PLANNED COURSE STATEMENT Course Title: Algebra 1 Length of Course: 2 semesters Grade Level: 9 - 12 Prerequisite: Pre-Algebra Credit: 1.5 Credit is awarded based on the completion of mathematics standards.Course Overview: This curriculum emphasizes a multi-representational approach to algebra, with concepts, results, and problems being expressed graphically, analytically, and verbally. It develops algebraic fluency by providing students with the skills needed to solve equations and perform important manipulations with numbers, variables, equations, and inequalities. In addition, the course develops proficiency with operations involving monomial and polynomial expressions. The main unifying themes of the course include understanding, writing, solving, and graphing linear equations, systems of linear equations and inequalities, quadratic equations, rational equations, as well as data representations and probability concepts.Course Goals: Upon completion of this course students will: • Perform operations with real numbers • Simplify and evaluate algebraic expressions • Use equations to solve word problems • Graph and solve problems involving inequalities and absolute value • Graph and solve linear equations • Solve systems of equations • Solve many types of real-world problems • Factor polynomial equations • Understand relations and functions • Solve quadratic equations • Work with radical expressions and rational equationsContent Outline:Algebra 1A Data exploration Bar graphs and dot plots; Measures of center; Five-number summaries and box plots; Histograms
Basic algebra principles Real numbers & algebraic expressions; Simplifying expressions; Solving equations; More on solving equations Inequalities & absolute values Sets, intersections & unions; Inequalities & their graphs; Using inequalities; Solving equations involving absolute values; More solving inequalities involving absolute values Graphs of linear equations Graphing linear equations; Slope in graphs & equations; Linear & nonlinear equations; Finding the equation of a line; Parallel & Perpendicular lines; & linear inequalities Systems of equations & inequalities Systems of linear equations & their graphs; Solving systems of linear equations by substitution; Solving systems of linear equations by elimination; Rate, work, digit, & coin problems; Systems of linear inequalitiesAlgebra 1B Exponents, monomials, and polynomials Properties of exponents; Monomials; Polynomials; Factoring polynomials; Factoring special polynomials Relations, functions, & quadratic equations Introduction to quadratic equations & their graphs; Solving quadratic equations by factoring; Solving quadratic equations by completing the square; The quadratic formula; Applications of quadratic equations; Functions & function notation Rational & radical expressions & equations Rational expressions; Special rational equations; Rational equations; Radical expressions; Finding square roots; Radical equations Transformations Symmetry; Translations; Reflections; Rotations; Size transformations Probability Experimental and theoretical probabilities; Independent and dependent probabilities; Multiple-stage experimentsLearning Activities:This course is organized into ten units.Each unit is comprised of lessons, and each lesson is broken down into two sections… • Readings (textbook and/or objectives) o This section provides the suggested readings from the course textbook and/or the learning objectives for the lesson. Students must use this as a resource to guide them through the lesson. • Content/Multimedia (lectures, homework, and/or projects) o Most lessons contain a multimedia presentation that provides the "lecture" portion of this course. Students must participate in each lecture before moving on through the lesson. o Included in the content/multimedia portion of each lesson are various homework assignments. Students must complete each homework assignment with at least a 70% level of proficiency. Answers are provided for students to self-correct their work. o The last lesson in each unit contains a project related to the unit concepts. Students must complete this project and turn it in before they will be allowed to take the unit test.
Assessment Procedures:All assessments will be proficiency based. This section must be completed at the RPA building. It is important that students do not take the Unit Test unless they have completed their homework assignments, turned in their project, and feel confident that they have mastered the content. **Students who do not demonstrate proficiency on one or more standards for a unit will be required to do test corrections and show evidence of completed extra practice assignments before they will be allowed to attempt the retake**Standards Addressed:Algebra 1A Data exploration 1S.3 – Use plots, graphs, range, and measures of center to compare and make conclusions about data sets. 1S.5 – Construct, analyze, and interpret tables, plots, and graphs of data sets. Basic algebra principles 1A.1 – Compare, order, and locate real numbers on a number line. 1A.4 – Apply algebraic properties to validate the equivalence of two expressions. 1A.7 – Simplify and evaluate algebraic expressions. 1A.8 – Solve algebraic equations for a given variable. Inequalities & absolute values 1A.2 – Evaluate, compute with, and determine equivalent numeric and algebraic expressions with real numbers. 2A.7 – Write, use, and solve linear inequalities using graphical and symbolic methods. Graphs of linear equations 1A.1 – Compare, order, and locate real numbers. 2A.1 – Identify, construct, extend, and analyze linear patterns that are expressed numerically, algebraically, graphically, or in tables. 2A.2 – Identify and interpret the meaning of the slope and intercepts, given a rule, context, two points, table, graph, or linear equation. 2A.3 – Determine the equation of a linear relationship. 2A.4 – Convert among representations of linear relationships. 2A.7 – Write, use, and solve linear inequalities using graphical and symbolic methods. Systems of equations & inequalities 1A.2 – Evaluate, compute with, and determine equivalent numeric and algebraic expressions with real numbers. 2A.8 – Solve systems of linear inequalities graphically. 2A.9 – Compare and contrast the rate of change for various contexts.Algebra 1B Exponents, monomials, and polynomials 1A.2 – Evaluate, compute with, and determine equivalent numeric and algebraic expressions with real numbers. 1A.5 – Factor quadratic expressions of the form ax 2 + bx + c . 1A.7 – Simplify and evaluate algebraic expressions.
Relations, functions, & quadratic equations 1A.2 – Evaluate, compute with, and determine equivalent numeric and algebraic expressions with real numbers. 1A.5 – Factor quadratic expressions of the form ax 2 + bx + c . 1A.8 – Solve algebraic functions for a given variable. 3A.3 – Compare the characteristics of and distinguish among various types of functions that are expressed algebraically or graphically, and interpret the domain and range of each. 3A.5 – Given a quadratic function of the form ax 2 + bx + c , determine and interpret the roots, vertex, and equation for axis of symmetry both graphically and algebraically. 3A.6 – Use the quadratic formula to find the roots of quadratic equations. 3A.7 – Use quadratic equations in context to solve problemsRational & radical expressions & equations 1A.3 – Express square roots in equivalent radical form and their decimal approximations when appropriate. 1A.7 – Simplify and evaluate algebraic expressions. 1A.8 – Solve algebraic equations for a given variable. 3G.4 – Apply the distance formula to solve problems.Transformations 3G.1 – Recognize and identify line and rotational symmetry of figures. 3G.2 – Identify and perform transformations of figures.Probability 2S.1 – Identify, analyze, and use both experimental and theoretical probability to estimate and calculate the probability of simple events. 2S.3 – Compute and interpret probabilities for independent, dependent, conditional, and compound events using various methods.