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 Students begin this module with Topic A, Constructions. Major constructions include an equilateral triangle, an angle bisector, and a perpendicular bisector. Students synthesize their knowledge of...

 Constructions segue into Topic B, Unknown Angles, which consists of unknown angle problems and proofs. These exercises consolidate students’ prior body of geometric facts and prime students’...

 Topic C, Transformations, builds on students’ intuitive understanding developed in Grade 8. With the help of manipulatives, students observed how reflections, translations, and rotations behave...

 In Topic D, Proving Properties of Geometric Figures, students use what they have learned in Topics A through C to prove properties—those that have been accepted as true and those that are new—of...

 The module closes with a return to constructions in Topic E (G.CO.13).

 Topic F is a review that highlights how geometric assumptions underpin the facts established thereafter.

 In Topic G, students review material covered throughout the module. Additionally, students discuss the structure of geometry as an axiomatic system.

 In Topic A, students explore the main functions that they will work with in Grade 9: linear, quadratic, and exponential. The goal is to introduce students to these functions by having them make...

 In middle school, students applied the properties of operations to add, subtract, factor, and expand expressions (6.EE.3, 6.EE.4, 7.EE.1, 8.EE.1). Now, in Topic B, students use the structure of...

 Throughout middle school, students practice the process of solving linear equations (6.EE.5, 6.EE.7, 7.EE.4, 8.EE.7) and systems of linear equations (8.EE.8). Now, in Topic C, instead of just...

 In Topic D, students are formally introduced to the modeling cycle (see page 61 of the CCLS) through problems that can be solved by creating equations and inequalities in one variable, systems of...

 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...

 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...

 In Topic C, students reconnect with previous work in Grade 8 involving categorical data. Students use a twoway frequency table to organize data on two categorical variables. Students calculate the...

 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...

 In Topic A, students explore arithmetic and geometric sequences as an introduction to the formal notation of functions (FIF.A.1, FIF.A.2). They interpret arithmetic sequences as linear functions...

 In Topic B, students connect their understanding of functions to their knowledge of graphing from Grade 8. They learn the formal definition of a function and how to recognize, evaluate, and...

 In Topic C, students extend their understanding of piecewise functions and their graphs including the absolute value and step functions. They learn a graphical approach to circumventing complex...

 Topic A introduces polynomial expressions. In Module 1, students learned the definition of a polynomial and how to add, subtract, and multiply polynomials. Here, their work with multiplication is...

 Students apply their experiences from Topic A as they transform quadratic functions from standard form to vertex form, (x) = a(x  h)2 + k in Topic B. The strategy known as completing the square is...

 In Topic C, students explore the families of functions that are related to the parent functions, specifically for quadratic (f(x) = x2), square root (f(x) = the square root of x), and cube root (f(x...

 Topic A focuses on the skills inherent in the modeling process: representing graphs, data sets, or verbal descriptions using explicit expressions (FBF.A.1a) when presented in graphic form in Lesson...

 Tables, graphs, and equations all represent models. We use terms such as “symbolic” or “analytic” to refer specifically to the equation form of a function model; “descriptive model” refers to a...

 The focus in this topic is on polynomial arithmetic and how it is analogous to operations with integers. The module opens with a lively lesson that engages students in writing polynomial expressions...