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Name of course: Algebra 1B

Motif:

Prerequisites: Algebra 1A

Credit 1.0

Grade levels: Grades 9-12

Estimated Completion Time: 2 semesters / 36 weeks

Course Description

Many people, not just math students, wonder why mathematics is important in the real world. This course is designed to answer that question by developing algebraic concepts and processes that can be used to solve a variety of real world and mathematical problems. This is the second of a two year sequence of courses, Algebra Ia and Algebra Ib. Algebra Ia and Ib meets the Algebra 1 requirement. Along with algebraic strategies and properties students will incorporate data analysis concepts and techniques including introductory statistics and probability. Students will learn varied strategies for solving linear and quadratic equations and inequalities and systems of equations and inequalities as related to real world examples. Each module is designed to pretest, read, observe, practice and posttest activities as needed for mastery of concepts. Learn how algebra integrates with other topics of mathematics and connects with other subjects you study while applying these concepts to real-world uses!

Scope and Sequence

Module 1: Review Algebra 1A A. Algebra 1A Diagnostic Test B. Algebraic Expressions Exponents Order of operations Variables Write expressions Evaluate expressions Simplifying algebraic expressions C. Real Number System Identify property of real number Absolute values Properties of Real Numbers D. Writing and solving equations and inequalities Formulas Literal Equations Using Formulas E. Solving Absolute Value Equations Module 2: Functional Relationships A. Dependent and Independent Variables Numerically Graphically Algebraically B. Definition of a Function Numerically Graphically Algebraically C. Domain and Range Discrete Continuous D. Representing Relationships Numerically Graphically Algebraically Verbally E. Functional Notation F. Evaluating and interpreting the solution of a function for a given value G. Formula Linear Nonlinear Area Surface Area Volume Module 3: Linear Relationships, Equations and Graphs A. Direct Variations in linear relationships Numeric Graphic B. Slope and rate of change Numeric Graphic Linear models of relationships C. Linear models of relationships Models from a verbal description of the slope and –intercept Models from a verbal description of two points of the relationship Models of the form Ax + B y = C D. Linear regression models Scatter plots from data Correlations Estimation of modeling lines Line of best fit Predicting, using the line of best fit E. Absolute value functions 1. Characteristic Graphic Vertex Line of Symmetry Algebraic Module 4: Systems Linear Equations and Inequalities A. Relationships between lines on a plane Parallel Intersecting: Perpendicular Coincident Consistent and Inconsistent systems B. Determine the equation of a line Parallel to another line Perpendicular to another line C. Solving systems of equations Graphing Substitution Linear combinations D. Solving systems of linear inequalities Graphing a linear inequality Determining the solution of a system of linear inequalities Module 5: Polynomials A. Polynomial expressions B. Multiplying and dividing polynomials C. Multiplying and factoring D. Multiplying binomials E. Special products Square trinomial Difference of two squares F. Factoring polynomials Common factor Square trinomial Difference of two squares Trinomials Module 6: Quadratic Functions A. Pattern of change in quadratic functions Numeric Graphic B. Characteristics of the quadratic function: y = x² Graphic Vertex Symmetry Algebraic Domain Range C. Quadratics functions: y=ax²+bx+c Identifying quadratic functions and their coefficients Comparison to y = x² Rate of change and finite differences Graphs of quadratics function Functions of the form y = ax² Functions of the form y=a(x-h) ²+k Functions of the form y=a(x-p)(x-q) 5. Modeling with quadratic functions Module 7: Solving Quadratic Equations A. In the form of ax²=d: Squares and square roots Geometric model Irrational numbers and the Real Number System Evaluating square roots B. Graphically C. Numerically D. In standard form: 0=ax²+bx+c Graphically: Zeroes of the function Numerically By factoring: Zero Product Property The Quadratic Formula E. Determining the number and types of solutions Graphically Algebraically: The discriminant F. Modeling with quadratic equations Module 8: Exponential Functions A. Exponents and powers Repeated factors rewritten with exponents Integer exponents Properties of exponents B. Exponential functions: f(x)=ab^x+k Patterns of change Characteristics Graphical y-intercept Asymptote Algebraic Domain Range C. Modeling with exponential growth patterns D. Modeling with exponential decay patterns Module 9: Data Analysis and Probability A. Data analysis Collecting, organizing and displaying data Tables, graphs and plots Relationship between data Measures of central tendency Measures of variability B. Probability Experiamental versus theoretical probability Simulation C. Permutations and Combinations

Course Objectives

structure and properties of the real number system, including rational and irrational numbers exponents, square roots, radicals, rational expressions, absolute value, and scientific notation varied means for analyzing and expressing patterns, relations, and functions, including words, tables, sequences, graphs, and algebraic equations variables, algebraic expressions, polynomials, and operations with polynomials coordinate geometry and graphing of equations and inequalities data analysis concepts and techniques including introductory statistics and probability varied solution strategies, algebraic and graphic, for inequalities, linear and quadratic equations, and for systems of equations

Grading Policy

Grades will be based upon the quality of the student submissions, participation in discussions, and the ability to maintain consistent communication with the instructor. The grading scale that is used for this course is as follows: A 90-100 B 80-89 C 70-79 D 60-69 F 59 or below All forms of academic dishonesty are prohibited. This includes, but is not limited to, plagiarism, cheating, furnishing false information, forgery, alteration or misuse of documents or software, and misconduct during a testing situation. Any student cheating on an exam will receive a zero on the exam and may be withdrawn from the class at the instructor's discretion.

Communication/Participation Requirements

Only through continuous communication can students be successful in an online course. Within each course the instructor outlines the weekly minimum work requirements. It is essential that the student and instructor maintain regular contact. Failure to complete assignments on a consistent basis will result in students being removed from the course.