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 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 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,...

 Student Outcomes Students learn the meaning and notation of recursive sequences in a modeling setting. Following the modeling cycle, students investigate the double and add 5 game in a simple case in...

 Student Outcomes Students learn the meaning and notation of recursive sequences in a modeling setting. Students use recursive sequences to model and answer problems. Students create equations and...

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

 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.

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

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

 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 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 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 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 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...

 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 create tables and graphs of functions and interpret key features including intercepts, increasing and decreasing intervals, and positive and negative intervals.

 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 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 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 vertical translation of the graph of y = f(x) corresponds to changing the equation from y = f(x) to y = f(x) + k. Students examine that a vertical scaling of...

 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).

 Student Outcomes Students examine that a horizontal scaling with scale factor k of the graph of y = f(x) corresponds to changing the equation from y = f(x) to y = f[(1/k)(x)].