Getting Started 
Misconception/Error The student is unable to write an equation that models the problem. 
Examples of Student Work at this Level The student attempts to solve the problem computationally.
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The student uses a guess and check approach to solve the problem.

Questions Eliciting Thinking What is this word problem about? What are you being asked to do?
How did you start to solve this problem? Explain to me what you did.
What necessary information is given in the problem?
What should you do when you have an unknown amount in a problem? 
Instructional Implications Provide instruction on writing onestep equations that model simple problem situations. Gradually increase the complexity of the problems to those modeled by twostep and multistep equations. Guide the student to explicitly identify the unknown and to create a variable to represent it. Ask the student to justify his or her equation by relating each term and operation to a specific feature of the problem. If necessary, provide instruction on solving equations, and encourage the student to always assess the reasonableness of solutions. Guide the student to use the solution of the equation to explicitly answer any question asked in the problem.
Provide additional examples of representing two related quantities in terms of the same variable. Give the student additional opportunities to write representations of related quantities in terms of the same variable. 
Moving Forward 
Misconception/Error The student makes an error representing some component of the equation. 
Examples of Student Work at this Level The student writes an incorrect equation.Â
The student uses two different variables to represent the cost of a student ticket and the cost of a chaperone ticket but is unable to write two independent equations to model the problem.

Questions Eliciting Thinking Can you explain the problem in your own words?
What was the unknown in the problem? What variable did you use? What does your variable represent?
How did you decide what to include in your equation?
Do both types of tickets cost the same amount? Can you write the price of a chaperone ticket in terms of the price of a student ticket? Now can you write an equation using only one variable? 
Instructional Implications Ask the student to justify his or her equation by relating each term and operation to a specific feature of the problem. Provide feedback and encourage the student to revise the equation as needed. Provide additional opportunities to write and solve equations that model problems. Encourage the student to selfassess by justifying each component of his or her equation 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 of the equation to explicitly answer any question asked in the problem.
Provide additional examples of representing two related quantities in terms of the same variable. Give the student additional opportunities to write representations of related quantities in terms of the same variable. 
Almost There 
Misconception/Error The student correctly writes the equation but makes minor errors solving the equation or does not answer the question being asked. 
Examples of Student Work at this Level The student assigns the variable x to represent the number of student tickets sold and writes the equation 59x + 6(x â€“ 2) = 508 but makes errors solving the equation.
The student assigns the variable x to represent the number of chaperone tickets and writes the equation 59(x + 2) + 6xÂ = 508 and solves correctly stating that x = 6, but incorrectly states that a student ticket costs six dollars.

Questions Eliciting Thinking There is a minor mistake in your work. Can you find it?
What was your first step in trying to solve the equation?
What did you do when you distributed?
Where are the like terms?
What unknown did your variable represent? Is that what you were being asked to find? Can you go back and determine the cost of the student ticket now that you know the price of the chaperone ticket? 
Instructional Implications Provide student with additional instruction and practice with solving multistep equations. Encourage the student to always go back to the problem and make sure the question asked was answered.
Pair the student with another Almost There student to compare equations and solutions. Ask the student s to reconcile any differences in their work. 
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 assigns the variable c to represent the cost of a student ticket, represents the cost of a chaperone ticket as c â€“ 2, and writes the equation 59c + 6(c â€“ 2) = 508. The student correctly solves the equation (c = 8) and states that a student ticket costs eight dollars.
The student assigns the variable c to represent the cost of a chaperone ticket, represents the cost of a student ticket as c + 2, and writes the equation 59(c + 2) + 6c = 508. The student correctly solves the equation (c = 6) and states that a student ticket costs eight dollars.

Questions Eliciting Thinking What does c â€“ 2 (or c + 2) represent in your equation?
Could you have written a different equation and still have gotten the correct price for a student ticket?
Can you determine the cost of the chaperone ticket? 
Instructional Implications Encourage the student to write another equation or a system of equations to solve the problem. Emphasize that there is often more than one approach to solving a mathematical problem. 