Getting Started 
Misconception/Error The student is unable to identify the value of the slope. 
Examples of Student Work at this Level The student:
 Provides an incorrect value of the slope (e.g., 7.5a, m, minutes per day, a, age of the infant, or 930).
 Provides a general description of slope (e.g., rate of change).
 States that slope is needed to solve the equation or find out how long the baby sleeps.
 Attempts to solve (or describes how to solve) the equation.
 Does not refer to the value 7.5 or its significance.

Questions Eliciting Thinking In general, what is the meaning of the slope of a line?
Can you identify the slope in the equation? What is the meaning of the slope in this situation?
What are the units of the slope? What does this slope tell you about the relationship between minutes spent sleeping and age? 
Instructional Implications Review the concepts of slope and linear functions. Focus on the slopeintercept form of the equation of a linear function. Review how to identify the slope graphically and from an equation written in slopeintercept form. 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., minutes per day spent sleeping) associated with a oneunit change in the independent variable (e.g., age in months). Review the implications of slopes that are positive (e.g., the values of the independent and dependent variables increase together) and negative (e.g., as the values of the independent variable increase, the values of the dependent variable decrease). Have the student initially describe the slope as a unit rate including the units of measure (e.g., 7.5 minutes/1 month). Then guide the student to interpret the slope in terms of the independent and dependent variables. Model explaining, “For every one month increase in age, time spent sleeping decreases by 7.5 minutes.”
Provide additional opportunities to identify and interpret the slope of a linear function that models a set of data. 
Making Progress 
Misconception/Error The student is unable to explain the meaning of the slope. 
Examples of Student Work at this Level The student describes slope as:
 Number of minutes per day or age of the infant.
 The decrease in the number of minutes the infant sleeps per day.
 The increase in the number of minutes the infant sleeps per month or day.
 The student does not refer to the context of the problem.

Questions Eliciting Thinking Can you explain what the slope means in terms of infants and the time they spend sleeping?
What is the slope? What are the units of the slope? What does this slope tell you about the relationship between minutes spent sleeping and age?
What does it mean for a slope to be negative? 
Instructional Implications Describe slope as a unit rate. Guide the student to explain the meaning of slope as an amount of change in the dependent variable (e.g., minutes per day spent sleeping) associated with a oneunit change in the independent variable (e.g., age in months). Review the implications of slopes that are positive (e.g., the values of the independent and dependent variables increase together) and negative (e.g., as the values of the independent variable increase, the values of the dependent variable decrease). Have the student initially describe the slope as a unit rate including the units of measure (e.g., 7.5 minutes/1 month). Then guide the student to interpret the slope in terms of the independent and dependent variables. Model explaining, “For every one month increase in age, time spent sleeping decreases by 7.5 minutes.”
Provide additional opportunities to identify and interpret the slope of a linear function that models a set of data. 
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 explains that the slope indicates that for each one month increase in age, the amount of time an infant sleeps per day decreases by 7.5 minutes.

Questions Eliciting Thinking Can you give an example of how someone might use this equation?
Can this equation be used to find the exact amount of time a baby will sleep? Why?
Can you describe the decrease in time spent sleeping in more detail? Is the rate of change constant?
What do you think is the domain of this function? 
Instructional Implications Ask the student to:
 Use the linear model to predict the amount of time a sixmonthold infant spends sleeping.
 Explain the meaning of the yintercept in the context of the linear model.
 Consider if the model could be used to predict the amount of time a person spends sleeping through their entire life.
Consider implementing other MFAS tasks for this standard (8.SP.1.3).
