CURRICULUM PACING GUIDE GRADE/SUBJECT: Precalculus Vertical Alignment. 1st Nine Weeks 1

Transcription

1 1st Nine Weeks 17 Days B. Exploring the Skills and Strategies Underlying Mathematics 1. Mathematical Processes Learned in the Context of Increasingly Complex Mathematical and Real-Word Problems a. Apply problem-solving skills (e.g., identifying irrelevant or missing information, making conjectures, extracting mathematical meaning, recognizing and performing multiple steps when needed, verifying results in the context of the problem) to the solution of real-world problems. d. Use the language of mathematics to communicate increasingly complex ideas orally and in writing, using symbols and notations correctly. g. Demonstrate the appropriate role of technology (e.g., calculators, software) in mathematics (e.g., organize data develop concepts, explore relationships, decrease time spent on computation after a skill has been established) C. Establishing Number Sense and Operation Skills 1. Foundations a. Identify ad graph piecewise functions, including greatest integer, step, and absolute value functions (CCRS 18) b. Identify, graph, and write equations for inverses and transformations of various functions including polynomial, rational, radical, absolute value, and trigonometric with and without technology (CCRS 20,21,22,23) E. Exploring Polynomial Expressions, Equations, and 2. a. Use algebraic tests to determine whether the graph of a relation is symmetrical (CCRS 16) b. Classify functions as even, odd, or neither. (CCRS 16) F. Exploring Advanced 1. Rational and Radical Expressions, Equations, and a. Graph and analyze radical functions, including square root and cube root functions, with and without technology (CCRS 18) piecewise absolute value polynomial rational radical functions constant decreasing increasing even odd extrema maximum minimum symmetry inverse one-to-one parent function reflection translation roots zeros intercepts ACT Quality Core Unit 1:, Graphs and Their Transformations Analyzing Graphs of and Relations 1.5 Parent and Transformations 1.6 Function Operations and Composition of 1.7 Inverse Relations and 2.1 Power and Radical Brooks/Cole Precalculus with Limits 1.1 Lines in the Plane Graphs of 1.4 Shifting, Reflecting, and Stretching Graphs 1.5 Combination of 1.6 Inverse 1.7 Linear Models Benchmark Mid-unit Test Unit Test 18 Days B. Exploring the Skills and Strategies Underlying Mathematics ACT Quality Core Unit 2: Polynomial and Rational 1st Nine Weeks 1

2 1. Mathematical Processes Learned in the Context of Increasingly Complex Mathematical and Real-Word Problems a. Apply problem-solving skills (e.g., identifying irrelevant or missing information, making conjectures, extracting mathematical meaning, recognizing and performing multiple steps when needed, verifying results in the context of the problem) to the solution of real-world problems. b. Use a variety of strategies to set up and solve increasingly complex problems c. Represent data, real-world situations and solutions in increasingly complex contexts (e.g., expressions, formulas, tables, charts, graphs, relations, functions) and understand the relationships. d. Use the language of mathematics to communicate increasingly complex ideas orally and in writing, using symbols and notations correctly. e. Make appropriate use of estimation and mental mathematics in computations and to determine the reasonableness of solutions to increasingly complex problems. f. Make mathematical connections among concepts, across disciplines, and in everyday experiences. g. Demonstrate the appropriate role of technology (e.g., calculators, software) in mathematics (e.g., organize data develop concepts, explore relationships, decrease time spent on computation after a skill has been established) h. Apply previously learned algebraic and geometric concepts to more advanced problems. E. Exploring Polynomial Expressions, Equations, and 1. Expressions and Equations a. Solve polynomial equations using a variety of methods (e.g., factoring, rational roots theorem) (CCRS 19) b. Use technology to approximate the real roots of a polynomial equation (CCRS 16) 2. a. Use algebraic tests to determine whether the graph of a relation is symmetrical (CCRS 16) Polynomial and Rational 2.2 Polynomial 2.4 Zeros of Polynomial 2.5 Rational Brooks/Cole Precalculus 2.1 Quadratic 2.2 Polynomial of High Degree 2.3 Real Zeros of Polynomial 2.4 Complex Numbers 2.5 The Fundamental Theorem of Algebra 2.6 Rational and Asympototes 2.7 Graphs of Rational 2.8 Quadratic Models 1st Nine Weeks 2

3 b. Classify functions as even, odd, or neither (CCRS 16) F. Exploring Advanced 1. Rational and Radical Expressions, Equations, and b. Graph rational functions using intercepts, symmetry, asymptotes, and removable discontinuities (CCRS 4,16) 1st Nine Weeks 3

4 2nd Nine Weeks 10 Days B. Exploring the Skills and Strategies Underlying Mathematics 1. Mathematical Processes Learned in the Context of Increasingly Complex Mathematical and Real-Word Problems a. Apply problem-solving skills (e.g., identifying irrelevant or missing information, making conjectures, extracting mathematical meaning, recognizing and performing multiple steps when needed, verifying results in the context of the problem) to the solution of real-world problems. b. Use a variety of strategies to set up and solve increasingly complex problems c. Represent data, real-world situations and solutions in increasingly complex contexts (e.g., expressions, formulas, tables, charts, graphs, relations, functions) and understand the relationships. d. Use the language of mathematics to communicate increasingly complex ideas orally and in writing, using symbols and notations correctly. e. Make appropriate use of estimation and mental mathematics in computations and to determine the reasonableness of solutions to increasingly complex problems. f. Make mathematical connections among concepts, across disciplines, and in everyday experiences. g. Demonstrate the appropriate role of technology (e.g., calculators, software) in mathematics (e.g., organize data develop concepts, explore relationships, decrease time spent on computation after a skill has been established) h. Apply previously learned algebraic and geometric concepts to more advanced problems. Conic sections Standard form of conics Elipse, hyperbola, circle, parabola Locus Focus, directrix Major axis, minor axis Vertices, co-vertices ACT Quality Core Unit 7: Conics 7.1 Parabolas 7.2 Elipses and Circles 7.3 Hyperbolas Brooks/Cole Precalculus with Limits 9.1 Conics: Circles and Parabolas 9.2 Ellipses 9.3 Hyperbolas Benchmark Unit Test 2nd Nine Weeks 4

5 D. Exploring Quadratic Equations and 1. Conic Sections a. Graph ellipses and hyperbolas and their translations from given equations or characteristics (CCRS 15) b. Solve systems of conics with and without technology (CCRS 15) c. Convert conic equations in genera form to standard form (CCRS 15,36) d. Determine characteristics of ellipses and hyperbolas from given characteristics ad graphs (CCRS 15) e. Identify and write equations for ellipses and hyperbolas from given characteristics and graphs (CCRS 15,37) A. Prerequisites 18 Days Exponents a. Solve linear, quadratic, rational, and radical equations B. Exploring the Skills and Strategies Underlying Mathematics 1. Mathematical Processes Learned in the Context of Increasingly Complex Mathematical and Real-Word Problems d. Use the language of mathematics to communicate increasingly complex ideas orally and in writing, using symbols and notations correctly. e. Make appropriate use of estimation and mental mathematics in computations and to determine the reasonableness of solutions to increasingly complex problems. f. Make mathematical connections among concepts, across disciplines, and in everyday experiences. Logarithms Exponential functions ACT Quality Core Unit 3: Exponential and Logarithmic 3.1 Exponential 3.2 Logarithmic 3.3 Properties of Logarithms 3.4 Exponential and Logarithmic Equations Brooks/Cole Precalculus with Limits 3.1 Exponential and Their Graphs 3.2 Logarithmic and Their Graphs 3.3 Properties of Logarithms 3.4 Solving Exponential and 2nd Nine Weeks 5

6 g. Demonstrate the appropriate role of technology (e.g., calculators, software) in mathematics (e.g., organize data develop concepts, explore relationships, decrease time spent on computation after a skill has been established) h. Apply previously learned algebraic and geometric concepts to more advanced problems. F. Exploring Advanced 2. Exponential and Logarithmic a. Use properties of exponents to simplify and evaluate expressions involving real exponents. b. Use properties of logarithms to simplify and evaluate expressions involving logarithms (CCRS 18) 3.4 Solving Exponential and Logarithmic Equations 3.5 Exponential and Logarithmic Models c. Solve equations involving real exponents 5 Days d. Solve equations with variable exponents by using logarithms e. Use the natural base e to evaluate exponential expressions, solve exponential expressions, solve exponential equations and graph exponential functions (CCRS 18,25) f. Solve exponential and logarithmic equations and realworld problems involving exponential and logarithmic equation (e.g., compound interest, exponential growth/decay) (CCRS 18,24) H. Using Matrices to Organize Data and Solve Problems 1. Sequences and Series Matrix Reduced row-echelon form ACT Quality Core Unit 6:Matrices, Vectors, and Polar Coordinates 6.1 a. Use matrices to determine the coordinates of polygons under a given transformation (CCRS 11) b. Find the reduced row-echelon form of an augmented matrix to solve systems of equations (CCRS 14) Multivariable Linear Systems and Row Operations Brooks/Cole Precalculus with Limits 7.4 Matrices and Systems of Equations 2nd Nine Weeks 6

7 2nd Nine Weeks 7

8 3rd Nine Weeks 12 Days B. Exploring the Skills and Strategies Underlying Mathematics 1. Mathematical Processes Learned in the Context of Increasingly Complex Mathematical and Real-Word Problems a. Apply problem-solving skills (e.g., identifying irrelevant or missing information, making conjectures, extracting mathematical meaning, recognizing and performing multiple steps when needed, verifying results in the context of the problem) to the solution of real-world problems. b. Use a variety of strategies to set up and solve increasingly complex problems c. Represent data, real-world situations and solutions in increasingly complex contexts (e.g., expressions, formulas, tables, charts, graphs, relations, functions) and understand the relationships. d. Use the language of mathematics to communicate increasingly complex ideas orally and in writing, using symbols and notations correctly. e. Make appropriate use of estimation and mental mathematics in computations and to determine the reasonableness of solutions to increasingly complex problems. f. Make mathematical connections among concepts, across disciplines, and in everyday experiences. g. Demonstrate the appropriate role of technology (e.g., calculators, software) in mathematics (e.g., organize data develop concepts, explore relationships, decrease time spent on computation after a skill has been established) h. Apply previously learned algebraic and geometric concepts to more advanced problems. F. Exploring Advanced 3. Trigonometric and Periodic a. Use various methods to find the area of a triangle (e.g., given the length of two sides and the included angle) (CCRS 35) Heron's Formula Period, phase shift, vertical translations, stretch, shrink Sine, cosine, tangent, secant, secant, cotangent Arcine, arccosine, arctangent ACT Quality Core Unit 4: Trigonometric 4.1 Right Triangle Trigonometry 4.2 Degrees and Radians 4.3 Trigonometric on the Unit Circle 4.4 Graphing Sine and Cosine 4.5 Graphing Other Trigonometric 4.6 Inverse Trigonometric 4.7 Law of Sines and Law of Cosines Brooks/Cole Precalculus with Limits 4.1 Radian and Degree Measure 4.2 Trigonometric : The Unit Circle 4.3 Right Triangle Trigonometry 4.4 Trigonometric of Any Angle 4.5 Graphs of Sine and Cosine 4.6 Graphs of Other Trigonometric 4.7 Inverse Trigonometric Benchmark Mid-Unit Test Unit Test 3rd Nine Weeks 8

9 3rd Nine Weeks 16 Days b. Graph tangent, cotangent, secant, and cosecant functions and their transformations c. State the amplitude, period, phase, and vertical translation of transformations of the sine and cosine functions (CCRS 26) d. Graph transformations (e.g., vertical and horizontal translations, reflections, stretches) of the sine and cosine functions (CCRS 29) e. Determine periodicity and amplitude from graphs, stretch and shrink graphs both vertically and horizontally, and translate graphs (CCRS 30) f. Graph and write the equations of sine and cosine functions given the amplitude, period, phase shift, and vertical translation; use the functions to model real-life situations (e.g. spring problems, ocean tides) (CCRS 31,32) B. Exploring the Skills and Strategies Underlying Mathematics 1. Mathematical Processes Learned in the Context of Increasingly Complex Mathematical and Real-Word Problems a. Apply problem-solving skills (e.g., identifying irrelevant or missing information, making conjectures, extracting mathematical meaning, recognizing and performing multiple steps when needed, verifying results in the context of the problem) to the solution of real-world problems. b. Use a variety of strategies to set up and solve increasingly complex problems c. Represent data, real-world situations and solutions in increasingly complex contexts (e.g., expressions, formulas, tables, charts, graphs, relations, functions) and understand the relationships. d. Use the language of mathematics to communicate increasingly complex ideas orally and in writing, using symbols and notations correctly. e. Make appropriate use of estimation and mental mathematics in computations and to determine the reasonableness of solutions to increasingly complex problems. Trigonometric identity Sum and Difference identities Double-angle, Half-angle formulas 4.7 Inverse Trigonometric 4.8 Applications and Models ACT Quality Core Unit 5: Trigonometric Identities and Equations 5.1 Trigonometric Identities 5.2 Verifying Trigonometric Equations 5.3 Solving Trigonometric Equations 5.4 Sum and Difference Identities 5.5 Multiple-Angle and Productto-Sum Identities Brooks/Cole Precalculus with Limits 5.1 Using Fundamental Identities 5.2 Verifying Trigonometric Identities 5.3 Solving Trigonometric Equations 3rd Nine Weeks 9

10 f. Make mathematical connections among concepts, across disciplines, and in everyday experiences. g. Demonstrate the appropriate role of technology (e.g., calculators, software) in mathematics (e.g., organize data develop concepts, explore relationships, decrease time spent on computation after a skill has been established) h. Apply previously learned algebraic and geometric concepts to more advanced problems. E. Exploring Polynomial Expressions, Equations, and 1. Expressions and Equations a. Solve polynomial equations using a variety of methods (e.g., factoring, rational roots theorem) (CCRS 16) b. Use technology to approximate the real roots of a polynomial equation (CCRS 18) 2. a. Use algebraic tests to determine whether the graph of a relation is symmetrical (CCRS 16,18) b. Classify functions as even, odd, or neither (CCRS 16) F. Exploring Advanced 3. Trigonometric and Periodic g. Identify the sum and difference identities for sine, cosine, and tangent functions; apply the identities to solve mathematical problems (CCRS 27) h. Derive, identify, and apply double-angle and half-angle formulas to solve mathematical problems (CCRS 33,34) I Apply the fundamental trigonometric identities, the doubleangle and half-angle identities, and the sum and difference identities to simplify and evaluate trigonometric expressions and prove trigonometric identities (CCRS 33,34) j. Use trigonometric identities or technology to solve trigonometric equations (CCRS 34) l. Use and evaluate inverse sine, cosine, and tangent functions to solve trigonometric equations (CCRS 22,23) Equations 5.4 Sum and Difference Formulas 5.5 Multiple-Angle and Productto-Sum Formulas 3rd Nine Weeks 10

11 3rd Nine Weeks 7 Days B. Exploring the Skills and Strategies Underlying Mathematics 1. Mathematical Processes Learned in the Context of Increasingly Complex Mathematical and Real-Word Problems a. Apply problem-solving skills (e.g., identifying irrelevant or missing information, making conjectures, extracting mathematical meaning, recognizing and performing multiple steps when needed, verifying results in the context of the problem) to the solution of real-world problems. b. Use a variety of strategies to set up and solve increasingly complex problems c. Represent data, real-world situations and solutions in increasingly complex contexts (e.g., expressions, formulas, tables, charts, graphs, relations, functions) and understand the relationships. d. Use the language of mathematics to communicate increasingly complex ideas orally and in writing, using symbols and notations correctly. e. Make appropriate use of estimation and mental mathematics in computations and to determine the reasonableness of solutions to increasingly complex problems. f. Make mathematical connections among concepts, across disciplines, and in everyday experiences. g. Demonstrate the appropriate role of technology (e.g., calculators, software) in mathematics (e.g., organize data develop concepts, explore relationships, decrease time spent on computation after a skill has been established) h. Apply previously learned algebraic and geometric concepts to more advanced problems. I. Exploring Polar Coordinates and Vectors 1. Polar Coordinates and Vectors a. Define polar coordinates to locate a point on a graph (CCRS 1) b. Graph polar functions by plotting points and by using technology (CCRS 1) Polar coordinates DeMoivre's theorem ACT Quality Core Unit 6: Polar Coordinates 9.1 Polar Coordinates 9.2 Graphs of Polar Equations 9.3 Polar and Rectangular Forms of Equations 9.5 Complex Numbers and DeMoivre's Theorem Brooks/Cole Precalculus with Limits 9.4 Parametric Equations 9.5 Polar Coordinates 9.6 Graphs of Polar Equations 10.2 Vectors in Space 103 Vecctors in Space 3rd Nine Weeks 11

12 c. Express two-dimensional points and equations in rectangular and polar coordinates (CCRS 1) d. Find powers and roots of complex numbers in polar form using De Moivre s Theorem (CCRS 1) 3rd Nine Weeks 12

13 Time Frame 4th Nine Weeks 10 Days B. Exploring the Skills and Strategies Underlying Mathematics 1. Mathematical Processes Learned in the Context of Increasingly Complex Mathematical and Real-Word Problems a. Apply problem-solving skills (e.g., identifying irrelevant or missing information, making conjectures, extracting mathematical meaning, recognizing and performing multiple steps when needed, verifying results in the context of the problem) to the solution of real-world problems. b. Use a variety of strategies to set up and solve increasingly complex problems c. Represent data, real-world situations and solutions in increasingly complex contexts (e.g., expressions, formulas, tables, charts, graphs, relations, functions) and understand the relationships. d. Use the language of mathematics to communicate increasingly complex ideas orally and in writing, using symbols and notations correctly. e. Make appropriate use of estimation and mental mathematics in computations and to determine the reasonableness of solutions to increasingly complex problems. f. Make mathematical connections among concepts, across disciplines, and in everyday experiences. g. Demonstrate the appropriate role of technology (e.g., calculators, software) in mathematics (e.g., organize data develop concepts, explore relationships, decrease time spent on computation after a skill has been established) h. Apply previously learned algebraic and geometric concepts to more advanced problems. I. Exploring Polar Coordinates and Vectors e. Graphically add and subtract vectors and perform scalar multiplication (CCRS 8,9) f. Use coordinates to perform vector operations and to determine the magnitude and direction of vector (CCRS 2,5,8) g. Use the dot product to calculate the angle between two vectors (CCRS 7) h. Resolve a vector into horizontal and vertical components. (CCRS 6) i. Solve real world problems involving vector displacements (e.g. airplane in the wind, weight of an object on a ramp) (CCRS 7) j. Graph parametric equations and write parametric equations of lines. (CCRS 28) College/Career- Ready Academic magnitude, direction, dot product, components, parametric equations ACT Quality Core 6: Vectors 8.1 Introduction to Vectors 8.2 Vectors in the Coordinate Plane 8.3 Dot Products and Vector Projections Brooks/Cole Precalculus with Limits 10.2 Vectors in space 10.3 Vectors in space Benchmark Mid-Unit Test Unit Test 4th Nine Infinite sequence ACT Quality Core Unit 8: 4th Nine Weeks 13

14 Time Frame 4th Nine Weeks 10 Days 4th nine weeks B. Exploring the Skills and Strategies Underlying Mathematics 1. Mathematical Processes Learned in the Context of Increasingly Complex Mathematical and Real-Word Problems a. Apply problem-solving skills (e.g., identifying irrelevant or missing information, making conjectures, extracting mathematical meaning, recognizing and performing multiple steps when needed, verifying results in the context of the problem) to the solution of real-world problems. b. Use a variety of strategies to set up and solve increasingly complex problems c. Represent data, real-world situations and solutions in increasingly complex contexts (e.g., expressions, formulas, tables, charts, graphs, relations, functions) and understand the relationships. d. Use the language of mathematics to communicate increasingly complex ideas orally and in writing, using symbols and notations correctly. e. Make appropriate use of estimation and mental mathematics in computations and to determine the reasonableness of solutions to increasingly complex problems. f. Make mathematical connections among concepts, across disciplines, and in everyday experiences. g. Demonstrate the appropriate role of technology (e.g., calculators, software) in mathematics (e.g., organize data develop concepts, explore relationships, decrease time spent on computation after a skill has been established) h. Apply previously learned algebraic and geometric concepts to more advanced problems. E. Exploring Polynomial expressions, Equations, and 2. f. Use limits to approximate the slope of a curve at a point (CCRS 4,17) g. Use limits to approximate the area under a curve (CCRS 4) G.Organizing and Analyzing Data and Applying Probability 2. Series and Sequences a. find the sum of a infinite geometric series (CCRS 12) b. Find or estimate the limit of an infinite sequence or determine that the limit does not exist (CCRS 12) c. Use the mathematical induction to prove the validity of mathematical sequences (CCRS 12) B. Exploring the Skills and Strategies Underlying Mathematics College/Career- Ready Academic Infinite sequence Geometric series limit normal distribution variance ACT Quality Core Unit 8: Sequence and Series 10.3 Geometric Sequences and Series 10.4 Mathematical Induction Brooks/cole Precalculus with Limits 8.1 Sequences and Series 8.3 Geometric Sequences and Series 11.1 Introduction to Limits 11.2 Techniques for Evaluating Limits 11.3 The Tangent ACT Quality Core Unit 9: Data Relations, Probability and Statistics Benchmark Mid-Unit Test Unit Test 4th Nine Weeks 14

15 Time Frame weeks 7days 1. Mathematical Processes Learned in the Context of Increasingly Complex Mathematical and Real-Word Problems a. Apply problem-solving skills (e.g., identifying irrelevant or missing information, making conjectures, extracting mathematical meaning, recognizing and performing multiple steps when needed, verifying results in the context of the problem) to the solution of real-world problems. b. Use a variety of strategies to set up and solve increasingly complex problems c. Represent data, real-world situations and solutions in increasingly complex contexts (e.g., expressions, formulas, tables, charts, graphs, relations, functions) and understand the relationships. d. Use the language of mathematics to communicate increasingly complex ideas orally and in writing, using symbols and notations correctly. e. Make appropriate use of estimation and mental mathematics in computations and to determine the reasonableness of solutions to increasingly complex problems. f. Make mathematical connections among concepts, across disciplines, and in everyday experiences. g. Demonstrate the appropriate role of technology (e.g., calculators, software) in mathematics (e.g., organize data develop concepts, explore relationships, decrease time spent on computation after a skill has been established) h. Apply previously learned algebraic and geometric concepts to more advanced problems. G. Organizing and Analyzing Data and Applying Probability 1. Data relations, Probability, and Statistics a. Use the standard normal curve to study properties of normal distributions of date (e.g., give percent of data within a given interval) (CCRS 39,49) b. Identify uniform, skewed, and normal distributions in a set of of data (CCRS 40) c. Determine the quartiles and interquartile range for a set of data (CCRS 39) d. Recognize different types of sampling procedures and identify their strengths and limitations.(ccrs 45,46) e. Estimate population characteristics based on samples.(43,44,47,48,50) f. Find the variance and standard deviation of a set of data and convert data to standard values (CCRS 41,42) College/Career- Ready variance Academic standard deviation normal distribution variance standard deviation Statistics Brooks/Precalculus with limits 8.6 Probability 4th Nine Weeks 15

16 Time Frame College/Career- Ready Academic 4th Nine Weeks 16