Amarillo ISD Math Curriculum

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Vanessa Lewis
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1 Amarillo Independent School District follows the Texas Essential Knowledge and Skills (TEKS). All of AISD curriculum and documents and resources are aligned to the TEKS. The State of Texas State Board of Education has defined the focal points for PreAP PreCalculus in mathematics in the first paragraph of the introduction to the Texas Essential Knowledge and Skills. In Precalculus, students continue to build on the K-8, Algebra I, Algebra II, and Geometry foundations as they expand their understanding through other mathematical experiences. Students use symbolic reasoning and analytical methods to represent mathematical situations, to express generalizations, and to study mathematical concepts and the relationships among them. Students use functions, equations, and limits as useful tools for expressing generalizations and as means for analyzing and understanding a broad variety of mathematical relationships. Students also use functions as well as symbolic reasoning to represent and connect ideas in geometry, probability, statistics, trigonometry, and calculus and to model physical situations. Students use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools, and technology (including, but not limited to, calculators with graphing capabilities, data collection devices, and computers) to model functions and equations and solve real-life problems. Unit 1 Functions and their Graphs Unit 2 Polynomial and Rational Functions Unit 3 Exponential and Logarithmic Functions Unit 4 Systems of Equations and Inequalties Unit 5 Topics of Analytic Geometry Unit 6 Trigonometry Unit 7 Analytic Trigonometry Unit 8 Additional Topics in Trigonometry Unit 9 Sequesnces and Series Unit 10 Analytic Geometry in Three Dimensions Page 1 of 7

2 Unit 1 Functions and their Graphs 5 Weeks P.01 The student defines functions, functions. The student is expected is expected these procedures and results verbally, numerically, symbolically, and graphically; Unit 2 Polynomial and Rational Functions 4 Weeks Page 2 of 7

3 P.01 The student defines functions, functions. The student is expected is expected Amarillo ISD PreAP PreCalculus Standards these procedures and results verbally, numerically, symbolically, and graphically; (A) investigate properties of trigonometric and polynomial functions; (B) use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data; Unit 3 Exponential and Logarithmic Functions P.01 The student defines functions, functions. The student is expected 4 Weeks Page 3 of 7

4 is expected Amarillo ISD PreAP PreCalculus Standards these procedures and results verbally, numerically, symbolically, and graphically; and (C) investigate identities graphically and verify them symbolically, including logarithmic properties, trigonometric identities, and exponential properties (B) use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data; Unit 4 Systems of Equations and Inequalties 1 Weeks No TEKS Unit 5 Topics of Analytic Geometry 1 Weeks P.05 The student uses conic sections, their properties, and parametric representations, as well as tools and technology, to model (A) use conic sections to model motion, such as the graph of velocity vs. position of a pendulum and motions of planets; (B) use properties of conic sections to describe physical phenomena such as the reflective properties of light and sound; Unit 6 Trigonometry 6 Week P.01 The student defines functions, functions. The student is expected Page 4 of 7

5 is expected Amarillo ISD PreAP PreCalculus Standards these procedures and results verbally, numerically, symbolically, and graphically; and (C) investigate identities graphically and verify them symbolically, including logarithmic properties, trigonometric identities, and exponential properties (A) investigate properties of trigonometric and polynomial functions; (B) use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data; Unit 7 Analytic Trigonometry 3 weeks is expected (C) investigate identities graphically and verify them symbolically, including logarithmic properties, trigonometric identities, and exponential properties (A) investigate properties of trigonometric and polynomial functions; Unit 8 Additional Topics in Trigonometry is expected P.06 The student uses vectors to model 3 weeks (E) solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas and incorporate radian measure where needed (A) use the concept of vectors to model situations defined by magnitude and direction; and (B) analyze and solve vector problems generated by real-life situations Page 5 of 7

6 Unit 9 Sequences and Series 2 weeks P.04 The student uses sequences and series as well as tools and technology to represent, analyze, and solve real-life problems. The student is expected Unit 10 Analytic Geometry in Three Dimensions P.05 The student uses conic sections, their properties, and parametric representations, as well as tools and technology, to model P.06 The student uses vectors to model (A) represent patterns using arithmetic and geometric sequences and series; (B) use arithmetic, geometric, and other sequences and series to solve real-life problems; (C) describe limits of sequences and apply their properties to investigate convergent and divergent series; (D) apply sequences and series to solve problems including sums and binomial expansion 2 weeks (C) convert between parametric and rectangular forms of functions and equations to graph them; and (D) use parametric functions to simulate problems involving motion (A) use the concept of vectors to model situations defined by magnitude and direction; and (B) analyze and solve vector problems generated by real-life situations Page 6 of 7

7 To ensure that every student has an opportunity to learn, understand and demonstrate the Texas Essential Knowledge and Skills. Amarillo Independent has adopted the following protocols for teachers, curriculum and others to use in reference to Curriculum, Instruction and Assessment. Curriculum 1) Prioritize essential learning based on AISD written curriculum and adhere to the scope and sequence. 2) Develop deep understandings of the AISD written curriculum with an emphasis on the essential learning outcomes. 3) Create relevant learning environments in every classroom using the AISD written curriculum. 4) Analyze vertical and horizontal alignment to ensure grade level curriculum is being taught. Instruction 1) Common lessons are developed based on strategically selected grade level TEKS and include learning opportunities for students that: are at the expected level of thinking and rigor utilize research based instructional strategies are actively engaging have real world applications 2) Collaboratively align instruction to assessment. 3) Individual student instructional needs are considered and addressed in the lessons. 4) Strategic re-teaching when students do not understand. 5) Common lessons are analyzed and strengthened through a continuous improvement process such as the Professional Teaching Model, Lesson Study or other method for collaborative study and sharing. Assessment 1) Collaboratively align all assessment to the AISD written curriculum and reflect appropriate rigor. 2) Collaboratively engage in purposeful dialogue about assessment tied to clearly defined essential learning outcomes. 3) Continuously improve and adjust instruction based on common assessment results and student work. 4) Provide feedback to the annual curriculum feedback and revision process. Page 7 of 7

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.