Algebra I
Course Title: Algebra I
Target Audience: Junior High or High School Students (Grades 8–10)
Prerequisites: Successful completion of Pre-Algebra or equivalent foundational mathematics course, including proficiency in arithmetic operations, fractions, decimals, ratios, and basic geometry.
Course Description
Algebra I is a foundational mathematics course designed to transition students from arithmetic reasoning to abstract algebraic thinking. This course introduces variables, functions, and relationships among quantities, emphasizing the ability to represent real-world situations using mathematical models. Students will develop fluency in manipulating algebraic expressions, solving equations and inequalities, analyzing patterns, and interpreting data.
Algebra I serves as the gateway to higher-level mathematics such as Geometry, Algebra II, Trigonometry, and Calculus. Students will explore both symbolic and graphical representations of relationships and will use technology and reasoning to analyze linear, quadratic, and exponential functions. The course encourages mathematical communication, critical thinking, and problem-solving, aligning with the Common Core State Standards for Mathematics (CCSSM) and the National Council of Teachers of Mathematics (NCTM) recommendations.
Intended Audience
This course is intended for students who are beginning formal study in algebra, typically in Grades 8 through 10. It provides essential preparation for college- and career-readiness by building the quantitative reasoning skills required in science, technology, engineering, and mathematics (STEM) disciplines.
Major Concepts Covered
1. Algebra Foundations
- Properties of operations and order of operations
- Writing, expanding, and factoring algebraic expressions
- Evaluating expressions with variables and exponents
2. Exponents and Radicals
- Integer and rational exponents
- Laws of exponents
- Simplifying and interpreting exponential expressions
3. Linear Equations and Inequalities
- Solving one-step, two-step, and multi-step equations
- Literal equations and formulas
- Solving and graphing linear inequalities and absolute value equations
4. Functions and Relations
- Understanding the function concept
- Function notation, domain, and range
- Interpreting graphs and tables
- Piecewise and step functions
5. Linear Relationships
- Slope and rate of change
- Writing linear equations in multiple forms (slope-intercept, point-slope, standard)
- Graphing lines and modeling linear relationships
- Solving and interpreting systems of linear equations and inequalities
6. Polynomials and Factoring
- Adding, subtracting, and multiplying polynomials
- Factoring by GCF, trinomials, and difference of squares
- Using factoring to solve quadratic equations
7. Quadratic and Exponential Functions
- Graphing quadratic functions and identifying vertex and axis of symmetry
- Solving quadratics by factoring, square roots, completing the square, and the quadratic formula
- Modeling real-world data using quadratic and exponential functions
8. Statistics and Data Analysis
- Creating and interpreting data displays and scatterplots
- Analyzing correlation and line of best fit
- Comparing linear and exponential models
- Arithmetic and geometric sequences
Concepts Not Included
- Calculus
- Integrals
- Derivatives
Learning Objectives
After this course, students will be able to:
Remembering
- Recall and apply key algebraic properties (commutative, associative, distributive)
- Identify the components of expressions, equations, and inequalities
- Recognize linear, quadratic, and exponential forms
Understanding
- Explain the meaning of variables, constants, coefficients, and exponents
- Describe relationships between graphical, tabular, and symbolic representations
- Interpret slope and intercepts in context of real-world problems
Applying
- Solve linear, quadratic, and exponential equations using multiple methods
- Model real-world problems with algebraic equations and functions
- Apply rules of exponents and factoring in simplifying expressions
Analyzing
- Compare characteristics of linear, quadratic, and exponential functions
- Decompose complex expressions into simpler components
- Analyze the effects of changing parameters on graphs of functions
Evaluating
- Justify solutions to equations and systems through substitution and verification
- Evaluate the appropriateness of mathematical models in context
- Critically assess data to determine correlation and causation
Creating
- Construct new equations or inequalities to represent unfamiliar problems
- Design and interpret linear and quadratic models from real data
- Integrate algebraic methods to solve multi-step, multi-concept problems
Alignment to Common Core Domains
| Domain | Description |
|---|---|
| A-SSE (Seeing Structure in Expressions) | Interpret, simplify, and factor expressions |
| A-APR (Arithmetic with Polynomials) | Perform operations on polynomials |
| A-CED (Creating Equations) | Create and solve equations and inequalities to model real situations |
| A-REI (Reasoning with Equations and Inequalities) | Understand and solve equations and systems logically |
| F-IF (Interpreting Functions) | Understand functions and their representations |
| F-BF (Building Functions) | Write, transform, and compose functions |
| F-LE (Linear, Quadratic, and Exponential Models) | Model growth and decay phenomena |
| S-ID (Statistics and Probability) | Analyze data using scatterplots, correlation, and regression |
Course Outcomes Summary
By the end of Algebra I, students will be able to:
- Translate real-world scenarios into algebraic representations.
- Use graphs, tables, and equations to model and analyze data.
- Solve and interpret linear, quadratic, and exponential equations and inequalities.
- Reason quantitatively, verify solutions, and communicate mathematical thinking clearly.
- Build confidence and curiosity for further study in mathematics and STEM disciplines.
Standards Alignment:
Aligned with the Common Core State Standards for Mathematics (CCSSM), High School Algebra and Functions Domains.