PA.A.4.1
PA.A.4.1 Solve mathematical problems using linear equations with one variable where there could be one, infinitely many, or no solutions. Represent situations using linear equations and interpret solutions in the original context.
In a Nutshell
Students will extend their knowledge and skill of solving onevariable linear equations with one solution to linear equations containing infinitely many solutions and no solutions. The form of the equations will extend to include combining like terms as well as variables on both sides of the equation. Students will be asked to represent situations using equations and not only use the equations to solve the problem but to also determine if the solution is viable.
Student Actions

Teacher Actions


Develop Accurate and Appropriate Procedural Fluency when using efficient and accurate procedures with operations to solve more complex equations involving multiple steps and evaluate if a solution makes the equation true.

Develop the Ability to Communicate Mathematically when using words describing solutions to explain how the solution makes sense within the context of the situation through verbal, written, and visual explanations.

Develop a Deep and Flexible Conceptual Understanding when analyzing mathematical situations that have one solution, no solution, and infinitely many solutions and interpreting results within context.
 Develop the Ability to Make Conjectures, Model, and Generalize when determining whether an equation has one solution, no solution, or infinite solutions by looking for patterns or commonalities among different forms of equations.


Make mathematical connections by continuing to connect solutions to the mathematical situation they represent.

Promote procedural fluency by encouraging students to assess the reasonableness of a solution in the context of a situation and participate in the error analysis process.

Implement meaningful tasks that promote reasoning and problemsolving by allowing opportunities for students to examine onevariable linear equations in various forms and make sense of observed patterns and commonalities among the equations to categorize resulting solutions.
 Pose purposeful questions to lead students to discover the patterns and similarities between equations that have one solution, no solution, or infinitely many solutions.

Key Understandings

Misconceptions


Recognize a onevariable linear equation with one solution will result in a single variable with a coefficient of 1 which is equal to a constant that makes the equation true.

Recognize a onevariable linear equation with no solution results in the elimination of the variable terms and only constant terms remain when simplified. The result will be a statement that is not true.

Recognize a onevariable linear equation with infinitely many solutions has equivalent expressions on both sides of the equation and results in all variable terms and constant terms being eliminated when simplified.


Students may substitute a different value for the same variable on opposite sides of the equal signs.

Students may not recognize characteristics of equations with infinitely many and/or no solutions and assume a solution exists for the equation..

Students may forget to use and/or incorrectly use inverse operations when moving constants and variables across the equal sign.

Knowledge Connections

Prior Knowledge

Leads to



Use knowledge of solving equations with rational values to represent, use and apply mathematical models and interpret the solutions in the original context (A1.A.1.1).

Solve absolute value equations and interpret the solution in the original context (A1.A.1.2).

Solve equations involving several variables for one variable in terms of the others (A1.A.3.1).

OKMath Framework Introduction
PreAlgebra Introduction
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