Module 2: In this module, students reconnect with and deepen their understanding of statistics and probability concepts first introduced in Grades 6, 7, and 8. Students develop a set of tools for understanding and interpreting variability in data, and begin to make more informed decisions from data. They work with data distributions of various shapes, centers, and spreads. Students build on their experience with bivariate quantitative data from Grade 8. This module sets the stage for more extensive work with sampling and inference in later grades.

Unit 1: Shapes and Centers of Distributions                         (A.SSE.2, A.APR.4)

In Topic A, students observe and describe data distributions.  They reconnect with their earlier study of distributions in Grade 6 by calculating measures of center and describing overall patterns or shapes.  Students deepen their understanding of data distributions recognizing that the value of the mean and median are different for skewed distributions and similar for symmetrical distributions.  Students select a measure of center based on the distribution shape to appropriately describe a typical value for the data distribution.  Topic A moves from the general descriptions used in Grade 6 to more specific descriptions of the shape and the center of a data distribution.

M2.U1 Lessons:

M1.U1.L1
M1.U1.L2
M1.U1.L3

Unit 2: Describing Variability and Comparing Distributions                 (N.Q.2, A.SSE.2, A.APR.2)

In Topic B, students reconnect with methods for describing variability first seen in Grade 6.  Topic B deepens students’ understanding of measures of variability by connecting a measure of the center of a data distribution to an appropriate measure of variability.  The mean is used as a measure of center when the distribution is more symmetrical.  Students calculate and interpret the mean absolute deviation and the standard deviation to describe variability for data distributions that are approximately symmetric.  The median is used as a measure of center for distributions that are more skewed, and students interpret the interquartile range as a measure of variability for data distributions that are not symmetric.  Students match histograms to box plots for various distributions based on an understanding of center and variability.  Students describe data distributions in terms of shape, a measure of center, and a measure of variability from the center.

​M2.U2 Lessons:

M2.U2.L4
M2.U2.L5
M2.U2.L6
M2.U2.L7
M2.U2.L8

Unit 3: Categorial Data on Two Variables                               (A.APR.6, A.REI.1, 2)

In Topic C, students reconnect with previous work in Grade 8 involving categorical data.  Students use a two-way frequency table to organize data on two categorical variables.  Students calculate the conditional relative frequencies from the frequency table.  They explore a possible association between two categorical variables using differences in conditional, relative frequencies.   Students also come to understand the distinction between association between two categorical variables and a causal relationship between two variables.  This provides a foundation for work on sampling and inference in later grades.

​​M2.U3 Lessons:

M2.U3.L9
M2.U3.L10
M2.U3.L11

Unit 4: Numerical Data on Two Variables             (N.CN.1, 2, 7)

In Topic D, students analyze relationships between two quantitative variables using scatterplots and by summarizing linear relationships using the least squares regression line.  Models are proposed based on an understanding of the equations representing the models and the observed pattern in the scatter plot.  Students calculate and analyze residuals based on an interpretation of residuals as prediction errors.  

​​M2.U4 Lessons:

M1.U2.L12
M1.U2.L20

Module 1: Students connect polynomial arithmetic to computations with whole numbers and integers.  Students learn that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers.  This unit helps students see connections between solutions to polynomial equations, zeros of polynomials, and graphs of polynomial functions.  Polynomial equations are solved over the set of complex numbers, leading to a beginning understanding of the fundamental theorem of algebra.  Application and modeling problems connect multiple representations and include both real world and purely mathematical situations. 

M1.U3.L22
M1.U3.L35
M1.U4.L36
M1.U3.L40

Module 1: Students connect polynomial arithmetic to computations with whole numbers and integers.  Students learn that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers.  This unit helps students see connections between solutions to polynomial equations, zeros of polynomials, and graphs of polynomial functions.  Polynomial equations are solved over the set of complex numbers, leading to a beginning understanding of the fundamental theorem of algebra.  Application and modeling problems connect multiple representations and include both real world and purely mathematical situations.