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Common Core: Math
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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...

 Student Outcomes Students write sequences with recursive and explicit formulas.

 Student Outcomes Students use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Students create functions...

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

 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...

 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...

 Student Outcomes Students are able to model with and solve problems involving exponential formulas.

 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.

 Student Outcomes Students understand that a function from one set (called the domain) to another set (called the range) assigns each element of the domain to exactly one element of the range....

 Student Outcomes Students describe and analyze exponential decay models; they recognize that in a formula that models exponential decay, the growth factor b is less than 1; or, equivalently, when b ...

 Student Outcomes Students understand that a function from one set (called the domain) to another set (called the range) assigns each element of the domain to exactly one element of the range and...

 Student Outcomes Students examine the features of piecewise functions including the absolute value function and step functions. Students understand that the graph of a function f is the graph of the...

 Student Outcomes Students compare linear and exponential models of population growth.

 Student Outcomes Students understand set builder notation for the graph of a realvalued function: {(x, f(x))  x ∈ D}. Students learn techniques for graphing functions and relate the domain of a...

 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...

 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...

 Student Outcomes Students examine quadratic equations in two variables represented graphically on a coordinate plane and recognize the symmetry of the graph. They explore key features of graphs of...

 Student Outcomes Students compare linear and exponential models by focusing on how the models change over intervals of equal length. Students observe from tables that a function that grows...

 Student Outcomes Students use the factored form of a quadratic equation to construct a rough graph, use the graph of a quadratic equation to construct a quadratic equation in factored form, and...

 Student Outcomes Students understand the meaning of the graph of y = f(x), namely {(x,y)  x ∈ D and y = f(x)}. Students understand the definitions of when a function is increasing or decreasing.