Curriculum Guide. Additional instructional supplements are indicated as needed

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1 Revised: July, 2012 Teachers: For the most recent revision, please check the interactive guide that has been posted within Secondary Math s NEW website Curriculum Guide Aligned to benchmarks as indicated in the course description below Course#: Pre-Calculus Main Textbook Resource Precalculus: Graphical, Numerical, Algebraic, Florida Edition, Glencoe 2011 Additional instructional supplements are indicated as needed

Curriculum Guide This guide was created to help direct your instructional focus during the school year. This guide is a STANDARDS based, NOT textbook based document.

2 Curriculum Guide This guide was created to help direct your instructional focus during the school year. This guide is a STANDARDS based, NOT textbook based document. As such, there will be times that alternative resources may have to be utilized in order to properly cover the learning goals and associated benchmarks. The timing of this guide was set up to provide ample time and opportunity to utilize pedagogically sound practices while covering the state benchmarks thoroughly by the end of the fourth quarter. In order to accomplish this, the following four pedagogical techniques must be effectively utilized over the course of the school year. Pedagogical Technique Fair game policy Content taught previously is expected to be retained. However, in order to aid student retention, review and/or incorporation of previously learned content may need to be infused within instruction ( just in time review). * Example Once students have been instructed on how to simplify rational expressions, then rational expressions should be included in the assigned scenarios and assessments for the remainder of the year. Content Clumping Where possible, instruct students several related concepts at once. This technique allows the students to make connections and utilize skill sets across various concepts at once, strengthening their conceptual understanding of mathematics Although there are various aspects to proportional relationships, the methodology of solving proportional scenarios is effectively the same. Thus, students could be taught how to distinguish situations that are proportional or are not proportional, solve proportion situations such as percent problems, similar figure problems, and measurement problems at relatively the same time. Teach for understanding not for content coverage. This can be accomplished by assigning fewer tasks, but requiring a deeper understanding to be demonstrated by the student(these tasks can be on content that has been clumped) Instead of drilling students and assigning 35 homework problems solving systems of linear equations, assign 4 scenarios in which students demonstrate their understanding of the solution of the system by solving using a table, graph, analytically, and then having them create a word problem for the given system. Standards for Mathematical Practice(MP) Demonstrate during instruction and instruct students how to utilize the eight standards of mathematical practice *Note: Level 1 and 2 students can receive these reviews during their Intensive Math class. The core content and Intensive Math teacher should be the same person or should communicate often about common students and their content deficiencies. In NO order of importance: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

3 Finally, the curriculum guide that follows is meant to be used as its name implies, it is just a GUIDE. The guide delineates the MINIMUM amount of material that MUST be presented to the students according to state law and according to course descriptions that have been approved by the state board of education. The guide in NO WAY dictates the exact teaching strategy or supportive content that may be needed to be presented to the students in accordance to Differentiated Instruction (DI) or Response To Intervention (RTI) methodologies. Due to various extenuating circumstances, there is a possibility that a class may not be able to fully keep up with the pacing of the guide. However, for assessed courses, it is a district expectation that students have been exposed to the content of the course as dictated in the guides prior to the administration of the interim assessments. If this is not possible, please inform your administration. Interactive Curriculum Guide This guide is available online through our districts SharePoint website. It will be kept as up to date as possible as new information and resources are added. For the best experience PLEASE CHOOSE this guide. Link to Secondary Mathematics Curriculum Site Printable Documents This guide is part of a subset of printable documents that have been posted online for the end user to print. A majority of these documents have not been uniformly formatted nor are they in a necessarily userfriendly format. Also, essential questions and resources have not been inserted into the guide and are thus separate documents. Please try to save paper and use the interactive guide whenever possible.

4 Pre- Calculus benchmarks to be incorporated throughout the curriculum Mathematics Benchmark Description Benchmark LACC.1112.RST.2.4 LACC.910.RST.2.4 LACC.1112.RST.3.7 LACC.910.RST.3.7 Language Arts Description Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades texts and topics. Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9 10 texts and topics. Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem. Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.

5 Learning Goal 1: Pre - Calculus # QUARTER 1 Weeks 1-3 Textbook sections: August 20 th September 7 th ; September 3 rd No School-Labor Day Students will be able to proficiently work with polynomial functions. This goal includes students being able to graph polynomial functions with and without technology and describe end behavior; being able to use theorems of polynomial behavior (including but not limited to the Fundamental Theorem of Algebra, Remainder Theorem, the Rational Root Theorem, Descartes' Rule of Signs, and the Conjugate Root Theorem) to find the zeros of a polynomial function; being able to write a polynomial equation for a given set of real and/or complex roots; and being able to describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression with and without technology. In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught such as the skill to teach other students how to work with literal equations. No major errors or omissions regarding any of the information and/or processes (simple or complex) that were explicitly taught for working with literal equations. involved in working with literal equations. With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes involved in working with literal equations. Even with help, no understanding or skill in working with literal equations is demonstrated. MA.912.A.4.5 MA.912.A.4.6 MA.912.A.4.7 MA.912.A.4.8

6 QUARTER 1 Weeks 4-6 Textbook sections: 2.6 September 10 th - September 28 th ; September 17 th Early Dismissal, September 19 th End of Interim, September 26 th Early Dismissal Learning Goal 2: Students will be able to work with and be able to sketch the graph of a complex rational function This goal includes students being able to identify removable and non-removable discontinuities, and vertical, horizontal, and oblique asymptotes of a graph of a rational function f ( x) N( x) = Dx ( ) (both simple [where the simplified degree of D(x) =1] and complex[where the degree of N(x) and/or D(x) is at least greater than or equal to 2]), find the zeros, and graph the function. MA.912.A.5.6

7 Learning Goal 3: Pre - Calculus # QUARTER 1 Weeks 7-9 Textbook sections: October 1 st October 18 th ; October 18 th Early release and End of 1 st Quarter Students will be able to proficiently work with angles given in radian measure. This goal includes students being able to convert between degree and radian measure; being able to state and use exact values of trigonometric functions for special angle (multiples of 30, 45, 60, &90*) given in both radian and degree measure; being able to find approximate values of trigonometric and inverse trigonometric functions using appropriate technology. MA.912.T.1.1 MA.912.T.1.2 MA.912.T.1.3 MA.912.T.1.4

8 QUARTER 2 Weeks Textbook Sections: October 22 nd November 9 th ; November 6 th Early release, Learning Goal 4: Students will be able to work with the trigonometric functions. This goal includes students being able to make connections between right triangle ratios, trigonometric functions and circular functions; being able to define and graph trigonometric functions using domain, range, intercepts, period, amplitude, phase shift, vertical shift, and asymptotes with and without the use of graphing technology; being able to define and graph inverse trigonometric relations and functions; and be able to solve real-world problems involving applications of trigonometric functions using graphing technology when appropriate. MA.912.T.1.5 MA.912.T.1.6 MA.912.T.1.7 MA.912.T.1.8

9 QUARTER 2 Weeks Textbook sections: 4.8, 5.5, 5.6 November 13 th November 30 th ; November Fall Break Learning Goal 5: Students will be able to use the trigonometric ratios to solve scenarios involving right triangles. This goal includes students being able to define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of angles of right triangles; being able to solve real-world problems involving right triangles using technology when appropriate; being able to apply the laws of sines and cosines to solve real-world problems using technology; and being able to use the area of triangles given two sides and an angle or three sides to solve real-world problems. MA.912.T.2.1 MA.912.T.2.2 MA.912.T.2.3 MA.912.T.2.4

10 QUARTER 2 Weeks Textbook sections: December 3 rd December 21 st ; Dec Early release, December 21 st End of 2 nd Quarter Learning Goal 6: Students will be able to use basic trigonometric identities to verify other identities, to simplify expressions, and to solve trigonometric equations. This goal includes students being able to verify the basic Pythagorean identities and show that they are equivalent to the Pythagorean Theorem; being able to use the sum and difference, half-angle and double-angle formulas for sine, cosine, and tangent, when formulas are provided; and being able to solve trigonometric equations and real-world problems involving applications of trigonometric equations using technology when appropriate. MA.912.T.3.1 MA.912.T.3.2 MA.912.T.3.3 MA.912.T.3.4

11 QUARTER 3 Weeks 19 & 20 Textbook sections: 6.1 & 6.2 January 7 th January 18 th ; January 21 st No School Learning Goal 7: Students will be able to proficiently work with vectors This goal includes students being able to demonstrate an understanding of the geometric interpretation of vectors and vector operations including addition, scalar multiplication, dot product, and cross product in the plane and in three-dimensional space; being able to demonstrate an understanding of the algebraic interpretation of vectors and vector operations including addition, scalar multiplication, dot product, and cross product in the plane and in three-dimensional space; and being able to use vectors to model and solve application problems. MA.912.D.9.1 MA.912.D.9.2 MA.912.D.9.3

12 QUARTER 3 Weeks 21 & 22 Textbook sections: 6.3 January 22 February 1 st Learning Goal 8: Students will be able to work with proficiently work with parametric equations. This goal includes students being able to sketch the graph of a curve in the plane represented parametrically, indicating the direction of motion; being able to convert from a parametric representation of a plane curve to a rectangular equation and vice-versa; and being able to use parametric equations to model applications of motion in the plane. MA.912.D.10.1 MA.912.D.10.2 MA.912.D.10.3

13 QUARTER 3 Weeks 23 & 24 Textbook Sections: February 4 th February 15 th ; February 13 th End of Interim, February 15 th Early release, February 18 th No School Learning Goal 9: Students will be able to work with polar coordinates and the trigonometric form of complex numbers. This goal includes students being able to define polar coordinates and relate polar coordinates to Cartesian coordinates with and without the use of technology; being able to represent equations given in rectangular coordinates in terms of polar coordinates; being able to graph equations in the polar coordinate plane with and without the use of graphing technology; being able to define the trigonometric form of complex numbers, convert complex numbers to trigonometric form, and multiply complex numbers in trigonometric form; and being able to apply DeMoivre's Theorem to perform operations with complex numbers. MA.912.T.4.1 MA.912.T.4.2 MA.912.T.4.3 MA.912.T.4.4 MA.912.T.4.5 Florida Standards( National Standards)

14 QUARTER 3 Weeks 25 & 26 Textbook sections: February 19 th March 1 st Learning Goal 10: Students will be able to work with and solve real world problems involving conic sections. This goal includes students being able to write the equations of conic sections in standard form and general form, in order to identify the conic section and to find its geometric properties (foci, asymptotes, eccentricity, etc.); being able to graph conic sections WITH and without using graphing technology; and being able to solve real-world problems involving conic sections. MA.912.A.9.1 MA.912.A.9.2 MA.912.A.9.3

15 Learning Goal 11: Pre - Calculus # QUARTER 3 Week 27 Textbook sections: 9.5 (Recommend coverage of 9.4) March 4 th March 8 th ; March 11 th March 15 th Spring Break Students will be able to find sums of arithmetic and geometric series. This goal includes students being able to find partial sums of arithmetic and geometric series, and find sums of infinite convergent geometric series, while using Sigma notation where applicable. In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught such as the skill to teach other students how to work with arithmetic and geometric sequences and series. No major errors or omissions regarding any of the information and/or processes (simple or complex) that were explicitly taught for working with arithmetic and geometric sequences and series. involved in working with arithmetic and geometric sequences and series. With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes involved in working with arithmetic and geometric sequences and series. Even with help, no understanding or skill in working with arithmetic and geometric sequences and series is demonstrated. MA.912.D.11.4

16 QUARTER 3 Week 28 & 29 Textbook sections: 9.6 March 18 th March 28 th ; Mar. 26 th Early Release, Mar. 28 th End of 3 rd Quarter Learning Goal 12: Students will be able to prove theorems using mathematical induction. This goal includes students being able to use mathematical induction to prove various concepts in number theory (such as sums of infinite integer series, divisibility statements, and parity statements), recurrence relations, and other applications. MA.912.D.1.3

17 QUARTER 4 Weeks Textbook sections: 10.3 April 2 nd April 19 th ; April 1st No School Learning Goal 13: Students will understand the concept of a limit and be able to find limits. This goal includes students being able to understand the concept of a limit and estimate limits from graphs and table of values; being able to find limits by substitution; being able to find limits of sums, differences, products, and quotients; being able to find limits of rational functions that are undefined at a point; and being able to find one sided limits. MA.912.C.1.1 MA.912.C.1.2 MA.912.C.1.3 MA.912.C.1.4 MA.912.C.1.5

18 QUARTER 4 Weeks Continuity and Limits; Continuity; Intermediate Value and Continuity; Intermediate and Extreme Value Theorem; Worksheet on the Theorems April 22 nd May 10 th ; April 29 th & April 30 th No School Learning Goal 14: Students will understand the continuity of functions and be able to apply this knowledge to either the Intermediate or Extreme Value theorems. This goal includes students being able to understand continuity in terms of limits; being able to decide if a function is continuous at a point; being able to find the types of discontinuities of a function; being able to understand and use the Intermediate Value Theorem on a function over a closed interval; being able to understand and apply the Extreme Value Theorem. MA.912.C.1.9 MA.912.C.1.10 MA.912.C.1.11 MA.912.C.1.12 MA.912.C.1.13

19 QUARTER 4 Week May 13 th June 5 th School based - project based learning/ ACT/SAT/ District Final Exam Prep Utilize material within Agile Mind to enhance instruction or to develop projects for your students Common Core Correlation

20 Pre-Calculus Final Exam Duration: 90 minutes May 31 st, June 3 rd, and June 4 th This test is summative. As a summative assessment, it will count as the final exam grade or 5% of 2 nd semester s grade. This assessment will assess all of the Next Generation Sunshine State Standards that are assigned to this course, regardless of content coverage in the textbook resource. Benchmarks assessed by quarter Quarter 1 MA.912.A.4.5 MA.912.A.4.6 MA.912.A.4.7 MA.912.A.4.8 MA.912.A.5.6 MA.912.T.1.1 MA.912.T.1.2 MA.912.T.1.3 MA.912.T.1.4 Quarter 2 Quarter 3 MA.912.T.1.5 MA.912.T.1.6 MA.912.T.1.7 MA.912.T.1.8 MA.912.T.2.1 MA.912.T.2.2 MA.912.T.2.3 MA.912.T.2.4 MA.912.T.3.1 MA.912.T.3.2 MA.912.T.3.3 MA.912.T.3.4 MA.912.T.4.1 MA.912.T.4.2 MA.912.T.4.3 MA.912.T.4.4 MA.912.T.4.5 MA.912.D.10.1 MA.912.D.10.2 MA.912.D.10.3 MA.912.D.9.1 MA.912.D.9.2 MA.912.D.9.3 MA.912.A.9.1 MA.912.A.9.2 MA.912.A.9.3 MA.912.D.1.3 MA.912.D.11.4 Quarter 4 MA.912.C.1.1 MA.912.C.1.2 MA.912.C.1.3 MA.912.C.1.4 MA.912.C.1.5 MA.912.C.1.9 MA.912.C.1.10 MA.912.C.1.11 MA.912.C.1.12 MA.912.C.1.13

Syllabus ENGR 190 Introductory Calculus (QR)

Syllabus ENGR 190 Introductory Calculus (QR) Catalog Data: ENGR 190 Introductory Calculus (4 credit hours). Note: This course may not be used for credit toward the J.B. Speed School of Engineering B. S.