Course Overview

Algebra is the branch of mathematics that uses symbols, variables, and equations to describe patterns and relationships. It allows us to solve problems involving unknown quantities, make predictions, and model real-world situations. In this course, students will build a strong foundation in algebraic thinking by exploring variables, expressions, equations, proportions, and graphs. Through hands-on problem solving and real-world applications, students will discover how algebra serves as a powerful tool for understanding and describing the world around them.

Unit 1: Patterns, Variables, and Algebraic Thinking

Develop the foundational skills needed to think algebraically and recognize mathematical relationships.

1.1 Recognizing Patterns

Numerical sequences
Visual patterns
Extending and predicting patterns

1.2 Variables and Unknowns

Understanding variables
Representing unknown quantities
Using letters in mathematics

1.3 Algebraic Expressions

Terms and coefficients
Writing expressions
Translating words into algebra

1.4 Order of Operations

PEMDAS/BEDMAS
Evaluating expressions
Multi-step calculations

1.5 Algebra in Everyday Life

Modeling situations with variables
Real-world relationships
Problem-solving applications

Unit 2: Solving One-Step and Multi-Step Equations

Learn how equations can be used to find unknown values and solve problems.

2.1 Understanding Equations

Equality and balance
Components of an equation
Verifying solutions

2.2 Solving One-Step Equations

Addition and subtraction equations
Multiplication and division equations
Checking solutions

2.3 Solving Multi-Step Equations

Combining operations
Isolating variables
Verification strategies

2.4 Equations with Variables on Both Sides

Balancing techniques
Simplification strategies
Solving efficiently

2.5 Real-World Equation Problems

Translating situations into equations
Word problems
Practical applications

Unit 3: Algebraic Expressions and Formulas

Explore how algebra can represent and simplify mathematical relationships.

3.1 Combining Like Terms

Identifying like terms
Simplifying expressions
Equivalent expressions

3.2 The Distributive Property

Expanding expressions
Factoring simple expressions
Applications

3.3 Substitution and Evaluation

Replacing variables with values
Evaluating formulas
Real-world applications

3.4 Rearranging Simple Formulas

Solving formulas for different variables
Using inverse operations
Formula manipulation

3.5 Algebra and Measurement Formulas

Area formulas
Perimeter formulas
Science and geometry applications

Unit 4: Ratios, Proportions, and Linear Relationships

Investigate how quantities are related and how algebra can describe these relationships.

4.1 Review of Ratios and Rates

Ratio notation
Unit rates
Comparing quantities

4.2 Solving Proportions

Equivalent ratios
Missing-value problems
Cross multiplication

4.3 Direct Variation

Constant relationships
Proportional reasoning
Real-world examples

4.4 Introduction to Linear Relationships

Input-output tables
Patterns and rules
Constant rate of change

4.5 Modeling Relationships

Creating algebraic rules
Predicting values
Practical applications

Unit 5: Introduction to Graphing

Connect algebraic relationships to visual representations using coordinates and graphs.

5.1 The Coordinate Plane

The x-axis and y-axis
Ordered pairs
Plotting points

5.2 Tables and Graphs

Organizing information
Input-output tables
Identifying patterns

5.3 Graphing Linear Relationships

Plotting ordered pairs
Drawing graphs
Interpreting patterns

5.4 Slope as Rate of Change

Understanding slope
Comparing rates of change
Real-world interpretations

5.5 Algebraic Modeling Project

Creating equations from situations
Graphing relationships
Analyzing and presenting findings

Course Summary

By the end of this course, students will understand how algebra can be used to represent patterns, solve problems, and model relationships. They will be able to work confidently with variables, expressions, equations, proportions, and graphs while developing the logical reasoning skills needed for higher-level mathematics.

Students will learn to:

Recognize and extend mathematical patterns.
Use variables to represent unknown quantities.
Write, simplify, and evaluate algebraic expressions.
Solve one-step and multi-step equations.
Apply algebraic methods to real-world situations.
Solve ratio and proportion problems.
Model relationships using equations and tables.
Plot and interpret graphs on a coordinate plane.
Understand slope as a measure of change.

This course provides the essential bridge between arithmetic and advanced mathematics, preparing students for future studies in linear equations, functions, geometry, statistics, science, engineering, economics, and beyond. Through algebraic thinking, students develop powerful tools for analyzing relationships, solving problems, and understanding the patterns that shape our world.