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 Algebra I Module 3: Linear and Exponential Functions In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module,...

 Algebra I Module 4: Polynomial and Quadratic Expressions, Equations, and Functions In earlier modules, students analyze the process of solving equations and developing fluency in writing,...

 Algebra I Module 5: A Synthesis of Modeling with Equations and Functions In Module 5, students synthesize what they have learned during the year about functions to select the correct function type in...

 Student Outcomes Students examine sequences and are introduced to the notation used to describe them.

 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...

 Exponential and Logarithmic Functions In this module, students synthesize and generalize what they have learned about a variety of function families. They extend the domain of exponential functions...

 Student Outcomes Students write sequences with recursive and explicit formulas.

 Student Outcomes Students learn the structure of arithmetic and geometric sequences.

 Student Outcomes Students compare the rate of change for simple and compound interest and recognize situations in which a quantity grows by a constant percent rate per unit interval.

 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...

 Student Outcomes Students examine that a horizontal translation of the graph of y = f(x) corresponds to changing the equation from y = f(x) to y = f(x  k).

 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...

 In Topic D, students apply and reinforce the concepts of the module as they examine and compare exponential, piecewise, and step functions in a realworld context (FIF.C.9). They create equations...

 Student Outcomes Students apply their understanding of transformations of functions and their graphs to piecewise functions.

 Student Outcomes From a graphic representation, students recognize the function type, interpret key features of the graph, and create an equation or table to use as a model of the context for...

 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...

 Student Outcomes Students create piecewise and step functions that relate to reallife situations and use those functions to solve problems. Students interpret graphs of piecewise and step functions...

 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...

 Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots...

 Student Outcomes Students recognize and use parent functions for linear, absolute value, quadratic, square root, and cube root to perform vertical and horizontal translations. They identify how the...

 Student Outcomes Students recognize and use parent functions for absolute value, quadratic, square root, and cube root to perform transformations that stretch and shrink the graphs of the functions...

 Student Outcomes Students apply knowledge of exponential functions and transformations of functions to a contextual situation.

 Student Outcomes Students make a connection between the symbolic and graphic forms of quadratic equations in the completedsquare (vertex) form. They efficiently sketch a graph of a quadratic...

 Student Outcomes Students create a twovariable equation that models the graph from a context. Function types include linear, quadratic, exponential, square root, cube root, and absolute value. ...