SCHOOL DISTRICT OF THE CHATHAMS CURRICULUM PROFILE


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1 CONTENT AREA(S): Mathematics COURSE/GRADE LEVEL(S): Honors Algebra 2 (10/11) I. Course Overview In Honors Algebra 2, the concept of mathematical function is developed and refined through the study of real numbers, complex numbers, polynomials, conic sections, equations and inequalities, exponents, logarithms, trigonometry and probability This demanding course puts a premium on reasoning and problem solving. Along with reasoning activities and problem solving strategies, cooperative learning projects, critical thinking activities, manipulatives and technology are used to explore and develop concepts and connect algebra to daily life. This course is a prerequisite for Honors Precalculus. In connection with the Common Core Standards, this course examines the concepts of; Number and Quantity, Algebra, Functions, Modeling and Probability and Statistics. This course with also incorporate the 8 Standards for Mathematical Practices as identified by the Common Core. II. Units of Study Unit 1 Probability and Statistics Unit 2 Linear Functions: Equations and Inequalities Unit 3 Systems of Linear Equations and Inequalities Unit 4 Quadratic Functions: Equations and Inequalities Unit 5 Polynomials Unit 6 Powers, Roots and Radicals Unit 7 Exponential and Logarithmic Functions Unit 8 Rational Expressions and Equations Unit 9 Matrices III. Essential Questions (The openended, provocative questions that help frame inquiry) Unit 1 What is the Fundamental counting principal and how do we apply it? What are permutations and how do we apply them? What are combinations and how do we apply them? How do we find theoretical and experimental probabilities? How do we find geometric probabilities? What are unions, intersections and complements, and how do we find them? How do we find the probability of independent events? How do we find the probability of dependent events?
2 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 What are relations and functions? How do we graph and evaluate linear functions? How do we find slopes and use them in real world situations? What is slopeintercept form and how can it be used to graph an equation? What is standard form and how can it be used to graph an equation? What is direct variation? How can a scatterplot be used to identify correlation? How do we approximate a best fit line for a set of data? How do we graph linear inequalities in one and two variables? What are piecewise functions and how do we use them in modeling? What are absolute value functions and how do we use them in modeling? How do we graph and solve linear systems in two variables? How do we solve linear systems algebraically? How do we graph and solve systems of linear inequalities? What is linear programming and how can it be applied to real world examples? How do we graph quadratic functions? How do we factor quadratic functions? How do we find the zeros of quadratic functions? How do we use quadratic equations to solve real world examples? What are complex numbers and how are the integrated in quadratic functions? What is completing the square and how does it help us solve quadratic functions? What is the quadratic formula and how does it help us solve quadratic functions? How do we graph and solve quadratic inequalities? Given the characteristics of a quadratic function, how do we write its equation? What are the properties of exponents? How do we identify, evaluate and graph polynomial functions? How do we add, subtract, multiply and divide polynomials? How do we apply polynomials to real world situations? How do we factor polynomial expressions and equations? How do we divide polynomials and relate the result to the remainder theorem and the factor theorem? How do we find the rational zeros of a polynomial? What is the Fundamental Theorem of Algebra and how do we use it? How can we utilize technology to approximate real zeros? How can graphs of polynomials be used to solve real world situations? What are rational exponents and how do we solve for them? What are the properties of rational exponents and how do we apply them? What is a power function and how can it be used to model real world situations? What is relationship between a function and its inverse? How do we graph square root and cube root equations? How do we solve equations which contain radicals?
3 Unit 7 Unit 8 Unit 9 What is an exponential function and how do we graph them? What is exponential decay and how is it represented in an equation? What is the relevance of the number e and what are its applications? How do we simplify and solve logarithmic functions? What are the properties of logarithms and how do we apply them? How do we solve exponential and logarithmic equations? How do we use exponential and logarithmic equations to model real world situations? How do inverse and joint variation affect mathematical relationships? What are asymptotes and what is their role in the graphing of rational functions? How can rational functions be used to identify maximum and minimum values? How do we multiply and divide rational functions? What is a complex fraction and how can it be simplified? How can we use rational equations to solve real world situations? What are matrices, and what do they represent? How can Matrices be added or subtracted? What is scalar multiplication? How do you find the product of two matrices and how can you use it in real life? How do you solve a system of linear equations in three variables using the augmented matrix method? What is the multiplicative inverse of a matrix and how do you use it to solve a system of equations? How can a matrix be used to represent a system of equations? What are determinants and how do you apply Cramer s Rule to solve systems of equations? How do you solve problems involving several unknowns using matrix operations? How do you solve real life problems using systems of equations? IV. Learning Objectives Common Core State Standards for Mathematics: Seeing Structure in Expressions Interpret the structure of expressions Write expressions in equivalent forms to solve problems arithmetic with polynomials and rational expressions Perform arithmetic operations on polynomials Understand the relationship between zeros and factors of polynomials Use polynomial identities to solve problems Rewrite rational expressions creating equations Create equations that describe numbers or relationships reasoning with equations and inequalities
4 Understand solving equations as a process of reasoning and explain the reasoning Solve equations and inequalities in one variable Solve systems of equations Represent and solve equations and inequalities graphically mathematical practices Interpreting Functions Understand the concept of a function and use function notation Interpret functions that arise in applications in terms of the context Analyze functions using different representations building functions Build a function that models a relationship between two quantities Build new functions from existing functions linear, quadratic, and exponential models Construct and compare linear, quadratic, and exponential models and solve problems Interpret expressions for functions in terms of the situation they model Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on a single count or measurement variable Summarize, represent, and interpret data on two categorical and quantitative variables Interpret linear models making inferences and justifying conclusions Understand and evaluate random processes underlying statistical experiments Make inferences and justify conclusions from sample surveys, experiments and observational studies Conditional Probability and the Rules of Probability Understand independence and conditional probability and use them to interpret data Use the rules of probability to compute probabilities of compound events in a uniform probability model Using Probability to Make Decisions Calculate expected values and use them to solve problems Use probability to evaluate outcomes of decisions V. Instructional Materials Textbook: Algebra 2, Larson, Kanold, Stiff; Heath 2001 Graphing Calculator TI  Smartview Manipulatives Math Games Teacher Generated Materials Math Literature Challenge Materials
5 VI. Key Performance and Benchmark Tasks Unit Tests, Formative and Summative Assessment and Final Exam Content knowledge demonstrated on homework, unit quizzes and tests that include elements of traditional assessment tools such as short answer, definitions and problem solving. Content knowledge and understanding demonstrated by application of mathematical concepts to real world situations. Performance Tasks Content knowledge and mathematical skills demonstrated through the modeling of various projects and real world simulations. Class participation and graded discussion Content knowledge and mathematical skills demonstrated by in class dialogue and collaboration in addition to guided discussions.
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