Getting Started 
Misconception/Error The student does not understand the meaning of equation. 
Examples of Student Work at this Level The student:
 Refers to equations as inequalities.
Â Â Â
 Describes equations as â€śproblems.â€ť
 Does not refer to equations but describes a solution as the result of a computation.

Questions Eliciting Thinking Can you show me an example of an equation?
What do equations that need to be solved contain?
What is the difference between an equation and an inequality? 
Instructional Implications Review relevant vocabulary: variable (e.g., letter that stands for a number or numbers), expression (e.g., representation of a value that can include numbers, variables, and operations), equation (e.g., statement that two expressions are equal), inequality (e.g., statement using one of the symbols, <,,>, or ), and solution (e.g., number that makes an equation true when substituted for a variable). Model examples and nonexamples of equations (e.g., x + 9 = 17, 2aÂ > 10,Â z Â 1.5). Explain that an equation may have one, many, or no solutions and provide an example of each case [e.g., x + 9 = 17, 2aÂ + 2 = 2(a+1), nÂ =Â nÂ + 1]. Provide opportunities for the student to solve equations and demonstrate that the solution makes the equation true.
Provide examples of equations and sets of numbers from which the student must identify solutions. Ask the student to demonstrate that the solutions actually do satisfy the equations. 
Moving Forward 
Misconception/Error The student understands solutions of equations only in terms of the process of solving. 
Examples of Student Work at this Level The student provides an example of an equation and describes the solution as the result of solving the equation.
Â Â Â
Â
Â 
Questions Eliciting Thinking What is the meaning of the word solution?
Suppose I gave you an equation (e.g., x + 3 = 8) and a solution (e.g., five). How would you demonstrate that five is a solution? 
Instructional Implications Clarify the definition of solution emphasizing that a solution is a value that when substituted for the variable in the equation makes the equation a true statement. Explain that an equation may have one, many, or no solutions and provide an example of each case [e.g., x + 9 = 17, 2aÂ + 2 = 2(aÂ + 1), nÂ = nÂ + 1]. Provide opportunities for the student to solve equations and demonstrate that the solution makes the equation true. 
Almost There 
Misconception/Error The studentâ€™s response is not concise, focused, or wellwritten. 
Examples of Student Work at this Level The student demonstrates an understanding of what it means for a number to be a solution of an equation but the studentâ€™s response is lengthy, imprecise, or contains nonmathematical vocabulary.
Â Â Â

Questions Eliciting Thinking What mathematical word describes replacing the variable in the equation with a number?
Illustrating with an example is very good, but can you explain in general what it means for a number to be a solution of an equation?
Is it possible for an equation to have more than one solution?
Can you think of an example of an equation that has more than one solution? 
Instructional Implications Model precisely explaining what it means for a number to be a solution of an equation. Reinforce the definition of solution by asking the student to check solutions when solving equations. Guide the student to use precise mathematical terms correctly when explaining or justifying mathematical work.
Consider implementing the MFAS task Finding Solutions of Equations (6.EE.2.5). 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student describes the solution of an equation as a value that when substituted for the variable makes the equation a true statement. The student may provide an example and demonstrate how a particular value is a solution. 
Questions Eliciting Thinking How would you determine if 12 is a solution of the equation 2x â€“ 4 = x + 8?
Is it possible for an equation to have more than one solution?
Can you think of an example of an equation that has more than one solution?
What if there were two variables in the equation (e.g., x + y = 7)? What would a solution of this equation look like? 
Instructional Implications Provide opportunities for the student to solve and interpret the solutions of inequalities.
Challenge the student to write an equation that has no solutions, two solutions, or infinitely many solutions.
Consider implementing the MFAS tasks Solutions of Inequalities or Finding Solutions of Inequalities (6EE.2.5). 