Getting Started 
Misconception/Error The student is unable to correctly write an inequality to represent the given constraints. 
Examples of Student Work at this Level The student:
 Uses a direct numerical approach to solve rather than writing an inequality.
 Writes an incorrect inequality.
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 Writes an expression or equation instead of an inequality.

Questions Eliciting Thinking What is the difference between an equation and an inequality?
What are you asked to find? Can you represent it with a variable?
Are there exactly 80 tons of steel remaining? What does the phrase â€śfewer than 80 tons leftâ€ť tell you? 
Instructional Implications Provide instruction on modeling relationships among quantities with inequalities. Begin with situations that can be modeled by onestep inequalities. Then progress to situations leading to twostep inequalities. Ask the student to explicitly describe the meaning of any variables used in the inequality. Emphasize the relationship between algebraic expressions and the quantities they represent in the context of the situations in which they arise. For example, if x represents the number of days that have passed, then 15x represents the number of tons of recycled steel sold after x days, and 200 â€“ 15x represents the number of tons of steel remaining in the scrapyard. Use the meaning of 200 â€“ 15x to guide the student to determine its relationship to 80 and write an inequality.
If necessary, review solving onestep and twostep equations and inequalities. Provide additional opportunities to solve word problems by writing and solving inequalities involving rational numbers. 
Moving Forward 
Misconception/Error The student is unable to correctly solve the inequality. 
Examples of Student Work at this Level The student correctly writes an inequality to represent the relationship among the quantities in the problem but makes an error in solving the inequality. For example, the student:
 Errs in applying the Division Property of Equality.
 Adds 200 to each side of the inequality instead of subtracting.
 Reverts to using a numerical approach to solve the problem.
The student may also fail to realize that the solution consists of more than one value.

Questions Eliciting Thinking If this were an equation, would you be able to solve it?
Can you explain how you solved the inequality?
Can you solve this inequality algebraically, that is, without using repeated subtraction?
Does an inequality have just one solution? Are you able to tell exactly how much steel has been sold? 
Instructional Implications Provide direct feedback on any errors that the student made and allow the student to correct them. Review solving onestep and twostep equations and inequalities. Explain that the same properties that are used to solve equations are used to solve inequalities. Be sure the student understands considerations in multiplying or dividing both sides of an inequality by a negative number.
Provide additional opportunities to solve word problems by writing and solving inequalities involving rational numbers. Remind the student to use substitution to check several solutions in the original inequality. 
Almost There 
Misconception/Error The student makes a minor error in solving the inequality or interpreting the result. 
Examples of Student Work at this Level The student:
 Forgets to reverse the direction of the symbol when dividing by a negative integer.
 Does not recognize that the solution is a set of values.
 Partially solves the inequality using a numerical approach before writing it.

Questions Eliciting Thinking How did you decide which inequality symbol to use?
What happens to the direction of the symbol when you divide by a negative number?
Does an inequality have just one solution? Are you able to tell exactly how much steel has been sold?
Is there just one number that will make the inequality a true statement? 
Instructional Implications Provide feedback to the student regarding any errors made and allow the student to revise his or her work. Be sure the student understands that the solution of an inequality often consists of more than one value. Guide the student to use problem contexts to reason about any additional limitations on the solution set. For example, in the given problem, although the number of days must be greater than eight, it cannot be as large as, for example, 20. The inequality would indicate that the amount of steel remaining in the yard after 20 days would be a negative value which makes no sense in this context.
Provide additional opportunities to solve word problems by writing and solving inequalities involving rational numbers. Remind the student to use substitution to check several solutions in the original inequality.
Consider implementing the MFAS task Gift Card Inequality (7.EE.2.4). 
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 writes the inequality as 200 â€“ 15d < 80 and correctly represents the solution as d > 8. The student explains that more than eight days have passed.

Questions Eliciting Thinking What does the expression 200 â€“ 15d represent in the context of the problem?
How did you know which inequality symbol to use? 
Instructional Implications Challenge the student to determine the upper limit on the number of days that might have passed. Then introduce the student to compound inequalities. Show the student that since the number of tons of steel in the scrapyard can never be less than zero, the inequality 0 < 200 â€“ 15d < 80 represents this problem. Explain that inequalities of the form a < x < b indicate that x must be between the values given by a (the lower limit) and b (the upper limit). 