Algebra I

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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
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