Students will understand that all linear equations in one variable or pairs of simultaneous linear equations in one variable have a solution even if that solution is “no solution.” Students will also be able to understand that linear equations in one variable can have one or infinitely many solutions. Students often struggle with this concept because they are used to solving equations for one variable where the solution is simply one point rather than infinitely many points, or even no point, on a number line. The concept that there are an infinite number of points between two integers will be introduced in this unit.
Key Concepts:
 Linear equations in one variable may have one solution, no solution, or infinitely many solutions.
 We can solve equations by writing a succession of equivalent equations until we write one we can solve by inspection.
 Properties of operations hold for expressions as we can operate on and with expressions just as we do with numbers.
Prior Knowledge Needed:
 Writing expressions
 Writing and solving equations
 Properties of operations, integers and rational numbers
Units on the Horizon:
 Solving linear equations in two variables
 Solving systems of linear equations in two variables
Lessons

Lesson objective: Students understand that not every equation has a solution; some have one, some have none, and some have infinitely many solutions. Students bring prior knowledge of solving equations from 7.EE.A.1 and 7.EE.A.2. This prior knowledge is...

Lesson objective: Students understand that not every equation has a solution; some have no solution, some have one solution, and some have infinitely many solutions. This lesson helps to build fluency with solving linear equations in one variable with n...

Lesson objective: Students understand that verbal expressions can be translated into mathematical expressions and equations. This lesson provides an opportunity for students to apply their knowledge and understanding of linear equations in one variable ...

Lesson objective: Students understand that equations can be solved by writing a succession of equivalent equations. Students bring prior knowledge of solving equations from 7.EE.A.1 and 7.EE.A.2. This prior knowledge is extended to solving linear equati...

Lesson objective: Students fluently understand that not every equation has a solution; some have no solution, some have one solution, and some have infinitely many solutions. This lesson helps to build fluency with solving linear equations in one variab...

Lesson objective: Students understand that equations can be developed from given solutions. This lesson provides an opportunity for students to apply their knowledge and understanding of linear equations in one variable to a mathematical situation. Stud...

Lesson objective: Students understand that properties of operations hold for expressions. Students bring prior knowledge of solving equations from 7.EE.A.1 and 7.EE.A.2. This prior knowledge is extended to solving linear equations in one variable as stu...

Lesson objective: Fluently solve equations in a variety of ways and understand that properties of operations hold for expressions. This lesson helps to build fluency with solving equations in one variable. Direct engagement in solving equations supports...

Lesson objective: Students fluently understand that equations can be solved in a variety of ways using operations performed in a different order. This lesson helps to build fluency with solving linear equations in one variable with one, no, or infinitel...

Lesson objective: Students understand that verbal expressions can be translated into mathematical expressions and equations. This lesson provides an opportunity for students to apply their knowledge and understanding of linear equations in one variable ...