In this unit, students begin to extend their understanding of univariate data to bivariate data as they discover how center, spread, and shape affect the relationship between two variables. Students will also extend their knowledge of linear functions as they informally discover the line of best fit for a data set that shows a linear pattern.
Key Concepts:
 Patterns of association (clustering, outliers, positive or negative association) may emerge when bivariate data are displayed in a scatterplot (as one increases, the other increase or decreases, linear or nonlinear, etc.).
 Bivariate data may not have an exact linear association, but a linear model is often used to describe the association.
 A linear model of bivariate data which has a slope and intercept may be used to predict values in real world problems.
Prior Knowledge Needed:
 Graphing points; Grade 5, Unit 14, 5.G.A.2
 Understanding center, spread, and shape; Grade 6, Unit 12, 6.SP.A.2
 Finding patterns in data; Grade 6, Unit 13, 6.SP.B.5
 Constructing a linear model; Grade 8, Unit 7, 8.F.B.4
 Analyzing a linear graph; Grade 8, Unit 7, 8.F.B.5
Units on the Horizon:
 High School Algebra 1  Determine the equation of a regression line
 High School Algebra 1  Interpret the slope and intercept of a regression line
 High School Algebra 1  Determine the correlation between two variables
Lessons

Lesson objective: Understand that patterns of association between bivariate data can be determined by using scatter plots. Students bring prior knowledge of plotting points from 5.G.A.2. This prior knowledge is extended to creating scatter plots as stud...

Lesson objective: Create a scatter plot by identifying the dependent and independent variables. This lesson helps to build procedural skill with creating scatter plots. A scatter plot is used here because it supports finding patterns of association betw...

Lesson objective: Fluently determine patterns of association in a bivariate set of data. This lesson helps to build fluency with patterns of association in a bivariate set of data. A scatter plot is used here because it highlights associations between v...

Lesson objective: Apply patterns of association to scatter plots. This lesson provides an opportunity for students to apply their knowledge and understanding of patterns of association for scatter plots to a reallife situation. Students are asked to de...

Lesson objective: Understand that a linear model is often used to describe the relationship in a set of bivariate data. Students bring prior knowledge of using scatter plots to describe patterns of association from 8.SP.A.1. This prior knowledge is exte...

Lesson objective: Determine a line of best fit for a scatter plot by using two points to find the equation of a line. This lesson helps to build procedural skill with a line of best fit. A scatter plot is used here because it highlights the linear assoc...

Lesson objective: Fluently interpret the slope and intercept of a line of best fit for a scatter plot in the context of the independent and dependent variables. This lesson helps to build fluency with interpreting the slope and intercept of a line of be...

Lesson objective: Connect meaning of the slope and intercept to the line of best fit for a set of bivariate data. This lesson provides an opportunity for students to apply their knowledge and understanding of a line of best fit to a reallife situation....

Lesson objective: Understand that a linear model can be used to predict values in realworld problems. Students bring prior knowledge of finding a line of best fit from 8.SP.A.2. This prior knowledge is extended to use the equation of the line of best f...

Lesson objective: Solve problems by using a line of best fit to predict values for the dependent and independent variables. This lesson provides an opportunity for students to apply their knowledge and understanding of lines of best fit to a reallife s...

Lesson objective: Understand that bivariate categorical data can be displayed in a twoway table. Students bring prior knowledge of organizing data into categories from 1.MD.C.4. This prior knowledge is extended to bivariate categorical data as students...

Lesson objective: Understand that associations may be found in bivariate categorical data by looking at a twoway table. Students bring prior knowledge of organizing and interpreting univariate categorical data from 1.MD.C.4. This prior knowledge is ext...

Lesson objective: Find relative frequencies for a twoway table. This lesson helps to build procedural skill with relative frequencies. A twoway table is used here because it supports finding relative frequencies for bivariate categorical data. This wo...

Lesson objective: Identify possible associations in twoway tables for categorical data. This lesson helps to build procedural skill with identifying possible associations in categorical data. A twoway table is used here because it highlights possible ...

Lesson objective: Connect a Venn diagram to a twoway table. This lesson provides an opportunity for students to apply their knowledge and understanding of twoeay tables to a reallife situation. Students are asked to convert a Venn diagram to a twowa...