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Common Core: Standard
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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 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...

 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,...

 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...

 Student Outcomes Students write equations to model data from tables, which can be represented with linear, quadratic, or exponential functions, including several from Lessons 4 and 5. They recognize...

 Student Outcomes Students model functions described verbally in a given context using graphs, tables, or algebraic representations.

 Student Outcomes Students interpret the function and its graph and use them to answer questions related to the model, including calculating the rate of change over an interval, and always using an...

 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...

 Student Outcomes Students recognize linear, quadratic, and exponential functions when presented as a data set or sequence, and formulate a model based on the data.

 Student Outcomes Students make sense of a contextual situation that can be modeled with linear, quadratic, and exponential functions when presented as a word problem. They analyze a verbal...

 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. ...

 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 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 compare two different quadratic, square root, or cube root functions represented as graphs, tables, or equations. They interpret, contextualize and abstract various...

 Student Outcomes Students graph simple quadratic equations of the form y = a(x  h)2 + k (completedsquare or vertex form), recognizing that (h,k) represents the vertex of the graph and use a graph...

 Student Outcomes Students graph a variety of quadratic functions using the form f(x) = ax2 + bx + c (standard form). Students analyze and draw conclusions about contextual applications using the key...