Getting Started 
Misconception/Error The student is unable to find the numerical values of the unit rate and slope. 
Examples of Student Work at this Level The student incorrectly determines either the unit rate, the slope, or both. For example, the student determines:
 The unit rate is 10 and the slope is two.
 The unit rate is “1=400” and the slope is .
 The unit rate is 400 ft ^{2}/1 gallon but the slope is two.

Questions Eliciting Thinking How did you determine the unit rate?
How did you determine the slope? Did you take into account the scales on the axes when determining the slope?
Does it matter if the number one is in the numerator or denominator?
How does one gallon equal 400 square feet? What does the equal sign mean?
What point on the graph helps you determine the unit rate? 
Instructional Implications If needed, review the meaning of a unit rate and how to find it from the graph of a proportional relationship. Describe the unit rate as a comparison of some quantity to one unit of another quantity. Make explicit that the unit of one must be in the denominator for the ratio to be considered a unit rate. Explain how the point (1, 400) helps identify the unit rate. Distinguish between ordered pairs and unit rates [e.g., between (1, 400) and as they relate to unit rates]. Assist the student in correctly finding the unit rate and interpreting it in context.
If needed, review the meaning of slope and how to find it from a graph of a relationship. Explain that the slope of the line is the same as the rate of change (the change in y over the change in x). Emphasize the importance of considering the scale of each axis when determining the slope. Assist the student in correctly finding the slope and interpreting it in context.
Provide additional opportunities to find the unit rate and slope of graphed proportional relationships. 
Moving Forward 
Misconception/Error The student is unable to describe and interpret both the unit rate and slope. 
Examples of Student Work at this Level The student provides an incomplete or incorrect interpretation of the unit rate, the slope, or both. For example, the student:
 Describes each as a quantity rather than a rate.
 Uses an incorrect unit of measure.
 Interchanges the units of measure describing the slope as the number of gallons of paint per square foot.
 Provides a vague description such as the unit rate “goes up by 400 every time.”

Questions Eliciting Thinking Is the slope a quantity or a rate? What does a slope of 400 square feet mean?
How did you determine the units of the slope?
Can you be more specific in your interpretation? What goes up and by how much? 
Instructional Implications Encourage the student to be more specific when describing unit rates and slopes in context. Have the student assign units of measure to each part of the ratios and to incorporate the units of measure into the interpretation. Remind the student that the graph of a proportional relationship will always pass through the origin. Then help the student understand the relationship between the unit rate in a proportional relationship and the slope of its graph. Have the student rewrite slope ratios as unit rates in order to observe the relationship between the two concepts. Provide additional opportunities to calculate both unit rates and slopes, and to describe their relationship in context. 
Almost There 
Misconception/Error The student provides an incomplete or incorrect explanation of the relationship between unit rate and slope. 
Examples of Student Work at this Level The student correctly finds and describes both the unit rate and slope. However, the student provides an incomplete or incorrect explanation of their relationship.

Questions Eliciting Thinking To what is the unit rate referring? To what is the slope referring?
Is there a connection between the unit rate and the slope?
Will the unit rate and the slope always be the same in a proportional relationship? 
Instructional Implications Assist the student in understanding that the unit rate and the slope will always be equal in a proportional relationship. Guide the student to describe the relationship in terms of the meaning of each in context.
Provide additional opportunities to calculate both unit rates and slopes, and to describe their relationship in context. 
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:
 Describes both the unit rate and slope as 400 square feet per gallon and indicates that this means that 1 gallon of paint can cover 400 square feet of surface.
 Explains that the slope is the same as the unit rate, and, in the given problem, each indicates that every gallon of paint covers 400 square feet.

Questions Eliciting Thinking Since is equivalent to , can also represent the unit rate? Why or why not?
Since is equivalent to , can also represent the slope? Why or why not?
Will the unit rate and the slope always be the same in a proportional relationship? Why or why not? 
Instructional Implications Challenge the student to write an equation to represent the proportional relationship, and then use the equation to determine the number of gallons it would take to cover 3,000 square feet.
Consider implementing MFAS task Compare Slopes (8.EE.2.5). 