PreCal

PreCal

 

Pre-Calculus-1st Semester

Beaumont ISD

11th and 12th

Revision Date: 6/7/16

1st Nine Weeks

August 24-October 14

(37 School Days)

37 Instructional Days, 0 Flex Day

Pre-Test – August 24 – September 2

Mid 9-week Test – September 12 – 16

9-week Test with Pre-Test attached –

October 10 – 14

 

 2nd  Nine Weeks

October 17-December 16

(39 School Days)

39 Instructional Days, 0 Flex Days

Mid 9-week Test – November 7 – 11 

9-week Test with Pre-Test attached –

December 12 – 16

 

 

Refer to instructional timelines when planning units of instruction.

See list of Ongoing Process TEKS that should be embedded in all Units of Instruction.

ALL Process TEKS are eligible for incorporating into the assessment of at least 40% of Content TEKS.

 

STAAR Standard Key:    Blue= STAAR Readiness Standard

                                                Yellow= STAAR Supporting Standard

                                                           Bold= Highest Stakes TEKS (greatest need)

                             Italics= High Stakes TEKS

Units

Unit 1: Intro to Trigonometry (34 days)

 

 

 

 

 

TEKS/SEs

 

Unit 1: Intro to Trigonometry (34 days)

P.1.A  Apply mathematics to problems arising in everyday life, society, and the workplace

 

P.1.B  Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving  process and the reasonableness of the solution

 

P.1.C  Select tools, including real objects, manipulative, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems

 

P.1.D  communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate

 

P.1.E  Create and use representations to organize, record, and communicate mathematical ideas

 

P.1.F  Analyze mathematical relationships to connect and communicate mathematical ideas

 

P.1.G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

 

P.2.N  Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems

 

P.4.A  Determine the relationship between the unit circle and the definition of a periodic function to evaluate trigonometric functions in mathematical and real-world problems

 

P.4.B  Describe the relationship  between degree and radian measure on the unit circle

 

P.4.C   Represent angles in radians or degrees based on the concept of rotation and find the measure of reference angles and angles in standard position.

 

P.4.D  Represent angles in radians or degrees based on the concept of rotation in mathematical and real-world problems, including linear and angular velocity

 

P.4.E  Determine the value of trigonometric ratios of angles and solve problems involving trigonometric ratios in mathematical and real-world problems

 

P.4.F  Use trigonometry in mathematical and real-world problems, including directional bearing

 

P.2.F  Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions

 

P.2.G  Graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x – c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems

 

P.2.I  Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing

 

P.2.N  Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems

 

P.2.O  Develop and use a sinusoidal function that models a situation in mathematical and real-world problems

 

P.4.F  Use trigonometry in mathematical and real-world problems, including directional bearing

 

P.2.F  Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions

 

P.2.H  Graph arcsin x and arccos x and describe the limitations on the domain

 

P.2.I  Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing

 

P.2.N  Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems

 

P.4.F  Use trigonometry in mathematical and real-world problems, including directional bearing

 

P.4.F  Use trigonometry in mathematical and real-world problems, including directional bearing

 

P.5.M Use trigonometric identities such as reciprocal, quotient, Pythagorean, cofunctions, even/odd, and sum and difference identities for cosine and sine to simplify trigonometric expressions

 

Students will use problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution and evaluating the problem-solving process and the reasonableness of the solution. Students will select appropriate tools such as real objects, manipulatives, paper and pencil, and technology and techniques such as mental math, estimation, and reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, and language.  Students will use mathematical relationships to generate solutions and make connections and predictions. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

 

Units

Unit 2: Trigonometric Applications and Intro to Vectors (33 days)

 

 

 

 

TEKS/SEs

 

Unit 2: Trigonometric Applications and Intro to Vectors (33 days)

 P.4.F  Use trigonometry in mathematical and real-world problems, including

 directional bearing

 

P.5.N  Generate and solve trigonometric equations in mathematical and real-world problems

 

P.4.F  Use trigonometry in mathematical and real-world problems, including directional bearing

 

P.5.M Use trigonometric identities such as reciprocal, quotient, Pythagorean, cofunctions, even/odd, and sum and difference

 

P.5.N  Generate and solve trigonometric equations in mathematical and real-world problems

 

P.4.G  Use the Law of Sines in mathematical and real-world problems

 

P.4.H  Use the Law of Cosines in mathematical and real-world problems

 

P.4.I  Use vectors to model situations involving magnitude and direction

 

P.4.J  Represent the addition of vectors and the multiplication of a vector by a scalar geometrically and symbolically

 

P.4.K  Apply vector addition and multiplication of a vector by a scalar in mathematical and real-world problems

 

 

Students will use problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution and evaluating the problem-solving process and the reasonableness of the solution. Students will select appropriate tools such as real objects, manipulatives, paper and pencil, and technology and techniques such as mental math, estimation, and reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, and language.  Students will use mathematical relationships to generate solutions and make connections and predictions. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

 

Beaumont  22nd Century Skills

 

Critical Thinking and Reasoning:  Thinking Deeply,

Thinking Differently

Information Literacy: Untangling the Web

Collaboration: Working Together, Learning Together

Self-Direction: Own Your Learning

Invention: Creating Solutions

 

 

Pre-Calculus-2nd Semester

Beaumont ISD

11th and 12th

Revision Date: 6/13/16

3rd  Nine Weeks

January 3 – March 10

(47 School Days)

47 Instructional Days, 0 Flex Day

Mid 9-week Test – January 30 – February 3  

9-week Test – March 6 – 10

 

2nd  Nine Weeks

March 20 – June 1

(52 School Days)

52 Instructional Days, 0 Flex Days

Mid 9-week Test – April 10 – 13

9-week Test/Finals – May 22 – 26 (HS Seniors); May 30 – June 1

 

 

Refer to instructional timelines when planning units of instruction.

See list of Ongoing Process TEKS that should be embedded in all Units of Instruction.

ALL Process TEKS are eligible for incorporating into the assessment of at least 40% of Content TEKS.

 

STAAR Standard Key:   Blue= STAAR Readiness Standard

                                               Yellow= STAAR Supporting Standard

                                                          Bold= Highest Stakes TEKS (greatest need)

                           Italics= High Stakes TEKS

Units

Unit 3: Functions and their Graphs (3 days)

 

 

 

TEKS/SEs

 

Unit 3: Functions and their Graphs (3 days)

P.2.N  Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems

 

P.2.F  Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions

 

P.2.N  Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems

 

P.2.A  Use the composition of two functions to model and solve real-world problems

 

P.2.B  Demonstrate that function composition is not always commutative

 

P.2.C  Represent a given function as a composite function of two or more functions

 

P.2.E  Determine an inverse function, when it exists, for a given function over its domain or a subset of its domain and represent the inverse using multiple representations

 

P.2.N  Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems

 

P.2.F  Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions

 

P.2.G  Graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x – c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems

 

P.2.I  Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing

 

P.2.J  Analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and real-world problems

 

P.2.N  Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems

 

P.2.F  Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions

 

P.2.G  Graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x – c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems

 

P.2.I  Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing

 

P.2.J  Analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and real-world problems

 

P.2.L  Determine various types of discontinuities in the interval (-∞, ∞) as they relate functions and explore the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities

 

P.2.N  Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems

 

P.5.J  Solve polynomial equations with real coefficients by applying a variety of techniques in mathematical and real-world problems

 

P.2.I  Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing

 

P.2.N  Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems

 

P.5.J  Solve polynomial equations with real coefficients by applying a variety of techniques in mathematical and real-world problems

 

P.2.F  Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions

 

P.2.G  Graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x – c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems

 

P.2.I  Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing

 

P.2.J  Analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and real-world problems

 

P.2.L  Determine various types of discontinuities in the interval (-∞, ∞) as they relate functions and explore the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities

 

P.2.M  Describe the left-sided behavior and the right-sided behavior of the graph of a function around discontinuities

 

 

P.2.N  Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems

 

P.5.K  Solve polynomial inequalities with real coefficients by applying a variety of techniques and write the solution set of the polynomial inequality in interval notation in mathematical and real-world

 

P.5.L  Solve rational inequalities with real coefficients by applying a variety of techniques and write the solution set of the rational inequality in interval notation in mathematical and real-world problems

 

Students will use problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution and evaluating the problem-solving process and the reasonableness of the solution. Students will select appropriate tools such as real objects, manipulatives, paper and pencil, and technology and techniques such as mental math, estimation, and reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, and language.  Students will use mathematical relationships to generate solutions and make connections and predictions. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

 

Units

Unit 4: Exponential/Log Functions and Conics (42 days)

 

 

 

TEKS/SEs

 

Unit 4: Exponential/Log Functions and Conics (42 days)

 

P.2.F  Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions

 

P.2.G  Graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x – c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems

 

P.2.I  Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing

 

P.2.J  Analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and real-world problems

 

P.2.N  Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems

 

P.2.N  Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems

 

P.5.G  Use the properties of logarithms to evaluate ore transform logarithmic expressions

 

P.5.H  Generate and solve logarithmic equations in mathematical and real-world problems

 

P.5.I  Generate and solve exponential equations in mathematical and real-world problems

 

P.5.A  Evaluate finite sums and geometric series, when possible, written in sigma notation

 

P.5.B  Represent arithmetic sequences and geometric sequences using recursive formulas

 

P.5.D Represent arithmetic series and geometric series using sigma notation

 

P.1.A  Apply mathematics to problems arising in everyday life, society, and the workplace

P.1.B  Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving  process and the reasonableness of the solution

 

P.1.C  Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems

 

P.1.D  communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate

 

P.1.E  Create and use representations to organize, record, and communicate mathematical ideas

 

P.1.F  Analyze mathematical relationships to connect and communicate mathematical ideas

 

P.1.G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

 

P.1.A  Apply mathematics to problems arising in everyday life, society, and the workplace

 

P.1.B  Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving  process and the reasonableness of the solution

 

P.1.C  Select tools, including real objects, manipulative, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems

 

P.1.D  communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate

P.1.E  Create and use representations to organize, record, and communicate mathematical ideas

 

P.1.F  Analyze mathematical relationships to connect and communicate mathematical ideas

 

P.1.G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

 

P.3.G Make connections between the locus definition of conic sections and their equations in rectangular coordinates

 

P.3.G Make connections between the locus definition of conic sections and their equations in rectangular coordinates

 

P.3.H  Use the characteristics of an ellipse to write the equation of an ellipse with center (h, k)

 

P.3.I  Use the characteristics of a hyperbola to write the equation of a hyperbola with center (h, k)

 

Students will use problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution and evaluating the problem-solving process and the reasonableness of the solution. Students will select appropriate tools such as real objects, manipulatives, paper and pencil, and technology and techniques such as mental math, estimation, and reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, and language.  Students will use mathematical relationships to generate solutions and make connections and predictions. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

 

Beaumont  22nd Century Skills

 

Critical Thinking and Reasoning:  Thinking Deeply, Thinking Differently

Information Literacy: Untangling the Web

Collaboration: Working Together, Learning Together

Self-Direction: Own Your Learning

Invention: Creating Solutions