La Cañada High School. Course Outline LC Math 1 Advanced

Transcription

1 La Cañada High School Course Outline LC Math 1 Advanced I. Course Title Math 1 Advanced II. Grade Level(s) Grades 9-12 III. Length/Credit 1 Year units Satisfies Traditional Algebra I Graduation Requirement IV. Preparations Completion of CC Algebra 8 with a grade of high B and teacher recommendation. V. Course Description This is the first course in an accelerated common core based college preparatory math sequence. This course builds on, and deepens, the conceptual understanding of linear function from CC Math 8. As the first course in an accelerated three-year progression, it will include standards traditionally taught in Algebra 1, Algebra II, and Pre-Calculus. Successful completion of LC Math 1 Advanced positions students to reach advanced math classes, including Calculus, by the senior year. The main purpose of LC Math 1 Advanced is to develop students fluency with linear, quadratic, exponential, radical and polynomial functions. The critical areas of instruction involve deepening and extending students understanding of linear and exponential relationships by contrasting them with each other and by applying linear models to data that exhibit a linear trend. Vectors and matrices will be used to extend and apply linear relationships. Quadratic functions will be fully analyzed and extended to polynomial functions. In addition, students engage in methods for analyzing, solving, and using exponential and quadratic functions, with real and non-real solutions. Some of the overarching ideas in the LCM1 Advanced course include: the notion of function, solving equations and inequalities, rates of change and growth patterns, working with sequences, vectors and matrices, understanding absolute value relationships, graphs as representations of functions, and modeling. Since the Standards for Mathematical Practice will be woven throughout each unit of the course, students will analyze each other s work, make and prove conjectures, use tools to experiment and validate conclusions, and problem solve. VI. Standards/ESLRs Addressed 1. Standards for Mathematical Practices Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.

2 2. Number and Quantity The Real Number System Standards Abbreviation: N-RN Extend the properties of exponents to rational exponents. Use properties of rational and irrational numbers. Quantities Standards Abbreviation: N-Q Reason quantitatively and use units to solve problems. The Complex Number System Standards Abbreviation: N-CN Perform arithmetic with complex numbers. Use complex numbers in polynomial identities and equations. Vector and Matrix Quantities Standards Abbreviation: N-VM Represent and model with vector quantities. Perform operations on vectors. Perform operations on matrices and use matrices in applications. 3. Algebra Seeing Structure in Expressions Standards Abbreviation: A-SSE Interpret the structure of expressions. Write expressions in equivalent forms to solve problems. Arithmetic with Polynomials and Rational Expressions Standards Abbr.: A-APR Perform arithmetic operations on polynomials. Understand the relationship between zeros and factors of polynomials. Use polynomial identities to solve problems. Creating Equations Standards Abbreviation: A-CED Create equations that describe numbers or relationships. Reasoning with Equations and Inequalities Standards Abbreviation: A-REI 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. 4. Functions Interpreting Functions Standards Abbreviation: F-IF 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 Standards Abbreviation: F-BF Build a function that models a relationship between two quantities. Build new functions from existing functions. Linear, Quadratic, and Exponential Models Standards Abbreviation: F-LE Construct and compare linear, quadratic, and exponential models and solve problems. Interpret expressions for functions in terms of the situation they model. 5. Statistics and Probability Interpreting Categorical and Quantitative Data Standards Abbreviation: S-ID 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

3 VII. Brief Course Outline Essential Course Concepts: Quarter 1: Quantities, Functions, and Linearity Introduction to variables, quantities, functions, and equations Properties of real numbers Graphing and solving linear functions, equations and inequalities Apply rate of change and slope to describe linear function behavior Analyze lines of best fit and linear regression Problem solving with systems of linear equations and inequalities Common Core State Standards Addressed: N-RN.3, N-Q.1, N-Q.2, N-Q.3, A-SSE.1, A-CED.1, A-CED.2, A- CED.3, A-CED.4, A-REI.1, A-REI.3, A-REI.10, F-IF.1, F-IF.2, F-IF.3, F-IF.4, F-IF.5, F-IF.7, F-IF.9. Course Concepts Description: Create and solve linear equations and inequalities, model reallife contexts with linear functions, use proportional reasoning to solve problems involving business, geometry and other real-life applications, extend solving linear equations and inequalities to problems involving absolute value expressions, use function notation to describe (algebraically or graphically) a situation or pattern, and determining whether a situation is a function or relation, describe the domain and range of a function, Use rate of change to create, graph and analyze linear functions, transform between forms of linear functions and understand applications for each form, use slope to determine geometric properties of linear functions, create and analyze scatter plots for bivariate data, find trend lines and analyze residuals for linear regression, graph linear absolute value functions, solve problems using a system of linear equations and inequalities, Essential Course Concepts: Quarter 2: Extending Linearity, Building Exponentiation Apply matrices to solving systems of linear equations Perform operations on matrices and vectors Pattern recognition, arithmetic sequences, and geometric sequences Exponential expressions Graph and analyze exponential functions Common Core State Standards Addressed: N-Q.1, N-Q.2, N-Q.3, N-VM.4, N-VM.5, N-VM.6, N-VM.7, N- VM.8, N-VM.9, N-VM.10, N-NM.12, A-SSE.1, A-SSE.2, A-CED.2, A-CED.3, A-REI.5, A-REI.6, A-REI.8, A-REI.11, A- REI.10, A-REI.12, F-IF.1, F-IF.2, F-IF.3, F-IF.4, F-IF.5, F-IF.7, F-IF.9, F-BF.1, F-BF.2, F-BF.3, F-LE.1, F-LE.2, F-LE.5, G- GPE.5, S-ID6, S-ID.7, S-ID.8, S-ID.9, Course Concepts Description: Create matrices and vectors to represent systems of linear equations, use matrices (row reduction, inverse matrices, determinants) to solve systems of linear equations, perform operations on matrices and connect operations to context, create and solve systems of three linear equations in three variables, create recursive and explicit function rules for arithmetic and geometric sequences, extend properties of exponents to exponential functions, connect geometric sequences to exponential functions, compare and contract linear and exponential functions, graph exponential functions, apply transformations to graph and analyze exponential functions, model situations with linear and exponential functions. Essential Course Concepts: Quarter 3: Quadratic Functions Quadratic expressions Graph and analyze quadratic functions Complex number arithmetic

4 Model with linear, exponential and quadratic function Common Core Concepts Addressed: N-RN.1, N-RN.2, N-RN.3, N-CN.1, N-CN.2, N-CN.7, N-CN.8, A-SSE.1, A- SSE.2, A-SSE.3, A-APR.1, A-APR.3, A-CED.1, A-CED.2, A-CED.3, A-REI.7, A-REI.11, F-IF.4, F-IF.5, F-IF.7, F-IF.8, F-IF.9, F-BF.1, F-BF.1, F-BF.3, F-LE.1, F-LE.2, Course Concepts Description: Extend exponent rules to rational exponents, understand the distinction between rational and irrational numbers, simplify radicals, transform between forms of quadratic expressions, determine which factoring strategy best solves quadratic equations, create quadratic models, graph quadratic functions, analyze properties of quadratic graphs, solve quadratic equations using multiple methods (factoring, graphing, completing the square, or the quadratic formula), determine which method for solving quadratic equations is best, transform between forms of quadratic functions, find complex solutions to quadratic equations, perform operations on complex numbers, model problems with linear, quadratic or exponential functions, extend systems of equations to involve applications of linear and quadratic functions, compare and contrast linear, exponential and quadratic functions, determine when an application is linear, quadratic or exponential. Essential Course Concepts: Quarter 4: Building Polynomial and Radical Functions Model with linear, exponential and quadratic function Graph and analyze polynomial functions Graph and analyze radical functions Summarize, represent, and interpret data Common Core Concepts Addressed: N-RN.1, N-RN.2, N-Q.1, N-Q.2, N-Q.3, N-CN.7, N-CN.8, N-CN.9, A-SSE.1, A-SSE.2, A-SSE.3, A-APR.1, A-APR.2, A-APR.3, A-APR.4, A-APR.5, A-APR.6, A-CED.1, A-CED.2, A-CED.3, A-CED.4, A-REI.1, A-REI.2, A-REI.4, A-REI.7, A-REI.11, F-IF.4, F-IF.5, F-IF.6, F-IF.7, F-IF.8, F-IF.9, F-BF.1, F-BF.3, F-LE.1, F-LE.2, F-LE.3, S-ID.1, S-ID.2, S-ID.3, S-ID.6, Course Concepts Description: Extend analysis of quadratic function to polynomial functions, graph and apply polynomial functions and equations, connect factors of a polynomial to roots of its graph, identify key features of graphs of polynomial functions, graph and apply radical functions and equations, simplify expressions with rational exponents, model situations with linear, exponential, quadratic, polynomial and radical functions, collect and analyze univariate and bivariate data, represent univariate data in multiple formats (tables, histograms, plots, boxplots), calculate measures of central tendency (mean, median, mode) and variation (variance, standard deviation, range) to describe data sets. VIII. Methods of Assessment Evaluation: 1. Examinations: Examinations are a critical component in monitoring comprehension and in preparing students in the development of key critical thinking, operational and computational skills, data analysis, and reading skills. The examinations in this course will follow the district examination policies. Exams will take the form of tests and quizzes given at appropriate instructional periods. 2. Projects: Students will be asked to complete both individual and group projects related to key concepts of this course.. 3. Homework: Students will be assigned homework daily to provide independent practice opportunities to practice and deepen key concepts. Homework Intensity for this course expects that students will complete homework that will require approximately 60 minutes daily. 4. Class Participation: Class participation will be graded on a weekly basis.

5 5. Final Exam: A final exam will be given at the conclusion of both first and second semester. It will be a comprehensive exam based upon the course of study completed during the year. Grades: All work will be assigned a point value, although not all work will receive a letter grade. Grades are based on total points accumulated during each grading period. I have structured the class in such a way to approximate your grade breaking down into the following percentages: Examinations: 75% A-/A-= % Homework: 10% B-/B/B Final Exam: 15% C-/C/C+ = % D-/D/D % F = Below 59.5 % IX. Materials/Textbook(s) Algebra: Structure and Method, Book 1, Richard G. Brown, et al. MCDOUGAL LITTLE, Algebra: Structure and Method, Book 2, Richard G. Brown, et al. MCDOUGAL LITTLE, X. Seeking a-f Approval Yes/No Yes, this course will be submitted to the University of California for approval for the academic year in the subject domain C for mathematics. XI. Seeking AP Class Approval Yes/No This course does NOT seek AP approval. C:/Course.out/Proposed Course Outline Template