COURSE OVERVIEW

Order of the units

Unit 1: Functions, Graphs, and Features

Students:

• Are introduced to all of the main features of functions they will learn throughout the year through basic graphical modeling of contextual situations.
• learn function notation and use this to analyze and express features of functions represented in graphs and contextually.
• Use the tools of domain and range, rates of change, intercepts, and where a function is changing to describe contextual situations.

Unit 2: Statistics:

Students:

• Continue to analyze contextual situations, but in this unit, they focus on single-variable data and then bivariate data. This is the first unit where students are introduced to the concept of using data to make predictions and judgments about a situation.
• Begin to make judgments about whether data is consistent (analysis of spread) and whether mean or median is a better representation of a situation (center).
• Develop a linear model that can be used to predict future events.
• Are introduced to the modeling cycle and complete a project on univariate data analysis and another on bivariate data analysis.

Unit 3: Linear Expressions & Single-Variable Equations/Inequalities

• Students become proficient at manipulating and solving single-variable linear equations and inequalities, as well as using linear expressions to model contextual situations.
• Domain and range are introduced again through the lens of a “constraint” with inequalities. The understanding students develop in this unit builds the foundation for Unit 4, Unit 5, and Unit 6, as well as provides an algebraic outlet for modeling contextual situations started in Unit 1 and continued in Unit 2.

Unit 4: Linear Equations, Inequalities, and Systems,

• Students become proficient at manipulating, identifying features, graphing, and modeling with two-variable linear equations and inequalities.
• Students are introduced to inverse functions and formalize their understanding on linear systems of equations and inequalities to model and analyze contextual situations.

Unit 5: Piecewise Functions and Transformations

• Students revisit work in Units 1, 3, and 4 to formalize their understanding of domain and range to model linear piecewise functions.
• Students are introduced to the concept of a function transformation—a key concept in identifying functions that model situations but are shifted, reflected, or dilated to represent the characteristics of the particular situation.

Unit 6: Exponents and Exponential Functions

• Students review exponent rules studied in middle school and extend their understanding to include rational exponents.
• students will be operating with polynomials as an extension of work done in Unit 3 with expressions, and utilizing exponent rules reviewed in this unit.
• Formalize the conceptual understanding of the power of exponents to increase or decrease values at increasing or decreasing rates, respectively, to model with exponential functions.
• Students use the understanding about linear functions developed in Units 2, 3, 4, and 5 to make comparisons to exponential situations in terms of algebraic modeling, use of the function in contextual situations, and graphical analysis.

Unit 7: Quadratic Functions and Solutions

• Students begin a deep study of quadratic functions—a key function for students to master in Algebra 1.
• Students pull together their understanding of graphical analysis from Unit 1, algebraic manipulation from Unit 3, and linear equations and inequalities from Unit 4 to develop an understanding of what a solution means in context, graphically, and algebraically within quadratics.

Unit 8: Quadratic Equations and Applications

• Students wrap up their study of quadratic functions in Algebra 1, diving deep into all forms of quadratic equations, methods to solve quadratic equations, and methods to identify features from equations.
• Students apply their understanding of how to graphically and algebraically analyze, manipulate, and solve quadratic functions to model contextual situations.
• Students will be expected to be fluent in analyzing and solving quadratic functions and equations in Algebra 2.

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