Algebra I – 12 (hrs)
Nov 06, 2020 20201124 12:41Algebra I – 12 (hrs)
Algebra I – 12 (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 Copy
 Graphs of Quadratic Functions Copy
 Graphs of Exponential Functions Copy
 Algebraic ExpressionsβThe Distributive Property Copy
 Algebraic ExpressionsβThe Commutative and Associative Properties Copy
 Adding and Subtracting Polynomials Copy
 Multiplying Polynomials Copy
 True and False Equations Copy
 Solution Sets for Equations and Inequalities Copy
 Solving Equations Copy
 Some Potential Dangers when Solving Equations Copy
 Solving Inequalities Copy
 Solution Sets of Two or More Equations (or Inequalities) Joined by βAndβ or βOrβ Copy
 Solving and Graphing Inequalities Joined by βAndβ or βOr” Copy

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

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

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

A Synthesis of Modeling with Equations and Functions