Algebra I – 5 (hrs)
Sep 23, 2020 20201124 13:04Algebra I – 5 (hrs)
Algebra I – 5 (hrs)
Students are introduced to nonlinear equations and their graphs.Β Students formalize their understanding of equivalent algebraic expressions and begin their study of polynomial expressions. Students develop a set of tools for understanding and interpreting variability in data and begin to make more informed decisions from data.Β Students work with data distributions of various shapes, centers, and spreads.Β Measures of center and measures of spread are developed as ways of describing distributions.Β The choice of appropriate measures of center and spread is tied to distribution shape.Β Symmetric data distributions are summarized by the mean and mean absolute deviation, or standard deviation.Β The median and the interquartile range summarize data distributions that are skewed.Β Students calculate and interpret measures of center and spread and compare data distributions using numerical measures and visual representations.
Students are familiar with linear equations in one variable and have applied graphical and algebraic methods to analyze and manipulate equations in two variables. They use expressions and equations to solve reallife problems. They have experience with square and cube roots, irrational numbers, and expressions with integer exponents. They synthesize what they have learned during the year by selecting the correct function type in a series of modeling problems without the benefit of a module or lesson title that includes function type to guide them in their choices.

Relationships Between Quantities and Reasoning with Equations and Their Graphs
 Graphs of Piecewise Linear Functions
 Graphs of Quadratic Functions
 Graphs of Exponential Functions
 Algebraic ExpressionsβThe Distributive Property
 Algebraic ExpressionsβThe Commutative and Associative Properties
 Adding and Subtracting Polynomials
 Multiplying Polynomials
 True and False Equations
 Solution Sets for Equations and Inequalities
 Solving Equations
 Some Potential Dangers when Solving Equations
 Solving Inequalities
 Solution Sets of Two or More Equations (or Inequalities) Joined by βAndβ or βOrβ
 Solving and Graphing Inequalities Joined by βAndβ or βOr”

Descriptive Statistics
 Distributions and Their Shapes
 Describing the Center of a Distribution
 Estimating Centers and Interpreting the Mean as a Balance Point
 Summarizing Deviations from the Mean
 Measuring Variability for Symmetrical Distributions
 Interpreting the Standard Deviation
 Measuring Variability for Skewed Distributions (Interquartile Range)
 Comparing Distributions
 Summarizing Bivariate Categorical Data with Relative Frequencies
 Conditional Relative Frequencies and Association
 Relationships Between Two Numerical Variables
 Modeling Relationships with a Line
 Interpreting Residuals from a Line
 Analyzing Residuals
 Interpreting Correlation

Linear and Exponential Functions
 Recursive Formulas for Sequences
 Arithmetic and Geometric Sequences
 The Power of Exponential Growth
 Exponential Decay
 Representing, Naming, and Evaluating Functions
 The Graph of a Function
 The Graph of the Equation π¦=π(π₯)
 Interpreting the Graph of a functions
 Linear and Exponential ModelsβComparing Growth Rates
 Piecewise Functions
 Graphs Can Solve Equations Too
 Four Interesting Transformations of Functions

Polynomial and Quadratic Expressions, Equations, and Functions
 Multiplying and Factoring Polynomial Expressions
 Advanced Factoring Strategies for Quadratic Expressions
 The Zero Product Property
 Solving Basic OneVariable Quadratic Equations
 Creating and Solving Quadratic Equations in One Variable
 Exploring the Symmetry in Graphs of Quadratic Functions
 Graphing Quadratic Functions from Factored Form, π(π₯)=π(π₯βπ)(π₯βπ)
 Interpreting Quadratic Functions from Graphs and Tables
 Solving Quadratic Equations by Completing the Square
 Deriving the Quadratic Formula
 Using the Quadratic Formula
 Graphing Quadratic Equations from the Vertex Form, π¦=π(π₯ββ)2+π
 Graphing Quadratic Functions from the Standard Form, π(π₯)=ππ₯2+ππ₯+π

A Synthesis of Modeling with Equations and Functions