Getting Started 
Misconception/Error The student does not address the association or describes it incorrectly. 
Examples of Student Work at this Level The student:
 Describes the association as linear.
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 Does not describe the association but attempts to interpret the slope of a line of fit.
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 Describes the association in a manner that does not make mathematical sense such as having a â€śpositive exponential slope.â€ť
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Questions Eliciting Thinking What about this pattern caused you to describe it as linear? What kind of curve would better model this data than a line?
What is happening to the number of bacteria over time? Are they increasing at a constant rate? 
Instructional Implications Review terms used to describe functional relationships: constant, linear, nonlinear, exponential, increasing, decreasing, positive, and negative. Emphasize the distinction between linear and nonlinear patterns in scatterplots. Remind the student that a linear association can be approximated by a straight line fitted to the data points and explain why a linear function is not the best choice of a model for the data. Assist the student in recognizing that the association between the variables in the scatterplot can be described as a strong positive exponential relationship. Explain that the rate of change of an exponential model of the data is increasing over time. Guide the student to interpret the relationship in the context of the data (i.e., over time, the number of bacteria is increasing exponentially).
Provide additional scatterplots that display various types of associations, and model describing the relationship between the variables. Address any clustering or evidence of outliers and explain these features in terms of the context of the data. Provide additional opportunities for the student to construct and interpret scatterplots by describing associations and identifying clusters and outliers. 
Making Progress 
Misconception/Error The student provides an incomplete description of the association. 
Examples of Student Work at this Level The student:
 Describes the association as strong, positive, and/or nonlinear without regard to the context of the data.
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 Describes the association in context but does not address its nonlinearity.
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 Says that the bacteria are exponentially increasing over time but does not address the strength of the relationship.
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Questions Eliciting Thinking What are the two variables graphed on this scatterplot? Can you describe the association in the context of these variables?
Would you describe this association as linear or nonlinear? Positive or negative? How would you describe the strength of this association?
How would you describe the strength of this realtionship? 
Instructional Implications Review terms used to describe functional relationships: constant, linear, nonlinear, exponential, increasing, decreasing, positive, and negative. Model describing the association between the variables in the scatterplot as a strong positive exponential relationship. Explain that the rate of change of an exponential model of the data is increasing over time. Guide the student to interpret the relationship in the context of the data (i.e., over time, the number of bacteria is increasing exponentially). Provide additional scatterplots that display various types of associations and ask the student to describe the relationship between the variables.
Remind the student that a curve that models a set of data is a good fit if the distances between the data points and the curve are small. Explain that data points in strong associations show little deviation from a curve used to model the association. In weak associations, the data points are more scattered around the curve that models the relationship. Show the student several scatterplots (e.g., ones with a strong positive exponential association, strong negative exponential association, weak positive exponential association, and weak negative exponential association) and model a curve of good fit for each example. 
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 explains that over time, the number of bacteria are increasing. Additionally, the student states that the association is nonlinear (or exponential), positive, and strong (or does so upon questioning).
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Questions Eliciting Thinking Would you describe this association as linear or nonlinear? Positive or negative? How would you describe the strength of this association (if the student did not already address these qualities in his or her response)?
What is happening to the rate of change?
What kind of curve do you think would best model this data? 
Instructional Implications Challenge the student to model the growth of the bacteria with an exponential function. Have the student write the equation of the function and graph it on the scatterplot. Then have the student informally evaluate the degree of fit of the function.
Consider implementing other MFAS tasks forÂ this topic. 