Typically the first high school math class that students take is Algebra 1 (Algebra 1/2 for PPS). This class forms the foundation for all other mathematics courses in high school, therefore it is aimed at providing students with a robust understanding of the language and tools of algebra. In the Algebra 1 objectives the main focus is to introduce students to algebraic concepts such as operations with real numbers, variables, expressions, equations, inequalities, and their applications. Students will develop procedural fluency in solving a variety of equations and inequalities, including linear, quadratic, and rational. They will also explore the numerical and graphical characteristics of these functions.
An important area of focus in Algebra 1 is the understanding and manipulation of relations and more specifically functions. Students will learn how to interpret, analyze, and compare functions in different forms (verbal, symbolic, graphical, tabular). These modalities will allow students to model and solve problems. They will learn the concept of function families, understand the behavior of different types of functions, and gain insights into the interconnections between algebra and geometry through the graphical interpretation of functions.
The Algebra 1 course also places significant emphasis on problem-solving and real-world applications. It’s designed to provide students with an opportunity to apply algebraic concepts to solve complex, multi-step problems, making connections between the classroom learning and the world outside. As part of the Common Core emphasis on reasoning and making sense of problems, students will be encouraged to justify their reasoning, communicate their thought process, and critique the reasoning of others.
By the end of the Algebra 1 course, students should have a strong foundation in linear and quadratic functions. Students will also be able to show proficiency in Algebraic properties operations. Students should be able use these skills to demonstrate their understanding of algebraic principles through symbolic manipulation, graphical analysis, and problem-solving. With the skills and understanding developed in this course, students will be better equipped to take on the challenges of Geometry, Algebra II (Algebra 3/4 for PPS), Precalculus, Calculus, as well as other IB and AP classes.
Unit 1: Foundations for Algebra
- Real Numbers
- Operations with Real Numbers
- Algebraic Expressions
- Solving Basic Equations
Unit 2: Solving Equations and Inequalities
- Solving Multi-step Equations
- Solving Absolute Value Equations
- Solving and Graphing Inequalities
- Solving Absolute Value Inequalities
Unit 3: Functions and Relations
- Introduction to Functions
- Function Notation and Evaluation
- Graphing Functions
- Arithmetic Sequences as Functions
- Linear Functions
- Special Functions
Unit 4: Linear Equations and Their Graphs
- Slope and Rate of Change
- Graphing Linear Equations
- Writing Linear Equations
- Parallel and Perpendicular Lines
- Scatter Plots and Trend Lines
Unit 5: Systems of Linear Equations and Inequalities
- Solving Systems of Linear Equations by Graphing
- Solving Systems of Linear Equations by Substitution
- Solving Systems of Linear Equations by Elimination
- Systems of Linear Inequalities
Unit 6: Polynomials and Factoring
- Introduction to Polynomials
- Adding and Subtracting Polynomials
- Multiplying Polynomials
- Factoring Polynomials
- Solving Equations by Factoring
Unit 7: Quadratic Functions and Equations
- Graphing Quadratic Functions
- Solving Quadratic Equations by Factoring
- Solving Quadratic Equations by the Quadratic Formula
- The Discriminant and the Nature of Roots
- Applications of Quadratic Equations
Unit 8: Radical Expressions and Equations
- Simplifying Radical Expressions
- Operations with Radical Expressions
- Radical Equations
- Rational Exponents
Unit 9: Rational Expressions and Equations
- Simplifying Rational Expressions
- Multiplying and Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Solving Rational Equations
