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Recurring Themes Throughout the Course CLE: CLE 3103.1.1 Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning. CLE 3103.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution. CLE 3103.1.3 Develop inductive and deductive reasoning to independently make and evaluate mathematical arguments and construct appropriate proofs; include various types of reasoning, logic, and intuition. CLE 3103.1.4 Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies. CLE 3103.1.5 Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication. CLE 3103.1.6 Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world. CLE 3103.1.7 Use technologies appropriately to develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate and reliable models. CLE 3103.2.4 Understand the capabilities and limitations of technology when performing operations, graphing, and solving equations involving complex numbers. Checks for State Performance Understanding Indicators Assessments Instructional Connections Resources 3103.1.5 Determine the accuracy SPI 3103.1.4 Use mathematical A classroom set of TI- School-to-career Masters and reliability of a mathematical language, symbols, definitions, http://www.algebra2.com/careers model. proofs and counterexamples 84s or TI-spires. or resource kit correctly and precisely to 3103.1.9 Translate the syntax of effectively communicate kutasoftware.com has several Science and Mathematics Lab technology to appropriate reasoning in the process of worksheets for various topics Manual (Glencoe Resource Kit) mathematical notation for non- solving problems via linear and transcendental mathematical modeling with http://www.glencoe.com/se functions. both linear and non-linear c/math/algebra/algebra2/al functions. gebra2_05/extra_examples 3103.1.10 Interpret the results of /index.php4/tn mathematical modeling in SPI 3103.1.1 Move flexibly various contexts to answer between multiple representations http://www.regentsprep.or questions. (contextual, physical, written, g/Regents/math/ALGEBR verbal, conic/pictorial, graphical, A/math- 3103.1.1 Create and analyze tabular, and symbolic) of non- ALGEBRA.htm#Equations scatter-plots of non-linear and linear and transcendental _and_Inequalities__ transcendental functions. functions to solve problems, to model mathematical ideas, and to http://education.ti.com/edu 3103.1.2 Compare and contrast communicate solution strategies. cationportal/activityexchan sampling techniques and identify ge/activity_list.do?cid=us the best technique for a given SPI 3103.1.2 Recognize and situation. describe errors in data collection http://glencoe.mcgraw- and analysis as well as hill.com/sites/007873830x/ 1 3103.1.4 Identify the weaknesses identifying representations of student_view0/chapter7/les of calculators and other data as being accurate or son7/personal_tutor.html technologies in representing misleading. nonlinear data, such as graphs http://glencoe.mcgraw- approaching vertical asymptotes, SPI 3103.1.3 Use technology hill.com/sites/0078884829/ and use alternative techniques to tools to identify and describe student_view0/chapter7/les identify these issues and patterns in data using non-linear son1/personal_tutor.html correctly solve problems. and transcendental functions that approximate data as well as http://www.purplemath.co 3103.1.3 Use calculators to using those functions to solve m/modules/ identify regression equations for contextual problems. nonlinear data. http://www.onlinemathlear ning.com/unit-circle.html 3103.1.5 Determine the accuracy and reliability of a mathematical http://teachers.henrico.k12. model. va.us/math/HCPSAlgebra2 / 3103.1.9 Translate the syntax of technology to appropriate www.Mathorama.com mathematical notation for non- linear and transcendental http://www.fkss.ca/courses functions. /math/PMa12/index.html Online Assessment with instant feedback: http://education.jlab.org/so lquiz/index.html Scavenger Hunt: Tool to find resources, located in each chapter of Glencoe Algebra 2 http://www.glencoe.com/sec/mat h/algebra/algebra2/algebra2_05/p dfs/Algebra2Scavenger.pdf Reading to Learn Mathematics: Vocabulary for each chapter of Glencoe Algebra 2 (activity sheets) Reading & Writing in the Mathematics Classroom (Glencoe Resource Kit) 2 eGlossary-Math http://www.glencoe.com/apps/e Glossary612/landing.php Online Algebra 2 Lessons: http://yourteacher.com/browse- lessons Teaching Mathematics with Foldables, Dinah Zike Resource CDs in kit: Alge2Pass Tutorials, Electronic Text Book, Worksheets and Enrichment Vocabulary Help: http://mathwords.com CLE 3103.2.4 http://calculusapplets.com/graph 3103.2.11 Understand the errors.html capabilities and limitations of technology. Make estimations without a calculator to detect potential errors. 3 Course: Algebra 2 1st Nine Weeks Curriculum Guide Unit 1: Characteristics of Functions Estimated Time: 4 Weeks CLE: CLE 3103.3.2 Understand, analyze, transform and generalize mathematical patterns, relations and functions using properties and various representations. CLE 3103.3.3 Analyze and apply various methods to solve equations, absolute values, inequalities, and systems of equations over complex numbers. CLE 3103.3.5 Use mathematical models involving equations and systems of equations to represent, interpret and analyze quantitative relationships, change in various contexts, and other real-world phenomena. Essential Questions: How do you use the characteristics of each family of functions to distinguish between absolute value, step, piece-wise, linear, or quadratic functions? How would you determine the domain and range of a relation and how do they relate to the relation's inverse? What methods would you use to solve contextual problems involving 2 and 3-variable systems of linear equations and inequalities? Unit Academic Vocabulary: Inverse of a relation, inverse function, piece-wise function, step function Prerequisite Skills: Graph linear equations, solve linear equations Checks for State Understanding Performance Assessments Instructional Resources Connections Indicators CLE 3103.3.2 SPI 3103.3.5 Describe the Domain Representations Activity 3103.3.3 Determine and domain and range of Daily formative http://illuminations.nctm.org/LessonDetail.aspx?id=L6 graph the inverse of a functions and articulate 21 Cell Phone Plans (Step Functions) assessments function with and without restrictions imposed either Finance: Graphing Inequalities related to technology. by the operations or by the Unit test Graphing Piecewise Functions(Calc): dividend earnings, minimum projections, 3103.3.4 Analyze the contextual situations http://www.tc3.edu/instruct/sbrown/ti83/funcpc.htm share values or other related economics effect of changing various which the functions School-based topics parameters on functions represent. common Function Transformation Activities (Calc): and their graphs. assessments 1. http://education.ti.com/educationportal/activi ACT Standards: 3103.3.5 Graph piece-wise SPI 3103.3.10 Identify tyexchange/Activity.do?cid=US&aId=9797 Read tables and graphs and step functions. and/or graph a variety of District Benchmark Manipulate data from graphs 3103.3.11 Describe and functions and their Solve real-world problems Assessment? 2. http://education.ti.com/educationportal/activi using first-degree equations articulate the translations tyexchange/Activity.do?cid=US&aId=11930 Write equations and characteristics and inequalities that require parameters of a parent SPI 3103.3.7 Identify planning, manipulating, and/or function. whether a function has an Quadratic Function Transformations (Calc): http://education.ti.com/educationportal/activityexchang solving inverse, whether two Solve simple absolute value functions are inverses of e/Activity.do?cid=US&aId=9795 inequalities each other, and/or explain Analyze and draw conclusions why their graphs are How to Find an Inverse (TI) based on information from reflections over the line y http://education.ti.com/educationportal/activityexchang graphs in the coordinate plane = x. e/Activity.do?cid=US&aId=8211 Determine when an expression is undefined 4 CLE 3103.3.3 SPI 3103.3.8 Solve Escape from the Tomb (Answers the question “When Biology/Chemistry applications with 3103.3.8 Solve a three by systems of three linear am I ever going to use systems of equations?” Linear Programming three system of linear equations in three http://illuminations.nctm.org/LessonDetail.aspx?id=L6 equations algebraically and variables. 98 by using inverse matrices and determinants with and SPI 3103.3.9 Graph the Talk or Text (Application of Systems) without technology. solution set of two or three http://illuminations.nctm.org/LessonDetail.aspx?id=L7 3103.3.18 Solve compound linear or quadratic 80 inequalities involving inequalities. disjunction and Matrix Operations, Solving (Not Cramer's, Calc): conjunction and linear http://mathbits.com/mathbits/tisection/precalculus/matr inequalities containing ices.htm absolute values. 3103.3.19 Solve linear Cramer's Rule: programming problems. http://www.purplemath.com/modules/cramers.htm Linear Programming: http://teachers.henrico.k12.va.us/math/hcpsalgebra2/3- 6.htm Systems of Linear Equations: http://teachers.henrico.k12.va.us/math/hcpsalgebra2/3- 7.htm Linear Programming—Dirt Bike Dilemma http://illuminations.nctm.org/LessonDetail.aspx?id=L6 85 CLE 3103.3.5 SPI 3103.3.12 Interpret Contextual Quadratic Project: Social Studies graphs that depict real- http://www.glencoe.com/sec/math/algebra/algebra2/alg world phenomena. ebra2_05/webquest/unit2/webquest.php4/ny SPI 3103.3.13 Solve contextual problems using quadratic, rational, radical and exponential equations, finite geometric series or systems of equations. 5 Course: Algebra 2 1st Nine Weeks Curriculum Guide Unit 2: Algebraic Operations Estimated Time: 4 Weeks CLE: CLE 3103.3.1 Understand and apply properties of rational exponents and perform basic operations to simplify algebraic expressions. CLE 3103.3.5 Use mathematical models involving equations and systems of equations to represent, interpret and analyze quantitative relationships, change in various contexts, and other real-world phenomena. Essential Questions: How would you determine that a polynomial has been completely factored? How do you properly simplify fractions that include radicals? Unit Vocabulary: complete the square, rational function Prerequisite Skills: operations on rational numbers, properties of exponents, factor polynomials Checks for State Understanding Performance Assessments Instructional Resources Connections Indicators CLE 3103.3.1 SPI 3103.3.1 Add, Daily formative Polynomial operations: Cost Analyst Career Connection: Production Costs 3103.3.1 Perform operations subtract and multiply assessments http://teachers.henrico.k12.va.us/math/hcpsal and Factors on algebraic expressions and polynomials; divide a gebra2/5-1.htm Medicine: Estimating populations during epidemics justify the procedures. polynomial by a lower Unit test with equations 3103.3.21 Factor degree polynomial. Polynomial Modeling with Algebra Tiles polynomials using a variety School-based common Business of methods including the SPI 3103.3.3 Add, assessments Use graphing calculator to compare factored factor theorem, synthetic subtract, multiply, and un-factored forms to check for accuracy Entertainment division, long division, sums divide and simplify District Benchmark and differences of cubes, rational expressions Assessment? Factoring/Multiplying Polynomials ACT Standards: and grouping. including those with Activity/Game Find and use the least common multiple rational and negative http://www.regentsprep.org/Regents/math/A Work with numerical factors exponents. LGEBRA/AV3/GridPoly.htm Work with scientific notation Work with squares and square roots of numbers Work with problems involving positive integer exponents Work with cubes and cube roots of numbers Determine when an expression is undefined Add, subtract, and multiply polynomials Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions and 6 numbers Write expressions that require planning and/or manipulating to accurately model a situation SPI 3103.3.12 Interpreting Graphs (with or without Tech): Economics CLE 3103.3.5 Interpret graphs that http://www.glencoe.com/sec/math/algebra/al 3103.3.6 Simplify depict real-world gebra2/algebra2_05/usa_today/index.php4/n Social Studies expressions and solve phenomena. y equations containing radicals. 7

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