Algebra 1 Fundamentals equips students with essential algebraic skills, progressing from basic operations to solving complex equations and graphing linear functions. Through hands-on examples and practical problem-solving, students will develop a solid foundation in algebraic concepts, preparing them for advanced math courses and real-world applications. By the end of this course, participants will be able to confidently manipulate algebraic expressions, solve various types of equations, and interpret linear relationships graphically.

Order of Operations and Evaluating Expressions

• Master the order of operations (PEMDAS/BODMAS) — parentheses, exponents, multiplication, division, addition, and subtraction.
• Simplify complex expressions — working from innermost parentheses outwards.
• Evaluate algebraic expressions — substitute numerical values for variables and simplify.

Solving Linear Equations

• Apply inverse operations to isolate variables — addition, subtraction, multiplication, and division.
• Solve multi-step equations — combining like terms and simplifying before isolating the variable.
• Utilize the distributive property — to eliminate parentheses and simplify expressions.

Graphing Linear Equations

• Understand the coordinate plane — plotting points and interpreting graphs.
• Graph linear equations using slope-intercept form (y = mx + b) — identify slope and y-intercept.
• Write linear equations from graphs or given points — determining slope and intercept.

Linear Inequalities

• Solve linear inequalities — similar to equations, with an added rule for multiplying/dividing by negatives.
• Graph solutions on a number line — using open and closed circles to represent strict and inclusive inequalities.
• Represent solutions with interval notation — expressing the range of values that satisfy the inequality.

Absolute Value Inequalities

• Solve absolute value equations — isolating the absolute value expression.
• Solve absolute value inequalities — considering both positive and negative cases.
• Graph absolute value solutions — representing the range of values on a number line.

Systems of Equations

• Solve systems of linear equations graphically — finding the intersection point of two lines.
• Solve systems of equations algebraically — using substitution and elimination methods.
• Interpret solutions in context — determining if there's one solution, no solution, or infinitely many solutions.

Applications of Algebra

• Apply algebraic concepts to real-world scenarios — creating equations and inequalities to model situations.
• Solve word problems — translating verbal descriptions into mathematical expressions.
• Develop problem-solving strategies — using algebra to analyze and solve practical problems.