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Unit 3: Algebraic Expressions & Equations

Develop algebraic thinking skills through expression simplification, equation solving, and function exploration. Master the foundation of algebra through engaging real-world scenarios involving phone plans, savings, paint mixing, budgeting, and transportation costs.

Simplifying Algebraic Expressions

Learn to simplify expressions with like terms and apply the distributive property through phone plan scenarios.

50-65 minutes Scenario: Phone Plans
Expression SimplificationLike TermsDistributive PropertyReal-world ApplicationsCost Analysis
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Multi-step Equations

Solve complex equations with fractions and decimals using savings and planning scenarios.

55-70 minutes Scenario: Savings Planning
Multi-step EquationsFraction EquationsDecimal EquationsEquation PropertiesVerification
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Proportional Equations

Use equations to solve proportional problems involving mixing ratios and scaling.

60-75 minutes Scenario: Paint Mixing
Proportional EquationsCross MultiplicationRatio ProblemsScaling ApplicationsProblem Solving
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Inequalities

Solve inequalities and represent solutions on number lines using budget and constraint scenarios.

55-70 minutes Scenario: Shopping Budget
Inequality SolvingNumber Line RepresentationMulti-step InequalitiesBudget ConstraintsSolution Sets
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Function Basics

Explore function relationships and create function tables through transportation cost scenarios.

60-75 minutes Scenario: Taxi Fares
Function DefinitionFunction TablesInput-Output RelationshipsGraphing BasicsReal-world Functions
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Unit Learning Objectives

Key Concepts

  • Simplify algebraic expressions with like terms
  • Solve multi-step equations with fractions and decimals
  • Use equations to solve proportional problems
  • Solve inequalities and represent solutions

Real-World Applications

  • Phone plan cost calculations
  • Savings and financial planning
  • Paint mixing and ratio problems
  • Budget constraints and shopping