Mathematics 8 (Grade 7/8)
4: Patterns of Association (8.SP)
Prior to Mathematics 8, almost all of students’ statistical topics and investigations have dealt with univariate data, e.g., collections of counts or measurements of one characteristic. Eighth graders apply their experience with the coordinate plane and linear functions in the study of association between two variables related to a question of interest. As in the univariate case, analysis of bivariate measurement data graphed on a scatterplot proceeds by describing shape, center, and spread. But now “shape” refers to a cloud of points on a plane, “center” refers to a line drawn through the cloud that captures the essence of its shape, and “spread” refers to how far the data points stray from this central line. Students extend their understanding of “cluster” and “outlier” from univariate data to bivariate data. They summarize bivariate categorical data using twoway tables of counts and/or proportions, and examine these for patterns of association.
What should my child know and be able to do?
Students will:
Investigate patterns of association in bivariate data.
8.SP.A.1
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
8.SP.A.2
Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
8.SP.A.4
Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
Students will:
Investigate patterns of association in bivariate data.
8.SP.A.1
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
 Check for Understanding: Constructing Scatter Plots  Describing Trends in Scatter Plots
 Review/Rewind: Constructing a Scatter Plot  Scatter Plots: Studying, Shoe Size, and Test Scores
 Enrichment Tasks: Birds' Eggs  Texting and Grades 1
8.SP.A.2
Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
 Check for Understanding: Eyeballing the Line of Best Fit
 Review/Rewind: Fitting a Line to Data
 Enrichment Tasks: Animal Brains  Laptop Battery Charge
8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
 Check for Understanding: Interpreting Slope and yintercept of Lines of Best Fit
 Review/Rewind: Line of Best Fit: Smoking in 1945
 Enrichment Tasks: US Airports, Assessment Variation
8.SP.A.4
Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
 Check for Understanding: Interpreting TwoWay Tables
 Review/Rewind: Categorical Data Example
 Enrichment Tasks: What's Your Favorite Subject?  Music and Sports
What are some signs of student mastery?

Tools and Technology
NCTM's Advanced Data Grapher can be used to build and analyze data using box plots, scatterplots, histograms, stemandleaf plots, and bubble graphs. You can enter multiple rows and columns of data, select which set(s) to display in a graph, and choose the type of representation. 
More 4 U
What's a dot plot?' See if this resource and accompanying video help deepen your understanding. 