Northampton County Schools Algebra II Mathematics Pacing Guide

Transcription

1 Northampton County Schools Algebra II Mathematics Pacing Guide Grading Periods Included 1 st Nine Weeks 2 nd Nine Weeks Northampton County Schools Department of Curriculum & Instruction 9-12 Mathematics Geneva N. Squire, Coordinator Pacing guides are subject to change as a result of benchmark assessment results. Fall 2009

2 Northampton County Schools Algebra II Pacing Guide The pacing guide illustrates the relative weight of the goals and objectives within the course. The pacing guide should be used by teachers to plan the course of work for the year, prepare daily lesson plans, and construct instructionally valid summative and formative assessments. Interpretation of Columns on the Math Pacing Guide No. Heading Column information 1 Obj.# Obj. =Objective number (Goal and Objective within the goal). Some of the goals have sublevel content as well. 2 Objective Statements 3 Supplemental Resources Statements of unit titles and specific objectives. Each specific objective begins with an action verb and makes a complete sentence when combined with the stem The learner will be able to... Valuable formative assessments can be located at the links below. Indicators: DPI Resources: Shador: Listserv If you wish to receive announcements and updates relevant to high school mathematics for the state of North Carolina, you may join the listserv by providing your name, address, school name, school address and phone number to Secondary_Math@dpi.state.nc.us. Algebra 2 continues students study of advanced algebraic concepts including functions, polynomials, rational expressions, systems of functions and inequalities, and matrices. Students will be expected to describe and translate among graphic, algebraic, numeric, tabular, and verbal representations of relations and use those representations to solve problems. Emphasis should be placed on practical applications and modeling. Appropriate technology, from manipulatives to calculators and application software, should be used regularly for instruction and assessment. Prerequisites Skills to maintain during the course: Operate with matrices to solve problems. Create linear models, for sets of data, to solve problems. Use linear functions and inequalities to model and solve problems. Use quadratic functions to model problems and solve by factoring and graphing. Use systems of linear equations or inequalities to model and solve problems. Graph and evaluate exponential functions to solve problems.

3 Objective Statements Key Concepts Obj # (The Learner will be able to:) st Nine Weeks (Topics should have covered) 1.03 Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems. Properties of Real Numbers Algebraic Expressions Solving Equations Use composition and inverse of functions to model and solve problems; justify results Create and use best-fit models of linear functions to solve problems involving sets of data. a. Interpret the constants, coefficients, and bases in the context of the data. Solving Inequalities Relations and Functions Function Operations and Composition (Linear Functions Only) Inverses/Domain and Range (Linear Functions Only) Linear Models/Scatter Plots b. Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions Use equations and inequalities with absolute value to model and solve problems; justify results. b. Interpret the constants and coefficients in the context of the 2.10 Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, and algebraic properties. Absolute Value Functions/Graphs Vertical and Horizontal Translations Graphing Systems of Equations Systems of Inequalities Solving Systems Algebraically: Substitution Solving Systems Algebraically: Linear Combinations/Eliminations Graphs in Three-Dimensions Systems with Three Variables (Triangular Form Only)

4 Objective Statements Key Concepts Obj # (The Learner will be able to:) nd Nine Weeks 1.02 Define and compute with complex numbers. Complex Numbers 1.03 Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems. Factoring Quadratics: GCF, A=1 Factoring Quadratics: A>1 Factoring Quadratics: Special Cases Factoring Cubes/Quadratics Only Simplifying Rational Expression Adding and Subtracting Rational Expressions Polynomials and Linear Factors Dividing Polynomials Solving Polynomial Equations 1.04 Operate with matrices to model and solve problems. Organizing Data into Matrices Adding and Subtracting Matrices/Scalar Multiplication Matrix Multiplication Determinants 2x2 Determinants 3x3; Area of Triangles 2.02 Use quadratic functions and inequalities to model and solve problems; justify results. b. Interpret the constants and coefficients in the context of the 2.04 Create and use best-fit models of linear, exponential and quadratic functions to solve problems involving sets of data. a. Interpret the constants, coefficients, and bases in the context of the data. Inverses 2x2 Modeling Data with Quadratic Functions Properties of Parabolas Translating Parabolas Completing the Square Quadratic Formula Modeling Data with Quadratic Functions Polynomial Functions b. Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions Use cubic equations to model and solve problems. a. Solve using tables and graphs. Polynomial Functions b. Interpret constants and coefficients in the context of the

5 Objective Statements Key Concepts Obj # (The Learner will be able to:) Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix Inverse Matrices and Systems Systems in 3-Variables operations, and algebraic properties. 3 rd Nine Weeks 1.01 Simplify and perform operations with rational exponents and logarithms (common and natural) to solve problems Model and solve problems using direct, inverse, combined and joint variation. Use composition and inverse of functions to model and solve problems; justify results Use exponential functions to model and solve problems; justify results. Roots and Radical Expressions Multiplying and Dividing Radical Expressions Binomial Radical Expressions Rational Exponents Logarithmic Functions as Inverses Properties of Logarithms Exponential and Logarithmic Equations Natural Logarithms Inverse Variation Graphing Inverse Variation Rational Functions and Their Graphs Logarithmic Functions as Inverses Exponential and Logarithmic Equations Natural Logarithms Exploring Exponential Models Properties of Exponential Functions b. Interpret the constants and coefficients in the context of the 2.04 Create and use best-fit models of linear, exponential and quadratic functions to solve problems involving sets of data. a. Interpret the constants, coefficients, and bases in the context of the data. Properties of Exponential Functions b. Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.

6 Objective Statements Key Concepts Obj # (The Learner will be able to:) Use rational equations to model and solve problems; justify results. Inverse Variation Graphing Inverse Variation Rational Functions and Their Graphs b. Interpret the constants and coefficients in the context of the Solving Rational Equations c. Identify the asymptotes and intercepts graphically and algebraically Use equations with radical expressions to model and solve problems; justify results b. Interpret the degree, constants, and coefficients in the context of the 2.09 Use equations of parabolas and circles to model and solve problems; justify results. b. Interpret the constants and coefficients in the context of the Solving Equations Exploring Conic Sections Parabolas Circles Translating Conics (Parabolas and Circles Only)

7 1 st Nine weeks Grading Period Days in Objectives Concept Key Concept School Skills to Maintain Tools of Algebra Review Fractions, Decimals & Integers Properties of Real Numbers Algebraic Expressions Solving Equations Literal Equations Solving Inequalities Absolute Value Equations Absolute Value Inequalities a Functions, Equations and Graphs 2.04b 2.08a 2.08b Skills to Maintain Relations and Functions Function Operations and Composition (Linear Functions Only) Inverses/Domain and Range (Linear Functions Only) Review Linear Equations: Graphing Linear Equations (Table/Intercepts) Review Linear Equations: Graphing using Slope and Slope Intercept Form, Parallel and Perpendicular Lines Review Linear Equations: Writing Equations of Lines Direct Variations Linear Models/Scatter Plots Absolute Value Functions/Graphs Vertical and Horizontal Translations Linear Systems Graphing Systems of Equations Systems of Inequalities Linear Programming (Enrichment) Solving Systems Algebraically: Linear Combinations/ Elimination Graphs in Three-Dimensions Systems with Three Variables (Triangular Form Only) Remediation and Enrichment Unit Review and Mini-Assessment

8 1 st Nine weeks Grading Period Days in School Objectives Concept Key Concept Matrices Organizing Data into Matrices Adding and Subtracting Matrices/Scalar Multiplication Matrix Multiplication Geometric Transformations with Matrices (Enrichment) Determinants 2x2 Determinants 3x3; Area of Triangles Crammer s Rule Inverses 2x2 Inverse Matrices and Systems Systems in 3-Variables Augmented Matrices and Systems (Enrichment) Remediation and Enrichment Unit Review and Mini-Assessment b Skills to Maintain Quadratic Equations and Functions Cumulative Review Remediation and Enrichment Mid-Term Assessments Modeling Data with Quadratic Functions Properties of Parabolas Translating Parabolas Algebra Review (Skills to Maintain) Distributive Property and F.O.I.L. Factoring Quadratics: GCF, A=1 Factoring Quadratics: A>1 Factoring Quadratics: Special Cases Factoring Cubes/Quadratics Only

9 Days in Grading Period a 2.06b Algebra II PACING GUIDE 2 st Nine weeks Grading Period Objectives Concept Key Concept a 2.06b Skills to Maintain Quadratic Equations and Functions (Continued) Remediation and Enrichment Unit Review and Mini-Assessment Polynomials and Polynomial Functions Cumulative Review Remediation and Enrichment Mid-Term Assessments Radical Functions and Rational Exponents Simplifying Rational Expressions Adding and Subtracting Rational Expressions Review Simplifying Square Roots Solving Quadratics Complex Numbers Completing the Square Quadratic Formula Polynomial Functions Polynomials and Linear Factors Dividing Polynomials Solving Polynomial Equations Review Properties of Exponents Roots and Radical Expressions Multiplying and Dividing Radical Expressions Binomial Radical Expressions Rational Exponents Solving Equations Graphing Radical Functions Function Operations Inverse Relations and Functions

10 Days in Grading Period a 2.09b Algebra II PACING GUIDE Objectives Concept Key Concept 2.04a 2.04b 2.06a 2.06b a 2.08b 2.10 Cumulative Review Remediation and Enrichment Cumulative Assessment Exponential and Logarithmic Functions Exploring Exponential Models Properties of Exponential Functions Logarithmic Functions as Inverses Properties of Logarithms Exponential and Logarithmic Equations Natural Logarithms Rational Functions Inverse Variation Graphing Inverse Variation Rational Functions and Their Graphs Solving Rational Equations Quadratic Relations Exploring Conic Sections Parabolas Circles Translating Conics (Parabolas and Circles Only!) Full Year Review for EOCs A minimum of 75% of the Review time must be spent on objectives from Goal 2. The remaining 25% should come from Goal 1. Remind students of test taking strategies Some review websites are below. Please know that North Carolina Standard Course of Study is not identical to any other state. However, they are all based on National Standards for Mathematics and you should be able to utilize some of the resources. Use your understanding of

11 78-79 FIRST EOC ASSESSMENT Review for EOC Retest # EOC Retest #1 the curriculum to determine appropriateness of individual modules on each website