Getting Started 
Misconception/Error The student does not recognize the difference between inequality and equation or simply describes the meaning of the inequality symbols. 
Examples of Student Work at this Level The student:
 Refers to inequalities as equations.
 Describes inequalities as problems that have no solution.
 Describes the meaning of the inequality symbol.
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Questions Eliciting Thinking What is the difference between an inequality and an equation?
Can you show me an example of an inequality?
You told me the meaning of the inequality symbol. Can you tell me the meaning of solution? 
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 relating expressions using one of the symbols <,Â , >, or ), and solution (e.g., number that makes an equation or inequality true when substituted for a variable). Model examples and nonexamples of inequalities (e.g., x + 9 > 17, 2aÂ = 10, z Â 1.5). Explain that an inequality has a set of solutions, and this set of numbers is often infinite. Provide examples (e.g., x + 9 > 17 has the set of solutions x > 8 meaning any value greater than eight will make the inequality true). Provide opportunities for the student to solve inequalities and demonstrate that any number from the set of solutions makes the inequality true.
Provide examples of inequalities and sets of numbers from which the student must identify solutions. Ask the student to demonstrate that the solutions actually do satisfy the inequalities. 
Moving Forward 
Misconception/Error The student understands solutions of inequalities only in terms of the process of solving. 
Examples of Student Work at this Level The student provides an example of an inequality and describes the solution as the result of solving the inequality.

Questions Eliciting Thinking Is there only one value of the variable that makes the inequality a true statement?
Can you tell me what your solution means?
What makes a particular number a solution of the inequality? Is 24 a solution of the inequality x â€“ 15 > 6? 
Instructional Implications Clarify the definition of solution emphasizing that a solution is a value that when substituted for the variable makes the inequality a true statement. Explain that an inequality has a set of solutions, and this set of numbers can be infinite. Provide examples (e.g., x + 9 > 17 has the set of solutions x > 8 meaning any value greater than eight will make the inequality true). Provide opportunities for the student to solve inequalities and demonstrate that any number from the set of solutions makes the inequality true. 
Almost There 
Misconception/Error The studentâ€™s response is imprecise or fails to acknowledge that inequalities have multiple solutions. 
Examples of Student Work at this Level The student demonstrates an understanding of solutions of inequalities; however:
 The response is lengthy, imprecise, or contains nonmathematical vocabulary.
 The response does not acknowledge that the solution is a set of values.

Questions Eliciting Thinking How is the solution of an inequality different from the solution of an equation?
How would you determine if 12 is a solution of the inequality 2x â€“ 4 < x + 8? 
Instructional Implications Model precisely explaining what it means for a number to be in the set of solutions of an inequality. Reinforce that an inequality has a set of solutions, and this set of numbers may be infinite. Remind the student to use substitution to check several solutions when solving inequalities. Guide the student to use precise mathematical terms correctly when explaining or justifying mathematical work.
Consider using the MFAS task Finding Solutions of Inequalities. 
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 inequality as a set of values, any of which will make the inequality true when substituted for the variable. The student may provide an example and demonstrate how a particular value is a solution. 
Questions Eliciting Thinking Is it possible to name every single number that is a solution of an inequality?
How would you represent the solution of an inequality on the number line?
What if there were two variables in the inequality (e.g., x + y > 7)? What would a solution of this inequality look like? 
Instructional Implications Provide opportunities for the student to solve and graph the solutions of inequalities.
Consider using the MFAS tasks Transportation Number Lines or Rational Number Lines. 