Getting Started 
Misconception/Error The student is unable to sketch a graph to model the relationship between two quantities. 
Examples of Student Work at this Level The student’s graph does not show variations that correspond to the differing descriptions of bike rate over time. The student’s graph displays:
 A linearly increasing, decreasing, or constant relationship.
 Variations that do not correspond to features of the description.
 Instantaneous increase and/or decrease of rate or a rate of zero over an interval of time.
The student labels time on the yaxis, but makes a graph as if time is on the xaxis.
The student graphs a relationship between quantities other than rate and time (e.g., rate vs. distance or length vs. time).

Questions Eliciting Thinking What are the two quantities described in this problem?
Can you explain what each section of your graph represents? What parts of the description correspond to each section of your graph?
What must happen for the rider to get up to that rate? Does this happen instantaneously?
What do you mean by a zero rate lasting for several minutes? What is the rider doing during that time? 
Instructional Implications Guide the student to identify and describe the two related quantities in the problem description and to label the axes accordingly. Then ask the student to analyze the problem description by identifying each component part. Guide the student to sketch segments of the graph that correspond to the parts of the description.
Provide examples of completed graphs for the student to analyze as well as descriptions of the relationship between two quantities that the student can graph. Guide the student to address features of the graph such as intercepts, intervals where the function is increasing, decreasing, positive or negative, relative maximums and minimums, and rate of change. Assist the student in learning and using mathematical terminology to describe these features. 
Moving Forward 
Misconception/Error The student misinterprets or omits some portion of the description when sketching a graph. 
Examples of Student Work at this Level Some portions of the student’s graph are correct, but others are incorrect or missing. For example, the student:
 Begins the graph at a nonzero constant rate.
 Provides an incomplete graph.
 Stops the graph after the constant rate on the hill, but does not show the rate diminishing to zero.
 Shows an increase in rate after reaching the top of the hill.
 Does not show time intervals correctly (e.g., the portion of the graph that corresponds to a 5 min. interval is not half of the portion that corresponds to a 10 min. interval).

Questions Eliciting Thinking Can the bike rider start at a nonzero rate? What must happen before the rider gets up to a constant rate?
What happens after Sophia rides at a constant rate for 10 minutes? How did you show that on your graph?
How can you show a constant rate on the graph?
What does it say the rider does at the top of the hill? What must happen for the rider to stop?
Does the rider going up the hill mean the same thing as the rate increasing? What happened to the rider’s rate as the bike went up the hill?
How did you scale your time axis? How should the 5 minute and 10 minute intervals be related? 
Instructional Implications Provide feedback to the student with regard to both the correct and incorrect parts of his or her graph. Address any misconceptions the student might have about how the context relates to the graph (e.g., riding up the hill does not mean the graph increases; stopping at the top of the hill does not mean the graph stops above the xaxis). Ask the student to complete the graph or revise the incorrect portions.
Provide additional descriptions of the relationship between two quantities that the student can graph. Guide the student to relate features of the graph such as intercepts, intervals where the function is increasing, decreasing, positive or negative, relative maximums and minimums, and rate of change to particular aspects of the description. Assist the student in learning and using mathematical terminology to describe these features. 
Almost There 
Misconception/Error The student does not label the axes or title the graph appropriately. 
Examples of Student Work at this Level The student:
 Does not provide a title.
 Does not include the unit of measure with each axis label.

Questions Eliciting Thinking Did you give your graph a title?
How is each quantity measured? Did you include the unit of measure when you labeled the axes? 
Instructional Implications Ask the student to provide a title for the graph if it was omitted. Also, guide the student to label axes with both a term that describes the quantity represented and its unit of measure [e.g., label the xaxis as “Time (in minutes)” and the yaxis as “Rate (in miles per hour)”].
Provide the student with additional opportunities to draw graphs from verbal descriptions. Consider using MFAS task Bacterial Growth Graph (8.F.2.5). Also, provide opportunities to interpret a given graph by describing it verbally. Consider implementing MFAS tasks Jet Fuel and Population Trend (8.F.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 identifies the two related quantities and labels the axes appropriately (e.g., time on the xaxis and rate or speed on the yaxis). The graph shows a gradual increase from a rate of zero for an unspecified time, then a 10 minute interval where the rate is constant, followed by a decrease in rate which is maintained for five minutes, after which the rate drops to zero.
Note: Exact number labels may be missing on the xaxis due to nonspecific times given for the acceleration and deceleration phases, but the graph should show a correct proportional relationship between lengths of segments relative to the description. 
Questions Eliciting Thinking How would the graph change if Sophia had gone downhill instead of uphill?
How would you show stopping for a red light on a graph?
How would the graph change if each segment lasted for double the stated time? 
Instructional Implications Provide the student with additional opportunities to draw graphs from verbal descriptions. Consider using MFAS task Bacterial Growth Graph (8.F.2.5). Also, provide opportunities to interpret a given graph by describing it verbally. Consider implementing MFAS tasks Jet Fuel and Population Trend (8.F.2.5). 