Algebra I Competency Goal 1 The learner will perform operations with numbers and expressions to solve problems. 1.01 Write equivalent forms of algebraic expressions to solve problems. Apply the laws of exponents. Operate with polynomials. Factor polynomials. 1.02 Use formulas and algebraic expressions, including iterative and recursive forms, to model and solve problems. 1.03 Model and solve problems using direct variation. Competency Goal 2 The learner will describe geometric figures in the coordinate plane algebraically. 2.01 Find the lengths and midpoints of segments to solve problems. 2.02 Use the parallelism or perpendicularity of lines and segments to solve problems. Competency Goal 3 The learner will collect, organize, and interpret data with matrices and linear models to solve problems. 3.01 Use matrices to display and interpret data. 3.02 Operate (addition, subtraction, scalar multiplication) with matrices to solve problems. 3.03 Create linear models for sets of data to solve problems. Interpret constants and coefficients in the context of the data. Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions. Competency Goal 4 The learner will use relations and functions to solve problems. 4.01 Use linear functions or inequalities to model and solve problems; justify results. Solve using tables, graphs, and algebraic properties. Interpret constants and coefficients in the context of the problem. 4.02 Graph, factor, and evaluate quadratic functions to solve problems. 4.03 Use systems of linear equations or inequalities in two variables to model and solve problems. Solve using tables, graphs, and algebraic properties; justify results. 4.04 Graph and evaluate exponential functions to solve problems. Variables and Expressions Order of Operations Open Sentences Properties in Algebra; Identity and Equality Properties, The Distributive Property, Commutative and Associative Properties Logical Reasoning Graphs and Functions Statistics; Analyzing Data by Using Tables and Graphs Rational Numbers on the Number Line Operations with Rational Numbers; Adding, Subtracting, Multiplying, and Dividing Rational Numbers Statistics: Displaying and Analyzing Data Probability: Simple Probability and Odds Square Roots and Real Numbers Writing Equations Solving Equations; Solving Using Addition, Subtraction, Multiplication, and Division, Solving Multi-Step Equations, Solving Equations with Variables on Both Sides Ratios, Proportions, and Percent of Change Solving Equations and Formulas Weighted Averages The Coordinate Plane; Transformations on the Coordinate Plane Relations; Equations as Relations Graphing Linear Equations Functions Arithmetic Sequences Writing Equations from Patterns Slope and Direct Variation Forms of Equations; Writing Equations in Slope-Intercept Form, Writing Equations in Point-Slope Form Geometry: Parallel and Perpendicular Lines Statistics: Scatter Plots and Lines of Fit Solving Inequalities; Solving Inequalities by Addition, Subtraction, Multiplication, and Division, Solving Multi-Step Inequalities, Solving Compound Inequalities Solving Open-Sentences Involving Absolute Value Graphing Inequalities in Two Variables Systems of Equations; Graphing Systems of Equations Solving Systems of Equations and Inequalities; Graphing, Substitutions, Eliminations Using Addition and Subtractions, Elimination Using Multiplication Graphing Systems of Inequalities Operations with Monomials and Polynomials; Adding, Subtracting, Multiplying and Dividing Monomials and Polynomials Scientific Notation Special Products Factors and Greatest Common Factors Factoring Using the Distributive Property Factoring Trinomials with or without a Leading Coefficient Factoring Differences of Squares Perfect Squares and Factoring Graphing Quadratic Functions Solving Quadratic Equations; Solving Quadratic Equations by Graphing, Solving Quadratic Equations by Completing the Square, Solving Quadratic Equations by Using the Quadratic Formula Exponential Functions Growth and Decay Geometric Sequences Simplifying Radical Expressions Operations with Radical Expressions Radical Equations The Pythagorean Theorem The Distance Formula Similar Triangles Trigonometric Ratios Inverse Variation Operations with Rational Expressions; Multiplying and Dividing Rational Expressions and Polynomials Rational Expressions with Like and Unlike Denominators Mixed Expressions and Complex Fractions Solving Rational Equations Sampling and Bias Introduction to Matrices Organizing Data; Histograms and Box-and-Whisker Plots Measures of Variation Counting Outcomes Permutations and Combinations Probability of Compound Events Probability Distributions and Probability Simulations