Amarillo ISD Math Curriculum

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1 Amarillo ISD Precalculus Stards Amarillo Independent School District follows the Texas Essential Knowledge Skills (TEKS). All of AISD curriculum documents resources are aligned to the TEKS. The State of Texas State Board of Education has defined the focal points for Precalculus in mathematics in the third paragraph of the introduction to the Texas Essential Knowledge Skills. Precalculus is the preparation for calculus. The course approaches topics from a function point of view, where appropriate, is designed to strengthen enhance conceptual understing mathematical reasoning used when modeling solving mathematical real-world problems. Students systematically work with functions their multiple representations. The study of Precalculus deepens students' mathematical understing fluency with algebra trigonometry extends their ability to make connections apply concepts procedures at higher levels. Students investigate explore mathematical ideas, develop multiple strategies for analyzing complex situations, use technology to build understing, make connections between representations, provide support in solving problems. Unit 1 Functions & Graphs Unit 2 Polynomial, Power & Rational Function Unit 3 Exponential, Logistic & Logarithmic Functions Unit 4 Trigonometric Functions (include Law of Sines Law of Cosines) Unit 5 Analytic Trigonometry (Identities) Unit 6 Analytic Geometry (Conic Sections) Unit 7 Discrete Mathematics (Sequence Series) Unit 8 Applications of Trigonometry (Vectors, Parametric, Polar)

2 Amarillo ISD Precalculus Stards First Semester Unit 1 Functions & Graphs 5 Weeks P.1 Mathematical process stards. The acquire demonstrate mathematical understing. (A) apply mathematics to problems arising in everyday life, society, the workplace; a plan or strategy, determining a solution, justifying the solution, evaluating the problem-solving process the reasonableness of the solution; (C) select tools, including real objects, manipulatives, paper pencil, technology as appropriate, techniques, including mental math, estimation, number sense as (D) communicate mathematical ideas, reasoning, their implications using multiple representations, including symbols, diagrams, graphs, language as appropriate; (E) create use representations to organize, record, communicate mathematical (F) analyze mathematical relationships to connect communicate mathematical (G) display, explain, justify mathematical ideas arguments using precise P.2 Functions. The student uses process (A) use the composition of two functions to model solve real-world problems; stards in mathematics to explore, describe, (B) demonstrate that function composition is not always commutative; analyze the attributes of functions. The (C) represent a given function as a composite function of two or more functions; student makes connections between multiple (D) describe symmetry of graphs of even odd functions; representations of functions algebraically (E) determine an inverse function, when it exists, for a given function over its domain or a constructs new functions. The student subset of its domain represent the inverse using multiple representations; analyzes uses functions to model realworld (F) graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse problems. trigonometric, piecewise defined functions, including step functions; (G) graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, power functions their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, d, in mathematical real-world problems; (I) determine analyze the key features of exponential, logarithmic, rational,

3 Amarillo ISD Precalculus Stards polynomial, power, trigonometric, inverse trigonometric, piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, intervals over which the function is increasing or decreasing; (L) determine various types of discontinuities in the interval (-, ) as they relate to functions explore the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities; Unit 2 Polynomial, Power & Rational Functions P.1 Mathematical process stards. The acquire demonstrate mathematical understing. P.2 Functions. The student uses process stards in mathematics to explore, describe, analyze the attributes of functions. The student makes connections between multiple representations of functions algebraically constructs new functions. The student analyzes uses functions to model realworld problems. 5 Weeks (A) apply mathematics to problems arising in everyday life, society, the workplace; a plan or strategy, determining a solution, justifying the solution, evaluating the problem-solving process the reasonableness of the solution; (C) select tools, including real objects, manipulatives, paper pencil, technology as appropriate, techniques, including mental math, estimation, number sense as (D) communicate mathematical ideas, reasoning, their implications using multiple representations, including symbols, diagrams, graphs, language as appropriate; (E) create use representations to organize, record, communicate mathematical (F) analyze mathematical relationships to connect communicate mathematical (G) display, explain, justify mathematical ideas arguments using precise (F) graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, piecewise defined functions, including step functions; (G) graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, power functions their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, d, in mathematical real-world problems; (I) determine analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, intervals over which the function is increasing

4 P.5 Algebraic reasoning. The student uses process stards in mathematics to evaluate expressions, describe patterns, formulate models, solve equations inequalities using properties, procedures, or algorithms. Amarillo ISD Precalculus Stards or decreasing; (J) analyze describe end behavior of functions, including exponential, logarithmic, rational, polynomial, power functions, using infinity notation to communicate this characteristic in mathematical real-world problems; (K) analyze characteristics of rational functions the behavior of the function around the asymptotes, including horizontal, vertical, oblique asymptotes; (L) determine various types of discontinuities in the interval (-, ) as they relate to functions explore the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities; (M) describe the left-sided behavior the right-sided behavior of the graph of a function around discontinuities; (N) analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, power functions, to solve real-world problems; (J) solve polynomial equations with real coefficients by applying a variety of techniques in mathematical real-world problems; (K) solve polynomial inequalities with real coefficients by applying a variety of techniques write the solution set of the polynomial inequality in interval notation in mathematical real-world problems; (L) solve rational inequalities with real coefficients by applying a variety of techniques write the solution set of the rational inequality in interval notation in mathematical real-world problems; Unit 3 Exponential, Logistic & Logarithmic Functions 5 Weeks P.1 Mathematical process stards. The acquire demonstrate mathematical understing. (A) apply mathematics to problems arising in everyday life, society, the workplace; a plan or strategy, determining a solution, justifying the solution, evaluating the problem-solving process the reasonableness of the solution; (C) select tools, including real objects, manipulatives, paper pencil, technology as appropriate, techniques, including mental math, estimation, number sense as (D) communicate mathematical ideas, reasoning, their implications using multiple representations, including symbols, diagrams, graphs, language as appropriate;

5 P.2 Functions. The student uses process stards in mathematics to explore, describe, analyze the attributes of functions. The student makes connections between multiple representations of functions algebraically constructs new functions. The student analyzes uses functions to model realworld problems. P.5 Algebraic reasoning. The student uses process stards in mathematics to evaluate expressions, describe patterns, formulate models, solve equations inequalities using properties, procedures, or algorithms. Amarillo ISD Precalculus Stards (E) create use representations to organize, record, communicate mathematical (F) analyze mathematical relationships to connect communicate mathematical (G) display, explain, justify mathematical ideas arguments using precise (F) graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, piecewise defined functions, including step functions; (G) graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, power functions their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, d, in mathematical real-world problems; (I) determine analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, intervals over which the function is increasing or decreasing; (J) analyze describe end behavior of functions, including exponential, logarithmic, rational, polynomial, power functions, using infinity notation to communicate this characteristic in mathematical real-world problems; (N) analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, power functions, to solve real-world problems; (G) use the properties of logarithms to evaluate or transform logarithmic expressions; (H) generate solve logarithmic equations in mathematical real-world problems; (I) generate solve exponential equations in mathematical real-world problems; Second Semester Unit 4 Trigonometric Functions 8 Weeks

6 P.1 Mathematical process stards. The acquire demonstrate mathematical understing. P.2 Functions. The student uses process stards in mathematics to explore, describe, analyze the attributes of functions. The student makes connections between multiple representations of functions algebraically constructs new functions. The student analyzes uses functions to model realworld problems. P.4 Number measure. The student uses process stards in mathematics to apply appropriate techniques, tools, formulas to Amarillo ISD Precalculus Stards (A) apply mathematics to problems arising in everyday life, society, the workplace; a plan or strategy, determining a solution, justifying the solution, evaluating the problem-solving process the reasonableness of the solution; (C) select tools, including real objects, manipulatives, paper pencil, technology as appropriate, techniques, including mental math, estimation, number sense as (D) communicate mathematical ideas, reasoning, their implications using multiple representations, including symbols, diagrams, graphs, language as appropriate; (E) create use representations to organize, record, communicate mathematical (F) analyze mathematical relationships to connect communicate mathematical (G) display, explain, justify mathematical ideas arguments using precise (F) graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, piecewise defined functions, including step functions; (G) graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, power functions their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, d, in mathematical real-world problems; (H) graph arcsin x arccos x describe the limitations on the domain; (I) determine analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, intervals over which the function is increasing or decreasing; (O) develop use a sinusoidal function that models a situation in mathematical realworld problems; (P) determine the values of the trigonometric functions at the special angles relate them in mathematical real-world problems. (A) determine the relationship between the unit circle the definition of a periodic function to evaluate trigonometric functions in mathematical real-world problems; (B) describe the relationship between degree radian measure on the unit circle;

7 calculate measures in mathematical realworld problems. P.5 Algebraic reasoning. The student uses process stards in mathematics to evaluate expressions, describe patterns, formulate models, solve equations inequalities using properties, procedures, or algorithms. Amarillo ISD Precalculus Stards (C) represent angles in radians or degrees based on the concept of rotation find the measure of reference angles angles in stard position; (D) represent angles in radians or degrees based on the concept of rotation in mathematical real-world problems, including linear angular velocity; (E) determine the value of trigonometric ratios of angles solve problems involving trigonometric ratios in mathematical real-world problems; (F) use trigonometry in mathematical real-world problems, including directional bearing; (G) use the Law of Sines in mathematical real-world problems; (H) use the Law of Cosines in mathematical real-world problems; (N) generate solve trigonometric equations in mathematical real-world problems. Unit 5 Analytic Trigonometry (Identities) P.1 Mathematical process stards. The acquire demonstrate mathematical understing. 3 Weeks (A) apply mathematics to problems arising in everyday life, society, the workplace; a plan or strategy, determining a solution, justifying the solution, evaluating the problem-solving process the reasonableness of the solution; (C) select tools, including real objects, manipulatives, paper pencil, technology as appropriate, techniques, including mental math, estimation, number sense as (D) communicate mathematical ideas, reasoning, their implications using multiple representations, including symbols, diagrams, graphs, language as appropriate; (E) create use representations to organize, record, communicate mathematical (F) analyze mathematical relationships to connect communicate mathematical (G) display, explain, justify mathematical ideas arguments using precise

8 Amarillo ISD Precalculus Stards P.5 Algebraic reasoning. The student uses process stards in mathematics to evaluate expressions, describe patterns, formulate models, solve equations inequalities using properties, procedures, or algorithms. Unit 6 Analytic Geometry (Conic Sections) P.1 Mathematical process stards. The acquire demonstrate mathematical understing. P.3 Relations geometric reasoning. The student uses the process stards in mathematics to model make connections between algebraic geometric relations. (M) use trigonometric identities such as reciprocal, quotient, Pythagorean, cofunctions, even/odd, sum difference identities for cosine sine to simplify trigonometric expressions; (N) generate solve trigonometric equations in mathematical real-world problems. 2 Weeks (A) apply mathematics to problems arising in everyday life, society, the workplace; a plan or strategy, determining a solution, justifying the solution, evaluating the problem-solving process the reasonableness of the solution; (C) select tools, including real objects, manipulatives, paper pencil, technology as appropriate, techniques, including mental math, estimation, number sense as (D) communicate mathematical ideas, reasoning, their implications using multiple representations, including symbols, diagrams, graphs, language as appropriate; (E) create use representations to organize, record, communicate mathematical (F) analyze mathematical relationships to connect communicate mathematical (G) display, explain, justify mathematical ideas arguments using precise (F) determine the conic section formed when a plane intersects a double-napped cone; (G) make connections between the locus definition of conic sections their equations in rectangular coordinates; (H) use the characteristics of an ellipse to write the equation of an ellipse with center (h, k); (I) use the characteristics of a hyperbola to write the equation of a hyperbola with center

9 Amarillo ISD Precalculus Stards (h, k). Unit 7 Discrete Mathematics (Sequence Series) 2 Weeks P.1 Mathematical process stards. The acquire demonstrate mathematical understing. P.5 Algebraic reasoning. The student uses process stards in mathematics to evaluate expressions, describe patterns, formulate models, solve equations inequalities using properties, procedures, or algorithms. (A) apply mathematics to problems arising in everyday life, society, the workplace; a plan or strategy, determining a solution, justifying the solution, evaluating the problem-solving process the reasonableness of the solution; (C) select tools, including real objects, manipulatives, paper pencil, technology as appropriate, techniques, including mental math, estimation, number sense as (D) communicate mathematical ideas, reasoning, their implications using multiple representations, including symbols, diagrams, graphs, language as appropriate; (E) create use representations to organize, record, communicate mathematical (F) analyze mathematical relationships to connect communicate mathematical (G) display, explain, justify mathematical ideas arguments using precise (A) evaluate finite sums geometric series, when possible, written in sigma notation; (B) represent arithmetic sequences geometric sequences using recursive formulas; (C) calculate the n th term the n th partial sum of an arithmetic series in mathematical real-world problems; (D) represent arithmetic series geometric series using sigma notation; (E) calculate the n th term of a geometric series, the n th partial sum of a geometric series, sum of an infinite geometric series when it exists; (F) apply the Binomial Theorem for the expansion of (a + b) n in powers of a b for a positive integer n, where a b are any numbers; Unit 8 Applications of Trigonometry (Vectors, Parametric, Polar 3 Weeks P.1 Mathematical process stards. The (A) apply mathematics to problems arising in everyday life, society, the workplace;

10 acquire demonstrate mathematical understing. P.3 Relations geometric reasoning. The student uses the process stards in mathematics to model make connections between algebraic geometric relations. P.4 Number measure. The student uses process stards in mathematics to apply appropriate techniques, tools, formulas to calculate measures in mathematical realworld problems. The student is expected to Amarillo ISD Precalculus Stards a plan or strategy, determining a solution, justifying the solution, evaluating the problem-solving process the reasonableness of the solution; (C) select tools, including real objects, manipulatives, paper pencil, technology as appropriate, techniques, including mental math, estimation, number sense as (D) communicate mathematical ideas, reasoning, their implications using multiple representations, including symbols, diagrams, graphs, language as appropriate; (E) create use representations to organize, record, communicate mathematical (F) analyze mathematical relationships to connect communicate mathematical (G) display, explain, justify mathematical ideas arguments using precise (A) graph a set of parametric equations; (B) convert parametric equations into rectangular relations convert rectangular relations into parametric equations; (C) use parametric equations to model solve mathematical real-world problems; (D) graph points in the polar coordinate system convert between rectangular coordinates polar coordinates; (E) graph polar equations by plotting points using technology; (I) use vectors to model situations involving magnitude direction; (J) represent the addition of vectors the multiplication of a vector by a scalar geometrically symbolically; (K) apply vector addition multiplication of a vector by a scalar in mathematical real-world problems.

11 Amarillo ISD Precalculus Stards To ensure that every student has an opportunity to learn, underst demonstrate the Texas Essential Knowledge Skills. Amarillo Independent has adopted the following protocols for teachers, curriculum others to use in reference to Curriculum, Instruction Assessment. Curriculum 1) Prioritize essential learning based on AISD written curriculum adhere to the scope sequence. 2) Develop deep understings 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 horizontal alignment to ensure grade level curriculum is being taught. Instruction 1) Common lessons are developed based on strategically selected grade level TEKS include learning opportunities for students that: are at the expected level of thinking 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 addressed in the lessons. 4) Strategic re-teaching when students do not underst. 5) Common lessons are analyzed strengthened through a continuous improvement process such as the Professional Teaching Model, Lesson Study or other method for collaborative study sharing. Assessment 1) Collaboratively align all assessment to the AISD written curriculum reflect appropriate rigor. 2) Collaboratively engage in purposeful dialogue about assessment tied to clearly defined essential learning outcomes. 3) Continuously improve adjust instruction based on common assessment results student work. 4) Provide feedback to the annual curriculum feedback revision process.

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.