Pearson Georgia High School Mathematics Advanced Algebra

Transcription

1 A Correlation of Pearson Georgia High School Mathematics Advanced Algebra 2014 to the Gwinnett County Academic Knowledge and Skills (AKS) Mathematics

2 Table of Contents A - Process Skills... 1 C - Geometry... 8 E - Algebra F - Data Analysis and Probability G - Reading Across the Curriculum Copyright 2013 Pearson Education, Inc. or its affiliate(s). All rights reserved

3 INTEGRATED ALGEBRA II A - Process Skills use appropriate technology to solve mathematical problems (GPS) (MAM3_A2010-1) TECHNOLOGY LAB 4-1: Even and Odd Functions, TECHNOLOGY LAB 5-5: Graphing Rational Functions, TECHNOLOGY LAB 5-6: Oblique Asymptotes, TECHNOLOGY LAB 5-7b: Rational Inequalities, TECHNOLOGY LAB 7-5: Using Logarithms for Exponential Models, TECHNOLOGY LAB 8-4: Graphing Trigonometric Functions, TECHNOLOGY LAB 8-7: Plotting and Analyzing Residuals build new mathematical knowledge through problem solving (GPS) (MAM3_A2010-2) to explore problem situations: solve problems that arise in mathematics and in other contexts (GPS) (MAM3_A2010-3) to explore problem situations in mathematics and other areas: 1

4 apply and adapt a variety of appropriate strategies to solve problems (GPS) (MAM3_A2010-4) to practice problem-solving strategies: monitor and reflect on the process of mathematical problem solving (GPS) (MAM3_A2010-5) to monitor and reflect on the process of mathematical problem-solving: recognize reasoning and proof (evidence) as fundamental aspects of mathematics (GPS) (MAM3_A2010-6) ACTIVITY LAB 1-4c: Drawing Conclusions From Samples, 3-8 A New Look at Parabolas, 3-9 Circles in the Coordinate Plane, 4-6 Theorems About Roots of Polynomial Equations, LESSON LAB 4-6: Using Polynomial Identities, 4-7 The Fundamental Theorem of Algebra, 4-8 The Binomial Theorem, LESSON LAB 4-8: Mathematical Induction, TECHNOLOGY LAB 8-7: Plotting and Analyzing Residuals, 8-9 Trigonometric Identities, 8-10 Area and the Law of Sines, LESSON LAB 8-10: The Ambiguous Case, 8-11 The Law of Cosines 2

5 make and investigate mathematical conjectures (GPS) (MAM3_A2010-7) ACTIVITY LAB 1-4c: Drawing Conclusions From Samples, 3-8 A New Look at Parabolas, 3-9 Circles in the Coordinate Plane, 4-6 Theorems About Roots of Polynomial Equations, LESSON LAB 4-6: Using Polynomial Identities, 4-7 The Fundamental Theorem of Algebra, 4-8 The Binomial Theorem, LESSON LAB 4-8: Mathematical Induction, TECHNOLOGY LAB 8-7: Plotting and Analyzing Residuals, 8-9 Trigonometric Identities, 8-10 Area and the Law of Sines, LESSON LAB 8-10: The Ambiguous Case, 8-11 The Law of Cosines investigate, develop and evaluate mathematical arguments and proofs (GPS) (MAM3_A2010-8) ACTIVITY LAB 1-4c: Drawing Conclusions From Samples, 4-6 Theorems About Roots of Polynomial Equations, LESSON LAB 4-6: Using Polynomial Identities, 4-7 The Fundamental Theorem of Algebra, 4-8 The Binomial Theorem, LESSON LAB 4-8: Mathematical Induction, TECHNOLOGY LAB 8-7: Plotting and Analyzing Residuals, 8-9 Trigonometric Identities, 8-10 Area and the Law of Sines, LESSON LAB 8-10: The Ambiguous Case, 8-11 The Law of Cosines select and use various types of reasoning and methods of proof (GPS) (MAM3_A2010-9) 4-6 Theorems About Roots of Polynomial Equations, LESSON LAB 4-6: Using Polynomial Identities, 4-7 The Fundamental Theorem of Algebra, 4-8 The Binomial Theorem, LESSON LAB 4-8: Mathematical Induction, 8-9 Trigonometric Identities, 8-10 Area and the Law of Sines, LESSON LAB 8-10: The Ambiguous Case, 8-11 The Law of Cosines 3

6 organize and consolidate mathematics thinking (GPS) (MAM3_A ) to organize and consolidate mathematics thinking: communicate mathematical thinking coherently to peers, teachers and others (GPS) (MAM3_A ) to communicate mathematical thinking coherently to peers, teachers, and others: analyze and evaluate the mathematical thinking and strategies of others (GPS) (MAM3_A ) to analyze and evaluate the mathematical thinking and strategies of others: 4

7 use the terminology and language of mathematics to express mathematical ideas precisely (GPS) (MAM3_A ) to use the terminology and language of mathematics to express mathematical ideas precisely: recognize and use connections among mathematical ideas (GPS) (MAM3_A ) to recognize and use connections among mathematical ideas: 5

8 explain how mathematical ideas interconnect and build on one another to produce a coherent whole (GPS) (MAM3_A ) Students experience the connection between and the building upon mathematical ideas as they explore different types of functions, including their graphs, end behaviors, domains and ranges, and applications to data analysis and problem solving. Sample References: 2-3 Linear Functions and Slope-Intercept Form, 2-4 Families of Functions, 2-5 Absolute Value Functions and Graphs, LESSON LAB 2-5: Piecewise Functions, 3-1 Quadratic Functions and Transformations, 3-7 Quadratic Systems, 4-1 Polynomial Functions, TECHNOLOGY LAB 4-1: Even and Odd Functions, ACTIVITY LAB 4-7: Graphing Polynomials Using Zeros, 4-9 Polynomial Models in the Real World, 4-10 Transforming Polynomial Functions, 5-5 The Reciprocal Function Family, 5-6 Rational Functions and Their Graphs, 6-6 Function Operations, 6-7 Inverse Relations and Functions, 6-8 Graphing Radical Functions, 7-2 Properties of Exponential Functions, 7-3 Logarithmic Functions as Inverses, TECHNOLOGY LAB 8-4: Graphing Trigonometric Functions recognize and apply mathematics in contexts outside of mathematics (GPS) (MAM3_A ) 1-3 Samples and Surveys, ACTIVITY LAB 1-4c: Drawing Conclusions From Samples, 4-9 Polynomial Models in the Real World, 10-1 Applying Constructions, 10-2 Solving Density and Design Problems 6

9 create and use pictures, manipulatives, models and symbols to organize, record and communicate mathematical ideas (GPS) (MAM3_A ) select, apply and translate among mathematical representations to solve problems (GPS) (MAM3_A ) Students use pictures, manipulatives, and models in lesson labs, activity labs, and technology labs: LESSON LAB 2-5: Piecewise Functions, LESSON LAB 3-2: Identifying Quadratic Data, TECHNOLOGY LAB 4-1: Even and Odd Functions, LESSON LAB 4-6: Using Polynomial Identities, Zeros, LESSON LAB 4-8: Mathematical Induction, TECHNOLOGY LAB 5-5: Graphing Rational Functions, TECHNOLOGY LAB 5-6: Oblique Asymptotes, ACTIVITY LAB 5-7a: Systems With Rational Equations, TECHNOLOGY LAB 5-7b: Rational Inequalities, TECHNOLOGY LAB 7-5: Using Logarithms for Exponential Models, LESSON LAB 7-6: Exponential and Logarithmic Inequalities, TECHNOLOGY LAB 8-4: Graphing Trigonometric Functions, TECHNOLOGY LAB 8-7: Plotting and Analyzing Residuals, LESSON LAB 8-10: The Ambiguous Case, ACTIVITY LAB 9-5: LESSON LAB 1-2: An Introduction to Summation Notation, ACTIVITY LAB 1-4a: Probability Distributions, LESSON LAB 2-5: Piecewise Functions, LESSON LAB 3-2: Identifying Quadratic Data, 3-8 A New Look at Parabolas, 3-9 Circles in the Coordinate Plane, TECHNOLOGY LAB 4-1: Even and Odd Functions, ACTIVITY LAB 4-7: Graphing Polynomials Using Zeros, 4-9 Polynomial Models in the Real World, TECHNOLOGY LAB 5-5: Graphing Rational Functions, TECHNOLOGY LAB 5-6: Oblique Asymptotes, ACTIVITY LAB 5-7a: Systems With Rational Equations, TECHNOLOGY LAB 5-7b: Rational Inequalities, 7-1 Exploring Exponential Models, TECHNOLOGY LAB 7-5: Using Logarithms for Exponential Models, 8-1 Exploring Periodic Data, TECHNOLOGY LAB 8-4: Graphing Trigonometric Functions, TECHNOLOGY LAB 8-7: Plotting and Analyzing Residuals, 10-1 Applying Constructions, 10-2 Solving Density and Design Problems 7

10 use representations to model and interpret physical, social and mathematical phenomena (GPS) (MAM3_A ) 1-4 Normal Distributions, LESSON LAB 2-5: Piecewise Functions, LESSON LAB 3-2: Identifying Quadratic Data, 3-8 A New Look at Parabolas, 3-9 Circles in the Coordinate Plane, TECHNOLOGY LAB 4-1: Even and Odd Functions, Zeros, 4-9 Polynomial Models in the Real World, TECHNOLOGY LAB 5-5: Graphing Rational Functions, TECHNOLOGY LAB 5-6: Oblique Asymptotes, ACTIVITY LAB 5-7a: Systems With Rational Equations, TECHNOLOGY LAB 5-7b: Rational Inequalities, 7-1 Exploring Exponential Models, TECHNOLOGY LAB 7-5: Using Logarithms for Exponential Models, 8-1 Exploring Periodic Data, TECHNOLOGY LAB 8-4: Graphing Trigonometric Functions, TECHNOLOGY LAB 8-7: Plotting and Analyzing Residuals, 10-1 Applying Constructions, 10-2 Solving Density and Design Problems C - Geometry find equations of circles (GPS) (MAM3_C ) 3-9 Circles in the Coordinate Plane graph a circle given an equation in general form (GPS) (MAM3_C ) 3-9 Circles in the Coordinate Plane find the equation of a tangent line to a circle at a given point (GPS) (MAM3_C ) Advanced Algebra: 2-3 Linear Functions and Slope-Intercept Form Analytic Geometry: 8-3 Tangent Lines Coordinate Algebra: 3-6 Slopes of Parallel and Perpendicular Lines 8

11 solve a system of equations involving a circle and a line (GPS) (MAM3_C ) 3-7 Quadratic Systems solve a system of equations involving two circles (GPS) (MAM3_C ) 3-7 Quadratic Systems convert equations of conics by completing the square (GPS) (MAM3_C ) 3-1 Quadratic Functions and Transformations, 3-2 Standard Form of a Quadratic Function, 3-5 Completing the Square, 3-8 A New Look at Parabolas graph conic sections, identifying fundamental characteristics (GPS) (MAM3_C ) 3-1 Quadratic Functions and Transformations, LESSON LAB 3-2: Identifying Quadratic Data, 3-7 Quadratic Systems, 3-8 A New Look at Parabolas, 3-9 Circles in the Coordinate Plane write equations of conic sections (including parabolas, circles, ellipses and hyperbolas) given appropriate information (GPS) (MAM3_C ) 3-1 Quadratic Functions and Transformations, LESSON LAB 3-2: Identifying Quadratic Data, 3-7 Quadratic Systems, 3-8 A New Look at Parabolas, 3-9 Circles in the Coordinate Plane plot the point (x, y, z) and identify it as a vertex of a rectangular prism (GPS) (MAM3_C ) apply the distance formula in 3-space (GPS) (MAM3_C ) 2-9 Systems With Three Variables Advanced Algebra: 2-9 Systems With Three Variables, 7-6 Coordinate Algebra: Midpoint and Distance in the Coordinate Plane 9

12 recognize and use equations of planes and spheres (GPS) (MAM3_C ) 3-9 Circles in the Coordinate Plane E - Algebra graph simple polynomial functions as translations of the function f(x) = ax n (GPS) (MAM3_E ) 4-1 Polynomial Functions, TECHNOLOGY LAB 4-1: Even and Odd Functions, 4-3 Polynomials, Linear Factors, and Zeros, ACTIVITY LAB 4-7: Graphing Polynomials Using Zeros, 4-9 Polynomial Models in the Real World, 4-10 Transforming Polynomial Functions analyze the effects of the following on the graph of a polynomial function: degree, lead coefficient and multiplicity of real zeros (GPS) (MAM3_E ) 4-1 Polynomial Functions, TECHNOLOGY LAB 4-1: Even and Odd Functions, 4-3 Polynomials, Linear Factors, and Zeros, ACTIVITY LAB 4-7: Graphing Polynomials Using Zeros, 4-9 Polynomial Models in the Real World, 4-10 Transforming Polynomial Functions determine whether a polynomial function has symmetry and whether it is even, odd or neither (GPS) (MAM3_E ) 4-1 Polynomial Functions, TECHNOLOGY LAB 4-1: Even and Odd Functions investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior (GPS) (MAM3_E ) 4-1 Polynomial Functions, TECHNOLOGY LAB 4-1: Even and Odd Functions, 4-3 Polynomials, Linear Factors, and Zeros, ACTIVITY LAB 4-7: Graphing Polynomials Using Zeros, 4-9 Polynomial Models in the Real World, 4-10 Transforming Polynomial Functions define and understand the properties of nth roots (GPS) (MAM3_E ) 6-1 Roots and Radical Expressions, 6-2 Multiplying and Dividing Radical Expressions, 6-3 Binomial Radical Expressions 10

13 extend properties of exponents to include rational exponents (GPS) (MAM3_E ) 6-4 Rational Exponents define logarithmic functions as inverses of exponential functions (GPS) (MAM3_E ) 7-3 Logarithmic Functions as Inverses, 7-5 Exponential and Logarithmic Equations, TECHNOLOGY LAB 7-5: Using Logarithms for Exponential Models use and explain properties of logarithms by extending laws of exponents (GPS) (MAM3_E ) 7-4 Properties of Logarithms, 7-5 Exponential and Logarithmic Equations investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change (GPS) (MAM3_E ) 7-1 Exploring Exponential Models, 7-2 Properties of Exponential Functions, 7-3 Logarithmic Functions as Inverses, TECHNOLOGY LAB 7-5: Using Logarithms for Exponential Models, 7-6 Natural Logarithms graph functions as transformations of f(x) = a x, f(x) = log a x, f(x) = e x and f(x) = lnx (GPS) (MAM3_E ) 7-1 Exploring Exponential Models, 7-2 Properties of Exponential Functions, 7-3 Logarithmic Functions as Inverses, TECHNOLOGY LAB 7-5: Using Logarithms for Exponential Models, 7-6 Natural Logarithms 11

14 explore real phenomena related to exponential and logarithmic functions including half-life and doubling time (GPS) (MAM3_E ) 7-1 Exploring Exponential Models, 7-2 Properties of Exponential Functions, 7-3 Logarithmic Functions as Inverses, TECHNOLOGY LAB 7-5: Using Logarithms for Exponential Models, 7-6 Natural Logarithms find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem and fundamental theorem of algebra, incorporating complex and radical conjugates (GPS) (MAM3_E ) 4-4 Solving Polynomial Equations, 4-6 Theorems About Roots of Polynomial Equations, 4-7 The Fundamental Theorem of Algebra solve polynomial, exponential and logarithmic equations analytically, graphically and using appropriate technology (GPS) (MAM3_E ) 4-4 Solving Polynomial Equations, 4-6 Theorems About Roots of Polynomial Equations, 4-7 The Fundamental Theorem of Algebra, 7-5 Exponential and Logarithmic Equations, TECHNOLOGY LAB 7-5: Using Logarithms for Exponential Models, 7-6 Natural Logarithms solve polynomial, exponential and logarithmic inequalities analytically, graphically and using appropriate technology and represent solution sets of inequalities using interval notation (GPS) (MAM3_E ) 2-2 Solving Inequalities, 2-6 Two-Variable Inequalities, TECHNOLOGY LAB 5-7b: Rational Inequalities, LESSON LAB 7-6: Exponential and Logarithmic Inequalities solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology (GPS) (MAM3_E ) 2-1 Solving Equations, 3-4 Quadratic Equations, 3-5 Completing the Square, 3-6 The Quadratic Formula, 4-4 Solving Polynomial Equations, 4-6 Theorems About Roots of Polynomial Equations, 5-7 Solving Rational Equations, 6-5 Solving Square Root and Other Radical Equations, 7-5 Exponential and Logarithmic Equations 12

15 add, subtract, multiply and invert matrices choosing appropriate methods including technology (GPS) (MAM3_E ) 2-10 Solving Systems Using Matrices find the determinants and inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology (GPS) (MAM3_E ) 2-10 Solving Systems Using Matrices examine the properties of matrices, contrasting them with properties of real numbers (GPS) (MAM3_E ) 2-10 Solving Systems Using Matrices represent a system of linear equations as a matrix equation (GPS) (MAM3_E ) 2-10 Solving Systems Using Matrices solve matrix equations using inverse matrices (GPS) (MAM3_E ) 2-10 Solving Systems Using Matrices represent and solve realistic problems using systems of linear equations (GPS) (MAM3_E ) 2-7 Solving Systems of Equations, 2-9 Systems With Three Variables, 2-10 Solving Systems Using Matrices solve systems of inequalities in two variables, showing the solutions graphically (GPS) (MAM3_E ) 2-6 Two-Variable Inequalities, 2-8 Systems of Inequalities 13

16 represent and solve realistic problems using linear programming (GPS) (MAM3_E ) 2-6 Two-Variable Inequalities, 2-8 Systems of Inequalities apply matrix representations of vertexedge graphs to represent realistic situations (GPS) (MAM3_E ) 2-10 Solving Systems Using Matrices use matrices to solve problems that can be represented by vertex-edge graphs (GPS) (MAM3_E ) 2-10 Solving Systems Using Matrices F - Data Analysis and Probability create probability histograms of discrete random variables, using both experimental and theoretical probabilities (GPS) (MAM3_F ) 1-4 Normal Distributions solve problems involving probabilities by interpreting a normal distribution as a probability histogram for a continuous random variable (z-scores are used for a general normal distribution) (GPS) (MAM3_F ) 1-4 Normal Distributions, ACTIVITY LAB 1-4b: Margin of Error determine intervals about the mean that include a given percent of data (GPS) (MAM3_F ) 1-4 Normal Distributions, ACTIVITY LAB 1-4b: Margin of Error 14

17 determine the probability that a given value falls within a specified interval (GPS) (MAM3_F ) 1-4 Normal Distributions, ACTIVITY LAB 1-4b: Margin of Error estimate how many items in a population fall within a specified interval (GPS) (MAM3_F ) 1-4 Normal Distributions, ACTIVITY LAB 1-4b: Margin of Error compare experimental and observational studies by posing questions and collecting, analyzing and interpreting data (GPS) (MAM3_F ) 1-1 Analyzing Data, 1-2 Standard Deviation, 1-3 Samples and Surveys, ACTIVITY LAB 1-4a: Probability Distributions, 1-4 Normal Distributions, ACTIVITY LAB 1-4b: Margin of Error, ACTIVITY LAB 1-4c: Drawing Conclusions From Samples G - Reading Across the Curriculum read and discuss mathematical material to establish context for subject matter, develop mathematical vocabulary and to be aware of current research (GPS) (MAM3_G ) Students are provided with opportunities to read and discuss mathematical material throughout the curriculum. 15