VIEWS: 120 PAGES: 21 CATEGORY: Business POSTED ON: 8/13/2011
Teacher Edition Internet Investigations Guide document sample
ALGEBRA II CURRICULUM GUIDE ROANOKE COUNTY SCHOOLS 5937 Cove Road Roanoke, Virginia 24019 Summer 2000 Revised Summer 2001 Acknowledgements We would like to thank the following Roanoke County educators. For their work in developing the curriculum guide: Lynn Edmondson, Northside High School Emily Pack, Cave Spring High School For their work in revision: Linda Ankrom, Glenvar High School Nancy Hoffman, Cave Spring High School Roanoke County School Division Dr. Linda Weber, Superintendent Dr. Lorraine Lange, Assistant Superintendent of Instruction Mr. Gary Basham, Associate Director of Instruction Mr. Martin Misicko, Coordinator of Mathematics Table of Contents Page Textbook Overview ………………………………………………………………………1 Comments.……………………………………………..……………………….…….…..3 Sequence/Pacing Suggestions …………………………………………………………...5 Correlation of Sections to SOLs.……………………………………………………..….7 Virginia Standards of Learning.…….………………………….……………………….21 SOL Check List.…………………………………………………..…………………....23 2000 SOL Released Items.…………………………………………..…………………25 Mathematics Standards of Learning Teacher Resource Guide………………...Appendix I Resources.…………………..…………….………………………...…………Appendix II County Videos Outside Resources Supplementary Worksheets Textbook Overview Course Title: Algebra II Course Text: Glencoe Algebra 2, Integration, Application, Connections Publisher: McGraw Hill, 1998 Supplemental Materials: Teacher’s Classroom Resources Teacher’s Wraparound Edition Investigations and Project Masters Tech Prep Applications Masters Science and Math Lab Manual Practice Masters Study Guide Masters Enrichment Masters Graphing Calculator Masters Graphing Calculators in the Mathematics Classroom Modeling Mathematics Masters Assessment and Evaluation Masters SAT/ACT Study Guide Block Scheduling Booklet Lesson Planning Guide Lesson Planning Guide Virginia Edition Test/Review Software: One Copy Per School Electronic Teacher Classroom Resources Mindjogger Videoquiz 5-Minute Check Transparencies Teaching Transparencies Real World Transparencies Answer Key Transparencies Answer Key Masters Solutions Manual Multicultural Activity Masters Interactive Math Tools Virginia SOL Practice Worksheets for Algebra Two Multimedia Applications CD ROM Additional Resources Algebra Instructional Modules Teachers Resource Guide NCTM Curriculum Standards Comments 1. Please follow the suggested sequence and pacing for this course. Write in this guide any suggested improvements for subsequent years. 2. The timetable, at the end of second semester, has 19 days for cumulative review, SOL testing, exam review and exams. These days are also available to complete course work as needed. 3. The Virginia Mathematics Standards of Learning for Algebra II have been correlated with the sections in each chapter of this guide. The SOLs are also listed by section in the Virginia Lesson Planning Guide. The NCTM Standards listed throughout the materials are not up to date. A copy of the new NCTM Standards are in each school. 4. An updated copy of Mathematics Standards of Learning Teacher Resource Guide is located at the end of this guide. Note that the SOLs in the Resource Guide are grouped by topic. Under each topic the SOL is stated, followed by lists of Essential Understandings and Essential Knowledge and Skills. 5. Use of mixed reviews and spiraling on assessments is strongly recommended 6. A wide range of evaluation and assessment tools are provided. The student text furnishes mixed reviews, self tests, chapter highlights, study guides and assessments. At the end of the student text, a student handbook section provides additional assessments. The teacher wraparound edition has “Check for understanding” comments and replicas of 5-minute checks and other supplementary materials. The teacher’s resource package contains Assessment and Evaluation Masters and 5-minute check Transparencies. Additionally, each school is provided with Test/Review Software. 7. Since there is a such a wealth of supplementary materials for this text, each teacher is advised to be selective in their planning and use. 8. Test/Review Software Time is needed to familiarize yourself with the capabilities of this software The disk is not needed to run the program Difficulties occur if you use more than one computer to edit, add, or change a single file (test, worksheet). To avoid this problem, use one computer to complete and print a single document. 9. A list of Internet Connections is on page T15 of the Teacher’s Wraparound Edition. 10. Students use calculators throughout this course. The textbook examples/explanations use the TI82. Please note that adjustments may be needed with the TI83. 11. At the beginning of each chapter in the Teacher’s Wraparound Edition, there are four pages of organizational aids. Page a: Lists lesson objectives with corresponding pages Page b: Lesson planning chart organized by section materials and manipulatives extra practice pages (student edition) list of black line masters applications interactive software teaching transparencies Page c: Provides other chapter resources, outside and assessment resources Page d: Samples of materials for enhancing the chapter 12. In the Teacher’s Resources package, Glencoe provides an additional supplement of multiple choice questions. The worksheets are Glencoe’s interpretation of Virginia SOLs. Use discretion when selecting problems from the worksheets. 13. Space is provided for your comments in the guide under each chapter outline. 14. The Mind Jogger Video quizzes are provided for each chapter. Each quiz has three rounds of 4 to 5 questions. The “game” plan is easy to follow. However, we recommend that teams be established before beginning. This activity is good but should not be overused. 15. The Electronic Teacher Classroom Resources is provided for each teacher. The CD ROM is needed to run the program. This resource requires a password to use teacher mode. Directions on “How do I get started” and password information are found on the inside cover of the disk container. This CD has all the teacher’s classroom resources. We found this CD ROM most helpful. 16. The Algebra Instructional Modules, developed by the Virginia Department of Education, were sent to each Algebra teacher last year. Incorporate the Algebra II modules where appropriate. It is advised that you preview activities before using. Sequence of Instruction and Pacing Suggestions Optional Ch. Page Topic Sections SOLs Days First Semester 1 4a Analyzing Equations and Inequalities 1.5A A2: 1,4,10,19 19 2 62a Graphing Linear Relations and Functions 2.2B A2: 8,9,13,19 22 3 122a Solving Systems of Linear Equations and 3.7B A2: 12,13 15 Inequalities 4 182a Using Matrices 4.1A,4.7, A2: 1,11,12 12 4.7B, 5 252a Exploring Polynomials and Radical Expressions A2: 1,2,3,5,7,17 16 Exam Reviews and Exams 6 First Semester Total 90 Second Semester 5 279 Exploring Polynomials and Radical Expressions A2: 1,2,3,5,7,17 24 9 546a Exploring Rational Expressions 9.1A, 9.1 A.2: 2,7,20 11 6 330a Exploring Quadratic Functions and Inequalities 6.5, 6.8-6.9 A2: 5,6,7,8,9,10,18 10 7 406a Analyzing Conic Sections 7.1,7.4A,7.6A A2: 14,18 18 ,7.6B,7.7A 8 476a Exploring Polynomial Functions 8.2,8.5, 8.6, A.2: 5,7,8,9,10,15 6 8.7B, 8.8B 10 592a Exploring Exponential and Logarithmic Functions 10.3-10.7 A.2: 8,9 4 11 644a Investigating Sequences and Series 11.5-11.8 A.2: 16 5 12 710a Investigating Discrete Mathematics and Probability All -- 13 770a Exploring Trigonometric Functions All -- Cumulative Reviews, SOL Testing, Exam Reviews and Exams 12 Second Semester Total 90 CHAPTER 1 ANALYZING EQUATIONS AND INEQUALITIES SECTION TOPICS SOL DAYS Supplement s Included 1-1A GRAPHING TECHNOLOGY: EXPRESSIONS A2.1 1 WS 1.1A 1-1 EXPRESSIONS AND FORMULAS A2.1 1 1-2 PROPERTIES OF REAL NUMBERS A2.1 3 Ws 1.2 A-F QUIZ 1 1-3 INTERGRATION: STATISTICS A2.19 1 1-4 SOLVING EQUATIONS A2.10 2 WS 1.4 See note TEST 1 1-6 SOLVING INEQUALITIES A2.4 2 WS 1.6 1-5 R REVIEW OF SETS 2 WS 1.5R & See note 1-5 SOLVING ABSOLUTE VALUE EQUATIONS A2.4 1 QUIZ 1 1-7 SOLVING ABSOLUTE VALUE INEQUALITIES A2.1, A2.4 2 WS 1.7 TEST 1 TIME: 19 DAYS COMMENTS: The TI-83 should be used extensively throughout the course. Put some MULTIPLE CHOICE SOL type questions on every test. 1.2 You may find it useful to introduce complex numbers at this point. A work sheet is provided for either choice. 1.3 Stem / Leaf and Line Plots are NOT in the Algebra II SOLs 1.4 Algebra with Pizzazz by Steve & Janis Marcy, Creative Publications, 1996 page 72 1.5R Teach some set terminology, including the connection between and/or and union/intersection. Pre-Algebra with Pizzazz by Steve & Janis Marcy, Creative Publications 1978 Edition pages DD50 – DD53 1996 Edition pages 226 - 229 CHAPTER 2 GRAPHING LINEAR RELATIONS AND FUNCTIONS SECTION TOPICS SOL DAYS Supplements Included 2-1 RELATIONS AND FUNCTIONS A2.8, A2.9 2 WS 2.1 8-7 COMPOSITION OF FUNCTION A2.9 1 QUIZ 1 2-2 LINEAR EQUATIONS A2.8 2 2-2A GRAPHING TECHNOLOGY: LINEAR EQUATIONS 2-3 SLOPE A2.8 3 WS 2.3 A WS 2.3 B 2-4 WRITING LINEAR EQUATIONS A2.8 2 Summary 2.4 WS 2.4 REVIEW 1 TEST 1 2-5 INTEGRATION A2.19 2 2-5B GRAPHING TECHNOLOGY: LINES OF REGRESSION: STATISTICS 2-6 SPECIAL FUNCTIONS A2.8 2 8-8 INVERSE FUNCTIONS AND RELATIONS A2.9 1 2-7 LINEAR INEQUALITIES A2.13 2 2.7A GRAPHING TECHNOLOGY: LINEAR INEQUALITIES REVIEW 1 TEST 1 TIME: 22 DAYS COMMENTS: 2-2 Content to include: Definition of Linear Equation Standard Form of a Linear Equation Solve an equation for y (when possible) Using TI-83 to set up a table of values Graph on paper and on calculator 2-3 Content to include: Determine Slope: Given a graph, 2 points, any form of the equation Classify Slope as Positive / Negative / Zero / Undefined Review Slope-intercept Form (Definition on page 88) Do Parallel / Perpendicular at end of Section 2-4 2-4 Include Parallel / Perpendicular at end of this section Use of TI-83 highly recommended, graphing by hand not required in SOLs See 2000 SOL Released Items #46, 47,48, 49, 50 2-6 Include Identity function CHAPTER 3 SOLVING SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES SECTION TOPICS SOL DAYS Supplements Included 3-1 GRAPHING SYSTEMS OF EQUATIONS A2.13 1 Summary 3.1 3-1A GRAPHING TECHNOLOGY: SYSTEMS OF A2.13 1 EQUATIONS 3-2 SOLVING SYSTEMS OF EQUATIONS A2.12 2 WS 3.2 A ALGEBRAICALLY WS 3.2 B QUIZ 1 3-3 CRAMER'S RULE A2.12 2 3-4 GRAPHING SYSTEMS OF INEQUALITIES A2.12, A2.13 2 3-4 A GRAPHING TECHNOLOGY: SYSTEMS OF LINEAR INEQUALITIES 3-5 LINEAR PROGRAMMING A2.13 3 WS 3.6 A-E 3-6 APPLICATIONS OF LINEAR PROGRAMMING 3-7 SOLVING SYSTEMS OF EQUATIONS IN A2.12 2 THREE VARIABLES TEST 1 TIME: 15 DAYS COMMENTS: 3-1 Additional practice found in Algebra with Pizzazz by Steve & Janis Marcy, Creative Publications 3-2 Additional word problems provided in Supplementary Materials 3-7 It is suggested that Cramer’s Rule not be used at this point to solve systems with more than 2 variables. 3 x 3 determinants are discussed in Chapter 5 CHAPTER 4 USING MATRICES SECTION TOPICS SOL DAYS Supplements Included 4-1 AN INTRODUCTION TO MATRICES A2.11 1 4-2 ADDING AND SUBTRACTING MATRICES A2.11 2 4-3 MULTIPLYING MATRICES A2.11 2 QUIZ 1 4-4 MATRICES AND DETERMINANTS A2.11 2 4-5 IDENTITY AND INVERSE MATRICES A2.1, A2.12 1 3-3 CRAMER'S RULE A2.12 1 (with 3 variables) 4-6 USING MATRICES TO SOLVE SYSTEMS OF A2.12 1 EQUATIONS TEST 1 TIME: 12 DAYS COMMENTS: 4-1 Newsstands have Logic Puzzle Magazines 4-2 First day by hand, second day using calculator Application: Translation matrix, (students lack percent probability background) 4-4 By determinants, diagonals, minors, and calculator 4-5 Be able to do the inverse of a 2 x 2 by hand 3-3 Use the calculator to do 3 x 3 determinants CHAPTER 5 EXPLORING POLYNOMIALS AND RADICAL EXPRESSIONS SECTION TOPICS SOL DAYS Supplements Included 5-1 MONOMIALS A2.1 3 5-2 POLYNOMIALS A2.1 3 5.2 5-3 DIVIDING POLYNOMIALS A2.2 3 TEST 1 5-4 FACTORING A2.5 5 See notes QUIZ 1 FIRST SEMESTER EXAMS START OF SECOND SEMESTER 5-4 FACTORING A2.5 5 See START OF SECOND SEMESTER notes REVIEW 1 TEST 1 5-5 ROOTS OF REAL NUMBERS A2.1 1 Summary 5.5 5-6 RADICAL EXPRESSIONS A2.2, A2.3 5 WS 5.6 A - C 5-7 RATIONAL EXPONENTS A2.2, A2.3 2 5-8 SOLVING RADICAL EQUATIONS AND A2.2, A2.3, 3 WS 5.8 A - B INEQUALITIES A2.7 TEST 1 5-9 COMPLEX NUMBERS A2.1, A2.2, 4 Summary 5.9, 5-10 SIMPLIFYING EXPRESSIONS CONTAINING A2.3, A2.17 Summary 5.9A COMPLEX NUMBERS WS 5.9 A-E TEST 1 TIME: 40 DAYS COMMENTS: 5.4 Get as far as possible into factoring before Exams Use Worksheets as needed to supplement WS 5.4 A-D flow GCF, Grouping, Master Product, Special binomial. Perfect square trinomials are mixed into 5.4 D WS 5.4 E – H flow GCF, Patterns, Trinomials, Special techniques Each has a Summary and an explanation of the Master Product Method is included GO TO CHAPTER 9 CHAPTER 9 EXPLORING RATIONAL EXPRESSIONS SECTION TOPICS SOL DAYS Supplements Included 9-2 DIRECT, INVERSE AND JOINT VARIATION A2.20 1 9-3 MULTIPLYING AND DIVIDING RATIONAL A2.2 3 WS 9.3 EXPRESSIONS A-C 9-4 ADDING AND SUBTRACTING RATIONAL A2.2 3 WS 9.4 EXPRESSIONS A-C 9-5 SOLVING RATIONAL EQUATIONS AND A2.7 3 WS 9.5 INEQUALITIES A-C TEST 1 TIME: 11 DAYS COMMENTS: 9.3 – 9.5 Summary provided CHAPTER 6 EXPLORING QUADRATIC FUNCTIONS AND INEQUALITIES SECTION TOPICS SOL DAYS Supplements Included 6-1 SOLVING QUADRATIC EQUATIONS BY A2.6, A2.7, 2 GRAPHING A2.8, A2.9, 6-1 A GRAPHING TECHNOLOGY: QUADRATIC A2.10 FUNCTIONS 6-2 SOLVING QUADRATIC EQUATIONS BY A2.5 1 FACTORING 6-3 COMPLETING THE SQUARE A2.5 2 QUIZ 1 6-4 QUADRATIC FORMULA AND A2.6,A2.7 1 WS 6.4 DISCRIMINANT 6-6A GRAPHING TECHNOLOGY: FAMILIES OF A2.18 1 PARABOLAS 6-7A GRAPHING TECHNOLOGY: QUADRATIC A2.18 1 INEQUALITIES 6-7 GRAPHING AND SOLVING QUADRATIC A2.18 INEQUALITIES TEST 1 TIME: 10 DAYS COMMENTS: 6-6 Will be done in 7-2. 6.7 Can be included if time allows. CHAPTER 7 ANALYZING CONIC SECTIONS SECTION TOPICS SOL DAYS Supplements Included 7-2 PARABOLAS A2.18 4 Text: 6-6 WS 7.2 A-B 7-3 CIRCLES A2.18 2 QUIZ 1 7-4 ELLIPSES A2.18 3 7-5 HYPERBOLAS A2.18 3 7-6 CONIC SECTIONS A2.18 2 WS 7.6 A-B 7-7 SOLVING QUADRATIC SYSTEMS A2.14 2 TEST 1 TIME: 18 DAYS COMMENTS: 7-2 Additional problems can be found in 6-6, Page 373 7-3 There is a built-in program in the TI-83 2nd DRAW 9: Data is entered as ( h, k, r ) ZOOM 5: SQUARE to scale axes correctly CHAPTER 8 EXPLORING POLYNOMIAL FUNCTIONS SECTION TOPICS SOL DAYS Supplements Included 8-1 POLYNOMIAL FUNCTIONS A2.8, A2.9, Mini Unit A2.15 8-3A GRAPHING TECHNOLOGY: POLYNOMIAL A2.7, A2.8, Mini Unit FUNCTIONS A2.9, A2.10 8-3 GRAPHING POLYNOMIAL FUNCTIONS AND A2.7, A2.8, Mini Unit APPROXIMATING ZEROES A2.9, A2.10 8-3B GRAPHING TECHNOLOGY: MODELING A2.7, A2.8, Mini Unit REAL-WORLD DATA A2.9, A2.10 8-4 ROOTS AND ZEROS A2.9, A2.10 Mini Unit 8-7 COMPOSITION OF FUNCTIONS A2.9 See Ch. 2 8-8 INVERSE FUNCTIONS AND RELATIONS A2.9 See Ch. 2 TIME: 6 DAYS COMMENTS: There is a Mini-Unit on Polynomials provided in the Supplementary Materials CHAPTER 10 EXPLORING EXPONENTIAL AND LOGARITHMIC FUNCTIONS SECTION TOPICS SOL DAYS Supplements Included 10-1 REAL EXPONENTS AND EXPONENTIAL A2.8 2 FUNCTIONS 10-2 LOGARITHMS AND LOGARITHMIC A2.9 1 FUNCTIONS QUIZ 1 TIME: 4 DAYS COMMENTS: CHAPTER 11 INVESTIGATING SEQUENCES AND SERIES SECTION TOPICS SOL DAYS Supplements Included GRAPHING TECHNOLOGY: ARITHMETIC A2.16 SEQUENCES 11-1 ARITHMETIC SEQUENCES A2.16 11-1A 11-2 ARITHMETIC SERIES A2.16 11-3 GEOMETRIC SEQUENCES A2.16 11-4 GEOMETRIC SERIES A2.16 TIME: 5 DAYS COMMENTS: Check the SOLs Mathematics Standards of Learning Algebra II The standards below outline the content for a one-year course in Algebra II. Students enrolled in Algebra II are assumed to have mastered those concepts outlined in the Algebra I standards. A thorough treatment of advanced algebraic concepts is provided through the study of functions, polynomials, rational expressions, complex numbers, matrices, and sequences and series. Emphasis should be placed on practical applications and modeling throughout the course of study. Oral and written communication concerning the language of algebra, logic of procedures, and interpretation of results also should permeate the course. These standards include a transformational approach to graphing functions. Transformational graphing uses translation, reflection, dilation, and rotation to generate a "family of graphs" from a given graph and builds a strong connection between algebraic and graphic representations of functions. Students will vary the coefficients and constants of an equation, observe the changes in the graph of the equation, and make generalizations that can be applied to many graphs. Graphing utilities (graphing calculators or computer graphing simulators) and spreadsheets will be used by students and teachers. Graphing utilities enhance the understanding of realistic applications through mathematical modeling and aid in the investigation and study of functions and their inverses. They also provide an effective tool for solving/verifying equations and inequalities. Any other available technology that will enhance student learning should be used. AII.1 The student will identify field properties, axioms of equality and inequality, and properties of order that are valid for the set of real numbers and its subsets, complex numbers, and matrices. AII.2 The student will add, subtract, multiply, divide, and simplify rational expressions, including complex fractions. AII.3 The student will add, subtract, multiply, divide, and simplify radical expressions containing positive rational numbers and variables and expressions containing rational exponents; and write radical expressions as expressions containing rational exponents, and vice versa. AII.4 The student will solve absolute value equations and inequalities graphically and algebraically. Graphing calculators will be used both as a primary method of solution and to verify algebraic solutions. AII.5 The student will identify and factor completely polynomials representing the difference of squares, perfect square trinomials, the sum and difference of cubes, and general trinomials. AII.6 The student will select, justify, and apply a technique to solve a quadratic equation over the set of complex numbers. Graphing calculators will be used for solving and confirming algebraic solutions. AII.7 The student will solve equations containing rational expressions and equations containing radical expressions algebraically and graphically. Graphing calculators will be used for solving and confirming algebraic solutions. AII.8 The student will recognize multiple representations of functions (linear, quadratic, absolute value, step, and exponential functions) and convert between a graph, a table, and symbolic form. A transformational approach to graphing will be employed through the use of graphing calculators. AII.9 The student will find the domain, range, zeros and inverse of a function, the value of a function for a given element in its domain, and the composition of multiple functions. Functions will include those that have domains and ranges that are limited and/or discontinuous. The graphing calculator will be used as a tool to assist in investigation of functions, including exponential and logarithmic. AII.10 The student will investigate and describe the relationships between the solution of an equation, zero of a function, x-intercept of a graph, and factors of a polynomial expression through the use of graphs. AII.11 The student will use matrix multiplication to solve practical problems. Graphing calculators or computer programs with matrix capabilities will be used to find the product. AII.12 The student will represent problem situations with a system of linear equations and solve the system using the inverse matrix method. Graphing calculators or computer programs with matrix capability will be used to perform computations. AII.13 The student will solve systems of linear inequalities and linear programming problems and describe the results both orally and in writing. A graphing calculator will be used to facilitate solutions to linear programming problems. AII.14 The student will solve nonlinear systems of equations, including linear-quadratic and quadratic- quadratic, algebraically and graphically. The graphing calculator will be used as a tool to visualize graphs and predict the number of solutions. AII.15 The student will recognize the general shape of polynomial functions, locate the zeros, sketch the graphs, and verify graphical solutions algebraically. The graphing calculator will be used as a tool to investigate the shape and behavior of polynomial functions. AII.16 The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve problems, including writing the first n terms, finding the nth term, and evaluating summation formulas. Notation will include sigma and 'a sub n'. AII.17 The student will perform operations on complex numbers and express the results in simplest form. Simplifying results will involve using patterns of the powers of i. AII.18 The student will identify conic sections (circle, ellipse, parabola, and hyperbola) from his/her equations. Given the equations in (h, k) form, students will sketch graphs of conic sections, using transformations. AII.19 The student will collect and analyze data to make predictions, write equations, and solve practical problems. Graphing calculators will be used to investigate scatterplots to determine the equation for a curve of best fit. AII.20 The student will identify, create, and solve practical problems involving a combination of direct and inverse variations. Outside Resources http://www.glencoe.com/sec/math For help with TI-83 http://education.ti.com To download TI-83 key fonts http://education.ti.com/product/tech/83/down/download.html UVa Curry School of Education http://teach.virginia.edu/k12algebra Algebra with Pizzazz by Steve & Janis Marcy, Creative Publications, 1996 http://www.mimosausa.com Cooperative Learning & Mathematics, Dina Kushnir, Kagan Publishing, 2001 www.KaganOnline.com