Pre-Calculus LAWRENCE HIGH SCHOOL PRE-CALCULUS CURRICULUM MAP Updated 8/10/15 + denotes a Honors level concept

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1 Pre-Calculus LAWRENCE HIGH SCHOOL PRE-CALCULUS CURRICULUM MAP Quarter 1 8/24-10/30 Chapter 1 - Analyzing Trigonometric Functions 1A - The Cosine and Sine Functions 1B - Other Trigonometric Functions 1C - Sinusoidal Fnctions and their Graphs Chapter 2 - Complex Numbers and Trigonometry 2A* - Graphing Complex numbers Quarter 2 11/2-1/22 2B - Trigonometric Identites Chapter 3 - Analysis of Functions 3A - Polynomial Functions 3B - Rational Functions 3C - Exponential and Logarithmic Functions Quarter 3 1/25-4/8 Chapter 4 - Combinatorics 4B* - Permutations and Combinations Chapter 5 - Functions and Tables 5B - Fitting Functions to Tables - Newton's Difference Formula Chapter 6 - Analytic Geometry 6A - Coordinate Geometry 6B - Conic Sections Quarter 4 4/11-6/14 Chapter 8 - Ideas of Calculus 8A - Finding Areas of Shapes 8B* - Finding Areas Under Curves 8C* - A Function Emerges

2 The following are a list of essential standards for this course and a brief map of where they will be addressed. Standard Quarter 1 Quarter 2 Quarter 3 Quarter 4 F.TF.1 F.TF.2 F.TF.3 F.TF.4 F.TF.5 F.TF.6 F.TF.7 F.TF.8 F.TF.9 F.IF.4 F.IF.5 F.IF.6 F.IF.7 F.IF.8 F.BF.1 F.BF.2 F.BF.3 F.BF.4 F.BF.5 A.SSE.1 A.SSE.2 A.SSE.3 A.SSE.4 A.REI.1 A.REI.4 G.SQRT.7 +N.CN.1

3 Standard Quarter 1 Quarter 2 Quarter 3 Quarter 4 +N.CN.2 +N.CN.3 N.CN.5 A.APR.2 A.APR.3 +A.APR.4 A.APR.6 A.APR.7 A.REI.2 A.REI.4 A.REI.10 A.REI.11 A.CED.2 A.CED.4 F.LE.1 F.LE.4 F.LE.5 N.VM.6 N.RN.2 G.GPE.1 G.GPE.2 G.GPE.3 G.GPE.4 G.GMD.4 N.Q.2 Note: Quarter Four covers introductory topics in Calculus which are not covered in the common core.

4 Chapter 1: Analyzing Trigonometric Functions CIA: 10/26-10/30/15 Data Meeting: Goals: Students will be introduced to radian measure. Students will review the graphs of the cosine and sine functions, and develop an understanding of a periodic function. They also begin to solve equations that involve cosine and sine. Students review the graphs of tangent, secant, cosecant, and cotangent. They look at how they fit on the unit circle and work with some basic identities. Students will also learn how domain, range, inverse, and one-to-one apply to these functions. Students will be able to apply the rules of functions to all sinusoidal functions and will be able to transform them on the coordinate plane. Where are the turning points of the cosine and sine functions? What is a radian? How can you use a graph to estimate solutions? How are the six trigonometric functions defined? Given the maximum and minimum values of cosine and sine function, how do you find the amplitude and vertical displacement? How can you make a sinusoidal function that has a specific period? How can you use sinusoidal functions to model periodic phenomena? Understand the relationship between degree and radian measure as the arc on the unit circle subtended by a central angle Relate the motion of an object around a circle to the graphs of the cosine and sine functions Solve equations that involve sine and cosine Understand several relationships between the tangent function and the unit circle Sketch and describe the graph of the tangent function Recognize three other trigonometric functions: secant, cosecant, and cotangent Make sense of sinusoidal functions in the context of previous experience Understand the geometry of sinusoidal functions Model with sinusoidal functions F.TF.1; F.TF.2; F.TF.3; F.TF.4; F.TF.5; F.TF.6; F.TF.7; F.TF.8; F.IF.4; F.IF.5; F.IF.6; F.IF.7; F.BF.1; F.BF.3; F.BF.4; A.SSE.1; A.SSE.3; A.REI.1; A.REI.4; G.SQRT.7 increasing; decreasing; maximum; minimum; amplitude; arc; asymptote; central angle; inverse function; period; periodic; phase shift; Pythagorean Identity; radian; secant line; sinusoidal function; turning point; vertical displacement investigation reflections; mid chapter test; end of unit test

5 11/9/15 Rubrics: 21 st Century Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Expectations Civic: Utilize networking skills and engage inclusively with others RETELL Strategies 7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around Texts/Resources Precalculus: common core CME Project

6 Chapter 2: Complex Numbers and Trigonometry CIA: 10/26-10/30/15 Data Meeting: 11/9/15 21 st Century Expectations RETELL Strategies Texts/Resources Goals: +Students will explore polar form as a way to represent complex numbers. +This chapter will highlight the connection between complex numbers and transformational geometry. Students will explore ways to build and prove trigonometric formulas and identities. +How can you write a complex number using trigonometry? +What are the magnitude and argument of a complex number, and how do you find them? +How do you use geometry to add and multiply complex numbers? How can you see if an equation might be an identity? How can you use complex numbers to find formulas for cos 2x and sin 2x? How can you use identities to prove other identities? +Represent complex numbers using both rectangular coordinates and polar coordinates +Determine the magnitude and argument of any complex number +Decide when its best to use either rectangular or polar coordinates to represent complex numbers Test trigonometric equations to predict Show the basic addition rules for cosine and sine using the Multiplication Law for complex numbers Use Pythagorean identities and algebra to prove that a trigonometric equation is an identity +N.CN.1; +N.CN.2; +N.CN.3; +A.APR.4; +A.REI.4; F.TF.8; F.TF.9; N.CN.5; A.SSE.1; A.SSE.2; A.CED.4; G.SRT.7 magnitude; norm; rectangular coordinates; identically equal; identity; absolute value of a complex number; argument; conjugate; modulus; polar coordinates; polar form of complex numbers; rectangular form of complex numbers investigation reflections; mid chapter test; end of unit test Rubrics: Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Civic: Utilize networking skills and engage inclusively with others 7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around Precalculus: common core CME Project

7 Chapter 3: Analysis of Functions Midterms: 1/19-1/22/16 Data Meeting: Goals: Students will explore the graphs of many different polynomial functions and develop a general description of the properties of these functions. Students will explore the graphs of rational functions. Students will analyze exponential and logarithmic functions. How can you graph a polynomial function given its factored form? How can you determine a polynomial s behavior at very large or very small inputs? How can you use long division to find equations of secant or tangent lines to the graph of a polynomial function? What happens to a rational function as x gets larger and larger? Why do some rational functions look so different from each other? How can you find tangent lines to rational functions? What happens when interest is compounded more and more frequently? What are some reasons to introduce the number e? How can you relate any exponential or logarithmic function to f(x) = e x and g(x) = ln x? State the Change of Sign Theorem and the Intermediate Value Theorem for Polynomials, and use them to analyze the graphs of polynomial functions Find the equation of a line secant to a polynomial function and the average rate of change of a function between two points Write the Taylor expansion for a polynomial function about a point Find the equation of the tangent to a polynomial curve at a point Sketch the graph of a rational function, including asymptotes and holes Evaluate limits of rational expressions Find the equation of the tangent to the graph of a rational function at a point State and use the limit and factorial definitions of e and e x Use the inverse relationship between e x and ln x to slove equations Find an equation for the line tangent to the graph of y = e x or y = ln x at a point A.SSE.3; A.SSE.4; A.APR.2; A.APR.3; A.APR.6; A.APR.7; A.CED.2; A.REI.2; A.REI.11; F.IF.4; F.IF.6; F.IF.7; F.IF.8; F.BF.1; F.BF.3; F.BF.4; F.BF.5; F.LE.1; F.LE.4; F.LE.5; N.VM.6; N.RN.2 average rate of change; continuous; hole; instantaneous speed; power function; rational function; removable discontinuity; continuously compounded interest; determinant; e; infinite discontinuity; linear fractional transformation; natural logarithm; reciprocal function; secant line; structure preserving map; tangent line; Taylor expansion investigation reflections; mid chapter test; end of unit test

8 2/1/16 Rubrics: 21 st Century Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Expectations Civic: Utilize networking skills and engage inclusively with others RETELL Strategies 7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around Texts/Resources Precalculus: common core CME Project

9 Chapter 4 Combinatorics CIA: 4/4-4/8/16 Data Meeting: 4/25/16 21 st Century Expectations RETELL Strategies Texts/Resources Goals: +Students will be formally introduced to permutations and combinations +In how many ways can you pick a certain number of objects, in order, from a defined set of distinct objects? +How many ways can you arrange a defined set of objects if the objects can be repeated? +How many ways can you arrange a defined set of objects if the objects cannot be repeated? +Develop and use formulas for finding the number of permutations of n objects, taken k at a time. +Find a formula for the number of combinations of n objects, taken k at a time. Find the number of anagrams for a word. A.CED.2; Prepares for S.CP.9 combination; permutation; anagram; nc k; np k Investigation quiz or test Rubrics: Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Civic: Utilize networking skills and engage inclusively with others 7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around Precalculus: common core CME Project

10 Chapter 5: Functions and Tables CIA: 4/4-4/8/16 Data Meeting: 4/25/16 21 st Century Expectations RETELL Strategies Texts/Resources Goals: Students will explore difference tables and learn about the connections between how difference tables are built and how Pascal s Triangle is constructed. What does a constant difference tell you about a function? What are the Mahler polynomials? How can you use differences to find a polynomial function that fits a table? Find a polynomial function that fits a difference table. Explain how the up-and-over rule of difference tables relates to Pascal s Triangle Quickly find rules for summations, like the sum of the first n squares. F.BF.1; F.BF.2; F.IF.8 difference table; hockey-stick property; up-and-over property Mahler Polynomials Investigation quiz or test Rubrics: Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Civic: Utilize networking skills and engage inclusively with others 7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around Precalculus: common core CME Project

11 Chapter 6: Analytic Geometry CIA: 4/4-4/8/16 Data Meeting: 4/25/16 21 st Century Expectations RETELL Strategies Texts/Resources Goals: Students will make connections between algebra and geometry by using algebraic techniques to prove geometric results. Students explore conic sections from many different perspectives. What is the set of points equidistant from the x-axis and a specific point? How can you use coordinates to prove geometric statements? How can you find the center and radius of a circle with an equation written in normal form? What does the intersection of a 3-D object and a plane look like? What is a locus? Sketch the graphs of equations in two variables. Use distance and slope relationships to prove geometric results Evaluate and use the signed power of a point with respect to a circle Visualize each of the conic sections as the intersection of a plane with an infinite double cone Give a locus definition for each of the conic sections Identify the equations for the graphs of the conic sections, and sketch their graphs. A.CED.2; A.REI.2; A.REI.4; A.REI.10; A.REI.11; A.SSE.3; G.GPE.1; G.GPE.2; G.GPE.3; G.GPE.4; G.GMD.4; N.Q.2 axis; conic sections; double cone; ellipse; focus; generator; major axis; midline; minor axis; parabola; parallelogram; point-tester; rhombus; trapezoid; apex; coordinatize; Dandelin sphere; directrix; eccentricity; hyperbola; locus; perpendicular bisector; power of a point; vertex investigation reflections; mid chapter test; end of unit test Rubrics: Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Civic: Utilize networking skills and engage inclusively with others 7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around Precalculus: common core CME Project

12 Chapter 8: Ideas in Calculus Finals: 6/7-6/10/16* 21 st Century Expectations RETELL Strategies Texts/Resources Goals: Students look at the area of familiar shapes and think about areas of irregular shapes. How can you find the area of an irregularly-shaped figure? How can you estimate the area under a curve? Estimate the areas of irregularly-shaped objects. Estimate the area under the graph of y = x m between x = 0 and x = 1. Calculate the area under the graph of y = x m between x = 0 and x = 1. Find the area under the graph y = e x between x = 0 and x = 1 Extends A.CED.3 area; sum lower sum; upper sum Investigation quiz or test Rubrics: Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Civic: Utilize networking skills and engage inclusively with others 7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around Precalculus: common core CME Project *Dates may be adjusted according to inclement weather cancellations