Algebra 1 Course Overview
This Algebra 1 course is designed to introduce students to the fundamental concepts and skills needed to succeed in high school mathematics and beyond. Students will develop a deep understanding of algebraic reasoning through engaging lessons, practice problems, real-world applications, and assessments. The course covers variables, expressions, equations, inequalities, functions, and graphing, with a focus on developing problem-solving skills and mathematical fluency.
Course Units Include:
- Introduction to Algebra: Variables, Expressions, and Equations
- Order of Operations (PEMDAS) and Evaluating Expressions
- Real Numbers and Their Properties
- Solving One-Step and Two-Step Equations
- Solving Multi-Step Equations and Inequalities
- Graphing Linear Equations and Functions
- Slope and Rate of Change
- Writing Linear Equations
- Systems of Equations: Graphing, Substitution, and Elimination
- Exponents and Exponential Functions
- Polynomials and Factoring
- Solving Quadratic Equations and Graphing Parabolas
Learning Objectives:
By the end of this course, students will be able to evaluate algebraic expressions, solve linear and quadratic equations, analyze functions, model relationships with graphs, and apply algebraic concepts to real-world problems.
Course Format:
The course consists of interactive lessons, instructional videos, practice assignments, quizzes, and unit tests. It is suitable for middle and high school students, homeschoolers, or learners reviewing algebra fundamentals.
Course Videos
Welcome to Algebra 1
Learning Videos
Introduction to Algebra
Objective:
Students will understand the foundational concepts of algebra including variables, constants, expressions, and basic equations. They will learn how to translate real-world situations into algebraic expressions and identify the parts of an algebraic expression.
Key Concepts:
- Definition and purpose of variables and constants
- Algebraic expressions and terms
- Coefficients and like terms
- Writing and interpreting expressions from word problems
- Introduction to one-step equations
Lesson Activities:
1. Warm-Up: Identify patterns and describe them using variables.
2. Direct Instruction: Interactive presentation on the components of algebraic expressions with examples.
3. Guided Practice: Students will work in pairs to identify variables and write expressions from context-based prompts.
4. Independent Practice: Worksheet with 10 problems including expression identification, simplification, and translating phrases.
5. Exit Ticket: A quick problem that asks students to write and evaluate a simple algebraic expression.
Learning Videos
Understanding Limits: Graphical, Numerical, and Algebraic Approaches
🎯 Lesson Objectives
By the end of this lesson, students will be able to:
Describe a limit as the value a function approaches
Evaluate limits using:
Graphs
Tables
Algebraic methods
Distinguish between left-hand and right-hand limits
Determine when a limit exists or does not exist
Explain limits in their own words using real-world context
🧠 Essential Question
What does it mean for a function to “approach” a value, and why does that matter?
Learning Videos
Continuity & the Intermediate Value Theorem: Understanding What Must Happen
🎯 Lesson Objectives
By the end of this lesson, students will be able to:
Define continuity using limits
Verify whether a function is continuous at a point
Identify types of discontinuities:
Removable
Jump
Infinite
Explain the three conditions of continuity
Apply the Intermediate Value Theorem (IVT)
Interpret IVT in both mathematical and real-world contexts
🧠 Essential Question
When a function is continuous, what are we guaranteed about its behavior?
Learning Videos
Definition of a Derivative: From Average Change to Instantaneous Change
🎯 Lesson Objectives
By the end of this lesson, students will be able to:
Define the derivative as a limit of the difference quotient
Interpret the derivative as:
Instantaneous rate of change
Slope of a tangent line
Compute derivatives using the limit definition
Distinguish between:
Average rate of change (secant line)
Instantaneous rate of change (tangent line)
Explain the derivative concept verbally, graphically, and algebraically
🧠 Essential Question
How can we measure how something is changing at an exact moment in time?
Learning Videos
Derivative Rules (Power, Product, Quotient, Chain): Efficiently Computing Rates of Change
Lesson Objectives
By the end of this lesson, students will be able to:
Apply the Power Rule to differentiate polynomial terms
Use the Product Rule for functions involving multiplication
Use the Quotient Rule for functions involving division
Apply the Chain Rule to composite functions
Identify the correct rule based on the structure of a function
Compute derivatives accurately and efficiently
Explain which rule was used and why
Essential Question
How can we quickly and correctly find derivatives by recognizing patterns in functions?
Learning Videos
Derivatives of Exponential, Logarithmic, and Trigonometric Functions
🎯 Lesson Objectives
By the end of this lesson, students will be able to:
Differentiate exponential functions:
e^x, a^x
Differentiate logarithmic functions:
ln x, ln(g(x))
Differentiate trigonometric functions:
sin x, cos x, tan x
Apply the chain rule to all function types
Identify the structure of a function and select the correct method
Interpret derivatives in real-world contexts (growth, decay, waves)
🧠 Essential Question
How do different types of functions change, and how can we measure that change efficiently?
Learning Videos
Implicit Differentiation: Finding Derivatives Without Solving for y
Lesson Objectives
By the end of this lesson, students will be able to:
Differentiate equations where y is not isolated
Apply the chain rule to y-terms
Use the product rule when x and y are multiplied
Solve for dy/dx after differentiating
Interpret dy/dx as the slope of a tangent line
Explain why implicit differentiation works conceptually
Essential Question
How can we find the rate of change when a function is not explicitly solved for y?