Getting Started 
Misconception/Error The student is unable to correctly apply algebraic properties to solve the inequality. 
Examples of Student Work at this Level The student is unable to solve the inequality. The student:
 Does not understand how to apply the distributive property.
 Attempts to add a quantity to an expression enclosed in parentheses that is a factor of another expression.
 Does not understand how to apply properties of equality and attempts to add or subtract a quantity twice from one side of the inequality.
 Does not understand how to combine like terms.

Questions Eliciting Thinking Can you explain what you did? Did you find any solutions?
What does the three in front of the parenthesis mean?
Are you familiar with the Distributive Property?
How confident are you in solving inequalities like this? Do you feel like there may be some things you do not understand? 
Instructional Implications Review the correct use of the Distributive Property, how to combine like terms, the concept of inverse operations, and the properties of equality. Provide the student with instruction on solving both equations and inequalities, beginning with twostep equations and inequalities, then moving on to multistep problems and those with variables on both sides. Provide additional opportunities to solve equations and inequalities and provide feedback as necessary. 
Moving Forward 
Misconception/Error The student correctly uses algebraic properties to solve the inequality but makes some errors. 
Examples of Student Work at this Level The student completes all steps of the solution process correctly except one in which he or she:
 Does not recognize an opportunity to combine like terms and subtracts six twice from the same side of the inequality.
 Subtracts 5x from 3x and gets 8x.
 Makes other computation errors such as 18 + 2 = 20 or 3x â€“ 5x = 2x.
 Divides by two instead of negative two and writes x = 6.

Questions Eliciting Thinking There is an error in your work. Can you find it?
Where did the 20 come from? Is the 18 positive or negative? Is the two positive or negative? 
Instructional Implications Review any error with the student and provide feedback. Ask the student to revise his or her work. Provide additional inequalities to solve and pair the student with another Moving Forward student to compare solution methods and reconcile any differences.
Provide the student with a completed problem that contains errors. Have the student identify and correct the errors. 
Almost There 
Misconception/Error The studentâ€™s only error involves the direction of the inequality symbol when multiplying or dividing each side of the inequality by a negative quantity. 
Examples of Student Work at this Level The student does not change the direction of the inequality sign after dividing by negative two.

Questions Eliciting Thinking What number did you divide by in the last step? What are you supposed to do when you multiply or divide both sides of an inequality by a negative number? 
Instructional Implications Guide the student in understanding why the direction of the inequality symbol is changed when multiplying or dividing an inequality by a negative number. Give the student a simple inequality such as 2x > 6 and ask the student to find solutions using â€śguess and test.â€ť Have the student find and graph on a number line as many solutions as is necessary to understand the solution set. Guide the student to summarize the solution set with an inequality and to compare the inequality symbol used in the solution to the symbol in the original problem. 
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 correctly solves the inequality and writes the solution set as x = 6.

Questions Eliciting Thinking How can you check your solution? Can you graph the solution set?
How many numbers satisfy this inequality? Can you give me examples of some other solutions?
Why did you change the direction of the inequality symbol when you divided by negative two? 
Instructional Implications Provide the student with more complex inequalities to solve.
Ask the student to partner with a Getting Started student to provide feedback on his or her solutions to inequalities. 