In former units, such as Grade 6, Unit 8, students learned that expressions are equivalent if they have the same value and that equations are equivalent if they have the same solution. This unit vastly expands these foundations by introducing rational number coefficients and factors, as well as introducing the idea of generating equivalent equations by using the properties of equality and the distributive, associative, and commutative properties. Students may struggle with many subtle details of how to handle combining like terms, how to rearrange terms, and how exactly to perform operations on both sides of an equation. Lastly, the unit covers how to represent reallife situations as equations and how specific words and contexts could help us do so.
Key Concepts:
 Equivalent expressions always have the same value.
 Equivalent equations have the same solution, and properties of equality allow us to transform equations into other equivalent equations.
 Properties of operations hold for expressions that may have an unknown value.
Prior Knowledge Needed:
 Working with algebraic expressions; (Grade 6, Unit 8; 6.EE.A.34)
 Understanding, writing, and solving inequalities and equations; (Grade 6, Unit 9; 6.EE.B)
 Using rational number operations; (Grade 7, Units 4, Unit 5; 7.NS.A)
Units on the Horizon:
 Solving Equations and Inequalities (Grade 7, Unit 7)
 Solving Linear Equations (Grade 8, Unit 10)
Lessons

Lesson objective: Understand that equivalent expressions always have the same value. Students bring prior knowledge of equivalent expressions from 6.EE.A.3 and 6.EE.A.4. This prior knowledge is extended to expressions that include rational numbers as st...

Lesson objective: Rewrite expressions in simplest form by combining like terms. This lesson helps to build fluency with writing equivalent expressions. Tape diagrams are used here because they help emphasize that you can only add like terms because they...

Lesson objective: Understand that we can use the same operation on both sides of an equation to solve. Students bring prior knowledge of solving 1step equations from 6.EEB.7. This prior knowledge is extended to multistep equations as students solve fo...

Lesson objective: Solve twostep equations by performing the same operation on both sides. This lesson helps to build procedural skill with twostep equations. This work develops students' understanding that performing operations to both sides of an equ...

Lesson objective: Fluently solve equations of the form px + q = r with rational coefficients by multiplying. This lesson helps to build fluency with twostep equations. This work develops students' understanding that performing the same operation on bot...

Lesson objective: Apply solving multistep equations to a realworld scenario. This lesson provides an opportunity for students to apply their knowledge and understanding of solving equations to a reallife situation. Students are asked to construct an ...

Lesson objective: Students will understand that the distributive property holds for variable expressions as well as numerical expressions. Students bring prior knowledge of equivalent expressions from 7.EE.A.1. This prior knowledge is extended to distri...

Lesson objective: Fluently rewrite algebraic expressions using the distributive property. This lesson helps to build procedural skill with the distributive property. Area/tape diagram models are used here because they help students understand what it lo...

Lesson objective: Write and solve equations of the form p(x+q) = r. This lesson helps to build procedural skill with solving equations that involve the distributive property. Area models are used here because it supports the understanding of two differe...

Lesson objective: Solve problems using equations with the distributive property. This lesson provides an opportunity for students to apply their knowledge and understanding of solving and the distributive property to a reallife situation. Students are ...

Lesson objective: Understand that arithmetic and algebraic approaches to problem solving are related and may use the same operations. Students bring their prior knowledge of solving problems arithmetically and solving equations. This prior knowledge is ...

Lesson objective: Practice finding the meaning of the expressions that model an algebraic approach to problem solving. This lesson helps to build procedural skill with translating mathematical expressions. Students are presented with variable expression...

Lesson objective: Compare arithmetic and algebraic approaches to solving problems. This lesson helps to build procedural skill with algebraic and arithmetic problem solving. Comparison of the two approaches is used here because it encourages students to...

Lesson objective: Compare algebraic and arithmetic approaches to problem solving using number puzzles. This lesson provides an opportunity for students to apply their knowledge and understanding of problem solving to a mathematical situation. Students a...