HADDONFIELD PUBLIC SCHOOLS Curriculum Map for Advanced Precalculus/Chapter 1
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1 Curriculum Map for Advanced Precalculus/Chapter 1 September 1 September 30 (16 days) Targeted Standard(s): NJCCCS 4.3A Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B Enduring Understandings (The big ideas): Algebraic representation can be used to generalize patterns and relationships Essential Questions: What is a relation? When is a relation also a function? How is the composite of functions formed? What are inverse functions? What is a zero of a function? Concepts What students will know Core Content/Objectives Skills What students will be able to do Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Instructional Actions Assessment How learning will be assessed Chapter 1 Linear Relations & Functions 1-1 Relations & Functions 1-2 Composition & Inverses of Functions 1-3 Linear Functions & Inequalities 1-4 Distance & Slope 1-5 Forms of Linear Equations 1-6 Parallel & Perpendicular Lines Determine whether a given relation is a function Identify the domain & range of any relation or function Perform operations with functions Find composite functions Find & recognize inverse functions Find zeros of linear functions Graph linear equations and inequalities Practice worksheets (1-1 to 1-6) Board races Quiz on Lessons 1-1 to 1-3 Quiz on Lessons 1-4 to 1-6 Test on Lessons 1-1 to 1-6 Reviewed 9-09 Page 1
2 Find the distance between 2 points Find the slope of a line through two points Find the midpoint of a line segment Write linear equations using slope-intercept form Write linear equations using point-slope form Write equations of parallel & perpendicular lines Write equations of lines in standard form Resources/Technology: TI83 graphing calculator TI83 overhead graphing calculator Reviewed 9-09 Page 2
3 Curriculum Map for Advanced Precalculus Chapter 2 October 1 October 22 (14 days) Targeted Standard(s): NJCCCS 4.3B Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B Enduring Understandings (The big ideas): Patterns and relationships can be represented graphically, numerically, symbolically or verbally. Essential Questions: What is a system of equations? How can a system of equations be solved algebraically? How can matrices be used to solve systems? How can we identify the solution of a system of inequalities? Concepts What students will know Core Content/Objectives Chapter 2 Systems of Equations & Inequalities 2-1 Solving Systems of Equations 2-2 Introduction to Matrices 2-3 Determinants & Multiplicative Inverses 2-4 Solving Systems of Equations by Using Matrices 2-5 Solving Systems of Inequalities Skills What students will be able to do Solve systems of equations graphically by hand and by the calculator Solve systems of equations algebraically by elimination and by substitution Add, subtract and multiply matrices Evaluate determinants Find inverses of matrices Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Practice worksheets (2-1 to 2-5) Solve a system by 5 methods Instructional Actions Assessment How learning will be assessed Quiz on Lessons 2-1 to 2-3 Quiz on Lessons 2-4 to 2-5 Test on Lessons 2-1 to 2-5 Reviewed 9-09 Page 3
4 Solve systems of equations by using inverses of matrices Solve systems of equations by using augmented matrices (calculator only) Graph systems of inequalities Resources/Technology: TI83 graphing calculator TI83 overhead graphing calculator Reviewed 9-09 Page 4
5 Curriculum Map for Advanced Precalculus Linear Programming October 23 November 5 (10 days) Targeted Standard(s): NJCCCS 4.3.C Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B Enduring Understandings (The big ideas): Mathematical models can be used to describe and quantify physical relationships. Essential Questions: How can linear programming be used to solve real world problems? Concepts What students will know Core Content/Objectives Skills What students will be able to do Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Instructional Actions Assessment How learning will be assessed Chapter Linear Programming 1. Find the maximum or minimum value of a function defined for a polygonal convex set 2. Use linear programming procedures to solve problems 3. Recognize situations where exactly one solution to a linear programming problem may not exist Practice sheet on inequalities & feasible regions Introductory problems on linear programming Linear programming problem set Problem set Quiz Reviewed 9-09 Page 5
6 Resources/Technology: TI83 graphing calculator TI83 overhead graphing calculator Reviewed 9-09 Page 6
7 Curriculum Map for Advanced Precalculus Chapter 3 Targeted Standard(s): NJCCCS 4.3.B Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B Enduring Understandings (The big ideas): Patterns and relationships can be represented graphically, numerically, symbolically or verbally. Essential Questions: How can symmetry be used in graphing relations? What are the basic graphs with which students should be familiar? What is an asymptote and how can we use asymptotes in graphing? What are even and odd functions? How do we determine when a graph has a hole? Concepts What students will know Core Content/Objectives Skills What students will be able to do Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Instructional Actions Assessment How learning will be assessed Chapter 3 The Nature of Graphs 3-1 Symmetry 3-2 Families of Graphs 3-3 Inverse Functions & Relations 3-4 Rational Functions & Asymptotes 3-5 Graphs of Inequalities 3-6 Tangent to a Curve 3-7 Graphs & Critical Points of Polynomial Functions Identify symmetrical graphs Use symmetry to complete a graph Identify an odd function and an even function Identify the graphs of simple polynomial functions, absolute value functions and step functions Sketch the graphs of these functions Determine the inverse Practice worksheets (3-1 to 3-7) Sheet on horizontal and vertical asymptotes and holes Quiz on Lessons 3-1 to 3-3 Quiz on Lessons 3-4 & 3-5 Quiz on Lessons 3-6 & 3-7 Test on Lessons 3-1 to 3-7 Reviewed 9-09 Page 7
8 of a relation or function Graph a function and its inverse Determine horizontal and vertical asymptotes and holes in graphs Graph rational functions Graph polynomial, absolute value and radical inequalities Find the derivative of a function Find the slope and the equation of the line tangent to the graph of a function at a given point Resources/Technology: TI83 graphing calculator TI83 overhead graphing calculator Reviewed 9-09 Page 8
9 Curriculum Map for Advanced Precalculus Chapter December 4 December 22 (13 days) Targeted Standard(s): NJCCCS 4.3.D Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B Enduring Understandings (The big ideas): Algebraic and numerous procedures are interconnected and build on one another to produce a coherent whole. Essential Questions: What is the fundamental theorem of Algebra? How can the remainder and the factor theorem be used to find roots? How is the discriminant used to analyze the roots of a quadratic? How is the rational root theorem used to solve a polynomial equation? Concepts What students will know Core Content/Objectives Skills What students will be able to do Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Instructional Actions Assessment How learning will be assessed Chapter 4 Polynomial & Rational Functions 4-1 Polynomial Functions 4-2 Quadratic Equation & Inequalities 4-3 The Remainder & Factor Theorem 4-4 The Rational Root Theorem 4-5 Locating the Zeros of a Function Determine roots of polynomial equations Apply the fundamental theorem of algebra Solve quadratic equations Use the discriminant to describe the roots of quadratic equations Graph quadratic equations and inequalities Find the factors of polynomials using the Practice worksheets (4-1 to 4-5) Long division sheet White board group activity to find the real roots Quiz on Lessons 4-1 to 4-2 Quiz on Lessons 4-3 to 4-5 White board activity Test on Lessons 4-1 to 4-5 Reviewed 9-09 Page 9
10 Resources/Technology: remainder and factor theorems Identify all possible rational roots of a polynomial equation by using the rational root theorem Determine the number of positive and negative real zeros a polynomial function has Approximate the real zeros of a polynomial function Graph polynomial functions TI83 graphing calculator TI83 overhead graphing calculator Reviewed 9-09 Page 10
11 Curriculum Map for Advanced Precalculus Chapter January 5 January 23 (14 days) Targeted Standard(s): NJCCCS 4.3.D Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B Enduring Understandings (The big ideas): Algebraic and numerous procedures are interconnected and build on one another to produce a coherent whole. Essential Questions: How can we use factoring and common denominators to solve rational algebraic equations? How do we solve an equation that contains a radical? How do we solve an equation with more than one radical? Concepts What students will know Core Content/Objectives Skills What students will be able to do Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Instructional Actions Assessment How learning will be assessed Chapter 4 - Polynomial & Rational Functions 4-6 Rational Equations & Partial Functions 4-7 Radical Equations & Inequalities Find the least common denominator of rational expressions Solve rational equations and inequalities Solve radical equations and inequalities Practice worksheets (4-6 & 4-7) Quiz on Lessons 4-6 to 4-7 Test on Lessons 4-6 to 4-7 Mid-Term Exam Reviewed 9-09 Page 11
12 Resources/Technology: TI83 graphing calculator TI83 overhead graphing calculator Reviewed 9-09 Page 12
13 Curriculum Map for Advanced Precalculus Chapter 10 February 2 March 4 (21 days) Targeted Standard(s): NJCCCS 4.3.C Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B Enduring Understandings (The big ideas): Physical models can be used to clarify mathematical relationships. Essential Questions: What are the conic sections? What are the basic forms of the equations for circles, parabolas, ellipses, and hyperbolas? How do we sketch graphs of the conics involving translations? Concepts What students will know Core Content/Objectives Skills What students will be able to do Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Instructional Actions Assessment How learning will be assessed Chapter 10 Conics 10-1 The Circle 10-2 The Parabola 10-3 The Ellipse 10-4 The Hyperbola 10-5 Conic Sections 10-6 Transformations of Conics 10-7 Systems of Second-Degree Equations and Inequalities (optional) Use the standard and general forms of the equation of a circle Graph circles Use the standard and general forms of the equation of a parabola Graph parabolas Use the standard and general forms of the equation of an ellipse Graph ellipses Use the standard and general forms of the equation of a hyperbola Graph hyperbolas Recognize conic sections by Practice worksheets (10-1 to 10-7) Review sheet on 10-1 to 10-3 Review sheet on 10-1 to 10-4 Rose garden authentic assessment Alternate authentic assessment using conics Quiz on Lesson 10-1 Quiz on Lesson 10-2 Quiz on Lesson 10-3 Quiz on Lesson 10-4 Quiz on Lesson 10-5 to 10-7 Test on Lesson 10-1 to 10-7 Reviewed 9-09 Page 13
14 Resources/Technology: their equations Find the equations of conic sections that have been translated Identify the equations of conic sections that have been rotated Graph and solve systems of second-degree equations and inequalities (optional) TI83 graphing calculator TI83 overhead graphing calculator Reviewed 9-09 Page 14
15 Curriculum Map for Advanced Precalculus Chapter 11 Targeted Standard(s): NJCCCS 4.3.C Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B March 5 April 2 (21 days) Enduring Understandings (The big ideas): Mathematical models can be used to describe and quantify physical relationships. Essential Questions: What are the properties of exponents and logarithms? How do we use the properties of exponents and logarithms? How do we solve equations using these properties? What are the graphs of exponential and logarithmic functions? Concepts What students will know Core Content/Objectives Skills What students will be able to do Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Instructional Actions Assessment How learning will be assessed Chapter 11 Exponential and Logarithmic Functions 11-1 Rational Exponents 11-2 Exponential Functions 11-3 The Number e 11-4 Logarithmic Functions 11-6 Exponential and Logarithmic Equations 11-7 Natural Logarithms Use the properties of exponents Evaluate and simplify expressions containing rational exponents Evaluate expressions with irrational exponents Graph exponential functions Graph exponential inequalities Use the exponential Practice worksheets on exponents Practice worksheets on logarithms Quiz on Lesson 11-1 Quiz on Lessons 11-2 & 11-3 Test on Lessons 11-1 to 11-4, 11-6 and 11-7 Reviewed 9-09 Page 15
16 Resources/Technology: function y=e^x Evaluate expressions involving logarithms Solve equations involving logarithms Graph logarithmic functions and inequalities Solve exponential and logarithmic equations Find natural logarithms of numbers Solve equations using natural logarithms TI83 graphing calculator TI83 overhead graphing calculator Reviewed 9-09 Page 16
17 Curriculum Map for Advanced Precalculus Chapter 9 Targeted Standard(s): NJCCCS 4.3.C Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B April 13 May 1 (15 days) Enduring Understandings (The big ideas): Physical models can be used to clarify mathematical relationships. Essential Questions: How are points graphed by their polar coordinates? How do we convert from polar to rectangular coordinates by calculator and by hand? How are complex numbers written in polar form? How is DeMoivre s Theorem used to find powers and roots of numbers in polar form? Concepts What students will know Core Content/Objectives Skills What students will be able to do Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Instructional Actions Assessment How learning will be assessed Chapter 9 Polar Coordinates & Complex Numbers 9-1 Polar Coordinates 9-2 Graphs of Polar Equations 9-3 Polar & Rectangular Coordinates 9-5 Simplifying Complex Numbers 9-6 Polar Form of Complex Numbers 9-7 Product & Quotients of Complex Numbers 9-8 Powers & Roots of Complex Numbers Graph polar coordinates and simple polar equations Graph polar equations Convert from polar coordinates to rectangular coordinates and vice versa Write the polar form of a linear equation Add, subtract, multiply, and divide complex numbers in rectangular form Change complex numbers from Practice worksheets (9-1 to 9-3, 9-5 to 9-8) Polar graph activity sheets Polar graph project Polar graph project Quiz on Lessons 9-1 & 9-2 Quiz on Lessons 9-3 & 9-5 Quiz on Lessons 9-6 to 9-8 Test on Lessons 9-1 to 9-3, 9-5 to 9-8 Reviewed 9-09 Page 17
18 rectangular to polar form and vice versa Find the product and quotient of complex numbers in polar form Find the powers and roots of complex numbers in polar form using DeMoivre s theorem Resources/Technology: TI83 graphing calculator TI83 overhead graphing calculator Reviewed 9-09 Page 18
19 Curriculum Map for Advanced Precalculus Chapter 12 Targeted Standard(s): NJCCCS 4.3.A Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B May 4 June 3 (22 days) Enduring Understandings (The big ideas): Algebraic representations can be used to generalize patterns and relationships. Essential Questions: How do you identify arithmetic, geometric and infinite sequences? How do you find the sum of arithmetic, geometric and infinite series? How do we use the binomial theorem to expand binomials? Concepts What students will know Core Content/Objectives Skills What students will be able to do Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Instructional Actions Assessment How learning will be assessed Chapter 12 Sequences and Series 12-1 Arithmetic Sequences and Series 12-2 Geometric Sequences and Series 12-3 Infinite Sequences and Series 12-4 Convergent and Divergent Series 12-5 Sigma Notation and the nth Term 12-6 The Binomial Theorem 12-7 Special Sequences and Series Find the nth term and arithmetic means of an arithmetic sequence Find the sum of n terms of an arithmetic series Find the nth term and geometric means of a geometric sequence Find the sum of n terms of a geometric series Find the limit of the terms of an infinite Practice worksheets 12-1 to 12-7 Quiz on 12-1 Quiz on 12-2 Quiz on 12-5 & 12-6 Mini-quizzes Test on Chapter 12 Final Exam Reviewed 9-09 Page 19
20 sequence Find the sum of an infinite geometric series Determine whether a series is convergent or divergent Use sigma notation Use the binomial theorem to expand binomials Evaluate e^x by using the exponential series (if time allows) Use Euler s formula to write the exponential form of a complex number (if time allows) Evaluate the logarithms of negative numbers (if time allows) Resources/Technology: TI83 graphing calculator TI83 overhead graphing calculator Reviewed 9-09 Page 20
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