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 is positive.
 The slope of the data is 4.3. This means the foot length increases 4.3 for every male.
 The slope is rise over run.

Questions Eliciting Thinking How did you determine the slope? What were you looking at?
How can you use the equation to find the slope?
How can you use the graph to find the slope?
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., foot length) associated with a one unit change in the independent variable (i.e., height). Have the student initially describe the slope as a unit rate including the units of measure (e.g., 1.5 mm/1 cm). Then guide the student to interpret the slope in terms of the independent and dependent variables. Model explaining, â€śFor every 1 cm increase in height, foot length increases 1.5 mm.' Â 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. 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, for example, by saying, â€śFor every one unit change in the independent variable, there is a corresponding m unit change in the dependent variable.â€ť 
Moving Forward 
Misconception/Error The student can determine the slope but is unable to explain its meaning in the context of the data. 
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 1.5. However, the student is unable to correctly interpret the slope in the context of the data. For example, the student says:
 The slope is the rise over run. It rises 1.5 for every one unit run.
 The slope tells us whether the line is positive or negative and how fast it is increasing or decreasing.
 The foot length goes up 1.5 and the height goes up 20 (since the horizontal axis is scaled by units of 20).
 For every 3 millimeters, there are 2 centimeters.

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., 1.5 mm in foot length to 1 cm of height). Then guide the student to interpret the slope in terms of the independent and dependent variables. Model explaining, â€śFor every 1 cm increase in height, foot length increases 1.5 mm.' 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. 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, for example, by saying, 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, explainÂ that 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 1.5 mm/cm. The student explains that for each 1 cm increase in height, there is a corresponding increase of 1.5 mm in foot length.

Questions Eliciting Thinking Suppose that Patâ€™s height is 150 cm. What foot length would this model predict?
Suppose Aaronâ€™s foot length is 210 mm. How could you use this model to predict his height?
Suppose the variables were interchanged so foot length now predicts height. Would you expect the slope to be the same as it is in the current model? 
Instructional Implications Ask the student to identify the yintercept and to consider if it has any meaning in this context.
Ask the student to interchange the variables so foot length now predicts height and to determine the slope for the new model.
Ask the student to consider how the equation would change if the foot length data were expressed in centimeters instead of millimeters. 