Algebra 1 – Course Overview The study of algebra involves finding patterns, balancing equations, and using graphs, lines, and arithmetic to understand quantities or dimensions. It also includes the study of ratios, percents, and probability. The concepts learned in Algebra I extend middle school math learning and prepare students for future high school learning in Algebra II and Geometry. Beginning algebra students learn concepts through lessons and practice. Online and offline projects allow students to practice their new skills in practical, real-life situations, building an appreciation for how what they are learning in school applies to life outside of school.

The Algebra I projects are designed to allow students to apply the algebra skills they have been learning to real life situations.Students use problem solving skills to run a profitable business in The Paddle Boat Trip. They compare and contrast interest rates and terms as they choose a loan for a new business in DRD Enterprises. The Architect puts students to work using spatial-reasoning skills as they fill in missing house dimensions and measure and compute the amount of carpeting needed. In The Neighborhood, students value properties and redraw property lines using visual skills, computation skills, and percents to find the information they need to complete the project. Real-life applications can help engage students in their mathematics learning as they see directly how what they’re learning applies to their lives.

Algebra 1 lessons are organized into 14 chapters that introduce and cover:

Real Numbers – Students will learn to work with the real number system, which includes lessons on how to identify the subsets of real numbers and perform arithmetic operations. Lessons will cover topics such as absolute values, operations with integers, square roots, and irrational numbers. Introduction to Algebra – Students will learn to work with algebraic expressions, evaluating them for variable values and combining like terms to simplify them. Lessons will include applying standardized problem solving plans and adding and subtracting algebraic expressions. Writing and Solving Equations – Students will learn to determine the values of variables in equations that involve varying degrees of complexity. Lessons include solving one and two step equations, solving multi-step equations, solving equations with variables on both sides, and solving for a variable and formulas. Proportional Reasoning – Students will learn to apply the rules of ratio and proportion to a variety of problems, including those involving percents and probabilities. Lessons cover topics that include percent increase and decrease, experimental and theoretical probability, and probabilities of independent and dependent events. Writing and Solving Inequalities – Students will learn to use skills for solving equations and apply them to finding solutions to inequalities of varying degrees of complexity. Lessons will include writing and graphing inequalities with one variable, solving and graphing inequalities with one, two, or three steps, solving compound inequalities, and absolute value equations and inequalities. Graphs and Functions – Students will learn to use a variety of data-gathering and interpreting skills useful in statistics. Students will also learn basic function descriptions and rules. Lessons will cover topics such as displaying data; the coordinate planes and relations; identifying functions; function rules, tables, and graphs; and arithmetic sequences. Graphing Equations – Students will explore linear equations and their characteristics including their graphs. Lessons will include slope, using x- and y- intercepts, the forms of linear functions, parallel and perpendicular lines, and scatter plots and correlations. Solving Systems of Equality and Inequality – Students will learn to graph and find the solutions to systems of equations and inequalities. Lessons include different strategies for solving systems of equality and inequality including graphing, substitution, and elimination. Lessons also include linear inequalities and parent functions. Exponents and Polynomials – Students will learn the rules for working with algebraic expressions that contain exponents and polynomials. Lessons include working with exponents, polynomials, and binomials. Factoring Polynomials – Students will learn techniques for factoring polynomials. Lessons include the basics of factoring, factoring quadratics, and factoring special products such as perfect square trinomials and the differences of perfect squares. Quadratic Equations and Functions – Students will learn to identify and graph quadratic functions and solve quadratic equations with real and complex solutions. Lessons will include examining graphs of quadratic functions, solving quadratic functions by graphing, simplifying radicals and complex numbers, solving quadratic equations, completing the square, and the quadratic formula and the discriminant. Exponential Equations and Functions – Students will learn to solve problems involving exponential functions. They will learn about exponential growth and decay, graphing exponential functions, and solving problems involving geometric sequences. Radical Expressions and Equations – Students will learn to simplify radicals and solve radical equations and work with trigonometry. Lessons will include graphing square root functions, the Pythagorean Theorem and trigonometry ratios, and the midpoint and distance formula. Rational Expressions and Equations – Students will learn to perform a variety of operations on rational expressions including simplifying quotients and solving equations. Lessons will include inverse variation, graphing rational functions, simplifying rational expressions, dividing polynomials, multiplying and dividing rational expressions, adding and subtracting rational expressions, mixed expressions and complex fractions, and solving rational expressions.