Getting Started 
Misconception/Error The student cannot use the table of values or a graph to identify and interpret key features in context. 
Examples of Student Work at this Level The student cannot identify minimum and maximum values, interpret the xintercepts in context, or determine how to identify xintercepts from a table of values. 
Questions Eliciting Thinking Can you restate the problem in your own words?
What are the two variables shown in the table?
How would you label the axes on the graph? Could you graph these points?
According to the table, how far is Brad from the shore after 6 minutes? When is he 10 yards from shore? What do you think Brad is doing?
What is Brad's maximum distance from shore? What is his minimum distance from shore? 
Instructional Implications Explain how the given data can be used to scale the time and distance axes using the given graph as a reference. Have the student graph the points given in the table and then verbally describe what is happening during each interval of time. Assist the student in translating the graph into a verbal description of Brad surfing.
Review the definitions of xintercept [the point(s) where the graph intersects the xaxis] and yintercept [the point(s) where the graph intersects the yaxis]. Be sure the student understands the form of each [e.g., an xintercept is always of the form (a, 0) and a yintercept is always of the form (0, b)]. Guide the student to understand the form of the intercepts in terms of graphing. Point out that a graph can have no intercepts, one intercept, or several intercepts. Provide additional opportunities to describe and interpret intercepts in the context of problems. Encourage the student to address the meaning of both coordinates when interpreting an intercept [e.g., when interpreting the intercept (20, 0), say that after 20 minutes Brad is on the shore].
Review the vocabulary associated with features of graphs: increasing, decreasing, minimum, maximum, intercepts, symmetry, end behavior, and periodicity. Provide additional opportunities to interpret key features of graphs that model the relationship between two variables.
Consider implementing MFAS tasks Taxi Ride (FIF.2.4) and Bike Race (FIF.2.4). 
Making Progress 
Misconception/Error The student is unable to identify xintercepts (i.e., the timeintercepts) from a table of values and interpret them in the context of the problem. 
Examples of Student Work at this Level The student provides an incorrect interpretation of the xintercepts or is unable to explain how to identify the intercepts from a table of values.

Questions Eliciting Thinking Can you show me where the xintercepts of this graph are located? What do you think Brad is doing at these points?
Can you write the xintercepts as ordered pairs? What are the units of each coordinate?
What do the coordinates of every point on the xaxis have in common? How can you recognize the xintercepts in the table? 
Instructional Implications Review the definitions of xintercept [the point(s) where the graph intersects the xaxis] and yintercept [the point(s) where the graph intersects the yaxis]. Be sure the student understands the form of each [e.g., an xintercept is always of the form (a, 0) and a yintercept is always of the form (0, b)]. Guide the student to understand the effect a coordinate of zero has on the location of a point in the coordinate plane (i.e., it places the point on an axis). Point out that a graph can have no intercepts, one intercept, or several intercepts. Provide additional opportunities to describe and interpret intercepts in the context of problems. Encourage the student to identify the units of measure and address the meaning of each coordinate when interpreting an intercept [e.g., when interpreting the intercept (20, 0), indicate that after 20 minutes Brad’s distance from shore is 0 yards meaning Brad is on the shore].
Review the vocabulary associated with features of graphs: increasing, decreasing, minimum, maximum, intercepts, symmetry, end behavior, and periodicity. Provide additional opportunities to interpret key features of graphs that model the relationship between two variables.
Consider implementing MFAS tasks Taxi Ride (FIF.2.4) and Bike Race (FIF.2.4). 
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 states that:
 Brad’s maximum distance from shore is 40 yards, and his minimum distance is 0 yards which means that he is on the shore.
 The data show that there are two xintercepts, (0, 0) and (20, 0). These points indicate that at 0 minutes, Brad starts surfing and after 20 minutes, Brad is on the shore.
 The xintercepts can be identified in the table by finding the ordered pairs that have a ycoordinate (or distance) of zero.

Questions Eliciting Thinking What does it mean for the distance from shore to be zero?
What do you think is happening in the problem at 0 minutes?
If you graphed the data, what would be happening when the graph is increasing? When it is decreasing?
According to this data, how many waves does Brad ride?
What do you think might be happening during the 15 – 18 minute interval? 
Instructional Implications Review the vocabulary associated with features of graphs: increasing, decreasing, minimum, maximum, intercepts, symmetry, end behavior, and periodicity. Provide additional opportunities to interpret key features of graphs that model the relationship between two variables.
Consider implementing MFAS tasks Taxi Ride (FIF.2.4) and Bike Race (FIF.2.4). 