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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 II Module 1: Polynomial, Rational, and Radical Relationships Students connect polynomial arithmetic to computations with whole numbers and integers. Students learn that the arithmetic of...

 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...

 Module 2 builds on students’ previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of...

 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...

 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 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 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 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.

 Student Outcomes Students discover that the multistep and exact way of solving 2x  5 = 3x + 1 using algebra can sometimes be avoided by recognizing that an equation of the form f(x) = g(x) can...

 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).

 This topic focuses on factoring polynomials and the advantages of factored form of a polynomial to both solve equations and sketch graphs of polynomial functions. Students solve problems involving...

 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 Students solve complex quadratic equations, including those with a leading coefficient other than 1, by completing the square. Some solutions may be irrational. Students draw...

 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...

 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...