Portville Study
Algebra 1
"Pure mathematics is, in its way, the
poetry of logical ideas."
Albert Einstein (1879-1955)
Unit 1
Lesson #1: Rates, Patterns, and Problem Solving
Lesson #2: Variables and Expressions
Lesson #3: The Commutative and Associative Properties
Lesson #4: The Distributive Property
Lesson #5: Equivalent Expressions
Lesson #6: Seeing Structure in Expressions
Lesson #7: Exponents as Repeated Multiplication
Lesson #8: More Complex Equivalency
Lesson #9: More Structure Work
Lesson #10: Translating English to Algebra
Lesson #11: Algebraic Puzzles

Unit 2
Lesson #1: Equations and Their Solutions
Lesson #2: Seeing Structure to Solve Equations
Lesson #3: Linear Equation Solving Review
Lesson #4: Justifying Steps in Solving an Equation
Lesson #5: Linear Word Problems
Lesson #6: More Linear Word Problems
Lesson #7: Solving Equations with Unspecified Constants
Lesson #8: Inequalities
Lesson #9: Solving Linear Inequalities
Lesson #10: Compound Inequalities
Lesson #11: More Work with Compound Inequalities
Lesson #12: Interval Notation
Lesson #13: Modeling with Inequalities

Unit 3
Lesson #1: Introduction to Functions
Lesson #2: Function Notation
Lesson #3: Graphs of Functions
Lesson #4: Graphical Features of Functions
Lesson #5: Exploring Functions on the Graphing Calculator (TI-84+)
Lesson #6: Average Rate of Change
Lesson #7: The Domain and Range of a Function

Unit 4
Lesson #1: Proportional Relationships
Lesson #2: Unit Conversions
Lesson #3: Non-proportional Linear Relationships
Lesson #4: More Work Graphing Lines
Lesson #5: Writing Equations of Lines
Lesson #6: Modeling with Linear Functions
Lesson #7: More Linear Modeling
Lesson #8: Vertical and Horizontal Lines
Lesson #9: Absolute Value and Step Functions
Lesson #10: The Truth About Graphs
Lesson #11: Graphs of Linear Inequalities
Lesson #12: Introduction to Sequences
Lesson #13: Arithmetic Sequences

Unit 5
Lesson #1: Solutions to Linear Systems and Solving by Graphing
Lesson #2: Solving Systems by Substitution
Lesson #3: Properties of Systems and Their Solutions
Lesson #4: The Method of Elimination
Lesson #5: Modeling with Systems of Equations
Lesson #6: Solving Equations Graphically
Lesson #7: Solving Systems of Inequalities
Lesson #8: Modeling with Systems of Inequalities

Unit 6
Lesson #1: Simplifying Expressions Involving Exponents
Lesson #2: Multiplying Polynomials
Lesson #3: Exponential Growth and Decay
Lesson #4: Introduction to Exponential Functions
Lesson #5: Percent Review
Lesson #6: Percent Increase and Decrease
Lesson #7: Exponential Models Based on Percent Growth
Lesson #8: Linear Versus Exponential

Unit 7
Lesson #1: Introduction to Polynomials
Lesson #2: Multiplying Polynomials
Lesson #3: Factoring Polynomials
Lesson #4: Factoring Based on Conjugate Pairs
Lesson #5: Factoring Trinomials
Lesson #6: More Trinomial Factoring

Unit 8
Lesson #1: Introduction to Quadratic Functions
Lesson #2: More Work with Parabolas
Lesson #3: The Shifted Form of a Parabola
Lesson #4: Completing the Square
Lesson #5: Stretching Parabolas and Completing the Square
Lesson #6: The Zeroes of a Quadratic
Lesson #7: More Zero Product Law
Lesson #8: Quadratic Word Problems

Unit 9
Lesson #1: Square Roots
Lesson #2: Irrational Numbers
Lesson #3: Square Root Functions and Shifting
Lesson #4: Solving Quadratics by Using Inverse Operations
Lesson #5: Finding Zeroes by Completing the Square
Lesson #6: The Quadratic Formula
Lesson #7: Final Work with Quadratic Equations
Lesson #8: Cube Roots

Unit 10
Lesson #1: Graphical Displays of Data
Lesson #2: Quartiles and Box Plots
Lesson #3: Measures of Central Tendency
Lesson #4: Measures of Variation
Lesson #5: Two Way Frequency Tables
Lesson #6: Bivariate Data Analysis
Lesson #7: Linear Regression on the Calculator
Lesson #8: Other Types of Regression
Lesson #9: Correlation Coefficients
Lesson #10: Residuals

Unit 11
Lesson #1: Function Transformations
Lesson #2: Horizontal Stretching of Functions
Lesson #3: Discrete Functions
Lesson #4: Another Look at Linear and Exponential Models
Lesson #5: Step Functions
Lesson #6: Piecewise Linear Functions
Lesson #7: Quadratic Models
Lesson #8: Limits to the Accuracy of Our Models
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