Getting Started 
Misconception/Error The student is unable to graph the proportional relationship. 
Examples of Student Work at this Level The student graphs coordinates incorrectly or graphs (x, y) as (y, x).

Questions Eliciting Thinking How do you use the numbers in the table to graph points (to form ordered pairs)?
Which column includes the x’s (independent variable)?
Can you rewrite the data in the table as ordered pairs? How do you graph ordered pairs?
How do you determine the slope of a line?
Do you expect the points to fall in a straight line? Why or why not? 
Instructional Implications Review graphing ordered pairs on the coordinate plane. Consider implementing CPALMS Lesson Plan Graphing Points on the Coordinate Plane (ID 29193), which addresses graphing only in quadrant one. Then consider implementing CPALMS Lesson Plan Bomb the Boat – Sink the Teacher’s Fleet! (ID 48848), which includes all four quadrants.
Provide explicit instruction on slope. Include both how to use the graphed line to find the slope (by counting the “rise” and the “run”) and how to calculate slope from the coordinates of two points on the line. Have the student calculate the slope using two ordered pairs given in the table, find the slope from the graph, and then compare the two.
The student may confuse “rise over run” with the procedure for plotting ordered pairs. Make explicit the difference between plotting ordered pairs and counting the rise and the run to determine the slope of a line. Provide additional practice opportunities for the student to graph proportionally related data and determine the slope of the graph. Point out that proportionally related data will be linear and will always be satisfied by the ordered pair (0, 0). 
Moving Forward 
Misconception/Error The student is unable to determine the slope of the proportional relationship. 
Examples of Student Work at this Level The student correctly graphs the proportional relationship but determines the slope of the line to be:

Questions Eliciting Thinking How are slopes written? Are they written the same way as ordered pairs?
How do you determine the slope of a line?
Is there a way to find the slope from the data? 
Instructional Implications Provide explicit instruction on slope. Include both how to use the graphed line to find the slope (by counting the “rise” and the “run”) and how to calculate slope from the coordinates of two points on the line. Have the student calculate the slope using two ordered pairs given in the table, find the slope from the graph, and then compare the two.
Review the concept of unit rate and explain how the slope of a line is related to this concept. Have the student calculate or find the unit rate using data in the table. Encourage the student to verbalize how the unit rate is related to the slope of the graphed line.
Provide additional opportunities to find the slopes of lines that represent proportional relationships from tables of values, equations, and graphs. 
Almost There 
Misconception/Error The student is unable to clearly interpret the meaning of the slope. 
Examples of Student Work at this Level The student correctly graphs the proportional relationship and identifies the slope of the line as . However, the student’s interpretation of the slope is unclear or incomplete. The student:
 Interprets the slope graphically rather than in context.
 Provides a vague or incomplete interpretation.
 Provides an incorrect interpretation.

Questions Eliciting Thinking What does the numerator and the denominator of the slope actually mean?
Can you be more specific? How much sea salt per how many gallons of water?
Can you determine the unit rate using the table (the graph)? Is there a connection between the unit rate and the slope of the line? Explain. 
Instructional Implications Have the student assign units of measure to each part of the slope ratio. Guide the student to explain the meaning of slope as an amount of the dependent variable (e.g., 1 cup of salt) associated with a corresponding amount of the independent variable (e.g., 2 gallons of water). Ask the student to convert the slope to a unit rate including the units of measure (e.g., cup of salt for every one gallon of water). Then guide the student to interpret the slope in terms of the context of the problem. Model explaining, “To maintain proper salinity, there should be cup of salt per gallon of water.”
Consider using other MFAS tasks such as Compare Slopes and Proportional Paint (8.EE.2.5). 
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 graphs the data in the table and identifies the slope of the line to be . In addition, the student describes the slope of the line as a unit rate. For example, the student says, “It means that there is a half cup of sea salt for every gallon of distilled water.”

Questions Eliciting Thinking How did you determine the slope?
What is the difference between the slope of the line and the unit rate?
What is ratio of salt to water?
What ordered pair represents the unit rate?
How can you determine the amount of salt needed for 12.5 gallons of water? 
Instructional Implications Challenge the student to write an equation to represent the proportional relationship.
Have the student show how to determine the amount of salt needed for 12.5 gallons of water using the table, the graph, and the equation. Ask the student to compare all three methods and discuss the efficiency of each.
Consider implementing MFAS task Proportional Paint (8.EE.2.5) to further assess the student. 