Getting Started 
Misconception/Error The student is unable to write an inequality that models the problem. 
Examples of Student Work at this Level The student attempts to solve the problem computationally.

Questions Eliciting Thinking Can you explain the problem in your own words? Can you explain what you did?
What is an inequality? Can you write an inequality that models this situation? 
Instructional Implications Provide instruction on writing onestep equations and inequalities that model simple problem situations. Gradually increase the complexity of the problems to those modeled by twostep and multistep equations and inequalities. Guide the student to explicitly identify the unknown and create a variable to represent it. Ask the student to justify his or her equation/inequality by relating each term and operation to a specific feature of the problem. If necessary, provide instruction on solving equations and inequalities, and encourage the student to always assess the reasonableness of solutions. Guide the student to use the solution(s) of the equation or inequality to answer any question asked in the problem.
Discuss the difference between equations and inequalities and how to determine which to use when modeling problems. Be sure the student understands the distinctions among the different inequality symbols. Encourage the student to identify words or phrases that indicate a relationship expressed in the problem (e.g., â€śis the same as,â€ť â€śno more than,â€ť â€śat leastâ€ť) and, consequently, which symbol to use. 
Moving Forward 
Misconception/Error The student makes an error representing some component of the problem in the inequality. 
Examples of Student Work at this Level The student:
 Writes an equation that does not model the problem.
 Writes an equation that includes the number of downloads per month as a component.
 Confuses the initial membership fee with the monthly charge.Â
 Does not include the membership fee or does not include the cost of the music player.Â

Questions Eliciting Thinking Can you explain the problem in your own words?
What is the unknown in the problem? What does your variable represent? What does each number in the problem (79, 25, 14.95, 30, 250)Â represent?
Did you write an inequality or an equation?
Why did you choose that inequality symbol? Can Kerry spend more than he has?
Can you tell me what the terms in your inequality represent? Does your inequality correspond to the description of the problem? 
Instructional Implications Ask the student to justify his or her inequality by relating each term and operation to a specific feature of the problem. Provide feedback and encourage the student to revise the inequality as needed. Provide additional opportunities to write and solve inequalities that model problems. Encourage the student to selfassess by justifying each component of his or her inequality and relating it to features of the original description of the problem. Encourage the student to always assess the reasonableness of solutions. Guide the student to use the solution(s) of the equation or inequality to answer any question asked in the problem.
Discuss the difference between equations and inequalities and how to determine which to use when modeling problems. Be sure the student understands the distinctions among the different inequality symbols. Encourage the student to identify words or phrases that indicate a relationship expressed in the problem (e.g., â€śis the same as,â€ť â€śno more than,â€ť â€śat leastâ€ť) and consequently, which symbol to use. 
Almost There 
Misconception/Error The student does not recognize there are multiple solutions to the problem. 
Examples of Student Work at this Level The student:
 Writes an equation and finds only one solution.
 Does not use the solution to the inequality to find all of the number of months of membership that Kerry can afford or does so incorrectly.

Questions Eliciting Thinking What were you being asked to write, an equation or an inequality? What symbol did you use? Why did you choose to use that symbol?
What were you being asked to find? Does your answer make sense?
How many solutions are there to your inequality? Can Kerry afford only nine months of membership or are there other numbers of months he can afford? 
Instructional Implications Discuss with the student that inequalities typically describe more than one value and problems that are modeled by inequalities typically have more than one solution. Using the problem in this task as an example, make explicit all of the possible numbers of months of membership that Kerry can afford. Remind the student to always check the reasonableness of solutions in the context of the problem. Provide the student with similar problems that require writing and solving inequalities and interpreting solutions in the context of the 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 describes the variable m as the number of months of membership and writes the inequality 79 + 25 + 14.95m Â 250. The student solves the inequality and writes mÂ 9.77. The student states that Kerry can pay for up to nine months of membership in the club. When asked, the student can explicitly state the numbers of months of membership that Kerry can afford. 
Questions Eliciting Thinking What are all of the possible numbers of months of membership that Kerry can afford?
If Kerry joins the club for five months, how much of his original $250 will be left over?
How would your inequality change if Kerry had only $200? How would your inequality change if there was no membership fee?
Why can this problem situation be modeled with an inequality rather than an equation? 
Instructional Implications Provide the student with more complex problems situations to model with equations and inequalities.
Ask the student to partner with a Getting Started or Moving Forward student to provide feedback on his or her equations and inequalities. 