Getting Started 
Misconception/Error The student is unable to interpret either the slope or yintercept. 
Examples of Student Work at this Level The student says that 45 is:
 The number of hours worked.
 The number of people.
 The charge for how many hours worked.
The student says that 80 is:
 The number of house calls.
 The number of customers.
 The overall charge.
The student can find the value of h corresponding to f(h) = 215 but cannot describe the meaning in context.
The student suggests that changing the coefficient of h in the equation from 45 to 35 means:
 Less people worked f.
 Fewer hours were worked.
 The total amount would change.

Questions Eliciting Thinking Can you explain the function in your own words? What does f(h) represent? What does h represent?
Is this function in slopeintercept form? What is the slope in this function? In this situation, why is 45 multiplied by h?
What is the yintercept in this function? In this situation, why is 80 added to 45h? 
Instructional Implications Review the concepts of linear function, slope, and yintercept. Initially, focus on the slopeintercept form of the equation of a linear function. Guide the student to carefully consider the context of the linear function given in this task, the specific variables that it relates, and their units of measure. Ask the student to graph the linear function and to label and scale the axes to fit the context. Relate the parameters in the equation to the slope of the graph and its yintercept. Then guide the student to explain the meaning of the constant term in the context of the data. Have the student initially identify the coordinates of the yintercept along with their units of measure [e.g., (0 hours, $80)]. Guide the student to relate the coordinates by saying, â€śWhen the number of hours worked is zero, the charge is $80.â€ť Ask the student to review the context of the problem and to consider why there might be a charge when the number of hours worked is zero.
Describe slope as a quality of a line but also describe it as a unit rate. Guide the student to explain the meaning of slope as an amount of change in the dependent variable (e.g., the cost or charge) associated with a one unit change in the independent variable (e.g., hours worked). Have the student initially describe the slope as a unit rate including the units of measure (e.g., $45 for every one hour). Then guide the student to interpret the slope in terms of the independent and dependent variables. Model explaining, â€śFor every one hour worked, the computer repair company charges $45.â€ť
Provide the student with additional examples of linear functions in context. Pose questions that can be answered by finding and interpreting a specific solution, the rate of change, and the initial value.
Consider using the MFAS task Lunch Account (FLE.2.5) if not used previously. 
Moving Forward 
Misconception/Error The student can interpret some of the parameters in context. 
Examples of Student Work at this Level The student can interpret the coefficient of h but not the initial value.
The student can interpret the initial value but not the coefficient of h.
The student identifies the coefficient of h as the slope and the initial value as the yintercept but cannot interpret either without prompting.

Questions Eliciting Thinking Can you explain the function in your own words? What does f(h) represent? What does h represent?
What role do you think 45 and 80 play in determining someoneâ€™s bill?
For question three, you found that h = 3? What does h represent in the problem? How is it related to 215?
For question four, you said the price dropped. What part of the companyâ€™s charge changed when the 45 was changed to 35? 
Instructional Implications Review the parameters of linear functions and how to use a function to find related pairs of values. Ask the student to write the meaning of h and of f(h) from the original problem [e.g., h = the number of hours worked and f(h) = the total repair bill] and to explain how they are related by the function (e.g., the total repair bill is equal to 45 times the number of hours worked plus 80). Clarify the units of measure for each variable and ask the student to consider why the number of hours worked might be multiplied by $45 and why $80 might be added to the bill. Then provide focused instruction and review of any parameter the student cannot completely interpret or explain.
Provide the student with additional examples of linear functions in context. Pose questions that can be answered by finding and interpreting a specific solution, the rate of change, and the initial value.
Consider using the MFAS task Lunch Account (FLE.2.5) if not used previously. 
Almost There 
Misconception/Error The student provides a correct response but with insufficient reasoning or imprecise language. 
Examples of Student Work at this Level The student uses the phrase â€śdaily payâ€ť to describe both the initial value and the total cost.
The student can find the value of h corresponding to f(h) = 215 but does not describe it in context.

Questions Eliciting Thinking What role do you think 45 and 80 play in determining someoneâ€™s bill?
For question three, you found that h = 3? What does h represent in the problem? How is it related to 215?
For question four, you said the price dropped. What part of the companyâ€™s charge changed when the 45 was changed to 35? 
Instructional Implications Make the student aware of any responses on his or her paper that are incomplete or unclear. Encourage the student to compose explanations and verbalize them before writing them on paper. Have the student rewrite his or her responses and provide feedback.
Give the student more experience explaining mathematics and justifying answers. Allow the student to work with a partner in order to compare interpretations and explanations before finalizing them on paper.
Share examples of complete, correct, and wellwritten responses prepared by other students.
Consider using the MFAS task Lunch Account (FLE.2.5) if not used previously. 
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 interprets the meaning of both 45 and 80 in context. The student says:
 The company charges $45 per hour worked.Â
 The company charges an $80 fee for making the house call.
The student substitutes 215 for f(h), determines that h = 3, and states that if the job took 3 hours, the bill would be $215. The student interprets the change from 45 to 35 in the equation as a rate change from $45 per hour to $35 per hour.

Questions Eliciting Thinking How would you find the xintercept of the graph of this function? Would it have any meaning in the context of this problem? 
Instructional Implications Provide other examples of linear functions in context and ask the student to interpret the parameters. 