Getting Started

The student does not address the association or describes it incorrectly.

The student:

• Describes the association as positive or says the higher the ESS score, the higher the math score.
• Describes the graph as nonlinear.
• Attempts to interpret the slope of a line that models the data but does so incorrectly.
  
  
   
• Does not take into account both variables.
  
  
   

What are the two variables graphed on this scatterplot?

What are the coordinates of this point (indicate a particular point on the graph)? Can you interpret this point in the context of the data?

What is happening to the ESS scores as you look from left to right on the horizontal axis? What is happening to math test scores as you look from left to right on the horizontal axis?

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. Point out that a linear association can be approximated by a straight line fitted to the data points. Remind the student that a positive linear association can be described by a line with a positive slope, and a negative linear association can be described by a line with a negative slope. Assist the student in recognizing that the association between the variables in the scatterplot can be described as a strong negative linear relationship. Guide the student to interpret the relationship in the context of the data (i.e., there is a strong, consistent tendency for math test scores to decline as ESS scores increase).

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

The student provides an incomplete description of the association.

The student:

• Describes the association simply as negative without regard to the context of the data.
  
  
   
• Describes the changes in each variable without making their association explicit.
  
  
   
• Makes a prediction rather than explicitly describing the association.
  
  
   
• Uses terminology incorrectly, for example, says, “The scatterplot shows a negative slope” rather than the scatterplot shows a negative association or the line of best fit would have a negative slope.
  
  
   
• Interprets the ESS score as indicating the student got less sleep rather than as an indication of daytime sleepiness.
  
  
   

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 complete this sentence, “As the ESS scores get higher, the…”?

Can a scatterplot “have slope”? What actually has slope?

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 negative linear relationship. Guide the student to interpret the relationship in the context of the data (i.e., there is a strong, consistent tendency for math test scores to decline as ESS scores increase). Provide additional scatterplots that display various types of associations and ask the student to describe the relationship between the variables.

Provide opportunities for the student to fit lines to linearly related data. Introduce the use of technology to construct scatterplots and generate lines of best fit. Ask the student to explain the relationship between the nature of the association and the slope of the line of best fit. Guide the student to observe that lines of best fit can be used to predict values of variables within a reasonable domain or range.

Got It

The student provides complete and correct responses to all components of the task.

The student explains that as ESS scores (or daytime sleepiness) increase, math test scores decrease. Additionally, the student states that the association is linear, negative, and strong (or does so upon questioning).

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)?

Do you think one of these variables is a cause and the other is an effect? Can you explain?

Do you see any evidence of outliers?

What feature of the scatterplot indicates the strength of the association?

Review the relationship between correlation and causation (i.e., a correlation does not imply causation). Group the student with other Got It students to brainstorm possible reasons for a given association (e.g., a change in Variable A may cause a change in Variable B, or the reverse may be true, or both may be affected by a third factor).

Provide the student with a sample data set. Ask the student to construct a scatterplot, draw a line of good fit, and approximate the equation of the line. Then ask the student to use the equation to make predictions about specific values of one or both variables.

Consider implementing other MFAS tasks for this topic.