Getting Started 
Misconception/Error The student is unable to use the equation to make a prediction. 
Examples of Student Work at this Level The student:
 Estimates based on values in the table.
 Substitutes a value for C and attempts to solve for t.
 Calculates an “average” cost and substitutes it for t in the equation.

Questions Eliciting Thinking How did you determine your prediction? Did you use the equation?
Why did you solve for t? What variable are you asked to find?
How did you find the value for t you used in the equation? Can you explain how you used the table to find the value of t? 
Instructional Implications Review as needed:
 Linear models and lines of best fit.
 Linear functions written in slopeintercept form, y = mx + b.
 Solutions of linear functions and using a linear function to find solutions given the value of one of the variables.
Provide instruction on how to use a linear model to make predictions about the value of one variable given a value of the other. Emphasize the meaning of each variable and its role (i.e., independent or dependent variable) in the equation. Guide the student to first determine the value of t for the year 2018. Then ask the student to find the cost of tuition when t = 15.
Ask the student to use the equation to make other predictions about the cost of tuition in a given year or the year that tuition will reach a certain cost. Introduce the issue of using values of t outside a reasonable domain of the model (e.g., attempting to make a prediction for the year 2050). 
Moving Forward 
Misconception/Error The student does not understand how to determine the value of t. 
Examples of Student Work at this Level The student understands that he or she must substitute a value for t into the equation and solve for C. However, the student does not understand how to find the value of t associated with the year 2018. The student determines that t equals some value other than 15 such as 10, 16, or 20.

Questions Eliciting Thinking How did you find the value of t?
What did the problem indicate about the meaning of t? What is the value of t for the year 2003? 
Instructional Implications Review the description of t given in the problem (e.g., t is the number of years since 2003). Ask the student to determine the value of t for each year given in the table and then find the value of t for 2018. Then have the student find the cost of tuition when t = 15.
Ask the student to use the equation to make other predictions about the cost of tuition in a given year or the year that tuition will reach a certain cost. Introduce the issue of using values of t outside a reasonable domain of the model (e.g., attempting to make a prediction for the year 2050). 
Almost There 
Misconception/Error The student makes a computational error. 
Examples of Student Work at this Level The student determines that t = 15 for the year 2018 and predicts the cost of tuition by substituting 15 for t but:
 Makes a computational error when multiplying 15 by 316.
 Makes an addition error when adding 4740 to 5827.

Questions Eliciting Thinking I think you made a mistake in your work. Can you find your error? 
Instructional Implications Provide feedback to the student regarding any error made and allow the student to revise the work. Ask the student to use the equation to make other predictions about the cost of tuition in a given year or the year that tuition will reach a certain cost. Introduce the issue of using values of t outside a reasonable domain of the model (e.g., attempting to make a prediction for the year 2050).
Consider implementing MFAS task Foot Length (8.SP.1.3) to assess the student’s understanding of slope and yintercept in linear models. 
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 determines that t = 15 for the year 2018 and predicts the cost of tuition by substituting 15 for t and solving for C: C = 316(15) + 5827 = $10,567.

Questions Eliciting Thinking How could you use the equation to determine when the cost of tuition will reach $13,000?
Why are the values in the table different from the values you get when you use the equation? 
Instructional Implications Have the student explain the meaning of the slope and yintercept in the context of the linear model.
Consider implementing MFAS task Foot Length (8.SP.1.3) to assess the student’s understanding of slope and yintercept in linear models. 