Algebra I (Advanced Algebra I)

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Course Overview

Algebra I, taught by Mark Rogers, presents algebraic concepts on a high school level, but in a more basic manner.  This course is recommended for high school and gifted middle school students -- especially for those planning careers in the trades or non-STEM college career paths.

 

Course topics include:

• Algebraic Expressions and Equations

• Proportions, Inequalities, and Absolute Values

• Introduction to Functions

• Linear Functions and Systems

• Exponential Properties and Functions

• Factoring

• Quadratic, Inverse, and Square Root Functions

• Statistical Analysis

Algebra I is taught by Instructor Mark Rogers.

 

Scope and Sequence

Unit 1 - Algebraic Expressions and Equations In this unit students explore variables, expressions, algebraic language, classifying numbers, evaluating algebraic expressions, equations, input, output, and analyzing equations, patterns, and graphs. They study solving one-step equations with addition, subtraction, multiplication, and division, as well as solving two-step equations and multi-step equations. They learn about solving equations with distributive property and with variables on both sides, solving special equations and solving literal equations and formulas.

Unit 2 - Proportions, Inequalities, and Absolute Values In this unit, students discuss ratios, rates, and conversions, as well as solving proportions in general and with maps. In addition, they explore proportions and similar figures. They also study percent change, graphing inequalities on a number line, solving positive and negative multi-step inequalities, solving special inequalities, solving inequalities with variables on both sides, compound inequalities, and absolute value equations and inequalities.

Unit 3 - Introduction to Functions In this unit students investigate mapping diagrams, distinguishing relations from functions, investigating patterns and linear functions, investigating patterns and nonlinear functions, and independent and dependent variables. They also discuss graphing a function rule, function notation, writing a function rule, identifying arithmetic sequences as linear functions, rate of change and slope, direct variation, slope-intercept form, and special linear equations.

Unit 4 - Linear Functions and Systems In this unit students learn about slope-intercept transformations, point-slope form, point-slope form alternative: y = mx + b inputs, finding X and Y intercepts with standard form, converting standard form to slope intercept form, and converting slope intercept form to standard form. They investigate parallel lines, perpendicular lines, solving systems by graphing, substitution, and elimination, applying linear systems in the real world, graphing linear inequalities in two variables, graphing systems of linear inequalities, applying systems of linear inequalities in the real world, and graphing positive and negative absolute value functions.  Following this unit students are presented with the Mid-Term Review and Exam.

Unit 5 - Exponential Properties and Functions In this unit students develop understanding of concepts including zero and negative exponents, multiplication and division properties of exponents, conversion from exponential to radical form, exponential functions, growth, and decay. Students also study geometric sequences, adding and subtracting polynomials, multiplying monomials by polynomials, multiplying binomials, and multiplying binomials raised to powers.

Unit 6 – Factoring In this unit students explore greatest common factor with coefficients, with variables, and with variables and coefficients. They also study trinomials, with a leading coefficient of one, as well as with prime leading coefficients, and with composite leading coefficients. In addition, they learn about factoring perfect square trinomials, factoring difference of squares binomials, and factoring four-term polynomials.

Unit 7 - Quadratic, Inverse, and Square Root Functions In this unit students discuss quadratics and leading coefficients, quadratics and axes of symmetry, quadratic zeroes and Y-intercept, quadratic domain and range, quadratic vertices as minima and maxima, and quadratic vertex form vs. standard form. They also explore solving quadratic equations by graphing, by factoring, by square roots, by completing the square, and with the quadratic formula, as well as linear, quadratic, and exponential functions, systems of linear and quadratic equations, inverse functions, solving square root equations, and graphing square root functions.

Unit 8 - Statistical Analysis In this unit students gain understanding of frequency and histograms, measures of central tendency and dispersion, and standard deviation. They also investigate box-and-whisker plots, scatter plots and correlation, correlation versus causation, trend lines in scatter plots, and interpolation versus extrapolation.  Following this unit students are presented with the Final Review and Exam.