ALGEBRA 1/ALGEBRA 1 HONORS


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1 ALGEBRA 1/ALGEBRA 1 HONORS CREDIT HOURS: 1.0 COURSE LENGTH: 2 Semesters COURSE DESCRIPTION The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics, with an emphasis on realworld applications throughout this yearlong algebra course. The first semester of the course includes an introduction to real numbers and variable expressions, methods for solving equations, understanding functions and relations, and an indepth study of linear and quadratic functions. The second semester of the course provides students with extensive instruction in topics including systems of equations and inequalities, exponential and radical functions, rational expressions and equations, as well as probability and statistics. Throughout the course are selfcheck quizzes, audio tutorials, interactive manipulatives, practice games, and plenty of review activities. The honors level course requires students to utilize higher order thinking skills such as analysis and synthesis, while completing more rigorous assignments. In addition, more emphasis is placed on research mastery and project based learning. COURSE OBJECTIVES Describe how mathematical properties are used to simplify numeric and variable expressions Solve one and multistep equations Solve equations involving absolute values Analyze relations and functions represented in a variety of forms Interpret functions based on real world situations Write and solve linear equations Graph lines written in different forms Define properties of polynomials and quadratic functions Demonstrate methods for factoring polynomials Solve quadratic equations
2 Solve systems of linear equations by graphing and algebraically Graph systems of linear inequalities and interpret the solution set Simplify expressions with exponents, including scientific notation Graph and analyze exponential and radical functions Solve exponential and radical equations Simplify rational expressions Write and solve rational equations Calculate theoretical probability Use statistical methods for analyzing and organizing data Solve problems involving ratios, rates, and unit conversion COURSE PREREQUISITES None REQUIRED TEXTBOOK (S) and/or MATERIALS Calculator TOPIC OUTLINE Module I: Numbers and Expressions Lesson 1 Real Numbers: Different Types of Numbers Lesson 2 Real Numbers: Describing Sets Lesson 3 Rational Numbers (Fractions): Simplest Form Lesson 4 Rational Numbers (Fractions): Improper Fractions and Mixed Numbers Lesson 5 Fractions, Decimals, and Percents: Classify Decimals Lesson 6 Fractions, Decimals, and Percents: Compare Decimal Values Lesson 7 Fractions, Decimals, and Percents: Equivalent Forms of Numbers Lesson 8 The Number Line Lesson 9 Exponents: Exponential, Composite, and Prime Numbers Lesson 10 Exponents: Prime Factorization Lesson 11 Roots: Square Roots Lesson 12 Roots: Cube Roots Lesson 13 Order of Operations
3 Lesson 14 Number Properties: Inverses, Zero Property, and Closure Lesson 15 Number Properties: Identities and Inverses Lesson 16 Commutative and Associative Properties: Commutative Lesson 17 Commutative and Associative Properties: Associative Properties Lesson 18 Distributive Property Module II: Solving Equations Lesson 1 Algebraic Expressions: Identify Parts of Expressions Lesson 2 Algebraic Expressions: Simplifying Expressions Lesson 3 Verbal Statements: Translate Written Statements into Algebraic Expressions Lesson 4 Verbal Statements: Represent Patterns Using Algebraic Expressions Lesson 5 OneStep Equations: Use Addition and Subtraction to Solve Lesson 6 OneStep Equations: Use Multiplication and Division to Solve Lesson 7 MultiStep Equations with Integers: Solving Equations with More than One Step Lesson 8 MultiStep Equations with Integers: Solving Equations by Combining Terms Lesson 9 MultiStep Equations with Integers: Solving Equations Using Distribution Lesson 10 Absolute Value: Distance on a Number Line Lesson 11 Absolute Value: Evaluate Absolute Value Expressions Lesson 12 Absolute Value Equations: OneStep Equations Lesson 13 Absolute Value Equations: MultiStep Equations and Extraneous Solutions Lesson 14 Complex MultiStep Equations: Combine Like Terms Lesson 15 Complex MultiStep Equations: Equations with Variables on Both Sides of the Equals Sign Lesson 16 Complex MultiStep Equations: Decimals and Fractions Lesson 17 Complex MultiStep Equations: Equations with Grouping Symbols Module III: Functions and Relations Lesson 1 Coordinate Plane: Parts of the Coordinate Plane Lesson 2 Coordinate Plane: Coordinates and Points
4 Lesson 3 Relations and Functions: Relations Lesson 4 Relations and Functions: Identify Relations that Are Functions Lesson 5 Function Notation and Rules: Function Rules Lesson 6 Function Notation and Rules: Independent and Dependent Variables Lesson 7 Evaluating Functions: Use a Table Lesson 8 Evaluating Functions: Use a Graph or a Rule Lesson 9 Domain and Range: The Domain of a Function Lesson 10 Domain and Range: The Range of a Function Lesson 11 Graph of a Function: Make a Table to Represent a Function Lesson 12 Graph of a Function: Make and Use a Graph Lesson 13 Function Operations: Add and Subtract Functions Lesson 14 Function Operations: Multiply and Divide Functions Lesson 15 Inverse of a Function: Inverse Functions Lesson 16 Inverse of a Function: Graph the Inverse of a Function Module IV: Linear Equations Lesson 1 Slope: Relate to the Slope of a Hill Lesson 2 Slope: Find the Slope of a Line Lesson 3 Rate of Change Lesson 4 Direct Variation: Equations, Tables, and Graphs Lesson 5 Direct Variation: Using Variation to Solve Problems Lesson 6 Linear Functions: Three Forms of Linear Equations Lesson 7 Linear Functions: Use Different Forms of Equations Lesson 8 Converting Between Forms: Different Forms of Lines Lesson 9 Converting Between Forms: Changing Between Forms of Lines Lesson 10 Writing the Equation of a Line: Pointslope and Slopeintercept Forms Lesson 11 Writing the Equation of a Line: Writing Equations When Given Two Points Lesson 12 Writing the Equation of a Line: Writing Equations Based on Graphs Lesson 13 Graphing Linear Functions: Pointslope forms of Lines Lesson 14 Graphing Linear Functions: Slopeintercept and Standard Forms of Lines Lesson 15 Line of Best Fit: Scatter Plots
5 Lesson 16 Line of Best Fit: Trend Lines Lesson 17 Vertical and Horizontal Lines: Slope of Vertical and Horizontal Lines Lesson 18 Vertical and Horizontal Lines: Equations of Vertical and Horizontal Lines Lesson 19 Parallel and Perpendicular Lines: Slopes of Parallel and Perpendicular Lines Lesson 20 Parallel and Perpendicular Lines: Equations of Parallel and Perpendicular Lines Module V: Polynomials and Quadratics Lesson 1 Adding and Subtracting Polynomials: Names and Degrees of Polynomials Lesson 2 Adding and Subtracting Polynomials: Add Polynomials Lesson 3 Adding and Subtracting Polynomials: Subtract Polynomials Lesson 4 Multiplying Polynomials: Multiply Polynomials Lesson 5 Multiplying Polynomials: Use FOIL to Multiply Polynomials Lesson 6 GCF of Polynomials: Greatest Common Factor (GCF) Lesson 7 GCF of Polynomials: Use GCF to Factor Polynomials Lesson 8 Guess and Check Factoring: Factor Trinomials Using Guess and Check Lesson 9 Guess and Check Factoring: Factor Trinomials With a Number in Front Lesson 10 Factoring Special Cases: Factor Perfect Square Trinomials Lesson 11 Factoring Special Cases: Factor a Difference of Two Squares Lesson 12 Factoring Special Cases: Factor a Sum of Cubes Lesson 13 Factoring Special Cases: Factor a Difference of Cubes Lesson 14 Solving Quadratic Equations: Quadratic Equations with Square Roots Lesson 15 Solving Quadratic Equations: Use the Zero Product Property Lesson 16 Solving Quadratic Equations: The Difference of Two Squares Lesson 17 Solving Quadratic Equations: Trinomials Lesson 18 Completing the Square: Create Perfect Square Trinomials Lesson 19 Completing the Square: Solve Quadratic Equations Lesson 20 Quadratic Formula: The Discriminant
6 Lesson 21 Quadratic Formula: Use the Quadratic Formula Lesson 22 Quadratic Graphs: Graph Quadratics Lesson 23 Quadratic Graphs: Parts of Parabolas Lesson 24 Maximum and Minimum: Find Maximum and Minimum Lesson 25 Maximum and Minimum: Write Quadratic Functions Semester 1 Exam Module VI: Inequalities and Systems Lesson 1 OneStep Inequalities: Solve Inequalities with Addition and Subtraction Lesson 2 OneStep Inequalities: The Solution Set and Graphs Lesson 3 OneStep Inequalities: Solve Inequalities with Multiplication and Division Lesson 4 MultiStep Inequalities: Solve Inequalities with More Than One Step Lesson 5 MultiStep Inequalities: Solve Inequalities with Grouping Symbols Lesson 6 Compound Inequalities: Solve Compound Inequalities with or Lesson 7 Compound Inequalities: Solve Compound Inequalities with and Lesson 8 Absolute Value Inequalities: Solve Absolute Value Inequalities Lesson 9 Absolute Value Inequalities: Other Types of Solutions and RealWorld Problems Lesson 10 Graphing Linear Inequalities: Solutions to Linear Inequalities Lesson 11 Graphing Linear Inequalities: Graph Linear Inequalities Lesson 12 Graphing Linear Inequalities: The Equation of the Boundary Line Lesson 13 Graphing Linear Inequalities: Write the Linear Inequality Lesson 14 Solve Systems of Linear Equations by Graphing: Number of Solutions Lesson 15 Solve Systems of Linear Equations by Graphing: Find Solutions Lesson 16 Solve Systems of Linear Equations by Substitution: Solve by Substitution Lesson 17 Solve Systems of Linear Equations by Substitution: Solve RealWorld Problems
7 Lesson 18 Solve Systems of Linear Equations by Elimination: Solve by Elimination Lesson 19 Solve Systems of Linear Equations by Elimination: Solve RealWorld Problems Lesson 20 Systems of Linear Inequalities: Use Systems of Linear Inequalities Lesson 21 Systems of Linear Inequalities: Write Systems of Linear Inequalities Lesson 22 Linear Programming: Critical Points Lesson 23 Linear Programming: Solve RealWorld Problems Module VII: Exponential and Radical Functions Lesson 1 Properties of Exponents: Exponents Lesson 2 Properties of Exponents: Multiply Powers Lesson 3 Properties of Exponents: Divide Powers Lesson 4 Scientific Notation: Write Numbers in Scientific Notation Lesson 5 Scientific Notation: Operations with Numbers in Scientific Notation Lesson 6 Exponential Functions: Graphs of Exponential Functions Lesson 7 Exponential Functions: Transformations of Exponential Functions Lesson 8 Solving Exponential Equations: Solve Problems Involving Exponential Functions Lesson 9 Exponential Growth and Decay: Explore Exponential Growth and Decay Lesson 10 Simplifying Radical Expressions: Simplify Radical Expressions Lesson 11 Simplifying Radical Expressions: Operations with Radical Expressions Lesson 12 Rational Exponents: Write Rational Exponents Lesson 13 Rational Exponents: Simplify Rational Exponent Expressions Lesson 14 Distance and Midpoint: Use the Distance Formula Lesson 15 Distance and Midpoint: Use the Midpoint Formula Lesson 16 Pythagorean Theorem: Use the Pythagorean Theorem Lesson 17 Radical Equations: Solve Radical Equations with One or Two Radicals Lesson 18 Radical Equations: Solve Radical Equations with Extraneous Solutions Lesson 19 Square Root Function: Graph Square Root Functions
8 Lesson 20 Square Root Function: Graph Transformations of Square Root Functions Module VIII: Rational Expressions and Equations Lesson 1 Simplifying Rational Expressions: Rational Expressions and Restrictions Lesson 2 Simplifying Rational Expressions: Simplify Using Greatest Common Factor (GCF) Lesson 3 Multiplying and Dividing Rational Expressions: Multiply Rational Expressions Lesson 4 Multiplying and Dividing Rational Expressions: Divide Rational Expressions Lesson 5 Adding and Subtracting Rational Expressions: Add and Subtract Rational Expressions Lesson 6 Adding and Subtracting Rational Expressions: Find Lowest Common Denominator (LCD) Lesson 7 Solving Rational Equations: Solve Rational Equations Lesson 8 Solving Rational Equations: Use Rational Equations to Solve Real World Problems Lesson 9 Characteristics of Rational Functions: The Domain and Asymptotes of Rational Functions Lesson 10 Characteristics of Rational Functions: Positive and Negative Parts and Increasing and Decreasing Intervals Lesson 11 Graphing a Rational Function: Graph Rational Functions Lesson 12 Graphing a Rational Function: Identify Vertical and Horizontal Translations Module IX: Probability, Statistics, and Discrete Math Lesson 1 Probability: Theoretical and Experimental Probability Lesson 2 Probability: Independent and Dependent Events Lesson 3 Counting and Permutations: Multiplication Counting Principle and Arrangements Lesson 4 Counting and Permutations: Permutations Lesson 5 Measures of Central Tendency: Mean and Median
9 Lesson 6 Measures of Central Tendency: Mode and Range Lesson 7 Histograms: Analyze Bar Graphs and Histograms Lesson 8 Histograms: Create Histograms Lesson 9 Box Plots: Minimum, Maximum, and Median Lesson 10 Box Plots: Identify Quartiles and Create Box Plots Lesson 11 Matrices: Represent Data with Matrices Lesson 12 Matrices: Operations with Matrices Lesson 13 Rates and Ratios: Unit Rates Lesson 14 Rates and Ratios: Proportions Lesson 15 Unit Conversions: Conversion Factors Lesson 16 Unit Conversions: Convert Units of Measure Lesson 17 Sequences: Arithmetic and Geometric Sequences Lesson 18 Sequences: Rules for Arithmetic and Geometric Sequences Semester 2 Exam Credits: 1 2 University of Miami Global Academy reserves the right to revise the course outline as needed throughout the duration of the course
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