Getting Started 
Misconception/Error The student is unable to identify a pattern, clustering, or outliers in the scatterplot. 
Examples of Student Work at this Level The student:
 Says, “there is no relationship” but adds, “the less land area the less population.”
 Does not identify any outliers or clustering.
 Draws an incorrect conclusion about the relationship between the variables.
 Says, “no relationship” without identifying outliers or clustering.

Questions Eliciting Thinking What do you mean by “no relationship?” Can you describe it to me further?
What patterns do you see in the data?
What is an outlier? What is clustering? Do you see either on the graph? 
Instructional Implications Review the concept of twovariable or bivariate data with the student and provide examples of both onevariable (e.g., the height of students at the school) and twovariable data (e.g., the ages and heights of students at the school). Explain that the scatterplot is a visual representation of twovariable data. Guide the student to observe that the axes are scaled to represent each of the variables and the points are graphed using the usual conventions of the coordinate plane. Using the given scatterplot, ask the student to (approximately) identify the coordinates of several points and explain their meaning in terms of the variables and the context of the data.
Review terms used to describe functional relationships: constant, linear, nonlinear, exponential, increasing, decreasing, positive, and negative. Provide a number of scatterplots displaying 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. Consider asking the student to use the virtual manipulatives Scatterplot (CPALMS ID 53932) and Line of Best Fit (CPALMS ID 11280) to construct scatterplots that include clusters, gaps, and outliers. Ask the student to identify and clearly describe any patterns and outliers in his or her scatterplots. 
Making Progress 
Misconception/Error The student is unable to clearly describe patterns in the scatterplot. 
Examples of Student Work at this Level The student identifies a pattern of clustering and/or several outliers, but has difficulty describing them accurately. The student:
 Lists the outliers by a single value of one variable (e.g., describes an outlier as “37” and the clustering by a range of a single variable “010”).
 Defines the terms, explaining clustering “is when the points are all in the same area” and an outlier “is when the points are far away from the others” but does not specifically identify the clustering or outliers in this context.
 Mentions that there is clustering and outliers without describing them specifically.
 Circles the cluster and outliers on the graph without describing them numerically.
 Makes an error reading the units on the vertical scale, saying the outlier is at about 57,000 (or 57,000,000) square miles rather than 570,000.
 Gives a vague or confusing description of the outliers and clustering.

Questions Eliciting Thinking Why did you label the outlier with one value? Does that pinpoint the specific spot on the graph where that point is located? How could you list that point using both variables?
Rather than list the definitions, can you list their positions numerically?
What are the specific parameters of the clustering and outliers?
Can you look at the scale again and write the value described in the units? What place value would a value of one have on the yaxis? 
Instructional Implications Review terms used to describe functional relationships: constant, linear, nonlinear, exponential, increasing, decreasing, positive, and negative. Provide a number of scatterplots displaying 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. Consider asking the student to use the virtual manipulatives Scatterplot (CPALMS ID 53932) and Line of Best Fit (CPALMS ID 11280) to construct scatterplots that include clusters, gaps, and outliers. Ask the student to identify and clearly describe any patterns and outliers in his or her scatterplots. 
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 describes a pattern of clustering of most data points at less than 15 million in population with a land area of less than 150,000 square miles. The student may say that there is a roughly constant relationship between population and land area, indicating that as the populations of states increase, their land areas stay about the same or vary within the 0 – 150,000 square mile range. Further, the student describes the potential outliers: (approximately 2 million and 580,000 ), (approximately 37 million and 170,000 ), (25 million, 280,000 ), (19 million, 500,000 ) and (18 million, 600,000 ). 
Questions Eliciting Thinking What makes each of the outliers you identified an outlier?
Are you able to make any inferences from the scatterplot about which points represent which states? Explain. 
Instructional Implications Ask the student to model the data with a line and calculate the residuals of the outliers. Ask the student to conjecture which states correspond to the outliers.
Consider implementing other tasks aligned to 8.SP.1.1. 