Getting Started 
Misconception/Error The student is unable to determine the slope either from the equation or the graph. 
Examples of Student Work at this Level The student is unable to determine the slope from either the equation or the graph. The student says:
 The slope of the line is 77. The average person will live to be 77.
 Roughly strong since it is close to 1 or 1.
 There is almost a full year of difference between each year.
 The older you get the shorter you live.

Questions Eliciting Thinking How did you determine the slope? What were you looking at?
Can you find the slope of the line from the graph?
Can you find the slope of the line from the equation?
What do m and b mean in the equation y = mx + b? 
Instructional Implications Review the concepts of linear function, slope, and yintercept. Focus on the slopeintercept form of the equation of a linear function. Review how to find slope graphically, quantitatively (as a change in y over a corresponding change in x), 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 (i.e., life expectancy) associated with a one unit change in the independent variable (i.e., age). Have the student initially describe the slope as a unit rate including the units of measure (e.g., 0.89 years of life expectancy/1 year of age). Then guide the student to interpret the slope in terms of the independent and dependent variables. Model explaining, â€śFor every additional year in age, average life expectancy decreases by 0.89 years.â€ť Explain the difference between a positive and negative change and how to discern this from both the graph and the equation.
Provide additional examples of linear functions that have been fitted to data. Ask the student to identify the slope from an equation or its graph. Encourage the student to initially describe the slope as a unit rate including the units of measure. Then have the student interpret the slope using appropriate terminology (e.g., â€śFor every one unit change in the independent variable, there is a corresponding m unit change in the dependent variableâ€ť). 
Moving Forward 
Misconception/Error The student can determine the slope but is unable to explain its meaning in context. 
Examples of Student Work at this Level The student estimates the slope using the graph or uses the equation to determine that the slope is 0.89. However, the student is unable to correctly interpret the slope in the context of the data. For example, the student:
 Identifies the variables but is unable to provide any interpretation.
 Provides a general interpretation that does not take into account the units of the variables.
 Provides an incorrect or incomplete interpretation.

Questions Eliciting Thinking How did you determine the slope?
In the computation of the slope, what unit would be in the numerator? What unit would be in the denominator?
How are the numerator and denominator of the slope related? What does the slope tell you? 
Instructional Implications Have the student initially describe the slope as a unit rate including the units of measure (e.g., 0.89 years of life expectancy/1 year of age). Then guide the student to interpret the slope in terms of the independent and dependent variables. Model explaining, â€śFor every additional year in age, average life expectancy decreases by 0.89 years.â€ť Explain the difference between a positive and negative change and how to discern this from both the graph and the equation.
Provide additional examples of linear functions that have been fitted to data. Ask the student to identify the slope from an equation or its graph. Encourage the student to initially describe the slope as a unit rate including the units of measure. Then have the student interpret the slope using ratio language by saying, for example, â€śFor every one unit change in the independent variable, there is a corresponding m unit change in the dependent variable.â€ť 
Almost There 
Misconception/Error The student correctly interprets the slope but estimates its value using the graph. 
Examples of Student Work at this Level The student estimates the coordinates of two points on the line and uses these points to calculate the slope. However, the studentâ€™s interpretation of the slope is correct given the calculated value. 
Questions Eliciting Thinking Do you know how to use the equation to find the slope?
How does your calculation compare to the slope given in the equation? Why might the slope you calculated differ from this value? 
Instructional Implications Review the parameters of a linear function and be sure the student understands that the slope or rate of change is the coefficient of the independent variable. Explain to the student that since the coordinates of points on the graph are not clearly given, any calculation involving these points would be an estimate. Additionally, identifying the slope from an equation is more efficient. 
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 the slope of the graph is 0.89 years of life expectancy/1 year of age. The student explains that the average life expectancy is reduced by 0.89 years when an individual ages by one year.

Questions Eliciting Thinking Can you use the graph to determine the oldest age a woman is expected to live?
On average, to what age would a woman who is currently aged 30 be expected to live? To what age would a woman who is currently aged 70 be expected to live? Why do you suppose the person who is currently 70 is expected to live to an older age? 
Instructional Implications Ask the student to identify the yintercept and to consider if it has any meaning in this context. Ask the student to consider why the model might not be valid for women younger than 30 or older than 70.
Ask the student to consider how the graph would differ if one used data from 100 years ago. 