanding that the relationship between variables can be used to write equations. Students begin to use equations to find missing values within the relationship. Students bring prior knowledge of unit rate from 6.RP.3. This ...

Lesson objective: Solve problems using the relationship between variables. This lesson provides an opportunity for students to apply their knowledge and understanding of ratio relationships to a reallife situation. Students are asked to determine which...

Lesson objective: Write equations that model the relationship between two proportional variables and use the equation to identify missing values within the relationship. This lesson helps to build procedural skill with writing equations that model propo...

Lesson objective: Find missing values in a data set using points on a graph. This lesson helps to build procedural skill with finding missing values within a data set by using the relationship between the variables. Graphs are used here because they dee...

Lesson objective: Apply knowledge of unit rates to convert various currencies to US dollars. This lesson provides an opportunity for students to apply their knowledge and understanding of relationships between variables to a reallife situation. Student...