In earlier units, students have written equivalent expressions and equations. In this unit, students will further develop their understanding by solving onestep equations and inequalities with nonnegative numbers. They will use a number line to represent their solutions to inequalities. Students may have difficulty understanding that problems and number lines with inequalities will have infinite solutions instead of just one. Students will continue to strengthen their understanding of variables as representations of unknown values.
Key Concepts:
 The solution of an equation is the set of values that make the equation true.
 Equivalent equations have the same solution.
 Because equations show a relationship between expressions, we can use the relational meaning of the equal sign to find a missing value in an equation.
Prior Knowledge Needed:
 Representing algebraic thinking, Grade 5, Unit 13, 5.OA.A
 Representing relationships, Grade 6, Unit 5, 6.EE.B6.C
 Algebraic expressions, Grade 6, Unit 8, 6.EE.A
Units on the Horizon:
 Solving Equations, Grade 7, Unit 6
 Solving Equations and Inequalities, Grade 7, Unit 7
 Solving Linear Equations, Grade 8, Unit 10
Lessons

Lesson objective: Understand how to substitute a given value for a variable into an equation and evaluate to determine if that value makes the equation true. Students bring prior knowledge of algebraic relationships from 5.OA.A. This prior knowledge is ...

Lesson objective: Fluently substitute and evaluate numbers in the specified set to determine which number makes the equation true. This lesson helps to build fluency with substituting numbers in for variables in an equation and evaluating the equation t...

Lesson objective: Apply understanding of substituting values in for variables and evaluting an inequality in order to solve realworld problems. This lesson provides an opportunity for students to apply their knowledge and understanding of substituting ...

Lesson objective: Understand that equivalent equations have the same solution. Students bring prior knowledge that mathematical relationships can be represented with expressions and that we can use those expressions as we use numbers from 6.EE.B6.C. Thi...

Lesson objective: Fluently identify equivalent equations. This lesson helps to build fluency with identifying equivalent equations. Tape diagrams and number lines are used here because they support students' understanding of how to informally solve equa...

Lesson objective: Apply understanding of equivalent equations to compare equation solutions. This lesson provides an opportunity for students to apply their knowledge and understanding of equivalent equations to a mathematical situation. Students are as...

Lesson objective: Use equations to solve problems. Students bring prior knowledge that mathematical relationships can be represented with expressions and that they can use those expressions as they use numbers from 6.EE.B6.C. This prior knowledge is ext...

Lesson objective: Fluently solve equations using inverse operations. This lesson helps to build procedural skills with using inverse operations to solve equations. Tape diagrams are used because it shows how students can determine the appropriate invers...

Lesson objective: Fluently solve equations with rational numbers by using inverse operations. This lesson helps to build procedural skill with using inverse operations to solve equations. Students apply their previous understanding of how to determine t...

Lesson objective: Apply understanding of how to solve equations in order to solve realworld problems. This lesson provides an opportunity for students to apply their knowledge and understanding of solving equations to a reallife situation. Students ar...

Lesson objective: Understand that inequalities show a relationship between expressions. Students bring prior knowledge of writing and solving equations to model equivalent relationships. This prior knowledge is extended to modeling relationships with in...

Lesson objective: Write inequalities to model situations. This lesson helps to build procedural skill using inequalities. Inequality symbols are used here because they model situations that have more than one solution. This work develops students' under...

Lesson objective: Solve onestep inequalities using the properties of equality for solving equations. This lesson helps to build procedural skill with solving inequalities. The structure of doing the same operation (addition, subtraction, multiplication...

Lesson objective: Understand that number lines are a visual way to represent inequalities. Students will critique the work of another student who has drawn several inequalities on number lines. Students bring prior knowledge of using number lines to loc...

Lesson objective: Graph inequalities on a number line using word problems and inequalities. This lesson helps to build the procedural skill of identifying inequality words with their corresponding number line graphs. A number line is used here because i...

Lesson objective: Write, solve and graph inequalites using word problems. This lesson provides an opportunity for students to apply their knowledge and understanding of inequalities to a reallife situation. Students are asked to write a recommendation ...