a correlation of precalculus - pearson · pdf filea correlation of . precalculus . graphical,...

A Correlation of

Precalculus Graphical, Numerical, Algebraic

Texas Edition, ©2015

To the Texas Essential Knowledge and Skills (TEKS)

for Pre-Calculus and the

Texas English Language Proficiency Standards (ELPS)

Chapter 111. Mathematics §111.42. Precalculus, Adopted 2012 (One-Half to One Credit). Proclamation 2015

Page 1 of 273 Pearson Education, Inc., publishing as Prentice Hall: 9781269614108 Student Material

SubjectSubchapterCoursePublisherProgram TitleProgram ISBN

Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location

(4) Statements that contain the word "including" reference content that must be mastered, while those containing the phrase "such as" are intended as possible illustrative examples.

(c) Knowledge and Skills.

9781269614108

(a) General requirements. Students shall be awarded one-half to one credit for successful completion of this course. Prerequisites: Algebra I, Geometry, and Algebra II.

(b) Introduction.

(1) The desire to achieve educational excellence is the driving force behind the Texas essential knowledge and skills for mathematics, guided by the college and career readiness standards. By embedding statistics, probability, and finance, while focusing on fluency and solid understanding, Texas will lead the way in mathematics education and prepare all Texas students for the challenges they will face in the 21st century.

(2) The process standards describe ways in which students are expected to engage in the content. The placement of the process standards at the beginning of the knowledge and skills listed for each grade and course is intentional. The process standards weave the other knowledge and skills together so that students may be successful problem solvers and use mathematics efficiently and effectively in daily life. The process standards are integrated at every grade level and course. When possible, students will apply mathematics to problems arising in everyday life, society, and the workplace. Students will 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. Students will select appropriate tools such as real objects, manipulatives, paper and pencil, and technology and techniques such as mental math, estimation, and number sense to solve problems. Students will effectively communicate mathematical ideas, 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 analyze mathematical relationships to connect and communicate mathematical ideas. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

(3) Precalculus is the preparation for calculus. The course approaches topics from a function point of view, where appropriate, and is designed to strengthen and enhance conceptual understanding and mathematical reasoning used when modeling and solving mathematical and real-world problems. Students systematically work with functions and their multiple representations. The study of Precalculus deepens students' mathematical understanding and fluency with algebra and trigonometry and extends their ability to make connections and apply concepts and procedures at higher levels. Students investigate and explore mathematical ideas, develop multiple strategies for analyzing complex situations, and use technology to build understanding, make connections between representations, and provide support in solving problems.

Precalculus: Graphical, Numerical, Algebraic, Texas Edition

Correlations to the Texas Essential Knowledge and Skills (TEKS): Student Material

Chapter 111. MathematicsSubchapter C. High School§111.42. Precalculus, Adopted 2012 (One-Half to One Credit).Pearson Education, Inc., publishing as Prentice Hall




(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

(A) apply mathematics to problems arising in everyday life, society, and the workplace

(i) apply mathematics to problems arising in everyday life Instruction 9781269614108 143 Example 5

Activity 9781269614108 172 Exercise 67



(ii) apply mathematics to problems arising in society

Instruction 9781269614108 304-305 Example 1




(iii) apply mathematics to problems arising in the workplace Instruction 9781269614108 166 Example 7



(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

(i) 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

Instruction 9781269614108 70-71 Problem solving







(ii) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the reasonableness of the solution

Instruction 9781269614108 332 Common Calculator Errors



(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

(i) select tools, including real objects as appropriate, to solve problems

Instruction 9781269614108 167-168 Vertical free fall motion




(ii) select tools, including manipulatives as appropriate, to solve problems

Instruction 9781269614108 582-583 Geometry of an ellipse

Activity 9781269614108 588 Exploration 2






(iii) select tools, including paper and pencil as appropriate, to solve problems

Instruction 9781269614108 576 Example 3 and the paragraph that follows it




(iv) select tools, including technology as appropriate, to solve problems

Instruction 9781269614108 120 Example 2




(v) select techniques, including mental math as appropriate, to solve problems

Instruction 9781269614108 8 Scientific Notation

Activity 9781269614108 10 Exercises 53-58






(vi) select techniques including estimation as appropriate, to solve problems





(vii) select techniques, including number sense as appropriate, to solve problems

Instruction 9781269614108 120 Example 2(c)(d)

Activity 9781269614108 121 Exercise 4 Exploration 1


(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate

(i) communicate mathematical ideas using multiple representations, including symbols as appropriate Instruction 9781269614108 140 Example 1







(ii) communicate mathematical ideas using multiple representations, including diagrams as appropriate Instruction 9781269614108 140-141 Example 2

Activity 9781269614108 77 Exercises 50, 52



(iii) communicate mathematical ideas using multiple representations, including graphs as appropriate Instruction 9781269614108 767-768 Example 3

Activity 9781269614108 150 Exercise 49(e)



(iv) communicate mathematical ideas using multiple representations, including language as appropriate Instruction 9781269614108 668 Principle of Mathematical Induction

Activity 9781269614108 150 Exercise 49(f)






(v) communicate mathematical reasoning using multiple representations, including symbols as appropriate Instruction 9781269614108 140 Example 1




(vi) communicate mathematical reasoning using multiple representations, including diagrams as appropriate Instruction 9781269614108 711-712 Normal Distribution




(vii) communicate mathematical reasoning using multiple representations, including graphs as appropriate Instruction 9781269614108 767-768 Example 3







(viii) communicate mathematical reasoning using multiple representations, including language as appropriate Instruction 9781269614108 668 Principle of Mathematical Induction




(ix) communicate [mathematical ideas'] implications using multiple representations, including symbols as appropriate Instruction 9781269614108 140 Example 1




(x) communicate [mathematical ideas'] implications using multiple representations, including diagrams as appropriate Instruction 9781269614108 683-684 Example 8

Activity 9781269614108 715 Exercise 39(a)






(xi) communicate [mathematical ideas'] implications using multiple representations, including graphs as appropriate Instruction 9781269614108 163 Example 3




(xii) communicate [mathematical ideas'] implications using multiple representations, including language as appropriate Instruction 9781269614108 162 Correlation vs. Causation

Assessment 9781269614108 675 Exercise 4



(xiii) communicate [mathematical reasoning's] implications using multiple representations, including symbols as appropriate Instruction 9781269614108 140 Example 1







(xiv) communicate [mathematical reasoning's] implications using multiple representations, including diagrams as appropriate Instruction 9781269614108 711-712 Normal Distributions




(xv) communicate [mathematical reasoning's] implications using multiple representations, including graphs as appropriate Instruction 9781269614108 767-768 Example 3




(xvi) communicate [mathematical reasoning's] implications using multiple representations, including language as appropriate Instruction 9781269614108 162 Correlation vs. Causation



(E) create and use representations to organize, record, and communicate mathematical ideas

(i) create representations to organize mathematical ideas








(ii) create representations to record mathematical ideas





(iii) create representations to communicate mathematical ideas Instruction 9781269614108 698 Example 6

Activity 9781269614108 701 Exercise 25-27 (Use together)



(iv) use representations to organize mathematical ideas





(v) use representations to record mathematical ideas








(vi) use representations to communicate mathematical ideas Instruction 9781269614108 698 Example 6

Activity 9781269614108 701 Exercise 25-27 (Use together)


(F) analyze mathematical relationships to connect and communicate mathematical ideas

(i) analyze mathematical relationships to connect mathematical ideas Instruction 9781269614108 180-181 Example 6




(ii) analyze mathematical relationships to communicate mathematical ideas Instruction 9781269614108 222 Example 5



(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication

(i) display mathematical ideas using precise mathematical language in written or oral communication

Instruction 9781269614108 677 Sample Spaces and Probability Functions







(ii) display mathematical arguments using precise mathematical language in written or oral communication

Instruction 9781269614108 668 Principle of Mathematical Induction

Review 9781269614108 674 Exercise 79



(iii) explain mathematical ideas using precise mathematical language in written or oral communication

Instruction 9781269614108 668 Principle of Mathematical Induction




(iv) explain mathematical arguments using precise mathematical language in written or oral communication

Instruction 9781269614108 667 Proof




(v) justify mathematical ideas using precise mathematical language in written or oral communication Instruction 9781269614108 667 Theorem proof

Activity 9781269614108 208 Exercise 69(c)






(vi) justify mathematical arguments using precise mathematical language in written or oral communication

Instruction 9781269614108 667 Theorem Proof


(2) Functions. The student uses process standards in mathematics to explore, describe, and analyze the attributes of functions. The student makes connections between multiple representations of functions and algebraically constructs new functions. The student analyzes and uses functions to model real-world problems. The student is expected to:

(A) use the composition of two functions to model and solve real-world problems

(i) use the composition of two functions to model real-world problems





(ii) use the composition of two functions to solve real-world problems







(B) demonstrate that function composition is not always commutative

(i) demonstrate that function composition is not always commutative

Instruction 9781269614108 111 Composition of Functions



(C) represent a given function as a composite function of two or more functions

(i) represent a given function as a composite function of two or more functions

Instruction 9781269614108 111 Composition of Functions diagram



(D) describe symmetry of graphs of even and odd functions

(i) describe symmetry of graphs of even functions

Instruction 9781269614108 90-91 Symmetry, Example 9(a)







(ii) describe symmetry of graphs of odd functions

Instruction 9781269614108 91 Symmetry



(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

(i) determine an inverse function, when it exists, for a given function over its domain or a subset of its domain Instruction 9781269614108 125 Example 7




(ii) represent the inverse using multiple representations







(F) graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions

(i) graph exponential functions





(ii) graph logarithmic functions





(iii) graph rational functions








(iv) graph polynomial functions





(v) graph power functions

Instruction 9781269614108 176 Exploration 1




(vi) graph trigonometric functions








(vii) graph inverse trigonometric functions

Instruction 9781269614108 378 Inverse Sine Function




(viii) graph piecewise defined functions, including step functions




(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

(i) graph functions, including exponential functions, in mathematical problems








(ii) graph functions, including exponential functions, in real-world problems





(iii) graph functions, including logarithmic functions, in mathematical problems


Review 9781269614108 314 Exercises 35-38



(iv) graph functions, including logarithmic functions, in real-world problems








(v) graph functions, including sine functions, in mathematical problems





(vi) graph functions, including sine functions, in real-world problems





(vii) graph functions, including cosine functions, in mathematical problems








(viii) graph functions, including cosine functions, in real-world problems





(ix) graph functions, including rational functions, in mathematical problems





(x) graph functions, including rational functions, in real-world problems








(xi) graph functions, including polynomial functions, in mathematical problems





(xii) graph functions, including polynomial functions, in real-world problems





(xiii) graph functions, including power functions, in mathematical problems








(xiv) graph functions, including power functions, in real-world problems





(xv) graph functions, including exponential transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614108 258 Example 5




(xvi) graph functions, including exponential transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614108 260 Example 7

Activity 9781269614108 262 Exercise 51Activity 9781269614108 796E Exercises 13-14






(xvii) graph functions, including logarithmic transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614108 279 Example 8




(xviii) graph functions, including logarithmic transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614108 280 Measuring Sound Using Decibels

Activity 9781269614108 282 Exercise 75Activity 9781269614108 796E Exercises 12 and 15

Instruction 9781269614108 796B Example 3



(xix) graph functions, including sine transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614108 353 Example 2







(xx) graph functions, including sine transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614108 355 Constructing a Sinusoidal Model Using

Time

Activity 9781269614108 358 Exercise 76 (c)Activity 9781269614108 796D Exercises 8-10



(xxi) graph functions, including cosine transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614108 352 Example 1




(xxii) graph functions, including cosine transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614108 356 Example 7

Activity 9781269614108 359 Exercise 77(d)Activity 9781269614108 796D Exercises 8-10






(xxiii) graph functions, including rational transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614108 220 Example 2




(xxiv) graph functions, including rational transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614108 231 Example 6

Activity 9781269614108 234 Exercise 35Activity 9781269614108 796D Exercises 5-6




(xxv) graph functions, including polynomial transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614108 185 Example 1







(xxvi) graph functions, including polynomial transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614108 167 Vertical Free-Fall Motion


Instruction 9781269614108 796A Example 1



(xxvii) graph functions, including power transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614108 178 Example 4




(xxviii) graph functions, including power transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614108 179-180 Example 5

Activity 9781269614108 183 Exercise 55Instruction 9781269614108 796A Examples 1 and 2






(xxix) graph functions, including exponential transformations, including f(x) + d , for specific values of d, in mathematical problems Instruction 9781269614108 256 Example 4




(xxx) graph functions, including exponential transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614108 297-298 Example 8




(xxxi) graph functions, including logarithmic transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614108 279 Example 8







(xxxii) graph functions, including logarithmic transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614108 280 Measuring Sound Using Decibels

Activity 9781269614108 282 Exercise 75Activity 9781269614108 796E Exercise 11

Instruction 9781269614108 796B-796C Examples 3-4



(xxxiii) graph functions, including sine transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614108 355 Modeling Periodic Behavior with

Sinusoids




(xxxiv) graph functions, including sine transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614108 356 Example 7







(xxxv) graph functions, including cosine transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614108 355 Example 6




(xxxvi) graph functions, including cosine transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614108 356 Example 7




(xxxvii) graph functions, including rational transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614108 220 Example 2







(xxxviii) graph functions, including rational transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 231 Example 6

Activity 234 Exercise 35



(xxxix) graph functions, including polynomial transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614108 130 Translations of Graphs




(xl) graph functions, including polynomial transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614108 185 Example 1








(xli) graph functions, including power transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614108 164 Example 4




(xlii) graph functions, including power transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614108 167 Vertical Free-Fall Motion





(xliii) graph functions, including exponential transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614108 256 Example 4







(xliv) graph functions, including exponential transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614108 266 Example 3




(xlv) graph functions, including logarithmic transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614108 279 Example 8




(xlvi) graph functions, including logarithmic transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614108 280 Measuring Sound Using Decibels







(xlvii) graph functions, including sine transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614108 354 Graphs of Sinusoids




(xlviii) graph functions, including sine transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614108 355-356 Modeling Periodic Behavior with

Sinusoids

Activity 9781269614108 359 Exercise 78Activity 9781269614108 796D Exercise 8



(xlix) graph functions, including cosine transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614108 352-355 Sinusoids and Transformations







(l) graph functions, including cosine transformations, including f(x - c), for specific values of c , in real-world problems Instruction 9781269614108 354 Example 4

Activity 9781269614108 357 Exercise 53Activity 9781269614108 796D-796E Exercises 9-10



(li) graph functions, including rational transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614108 220 Example 2




(lii) graph functions, including rational transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614108 230-232 Applications







(liii) graph functions, including polynomial transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614108 185 Example 1




(liv) graph functions, including polynomial transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614108 164-166 Quadratic Functions and Their Graphs

Activity 9781269614108 579-580 Exercise 63Activity 9781269614108 796D Exercise 4




(lv) graph functions, including power transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614108 185 Example 1







(lvi) graph functions, including power transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614108 164-166 Quadratic Functions and Their Graphs





(lvii) graph functions, including exponential transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614108 254 Example 3




(lviii) graph functions, including exponential transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614108 266 Example 3







(lix) graph functions, including logarithmic transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614108 279 Example 8




(lx) graph functions, including logarithmic transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614108 280 Measuring Sound Using Decibels


Instruction 9781269614108 796C Example 4



(lxi) graph functions, including sine transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614108 353 Example 2







(lxii) graph functions, including sine transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614108 355-356 Modeling Periodic Behavior with

Sinusoids




(lxiii) graph functions, including cosine transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614108 353 Example 2




(lxiv) graph functions, including cosine transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614108 356 Example 7

Activity 9781269614108 358-359 Exercise 77Activity 9781269614108 796D-796E Exercises 8-10






(lxv) graph functions, including rational transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614108 219-220 Transformations of the Reciprocal

Function




(lxvi) graph functions, including rational transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614108 230-232 Applications





(lxvii) graph functions, including polynomial transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614108 187 Exploration 1







(lxviii) graph functions, including polynomial transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614108 185 Example 1




(lxix) graph functions, including power transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614108 178 Example 4




(lxx) graph functions, power transformations, including f(bx) for specific values of b , in real-world problems


Activity 9781269614108 183 Exercise 57Activity 9781269614108 796D Exercises 1-2 and 5-6






(H) graph arcsin x and arccos x and describe the limitations on the domain

(i) graph arcsin x





(ii) graph arccos x

Instruction 9781269614108 380 Inverse Cosine Function




(iii) describe the limitations on the domain







(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

(i) determine the key features of exponential functions

Instruction 9781269614108 255 Exponential Function




(ii) determine the key features of logarithmic functions

Instruction 9781269614108 278 The Natural Logarithmic Function







(iii) determine the key features of rational functions





(iv) determine the key features of polynomial functions

Instruction 9781269614108 185 Definition







(v) determine the key features of power functions





(vi) determine the key features of trigonometric functions

Instruction 9781269614108 350 The Sine Function







(vii) determine the key features of inverse trigonometric functions





(viii) determine the key features of piecewise defined functions, including step functions








(ix) analyze the key features of exponential functions

Instruction 9781269614108 255 Exponential Function




(x) analyze the key features of logarithmic functions








(xi) analyze the key features of rational functions





(xii) analyze the key features of polynomial functions








(xiii) analyze the key features of power functions





(xiv) analyze the key features of trigonometric functions

Instruction 9781269614108 350 The Sine Function







(xv) analyze the key features of inverse trigonometric functions





(xvi) analyze the key features of piecewise defined functions, including step functions







(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

(i) analyze end behavior of functions, including exponential functions, using infinity notation to communicate this characteristic in mathematical problems

Instruction 9781269614108 256 Exponential Functions




(ii) analyze end behavior of functions, including exponential functions, using infinity notation to communicate this characteristic in real-world problems

Instruction 9781269614108 296-298 Newton’s Law of Cooling

Activity 9781269614108 796E Exercises 17, 18, 25, 26

Instruction 9781269614108 796D End Behavior and Real-World Models and Example 5



(iii) analyze end behavior of functions, including logarithmic functions, using infinity notation to communicate this characteristic in mathematical problems








(iv) analyze end behavior of functions, including logarithmic functions, using infinity notation to communicate this characteristic in real-world problems

Instruction 9781269614108 796C-796D End Behavior and Real-World Models box

Activity 9781269614108 796E Exercises 21-22



(v) analyze end behavior of functions, including rational functions, using infinity notation to communicate this characteristic in mathematical problems Instruction 9781269614108 175 Example 2




(vi) analyze end behavior of functions, including rational functions, using infinity notation to communicate this characteristic in real-world problems Instruction 9781269614108 796C-796D End Behavior and Real-World Models

box and Example 5







(vii) analyze end behavior of functions, including polynomial functions, using infinity notation to communicate this characteristic in mathematical problems





(viii) analyze end behavior of functions, including polynomial functions, using infinity notation to communicate this characteristic in real-world problems





(ix) analyze end behavior of functions, including power functions, using infinity notation to communicate this characteristic in mathematical problems Instruction 9781269614108 175 Example 2







(x) analyze end behavior of functions, including power functions, using infinity notation to communicate this characteristic in real-world problems Instruction 9781269614108 796C-796D End Behavior and Real World Models

box and Example 5




(xi) describe end behavior of functions, including exponential functions, using infinity notation to communicate this characteristic in mathematical problems

Instruction 9781269614108 256 Exponential Functions




(xii) describe end behavior of functions, including exponential functions, using infinity notation to communicate this characteristic in real-world problems

Instruction 9781269614108 796C-796D End Behavior and Real World Models box and Example 5

Activity 9781269614108 796E Exercises 17-18 and 23-26






(xiii) describe end behavior of functions, including logarithmic functions, using infinity notation to communicate this characteristic in mathematical problems





(xiv) describe end behavior of functions, including logarithmic functions, using infinity notation to communicate this characteristic in real-world problems

Instruction 9781269614108 796C-796D End Behavior and Real World Models box




(xv) describe end behavior of functions, including rational functions, using infinity notation to communicate this characteristic in mathematical problems Instruction 9781269614108 221 Graphs of Rational Functions







(xvi) describe end behavior of functions, including rational functions, using infinity notation to communicate this characteristic in real-world problems





(xvii) describe end behavior of functions, including polynomial functions, using infinity notation to communicate this characteristic in mathematical problems





(xviii) describe end behavior of functions, including polynomial functions, using infinity notation to communicate this characteristic in real-world problems








(xix) describe end behavior of functions, including power functions, using infinity notation to communicate this characteristic in mathematical problems Instruction 9781269614108 175 Example 2




(xx) describe end behavior of functions, including power functions, using infinity notation to communicate this characteristic in real-world problems Instruction 9781269614108 796C-796D End Behavior and Real World Models

box and Example 5



(K) analyze characteristics of rational functions and the behavior of the function around the asymptotes, including horizontal, vertical, and oblique asymptotes

(i) analyze characteristics of rational functions








(ii) analyze the behavior of the function around the asymptotes, including horizontal asymptotes Instruction 9781269614108 222 Example 5




(iii) analyze the behavior of the function around the asymptotes, including vertical asymptotes Instruction 9781269614108 223 Example 7




(iv) analyze the behavior of the function around the asymptotes, including oblique asymptotes Instruction 9781269614108 221-222 Example 4 and paragraph above






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

(i) determine various types of discontinuities in the interval (-∞, ∞) as they relate to functions





(ii) explore the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities Instruction 9781269614108 72 Example 9



(M) describe the left-sided behavior and the right-sided behavior of the graph of a function around discontinuities

(i) describe the left-sided behavior of the graph of a function around discontinuities Instruction 9781269614108 223 Example 7







(ii) describe the right-sided behavior of the graph of a function around discontinuities Instruction 9781269614108 223 Example 7



(N) analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems

(i) analyze situations modeled by functions, including exponential functions, to solve real-world problems Instruction 9781269614108 260 Example 7




(ii) analyze situations modeled by functions, including logarithmic functions, to solve real-world problems Instruction 9781269614108 280 Measuring Sound Using Decibels

Activity 9781269614108 281 Exercises 59–60






(iii) analyze situations modeled by functions, including rational functions, to solve real-world problems Instruction 9781269614108 231 Example 6




(iv) analyze situations modeled by functions, including polynomial functions, to solve real-world problems Instruction 9781269614108 167-168 Example 8




(v) analyze situations modeled by functions, including power functions, to solve real-world problems Instruction 9781269614108 180-181 Example 6






(O) develop and use a sinusoidal function that models a situation in mathematical and real-world problems

(i) develop a sinusoidal function that models a situation in mathematical problems Instruction 9781269614108 355 Example 6




(ii) develop a sinusoidal function that models a situation in real-world problems Instruction 9781269614108 356 Example 7




(iii) use a sinusoidal function that models a situation in mathematical problems








(iv) use a sinusoidal function that models a situation in real-world problems




(P) determine the values of the trigonometric functions at the special angles and relate them in mathematical and real-world problems

(i) determine the values of the trigonometric functions at the special angles





(ii) relate them in mathematical problems








(iii) relate them in real-world problems



(3) Relations and geometric reasoning. The student uses the process standards in mathematics to model and make connections between algebraic and geometric relations. The student is expected to:

(A) graph a set of parametric equations

(i) graph a set of parametric equations

Instruction 9781269614108 119 Example 1(c)



(B) convert parametric equations into rectangular relations and convert rectangular relations into parametric equations

(i) convert parametric equations into rectangular relations Instruction 9781269614108 476 Example 2




(ii) convert rectangular relations into parametric equations Instruction 9781269614108 125 Example 7






(C) use parametric equations to model and solve mathematical and real-world problems

(i) use parametric equations to model mathematical problems Instruction 9781269614108 125 Example 7




(ii) use parametric equations to model real-world problems

Instruction 9781269614108 478-481 Simulating Motion with a Grapher




(iii) use parametric equations to solve mathematical problems Instruction 9781269614108 119 Example 1




(iv) use parametric equations to solve real-world problems







(D) graph points in the polar coordinate system and convert between rectangular coordinates and polar coordinates

(i) graph points in the polar coordinate system





(ii) convert between rectangular coordinates and polar coordinates Instruction 9781269614108 616 Example 3



(E) graph polar equations by plotting points and using technology

(i) graph polar equations by plotting points





(ii) graph polar equations by using technology







(F) determine the conic section formed when a plane intersects a double-napped cone

(i) determine the conic section formed when a plane intersects a double-napped cone

Instruction 9781269614108 571-572 Conic Sections



(G) make connections between the locus definition of conic sections and their equations in rectangular coordinates

(i) make connections between the locus definition of conic sections and their equations in rectangular coordinates

Instruction 9781269614108 572 Geometry of a Parabola



(H) use the characteristics of an ellipse to write the equation of an ellipse with center (h, k)

(i) use the characteristics of an ellipse to write the equation of an ellipse with center (h, k)





(ii) use the characteristics of a hyperbola to write the equation of a hyperbola with center (h, k)






(4) Number and measure. The student uses process standards in mathematics to apply appropriate techniques, tools, and formulas to calculate measures in mathematical and real-world problems. The student is expected to:

(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

(i) determine the relationship between the unit circle and the definition of a periodic function to evaluate trigonometric functions in mathematical problems





(ii) determine the relationship between the unit circle and the definition of a periodic function to evaluate trigonometric functions in real-world problems




(B) describe the relationship between degree and radian measure on the unit circle

(i) describe the relationship between degree and radian measure on the unit circle Instruction 9781269614108 346 The 16-Point Unit Circle



(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

(i) represent angles in radians or degrees based on the concept of rotation Instruction 9781269614108 322 Example 2







(ii) find the measure of reference angles





(iii) find the measure of angles in standard position




(D) represent angles in radians or degrees based on the concept of rotation in mathematical and real-world problems, including linear and angular velocity

(i) represent angles in radians or degrees based on the concept of rotation in mathematical problems, including linear velocity





(ii) represent angles in radians or degrees based on the concept of rotation in real-world problems, including linear velocity








(iii) represent angles in radians or degrees based on the concept of rotation in mathematical problems, including angular velocity





(iv) represent angles in radians or degrees based on the concept of rotation in real-world problems, including angular velocity




(E) determine the value of trigonometric ratios of angles and solve problems involving trigonometric ratios in mathematical and real-world problems

(i) determine the value of trigonometric ratios of angles





(ii) solve problems involving trigonometric ratios in mathematical problems Instruction 9781269614108 333 Example 5







(iii) solve problems involving trigonometric ratios in real-world problems Instruction 9781269614108 334 Example 6



(F) use trigonometry in mathematical and real-world problems, including directional bearing

(i) use trigonometry in mathematical, including directional bearing Instruction 9781269614108 390 Example 4




(ii) use trigonometry in real-world problems, including directional bearing Instruction 9781269614108 390 Example 4



(G) use the Law of Sines in mathematical and real-world problems

(i) use the Law of Sines in mathematical problems








(ii) use the Law of Sines in real-world problems




(H) use the Law of Cosines in mathematical and real-world problems

(i) use the Law of Cosines in mathematical problems





(ii) use the Law of Cosines in real-world problems




(I) use vectors to model situations involving magnitude and direction

(i) use vectors to model situations involving magnitude and direction Instruction 9781269614108 458 Example 2






(J) represent the addition of vectors and the multiplication of a vector by a scalar geometrically and symbolically

(i) represent the addition of vectors geometrically





(ii) represent the addition of vectors symbolically





(iii) represent the multiplication of a vector by a scalar geometrically Instruction 9781269614108 459 Example 3




(iv) represent the multiplication of a vector by a scalar symbolically Instruction 9781269614108 459 Example 3






(K) apply vector addition and multiplication of a vector by a scalar in mathematical and real-world problems

(i) apply vector addition in mathematical problems





(ii) apply vector addition in real-world problems

Instruction 9781269614108 463 Chapter Opener




(iii) apply multiplication of a vector by a scalar in mathematical problems Instruction 9781269614108 459 Example 3




(iv) apply multiplication of a vector by a scalar in real-world problems Instruction 9781269614108 471 Example 6





(5) Algebraic reasoning. The student uses process standards in mathematics to evaluate expressions, describe patterns, formulate models, and solve equations and inequalities using properties, procedures, or algorithms. The student is expected to:

(A) evaluate finite sums and geometric series, when possible, written in sigma notation

(i) evaluate finite sums written in sigma notation

Instruction 9781269614108 658 Summation Notation




(ii) evaluate geometric series, when possible, written in sigma notation Instruction 9781269614108 663 Example 4



(B) represent arithmetic sequences and geometric sequences using recursive formulas

(i) represent arithmetic sequences using recursive formulas Instruction 9781269614108 650-651 Example 2

Activity 9781269614108 656 Exercise 21(c)-24(c)



(ii) represent geometric sequences using recursive formulas Instruction 9781269614108 653 Example 6

Activity 9781269614108 656 Exercise 25(c)-28( c )





(C) calculate the n th term and the n th partial sum of an arithmetic series in mathematical and real-world problems

(i) calculate the n th term of an arithmetic series in mathematical problems Instruction 9781269614108 652 Example 5(b)




(ii) calculate the n th term of an arithmetic series in real-world problems Instruction 9781269614108 660 Example 1




(iii) calculate the n th partial sum of an arithmetic series in mathematical problems Instruction 9781269614108 660 Example 1

Review 9781269614108 664 Exercise 3



(iv) calculate the n th partial sum of an arithmetic series in real-world problems Instruction 9781269614108 660 Example 1






(D) represent arithmetic series and geometric series using sigma notation

(i) represent arithmetic series using sigma notation

Instruction 9781269614108 659-660 Theorem

Review 9781269614108 674 Exercise 72



(ii) represent geometric series using sigma notation




(E) calculate the n th term of a geometric series, the n th

partial sum of a geometric series, and sum of an infinite geometric series when it exists

(i) calculate the n th term of a geometric series






(ii) calculate the n th partial sum of a geometric series


Review 9781269614108 674 Exercise 63







(iii) calculate the 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 and b for a positive integer n , where a and b are any numbers

(i) apply the Binomial Theorem for the expansion of (a + b) n in powers of a and b for a positive integer n , where a and b are any numbers




(G) use the properties of logarithms to evaluate or transform logarithmic expressions

(i) use the properties of logarithms to evaluate or transform logarithmic expressions Instruction 9781269614108 275 Example 2



(H) generate and solve logarithmic equations in mathematical and real-world problems

(i) generate logarithmic equations in mathematical problems Instruction 9781269614108 288 Example 7

Review 9781269614108 315 Exercise 72






(ii) generate logarithmic equations in real-world problems Instruction 9781269614108 288 Example 7




(iii) solve logarithmic equations in mathematical problems Instruction 9781269614108 276 Example 5

Review 9781269614108 315 Exercise 50



(iv) solve logarithmic equations in real-world problems Instruction 9781269614108 295 Example 5



(I) generate and solve exponential equations in mathematical and real-world problems

(i) generate exponential equations in mathematical problems Instruction 9781269614108 260 Example 7

Review 9781269614108 315 Exercise 68






(ii) generate exponential equations in real-world problems Instruction 9781269614108 260 Example 7

Review 9781269614108 315 Exercise 74



(iii) solve exponential equations in mathematical problems Instruction 9781269614108 292 Example 1




(iv) solve exponential equations in real-world problems Instruction 9781269614108 260 Example 7



(J) solve polynomial equations with real coefficients by applying a variety of techniques in mathematical and real-world problems

(i) solve polynomial equations with real coefficients by applying a variety of techniques in mathematical problems








(ii) solve polynomial equations with real coefficients by applying a variety of techniques in real-world problems

Instruction 9781269614108 166-168 Applications



(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 problems

(i) solve polynomial inequalities with real coefficients by applying a variety of techniques in mathematical and real-world problems





(ii) write the solution set of the polynomial inequality in interval notation in mathematical problems








(iii) write the solution set of the polynomial inequality in interval notation in real-world problems




(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

(i) solve rational inequalities with real coefficients by applying a variety of techniques Instruction 9781269614108 239 Example 5




(ii) write the solution set of the rational inequality in interval notation in mathematical problems Instruction 9781269614108 239 Example 5







(iii) write the solution set of the rational inequality in interval notation in real-world problems Instruction 9781269614108 241-242 Example 10



(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

(i) use trigonometric identities for cosine to simplify trigonometric expressions Instruction 9781269614108 408 Example 5




(ii) use trigonometric identities for sine to simplify trigonometric expressions







(N) generate and solve trigonometric equations in mathematical and real-world problems

(i) generate trigonometric equations in mathematical problems Instruction 9781269614108 442 Deriving the Law of Cosines




(ii) generate trigonometric equations in real-world problems Instruction 9781269614108 445-446 Example 5

Review 9781269614108 452 Exercise 63



(iii) solve trigonometric equations in mathematical problems Instruction 9781269614108 408-409 Example 6




(iv) solve trigonometric equations in real-world problems Instruction 9781269614108 389 Example 2



Page 86 of 273 Pearson Education, Inc., publishing as Prentice Hall: 9781269614108 Teacher Material



(2) The process standards describe ways in which students are expected to engage in the content. The placement of the process standards at the beginning of the knowledge and skills listed for each grade and course is intentional. The process standards weave the other knowledge and skills together so that students may be successful problem solvers and use mathematics efficiently and effectively in daily life. The process standards are integrated at every grade level and course. When possible, students will apply mathematics to problems arising in everyday life, society, and the workplace. Students will 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. Students will select appropriate tools such as real objects, manipulatives, paper and pencil, and technology and techniques such as mental math, estimation, and number sense to solve problems. Students will effectively communicate mathematical ideas, 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 analyze mathematical relationships to connect and communicate mathematical ideas. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

(3) Precalculus is the preparation for calculus. The course approaches topics from a function point of view, where appropriate, and is designed to strengthen and enhance conceptual understanding and mathematical reasoning used when modeling and solving mathematical and real-world problems. Students systematically work with functions and their multiple representations. The study of Precalculus deepens students' mathematical understanding and fluency with algebra and trigonometry and extends their ability to make connections and apply concepts and procedures at higher levels. Students investigate and explore mathematical ideas, develop multiple strategies for analyzing complex situations, and use technology to build understanding, make connections between representations, and provide support in solving problems.

(4) Statements that contain the word "including" reference content that must be mastered, while those containing the phrase "such as" are intended as possible illustrative examples.

(c) Knowledge and Skills.

Correlations to the Texas Essential Knowledge and Skills (TEKS): Teacher Material

Chapter 111. MathematicsSubchapter C. High School§111.42. Precalculus, Adopted 2012 (One-Half to One Credit).Pearson Education, Inc., publishing as Prentice HallPrecalculus: Graphical, Numerical, Algebraic, Texas Edition9781269614108

(a) General requirements. Students shall be awarded one-half to one credit for successful completion of this course. Prerequisites: Algebra I, Geometry, and Algebra II.

(b) Introduction.

(1) The desire to achieve educational excellence is the driving force behind the Texas essential knowledge and skills for mathematics, guided by the college and career readiness standards. By embedding statistics, probability, and finance, while focusing on fluency and solid understanding, Texas will lead the way in mathematics education and prepare all Texas students for the challenges they will face in the 21st century.






(i) apply mathematics to problems arising in everyday life Instruction 9781269614382 323-324 Example 5




(ii) apply mathematics to problems arising in society





(iii) apply mathematics to problems arising in the workplace Instruction 9781269614382 719-720 Example 3




(i) 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

Instruction 9781269614382 70-71 Problem Solving







(ii) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the reasonableness of the solution

Instruction 9781269614382 332 Common Calculator Errors




(i) select tools, including real objects as appropriate, to solve problems

Instruction 9781269614382 250 Modeling the height of a bouncing ball

Activity 9781269614382 250 Explorations 1-6



(ii) select tools, including manipulatives as appropriate, to solve problems

Instruction 9781269614382 582-583 Geometry of an ellipse







(iii) select tools, including paper and pencil as appropriate, to solve problems

Instruction 9781269614382 584, 594 Drawing Lessons

Activity 9781269614382 579 Exercises 31-36Instruction 9781269614382 594 Drawing Lessons



(iv) select tools, including technology as appropriate, to solve problems

Instruction 9781269614382 332 Last paragraph




(v) select techniques, including mental math as appropriate, to solve problems

Instruction 9781269614382 320 Degrees and Radians

Activity 9781269614382 325 Exercises 1-2, 5-6






(vi) select techniques including estimation as appropriate, to solve problems


Activity 9781269614382 208 Exercise 69(d)



(vii) select techniques, including number sense as appropriate, to solve problems

Instruction 9781269614382 43 Agreement About Approximate Solutions




(i) communicate mathematical ideas using multiple representations, including symbols as appropriate Instruction 9781269614382 125 Example 7







(ii) communicate mathematical ideas using multiple representations, including diagrams as appropriate Instruction 9781269614382 323-324 Angular and Linear Motion




(iii) communicate mathematical ideas using multiple representations, including graphs as appropriate Instruction 9781269614382 163 Example 3




(iv) communicate mathematical ideas using multiple representations, including language as appropriate Instruction 9781269614382 668 Principle of Mathematical Induction







(v) communicate mathematical reasoning using multiple representations, including symbols as appropriate Instruction 9781269614382 125 Example 7




(vi) communicate mathematical reasoning using multiple representations, including diagrams as appropriate Instruction 9781269614382 723 Normal Model




(vii) communicate mathematical reasoning using multiple representations, including graphs as appropriate Instruction 9781269614382 163 Example 3







(viii) communicate mathematical reasoning using multiple representations, including language as appropriate Instruction 9781269614382 668 Principle of Mathematical Induction




(ix) communicate [mathematical ideas'] implications using multiple representations, including symbols as appropriate Instruction 9781269614382 125 Example 7




(x) communicate [mathematical ideas'] implications using multiple representations, including diagrams as appropriate Instruction 9781269614382 644 Powers of Binomials







(xi) communicate [mathematical ideas'] implications using multiple representations, including graphs as appropriate Instruction 9781269614382 767-768 Example 3




(xii) communicate [mathematical ideas'] implications using multiple representations, including language as appropriate Instruction 9781269614382 162 Correlation vs. Causation




(xiii) communicate [mathematical reasoning's] implications using multiple representations, including symbols as appropriate Instruction 9781269614382 125 Example 7







(xiv) communicate [mathematical reasoning's] implications using multiple representations, including diagrams as appropriate Instruction 9781269614382 723 Normal Model




(xv) communicate [mathematical reasoning's] implications using multiple representations, including graphs as appropriate Instruction 9781269614382 163 Example 3




(xvi) communicate [mathematical reasoning's] implications using multiple representations, including language as appropriate Instruction 9781269614382 162 Correlation vs. Causation




(i) create representations to organize mathematical ideas








(ii) create representations to record mathematical ideas





(iii) create representations to communicate mathematical ideas Instruction 9781269614382 699 Example 7




(iv) use representations to organize mathematical ideas





(v) use representations to record mathematical ideas








(vi) use representations to communicate mathematical ideas Instruction 9781269614382 696 Example 5




(i) analyze mathematical relationships to connect mathematical ideas Instruction 9781269614382 199 Fundamental Connections for

Polynomial Functions




(ii) analyze mathematical relationships to communicate mathematical ideas Instruction 9781269614382 163 Example 3




(i) display mathematical ideas using precise mathematical language in written or oral communication

Instruction 9781269614382 677 Sample Spaces and Probability Functions







(ii) display mathematical arguments using precise mathematical language in written or oral communication


Review 9781269614382 674 Exercise 84



(iii) explain mathematical ideas using precise mathematical language in written or oral communication





(iv) explain mathematical arguments using precise mathematical language in written or oral communication





(v) justify mathematical ideas using precise mathematical language in written or oral communication Instruction 9781269614382 668 Example 1







(vi) justify mathematical arguments using precise mathematical language in written or oral communication





(i) use the composition of two functions to model real-world problems





(ii) use the composition of two functions to solve real-world problems







(B) demonstrate that function composition is not always commutative

(i) demonstrate that function composition is not always commutative

Instruction 9781269614382 118 Exercise 54 (First sentence teaches.)



(C) represent a given function as a composite function of two or more functions

(i) represent a given function as a composite function of two or more functions





(i) describe symmetry of graphs of even functions








(ii) describe symmetry of graphs of odd functions

Instruction 9781269614382 92 Example 9(c)




(i) determine an inverse function, when it exists, for a given function over its domain or a subset of its domain Instruction 9781269614382 123 Example 5




(ii) represent the inverse using multiple representations

Instruction 9781269614382 121-122 Inverse Relations and Inverse Functions







(i) graph exponential functions





(ii) graph logarithmic functions





(iii) graph rational functions

Instruction 9781269614382 219-220 Exploration 1

Activity 9781269614382 232 Exercise 13-18






(iv) graph polynomial functions





(v) graph power functions





(vi) graph trigonometric functions








(vii) graph inverse trigonometric functions

Instruction 9781269614382 380 Inverse Cosine and Tangent Functions

Activity 9781269614382 796D Exercise 7



(viii) graph piecewise defined functions, including step functions





(i) graph functions, including exponential functions, in mathematical problems


Review 9781269614382 315 Exercise 73






(ii) graph functions, including exponential functions, in real-world problems

Instruction 9781269614382 305-306 Example 3 and 4

Activity 9781269614382 156 Exercise 1, 2



(iii) graph functions, including logarithmic functions, in mathematical problems


Review 9781269614382 314 Exercise 35-38



(iv) graph functions, including logarithmic functions, in real-world problems


Review 9781269614382 315 Exercise 73






(v) graph functions, including sine functions, in mathematical problems





(vi) graph functions, including sine functions, in real-world problems





(vii) graph functions, including cosine functions, in mathematical problems








(viii) graph functions, including cosine functions, in real-world problems





(ix) graph functions, including rational functions, in mathematical problems

Instruction 9781269614382 219-220 Exploration 1




(x) graph functions, including rational functions, in real-world problems








(xi) graph functions, including polynomial functions, in mathematical problems





(xii) graph functions, including polynomial functions, in real-world problems





(xiii) graph functions, including power functions, in mathematical problems








(xiv) graph functions, including power functions, in real-world problems





(xv) graph functions, including exponential transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614382 256 Example 4




(xvi) graph functions, including exponential transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614382 297-298 Example 8







(xvii) graph functions, including logarithmic transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614382 279 Example 8




(xviii) graph functions, including logarithmic transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614382 280 Measuring Sound Using Decibels

Activity 9781269614382 282 Exercise 75Activity 9781269614382 796E Exercises 12 and 15




(xix) graph functions, including sine transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614382 353 Example 2







(xx) graph functions, including sine transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614382 355 Constructing a Sinusoidal Model Using

Time

Activity 9781269614382 359 Exercise 78(d)Activity 9781269614382 796D Exercises 8-10



(xxi) graph functions, including cosine transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614382 352 Example 1




(xxii) graph functions, including cosine transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614382 356 Example 7







(xxiii) graph functions, including rational transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614382 131-132 Example 3




(xxiv) graph functions, including rational transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614382 231-232 Example 7





(xxv) graph functions, including polynomial transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614382 187 Exploration 1







(xxvi) graph functions, including polynomial transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614382 167-168 Example 8

Activity 9781269614382 208 Exercise 72(b)Activity 9781269614382 796D Exercises 1-4




(xxvii) graph functions, including power transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614382 177 Example 3




(xxviii) graph functions, including power transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614382 180-181 Example 6

Activity 9781269614382 183 Exercise 57Instruction 9781269614382 796B Examples 1 and 2






(xxix) graph functions, including exponential transformations, including f(x) + d , for specific values of d, in mathematical problems Instruction 9781269614382 256 Example 4




(xxx) graph functions, including exponential transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614382 297-298 Example 8




(xxxi) graph functions, including logarithmic transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614382 279 Example 8







(xxxii) graph functions, including logarithmic transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614382 280 Measuring Sound Using Decibels

Activity 9781269614382 282 Exercise 75Activity 9781269614382 796E Exercise 11

Instruction 9781269614382 796B-796C Examples 3-4



(xxxiii) graph functions, including sine transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614382 355 Modeling Periodic Behavior with

Sinusoids




(xxxiv) graph functions, including sine transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614382 356 Example 7







(xxxv) graph functions, including cosine transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614382 355 Example 6




(xxxvi) graph functions, including cosine transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614382 356 Example 7




(xxxvii) graph functions, including rational transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614382 220 Example 2







(xxxviii) graph functions, including rational transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614382 231-232 Example 7




(xxxix) graph functions, including polynomial transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614382 185 Example 1




(xl) graph functions, including polynomial transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614382 185 Example 1








(xli) graph functions, including power transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614382 164 Example 4




(xlii) graph functions, including power transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614382 167 Vertical Free-Fall Motion





(xliii) graph functions, including exponential transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614382 256 Example 4







(xliv) graph functions, including exponential transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614382 267 Example 5




(xlv) graph functions, including logarithmic transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614382 279 Example 8




(xlvi) graph functions, including logarithmic transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614382 280 Measuring Sound Using Decibels







(xlvii) graph functions, including sine transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614382 354 Graphs of Sinusoids




(xlviii) graph functions, including sine transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614382 355-356 Modeling Periodic Behavior with

Sinusoids

Activity 9781269614382 359 Exercise 78Activity 9781269614382 796D Exercise 8



(xlix) graph functions, including cosine transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614382 352-355 Sinusoids and Transformations







(l) graph functions, including cosine transformations, including f(x - c), for specific values of c , in real-world problems Instruction 9781269614382 354 Example 5




(li) graph functions, including rational transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614382 219 Exploration 1




(lii) graph functions, including rational transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614382 230-232 Applications







(liii) graph functions, including polynomial transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614382 185 Example 1




(liv) graph functions, including polynomial transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614382 164-166 Quadratic Functions and Their Graphs





(lv) graph functions, including power transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614382 185 Example 1







(lvi) graph functions, including power transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614382 164-166 Quadratic Functions and Their Graphs





(lvii) graph functions, including exponential transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614382 258 Example 5




(lviii) graph functions, including exponential transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614382 266-267 Example 4







(lix) graph functions, including logarithmic transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614382 279 Example 8




(lx) graph functions, including logarithmic transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614382 280 Measuring Sound Using Decibels


Instruction 9781269614382 796C Example 4



(lxi) graph functions, including sine transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614382 353 Example 3







(lxii) graph functions, including sine transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614382 355-356 Modeling Periodic Behavior with

Sinusoids




(lxiii) graph functions, including cosine transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614382 353 Example 3




(lxiv) graph functions, including cosine transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614382 356 Example 7







(lxv) graph functions, including rational transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614382 219-220 Transformations of the Reciprocal

Function




(lxvi) graph functions, including rational transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614382 230-232 Applications





(lxvii) graph functions, including polynomial transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614382 188 Example 3







(lxviii) graph functions, including polynomial transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614382 185 Example 1




(lxix) graph functions, including power transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614382 177 Example 3




(lxx) graph functions, power transformations, including f(bx) for specific values of b , in real-world problems


Activity 9781269614382 183 Exercise 55Activity 9781269614382 796D Exercises 1-2 and 5-6







(i) graph arcsin x





(ii) graph arccos x





(iii) describe the limitations on the domain








(i) determine the key features of exponential functions





(ii) determine the key features of logarithmic functions

Instruction 9781269614382 101 Figure 1.47







(iii) determine the key features of rational functions





(iv) determine the key features of polynomial functions








(v) determine the key features of power functions

Instruction 9781269614382 174 Power Function and Variation




(vi) determine the key features of trigonometric functions

Instruction 9781269614382 354 Graphs of Sinusoidal Functions







(vii) determine the key features of inverse trigonometric functions





(viii) determine the key features of piecewise defined functions, including step functions

Instruction 9781269614382 101 Example Figure 1.46







(ix) analyze the key features of exponential functions





(x) analyze the key features of logarithmic functions

Instruction 9781269614382 101 Figure 1.47







(xi) analyze the key features of rational functions





(xii) analyze the key features of polynomial functions








(xiii) analyze the key features of power functions

Instruction 9781269614382 174 Power Function and Variation




(xiv) analyze the key features of trigonometric functions

Instruction 9781269614382 354 Graphs of Sinusoidal Functions







(xv) analyze the key features of inverse trigonometric functions

Instruction 9781269614382 380 Inverse Cosine and Tangent Functions




(xvi) analyze the key features of piecewise defined functions, including step functions

Instruction 9781269614382 101 Example Figure 1.46







(i) analyze end behavior of functions, including exponential functions, using infinity notation to communicate this characteristic in mathematical problems

Instruction 9781269614382 259 The Logistic Function




(ii) analyze end behavior of functions, including exponential functions, using infinity notation to communicate this characteristic in real-world problems

Instruction 9781269614382 296-298 Newton’s Law of Cooling

Activity 9781269614382 796E Exercises 17, 18, 25, 26

Instruction 9781269614382 796D End Behavior and Real-World Models and Example 5



(iii) analyze end behavior of functions, including logarithmic functions, using infinity notation to communicate this characteristic in mathematical problems

Instruction 9781269614382 287 Logarithmic Functions







(iv) analyze end behavior of functions, including logarithmic functions, using infinity notation to communicate this characteristic in real-world problems





(v) analyze end behavior of functions, including rational functions, using infinity notation to communicate this characteristic in mathematical problems Instruction 9781269614382 221-222 Example 4




(vi) analyze end behavior of functions, including rational functions, using infinity notation to communicate this characteristic in real-world problems Instruction 9781269614382 796C-796D End Behavior and Real-World Models

box and Example 5







(vii) analyze end behavior of functions, including polynomial functions, using infinity notation to communicate this characteristic in mathematical problems

Instruction 9781269614382 187 End Behavior of Polynomial Functions




(viii) analyze end behavior of functions, including polynomial functions, using infinity notation to communicate this characteristic in real-world problems





(ix) analyze end behavior of functions, including power functions, using infinity notation to communicate this characteristic in mathematical problems Instruction 9781269614382 175 Example 2







(x) analyze end behavior of functions, including power functions, using infinity notation to communicate this characteristic in real-world problems Instruction 9781269614382 796C-796D End Behavior and Real World Models

box and Example 5




(xi) describe end behavior of functions, including exponential functions, using infinity notation to communicate this characteristic in mathematical problems

Instruction 9781269614382 259 The Logistic Function




(xii) describe end behavior of functions, including exponential functions, using infinity notation to communicate this characteristic in real-world problems


Activity 9781269614382 796E Exercises 17-18 and 23-26






(xiii) describe end behavior of functions, including logarithmic functions, using infinity notation to communicate this characteristic in mathematical problems

Instruction 9781269614382 287 Logarithmic Functions




(xiv) describe end behavior of functions, including logarithmic functions, using infinity notation to communicate this characteristic in real-world problems





(xv) describe end behavior of functions, including rational functions, using infinity notation to communicate this characteristic in mathematical problems Instruction 9781269614382 221-222 Example 4







(xvi) describe end behavior of functions, including rational functions, using infinity notation to communicate this characteristic in real-world problems





(xvii) describe end behavior of functions, including polynomial functions, using infinity notation to communicate this characteristic in mathematical problems

Instruction 9781269614382 187 End Behavior of Polynomial Functions




(xviii) describe end behavior of functions, including polynomial functions, using infinity notation to communicate this characteristic in real-world problems








(xix) describe end behavior of functions, including power functions, using infinity notation to communicate this characteristic in mathematical problems Instruction 9781269614382 175 Example 2




(xx) describe end behavior of functions, including power functions, using infinity notation to communicate this characteristic in real-world problems Instruction 9781269614382 796C-796D End Behavior and Real World Models

box and Example 5




(i) analyze characteristics of rational functions








(ii) analyze the behavior of the function around the asymptotes, including horizontal asymptotes Instruction 9781269614382 221-222 Example 4




(iii) analyze the behavior of the function around the asymptotes, including vertical asymptotes Instruction 9781269614382 224 Example 8




(iv) analyze the behavior of the function around the asymptotes, including oblique asymptotes Instruction 9781269614382 221-222 Example 4 and paragraph above







(i) determine various types of discontinuities in the interval (-∞, ∞) as they relate to functions

Instruction 9781269614382 175 Example 2(b)




(ii) explore the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities Instruction 9781269614382 73 Example 10




(i) describe the left-sided behavior of the graph of a function around discontinuities Instruction 9781269614382 778 Example 6







(ii) describe the right-sided behavior of the graph of a function around discontinuities Instruction 9781269614382 777 Example 4




(i) analyze situations modeled by functions, including exponential functions, to solve real-world problems Instruction 9781269614382 261 Example 8




(ii) analyze situations modeled by functions, including logarithmic functions, to solve real-world problems Instruction 9781269614382 796B-796C Example 3







(iii) analyze situations modeled by functions, including rational functions, to solve real-world problems Instruction 9781269614382 230-231 Example 5




(iv) analyze situations modeled by functions, including polynomial functions, to solve real-world problems Instruction 9781269614382 167-168 Example 8




(v) analyze situations modeled by functions, including power functions, to solve real-world problems Instruction 9781269614382 179-180 Example 5







(i) develop a sinusoidal function that models a situation in mathematical problems Instruction 9781269614382 356 Example 7




(ii) develop a sinusoidal function that models a situation in real-world problems Instruction 9781269614382 356 Example 7




(iii) use a sinusoidal function that models a situation in mathematical problems








(iv) use a sinusoidal function that models a situation in real-world problems





(i) determine the values of the trigonometric functions at the special angles





(ii) relate them in mathematical problems








(iii) relate them in real-world problems




(A) graph a set of parametric equations

(i) graph a set of parametric equations





(i) convert parametric equations into rectangular relations Instruction 9781269614382 477 Examples 3–4




(ii) convert rectangular relations into parametric equations Instruction 9781269614382 344-345 Trigonometric Functions of Real

Numbers







(i) use parametric equations to model mathematical problems Instruction 9781269614382 125 Example 7




(ii) use parametric equations to model real-world problems





(iii) use parametric equations to solve mathematical problems Instruction 9781269614382 125 Example 7




(iv) use parametric equations to solve real-world problems








(i) graph points in the polar coordinate system





(ii) convert between rectangular coordinates and polar coordinates Instruction 9781269614382 616 Example 3




(i) graph polar equations by plotting points





(ii) graph polar equations by using technology







(F) determine the conic section formed when a plane intersects a double-napped cone

(i) determine the conic section formed when a plane intersects a double-napped cone

Instruction 9781269614382 571-572 Conic Sections



(G) make connections between the locus definition of conic sections and their equations in rectangular coordinates

(i) make connections between the locus definition of conic sections and their equations in rectangular coordinates

Instruction 9781269614382 572 Geometry of a Parabola




(i) use the characteristics of an ellipse to write the equation of an ellipse with center (h, k)





(ii) use the characteristics of a hyperbola to write the equation of a hyperbola with center (h, k)








(i) determine the relationship between the unit circle and the definition of a periodic function to evaluate trigonometric functions in mathematical problems





(ii) determine the relationship between the unit circle and the definition of a periodic function to evaluate trigonometric functions in real-world problems




(B) describe the relationship between degree and radian measure on the unit circle

(i) describe the relationship between degree and radian measure on the unit circle Instruction 9781269614382 346 The 16-Point Unit Circle




(i) represent angles in radians or degrees based on the concept of rotation Instruction 9781269614382 321 Example 1







(ii) find the measure of reference angles





(iii) find the measure of angles in standard position





(i) represent angles in radians or degrees based on the concept of rotation in mathematical problems, including linear velocity





(ii) represent angles in radians or degrees based on the concept of rotation in real-world problems, including linear velocity








(iii) represent angles in radians or degrees based on the concept of rotation in mathematical problems, including angular velocity





(iv) represent angles in radians or degrees based on the concept of rotation in real-world problems, including angular velocity





(i) determine the value of trigonometric ratios of angles





(ii) solve problems involving trigonometric ratios in mathematical problems Instruction 9781269614382 331 Example 3







(iii) solve problems involving trigonometric ratios in real-world problems Instruction 9781269614382 334 Example 6




(i) use trigonometry in mathematical, including directional bearing Instruction 9781269614382 390 Example 4




(ii) use trigonometry in real-world problems, including directional bearing Instruction 9781269614382 390 Example 4




(i) use the Law of Sines in mathematical problems








(ii) use the Law of Sines in real-world problems





(i) use the Law of Cosines in mathematical problems





(ii) use the Law of Cosines in real-world problems




(I) use vectors to model situations involving magnitude and direction

(i) use vectors to model situations involving magnitude and direction Instruction 9781269614382 461-462 Example 7







(i) represent the addition of vectors geometrically

Instruction 9781269614382 458-459 Vector Operations




(ii) represent the addition of vectors symbolically

Instruction 9781269614382 458-459 Vector Operations




(iii) represent the multiplication of a vector by a scalar geometrically Instruction 9781269614382 459 Example 3




(iv) represent the multiplication of a vector by a scalar symbolically Instruction 9781269614382 458 Definition







(i) apply vector addition in mathematical problems





(ii) apply vector addition in real-world problems





(iii) apply multiplication of a vector by a scalar in mathematical problems Instruction 9781269614382 471 Example 7




(iv) apply multiplication of a vector by a scalar in real-world problems Instruction 9781269614382 471 Example 7

Review 9781269614382 464 Quick Review 10






(i) evaluate finite sums written in sigma notation


Review 9781269614382 675 Exercise 75



(ii) evaluate geometric series, when possible, written in sigma notation Instruction 9781269614382 663 Example 4

Review 9781269614382 674 Exercise 77



(i) represent arithmetic sequences using recursive formulas Instruction 9781269614382 652 Example 5

Activity 9781269614382 656 Exercise 21(c)-24(c)



(ii) represent geometric sequences using recursive formulas Instruction 9781269614382 653 Example 6







(i) calculate the n th term of an arithmetic series in mathematical problems Instruction 9781269614382 652 Example 5(b)




(ii) calculate the n th term of an arithmetic series in real-world problems Instruction 9781269614382 660 Example 1




(iii) calculate the n th partial sum of an arithmetic series in mathematical problems Instruction 9781269614382 660 Example 1




(iv) calculate the n th partial sum of an arithmetic series in real-world problems Instruction 9781269614382 660 Example 1







(i) represent arithmetic series using sigma notation





(ii) represent geometric series using sigma notation


Review 9781269614382 674 Exercise 71




(i) calculate the n th term of a geometric series






(ii) calculate the n th partial sum of a geometric series









(iii) calculate the 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 and b for a positive integer n , where a and b are any numbers

(i) apply the Binomial Theorem for the expansion of (a + b) n in powers of a and b for a positive integer n , where a and b are any numbers

Instruction 9781269614382 644 Powers of Binomials



(G) use the properties of logarithms to evaluate or transform logarithmic expressions

(i) use the properties of logarithms to evaluate or transform logarithmic expressions Instruction 9781269614382 274 Example 1




(i) generate logarithmic equations in mathematical problems Instruction 9781269614382 288 Example 7







(ii) generate logarithmic equations in real-world problems Instruction 9781269614382 288 Example 7




(iii) solve logarithmic equations in mathematical problems Instruction 9781269614382 276 Example 5




(iv) solve logarithmic equations in real-world problems Instruction 9781269614382 296 Example 6




(i) generate exponential equations in mathematical problems Instruction 9781269614382 261 Example 8







(ii) generate exponential equations in real-world problems Instruction 9781269614382 261 Example 8

Review 9781269614382 315 Exercise 75



(iii) solve exponential equations in mathematical problems Instruction 9781269614382 292-293 Example 2




(iv) solve exponential equations in real-world problems Instruction 9781269614382 261 Example 8




(i) solve polynomial equations with real coefficients by applying a variety of techniques in mathematical problems








(ii) solve polynomial equations with real coefficients by applying a variety of techniques in real-world problems

Instruction 9781269614382 166-168 Applications




(i) solve polynomial inequalities with real coefficients by applying a variety of techniques in mathematical and real-world problems





(ii) write the solution set of the polynomial inequality in interval notation in mathematical problems








(iii) write the solution set of the polynomial inequality in interval notation in real-world problems





(i) solve rational inequalities with real coefficients by applying a variety of techniques Instruction 9781269614382 240 Example 6




(ii) write the solution set of the rational inequality in interval notation in mathematical problems Instruction 9781269614382 240 Example 8







(iii) write the solution set of the rational inequality in interval notation in real-world problems Instruction 9781269614382 241-242 Example 10




(i) use trigonometric identities for cosine to simplify trigonometric expressions Instruction 9781269614382 407 Example 3




(ii) use trigonometric identities for sine to simplify trigonometric expressions








(i) generate trigonometric equations in mathematical problems Instruction 9781269614382 413 Example 1

Review 9781269614382 451 Exercise 50



(ii) generate trigonometric equations in real-world problems Instruction 9781269614382 446 Example 6

Review 9781269614382 452 Exercise 63



(iii) solve trigonometric equations in mathematical problems Instruction 9781269614382 409 Example 7




(iv) solve trigonometric equations in real-world problems Instruction 9781269614382 390 Example 4



Page 171 of 273 Pearson Education, Inc., publishing as Prentice Hall: 9781269614108 ELPS: Student Material


Knowledge and Skills Statement Student Expectation Breakout Required Grade Level Component ISBN Page (s) Specific Location

1) Cross-curricular second language acquisition/learning strategies. The ELL uses language learning strategies to develop an awareness of his or her own learning processes in all content areas. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:

(A) use prior knowledge and experiences to understand meanings in English

(1) use prior knowledge to understand meanings in English

T: 9-12S: 9-12

9781269614108 110 Lesson 1.4

9781269614108 160 Lesson 2.19781269614108 428 Lesson 5.49781269614108 603 Lesson 8.4

9781269614108

The English language proficiency standards (ELPS) outline English language proficiency level descriptors and student expectations for English language learners (ELLs). School districts are required to implement the ELPS as an integral part of each subject in the required curriculum. This document outlines the ELPS that have been designated as appropriate for inclusion in instructional materials. Since the designated ELPS are included in student materials for English language arts and reading, the ELPS are not required to be included in Proclamation 2015 instructional materials for Kindergarten through grade 5 where students are typically taught in self-contained classroom settings rather than departmentalized classes. Additionally, many of the designated ELPS are most appropriate for inclusion in teacher materials and are only required to be included in student materials where specifically indicated.

(c) Cross-curricular second language acquisition essential knowledge and skills

Correlations to the English Language Proficiency Standards (ELPS): Student Material

Chapter 111. MathematicsSubchapter C. High School§111.42. Precalculus, Adopted 2012 (One-Half to One Credit).Pearson Education, Inc., publishing as Prentice HallPrecalculus: Graphical, Numerical, Algebraic, Texas Edition






(2) use prior experiences to understand meanings in English

T: 9-12S: 9-12

9781269614108 129 Lesson 1.6

9781269614108 363 Lesson 4.59781269614108 621 Lesson 8.6


(B) monitor oral and written language production and employ self-corrective techniques or other resources

(1) monitor oral language production and employ self-corrective techniques or other resources

T: 9-12



(2) monitor written language production and employ self-corrective techniques or other resources

NA





(C) use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary

(1) use strategic learning techniques to acquire basic and grade-level vocabulary

NA


(D) speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known)

(1) speak using learning strategies

T: 9-12S: 9-12

9781269614108 70 Lesson 1.1

9781269614108 737 Lesson 10.5


(E) internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment

(1) internalize new basic language by using and reusing it in meaningful ways in speaking activities that build concept and language attainment

NA






(2) internalize new basic language by using and reusing it in meaningful ways in writing activities that build concept and language attainment

NA



(3) internalize new academic language by using and reusing it in meaningful ways in speaking activities that build concept and language attainment

NA



(4) internalize new academic language by using and reusing it in meaningful ways in writing activities that build concept and language attainment

NA





(F) use accessible language and learn new and essential language in the process

(1) use accessible language and learn new and essential language in the process

T: 9-12


(G) demonstrate an increasing ability to distinguish between formal and informal English and an increasing knowledge of when to use each one commensurate with grade-level learning expectations

(1) demonstrate an increasing ability to distinguish between formal and informal English

NA



(2) demonstrate an increasing knowledge of when to use [formal and informal English] commensurate with grade-level learning expectations

NA





(H) develop and expand repertoire of learning strategies such as reasoning inductively or deductively, looking for patterns in language, and analyzing sayings and expressions commensurate with grade-level learning expectations

(1) develop and expand repertoire of learning strategies

NA

(2) Cross-curricular second language acquisition/listening. The ELL listens to a variety of speakers including teachers, peers, and electronic media to gain an increasing level of comprehension of newly acquired language in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in listening. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:

(A) distinguish sounds and intonation patterns of English with increasing ease

(1) distinguish sounds of English with increasing ease

NA



(2) distinguish intonation patterns of English with increasing ease

NA





(B) recognize elements of the English sound system in newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters

(1) recognize elements of the English sound system in newly acquired vocabulary

NA


(C) learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions

(1) learn new language structures heard during classroom instruction and interactions

T: 9-12



(2) learn new expressions heard during classroom instruction and interactions

T: 9-12






(3) learn basic vocabulary heard during classroom instruction and interactions

T: 9-12S: 9-12

9781269614108 212 Lesson 2.5

9781269614108 481 Lesson 6.39781269614108 774 Lesson 11.3



(4) learn academic vocabulary heard during classroom instruction and interactions

T: 9-12S: 9-12

9781269614108 603 Lesson 8.4

9781269614108 774 Lesson 11.3





(D) monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed

(1) monitor understanding of spoken language during classroom instruction and interactions

T: 9-12



(2) seek clarification [of spoken language] as needed

T: 9-12S: 9-12

9781269614108 244 Lesson 2.6

9781269614108 755 Lesson 11.1





(E) use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language

(1) use visual support to enhance and confirm understanding of increasingly complex and elaborated spoken language

NA



(2) use contextual support to enhance and confirm understanding of increasingly complex and elaborated spoken language

NA



(3) use linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language

T: 9-12S: 9-12

9781269614108 84 Lesson 1.2




9781269614108 670 Lesson 9.59781269614108 755 Lesson 11.1


(F) listen to and derive meaning from a variety of media such as audio tape, video, DVD, and CD ROM to build and reinforce concept and language attainment

(1) listen to and derive meaning from a variety of media to build and reinforce concept attainment

NA



(2) listen to and derive meaning from a variety of media to build and reinforce language attainment

NA





(G) understand the general meaning, main points, and important details of spoken language ranging from situations in which topics, language, and contexts are familiar to unfamiliar

(1) understand the general meaning of spoken language ranging from situations in which topics are familiar to unfamiliar

NA



(2) understand the general meaning of spoken language ranging from situations in which language [is] are familiar to unfamiliar

NA



(3) understand the general meaning of spoken language ranging from situations in which contexts are familiar to unfamiliar

NA






(4) understand the main points of spoken language ranging from situations in which topics are familiar to unfamiliar

NA



(5) understand the main points of spoken language ranging from situations in which language [is] are familiar to unfamiliar

NA



(6) understand the main points of spoken language ranging from situations in which contexts are familiar to unfamiliar

NA






(7) understand the important details of spoken language ranging from situations in which topics are familiar to unfamiliar

NA



(8) understand the important details of spoken language ranging from situations in which language [is] are familiar to unfamiliar

NA



(9) understand the important details of spoken language ranging from situations in which contexts are familiar to unfamiliar

NA





(H) understand implicit ideas and information in increasingly complex spoken language commensurate with grade-level learning expectations

(1) understand implicit ideas in increasingly complex spoken language commensurate with grade-level learning expectations

NA



(2) understand information in increasingly complex spoken language commensurate with grade-level learning expectations

NA


(I) demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs

(1) demonstrate listening comprehension of increasingly complex spoken English by following directions commensurate with content and grade-level needs

NA






(2) demonstrate listening comprehension of increasingly complex spoken English by retelling or summarizing spoken messages commensurate with content and grade-level needs

NA



(3) demonstrate listening comprehension of increasingly complex spoken English by responding to questions and requests commensurate with content and grade-level needs

T: 9-12S: 9-12

9781269614108 405 Lesson 5.1

9781269614108 582 Lesson 8.2






(4) demonstrate listening comprehension of increasingly complex spoken English by collaborating with peers commensurate with content and grade-level needs

T: 9-12



(5) demonstrate listening comprehension of increasingly complex spoken English by taking notes commensurate with content and grade-level needs

T: 9-12S: 9-12

9781269614108 42 Lesson P.5

9781269614108 521 Lesson 7.19781269614108 788 Lesson 11.4




(3) Cross-curricular second language acquisition/speaking. The ELL speaks in a variety of modes for a variety of purposes with an awareness of different language registers (formal/informal) using vocabulary with increasing fluency and accuracy in language arts and all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in speaking. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:

(A) practice producing sounds of newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters to pronounce English words in a manner that is increasingly comprehensible

(1) practice producing sounds of newly acquired vocabulary to pronounce English words in a manner that is increasingly comprehensible

NA


(B) expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication

(1) expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects

NA






(2) expand and internalize initial English vocabulary by retelling simple stories and basic information represented or supported by pictures

NA



(3) expand and internalize initial English vocabulary by learning and using routine language needed for classroom communication

T: 9-12S: 9-12

9781269614108 3 Lesson P.1

9781269614108 725 Lesson 10.4





(C) speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as more English is acquired

(1) speak using a variety of grammatical structures with increasing accuracy and ease as more English is acquired

NA



(2) speak using a variety of sentence lengths with increasing accuracy and ease as more English is acquired

NA






(3) speak using a variety of sentence types with increasing accuracy and ease as more English is acquired

NA



(4) speak using a variety of connecting words with increasing accuracy and ease as more English is acquired

T: 9-12S: 9-12

9781269614108 50 Lesson P.6

9781269614108 445 Lesson 5.6





(D) speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency

(1) speak using grade-level content area vocabulary in context to internalize new English words

T: 9-12S: 9-12

9781269614108 180 Lesson 2.2

9781269614108 503 Lesson 6.69781269614108 737 Lesson 10.5



(2) speak using grade-level content area vocabulary in context to build academic language proficiency

T: 9-12S: 9-12

9781269614108 14 Lesson P.2

9781269614108 424 Lesson 5.39781269614108 463 Lesson 6.1





(E) share information in cooperative learning interactions

(1) share information in cooperative learning interactions

T: 9-12S: 9-12

9781269614108 198 Lesson 2.4

9781269614108 285 Lesson 3.4


(F) ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments

(1) ask [for] information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments

T: 9-12S: 9-12

9781269614108 260 Lesson 3.1

9781269614108 788 Lesson 11.4






(2) give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments

T: 9-12S: 9-12

9781269614108 105 Lesson 1.3

9781269614108 260 Lesson 3.19781269614108 603 Lesson 8.4


(G) express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

(1) express opinions ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

T: 9-12






(2) express ideas ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

T: 9-12



(3) express feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

NA





(H) narrate, describe, and explain with increasing specificity and detail as more English is acquired

(1) narrate with increasing specificity and detail as more English is acquired

NA



(2) describe with increasing specificity and detail as more English is acquired

NA






(3) explain with increasing specificity and detail as more English is acquired

T: 9-12S: 9-12

9781269614108 188 Lesson 2.3



(I) adapt spoken language appropriately for formal and informal purposes

(1) adapt spoken language appropriately for formal purposes

NA






(2) adapt spoken language appropriately for informal purposes

NA


(J) respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept and language attainment

(1) respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept attainment

NA






(2) respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce language attainment

N/A

(4) Cross-curricular second language acquisition/reading. The ELL reads a variety of texts for a variety of purposes with an increasing level of comprehension in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in reading. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For kindergarten and grade 1, certain of these student expectations apply to text read aloud for students not yet at the stage of decoding written text. The student is expected to:

(A) learn relationships between sounds and letters of the English language and decode (sound out) words using a combination of skills such as recognizing sound-letter relationships and identifying cognates, affixes, roots and base words

(1) learn relationships between sounds and letters of the English language

NA






(2) decode (sound out) words using a combination of skills

NA


(B) recognize directionality of English reading such as left to right and top to bottom

(1) recognize directionality of English reading

NA





(C) develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials

(1) develop basic sight vocabulary used routinely in written classroom materials

T: 9-12S: 9-12

9781269614108 143 Lesson 1.7



(2) derive meaning of environmental print

T: 9-12S: 9-12

9781269614108 321 Lesson 4.1

9781269614108 692 Lesson 10.2






(3) comprehend English vocabulary used routinely in written classroom materials

T: 9-12S: 9-12

9781269614108 121 Lesson 1.5

9781269614108 529 Lesson 7.29781269614108 662 Lesson 9.4



(4) comprehend English language structures used routinely in written classroom materials

T: 9-12S: 9-12

9781269614108 21 Lesson P.3

9781269614108 529 Lesson 7.2





(D) use prereading supports such as graphic organizers, illustrations, and pretaught topic-related vocabulary and other prereading activities to enhance comprehension of written text

(1) use prereading supports to enhance comprehension of written text

T: 9-12S: 9-12

9781269614108 304 Lesson 3.6

9781269614108 494 Lesson 6.59781269614108 670 Lesson 9.5


(E) read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned

(1) read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned

T: 9-12





(F) use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language

(1) use visual and contextual support to read grade-appropriate content area text

T: 9-12S: 9-12

9781269614108 388 Lesson 4.8

9781269614108 547 Lesson 7.39781269614108 612 Lesson 8.5



(2) use visual and contextual support to enhance and confirm understanding

T: 9-12S: 9-12

9781269614108 346 Lesson 4.3







(3) use visual and contextual support to develop vocabulary needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614108 350 Lesson 4.4

9781269614108 463 Lesson 6.19781269614108 573 Lesson 8.1



(4) use visual and contextual support to develop grasp of language structures needed to comprehend increasingly challenging language

NA






(5) use visual and contextual support to develop background knowledge needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614108 294 Lesson 3.5




(6) use support from peers and teachers to read grade-appropriate content area text

T: 9-12S: 9-12

9781269614108 280 Lesson 3.3






(7) use support from peers and teachers to enhance and confirm understanding

T: 9-12S: 9-12

9781269614108 224 Lesson 2.6

9781269614108 428 Lesson 5.49781269614108 599 Lesson 8.3



(8) use support from peers and teachers to develop vocabulary needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614108 14 Lesson P.2

9781269614108 638 Lesson 9.1






(9) use support from peers and teachers to develop grasp of language structures needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614108 374 Lesson 4.6

9781269614108 445 Lesson 5.69781269614108 650 Lesson 9.3



(10) use support from peers and teachers to develop background knowledge needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614108 129 Lesson 1.6

9781269614108 467 Lesson 6.2





(G) demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

(1) demonstrate comprehension of increasingly complex English by participating in shared reading commensurate with content area and grade level needs

NA



(2) demonstrate comprehension of increasingly complex English by retelling or summarizing material commensurate with content area and grade level needs

T: 9-12S: 9-12

9781269614108 229 Lesson 2.7

9781269614108 616 Lesson 8.5






(3) demonstrate comprehension of increasingly complex English by responding to questions commensurate with content area and grade level needs

T: 9-12S: 9-12

9781269614108 237 Lesson 2.8

9781269614108 270 Lesson 3.29781269614108 285 Lesson 3.4



(4) demonstrate comprehension of increasingly complex English by taking notes commensurate with content area and grade level needs

T: 9-12S: 9-12

9781269614108 32 Lesson P.4





(H) read silently with increasing ease and comprehension for longer periods

(1) read silently with increasing ease for longer periods

NA



(2) read silently with increasing comprehension for longer periods

NA





(I) demonstrate English comprehension and expand reading skills by employing basic reading skills such as demonstrating understanding of supporting ideas and details in text and graphic sources, summarizing text and distinguishing main ideas from details commensurate with content area needs

(1) demonstrate English comprehension by employing basic reading skills commensurate with content area needs

NA



(2) expand reading skills commensurate with content area needs

NA





(J) demonstrate English comprehension and expand reading skills by employing inferential skills such as predicting, making connections between ideas, drawing inferences and conclusions from text and graphic sources, and finding supporting text evidence commensurate with content area needs

(1) demonstrate English comprehension and expand reading skills by employing inferential skills

NA


(K) demonstrate English comprehension and expand reading skills by employing analytical skills such as evaluating written information and performing critical analyses commensurate with content area and grade level needs

(1) demonstrate English comprehension and expand reading skills by employing analytical skills

NA




(5) Cross-curricular second language acquisition/writing. The ELL writes in a variety of forms with increasing accuracy to effectively address a specific purpose and audience in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in writing. In order for the ELL to meet grade-level learning expectations across foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For kindergarten and grade 1, certain of these student expectations do not apply until the student has reached the stage of generating original written text using a standard writing system. The student is expected to:

(A) learn relationships between sounds and letters of the English language to represent sounds when writing in English

(1) learn relationships between sounds and letters of the English language to represent sounds when writing in English

NA


(B) write using newly acquired basic vocabulary and content-based grade-level vocabulary

(1) write using newly acquired basic vocabulary

NA






(2) write using content-based grade-level vocabulary

NA


(C) spell familiar English words with increasing accuracy, and employ English spelling patterns and rules with increasing accuracy as more English is acquired

(1) spell familiar English words with increasing accuracy

NA






(2) employ English spelling pattern with increasing accuracy as more English is acquired

NA



(3) employ English spelling rules with increasing accuracy as more English is acquired

NA





(D) edit writing for standard grammar and usage, including subject-verb agreement, pronoun agreement, and appropriate verb tenses commensurate with grade-level expectations as more English is acquired

(1) edit writing for standard grammar and usage, including subject-verb agreement commensurate with grade-level expectations as more English is acquired

NA



(2) edit writing for standard grammar and usage, including pronoun agreement, commensurate with grade-level expectations as more English is acquired

NA






(3) edit writing for standard grammar and usage, including appropriate verb tenses, commensurate with grade-level expectations as more English is acquired

NA


(E) employ increasingly complex grammatical structures in content area writing commensurate with grade level expectations such as (i) using correct verbs, tenses, and pronouns/antecedents; (ii) using possessive case (apostrophe -s) correctly; and, (iii) using negatives and contractions correctly

(1) employ increasingly complex grammatical structures in content area writing commensurate with grade level expectations

NA





(F) write using a variety of grade-appropriate sentence lengths, patterns, and connecting words to combine phrases, clauses, and sentences in increasingly accurate ways as more English is acquired

(1) write using a variety of grade-appropriate sentence lengths in increasingly accurate ways as more English is acquired

NA



(2) write using a variety of grade-appropriate sentence patterns in increasingly accurate ways as more English is acquired

NA






(3) write using a variety of grade-appropriate connecting words to combine phrases, clauses, and sentences in increasingly accurate ways as more English is acquired

NA


(G) narrate, describe, and explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired

(1) narrate with increasing specificity and detail to fulfill content area writing needs as more English is acquired

NA






(2) describe with increasing specificity and detail to fulfill content area writing needs as more English is acquired

NA



(3) explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired

NA


Page 222 of 273 Pearson Education, Inc., publishing as Prentice Hall: 9781269614108 ELPS: Teacher Material





(1) use prior knowledge to understand meanings in English

T: 9-12S: 9-12

9781269614382 157b Lesson 2.6

9781269614108

The English language proficiency standards (ELPS) outline English language proficiency level descriptors and student expectations for English language learners (ELLs). School districts are required to implement the ELPS as an integral part of each subject in the required curriculum. This document outlines the ELPS that have been designated as appropriate for inclusion in instructional materials. Since the designated ELPS are included in student materials for English language arts and reading, the ELPS are not required to be included in Proclamation 2015 instructional materials for Kindergarten through grade 5 where students are typically taught in self-contained classroom settings rather than departmentalized classes. Additionally, many of the designated ELPS are most appropriate for inclusion in teacher materials and are only required to be included in student materials where specifically indicated.

(c) Cross-curricular second language acquisition essential knowledge and skills

Correlations to the English Language Proficiency Standards (ELPS): Teacher Material

Chapter 111. MathematicsSubchapter C. High School§111.42. Precalculus, Adopted 2012 (One-Half to One Credit).Pearson Education, Inc., publishing as Prentice HallPrecalculus: Graphical, Numerical, Algebraic, Texas Edition






(2) use prior experiences to understand meanings in English

T: 9-12S: 9-12

9781269614382 319b Lesson 4.7



(1) monitor oral language production and employ self-corrective techniques or other resources

T: 9-12

9781269614382 1b Lesson P.2

9781269614382 157b Lesson 2.5



(2) monitor written language production and employ self-corrective techniques or other resources

NA





(C) use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary

(1) use strategic learning techniques to acquire basic and grade-level vocabulary

NA


(D) speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known)

(1) speak using learning strategies

T: 9-12S: 9-12

9781269614382 63b Lesson 1.1



(1) internalize new basic language by using and reusing it in meaningful ways in speaking activities that build concept and language attainment

NA






(2) internalize new basic language by using and reusing it in meaningful ways in writing activities that build concept and language attainment

NA



(3) internalize new academic language by using and reusing it in meaningful ways in speaking activities that build concept and language attainment

NA



(4) internalize new academic language by using and reusing it in meaningful ways in writing activities that build concept and language attainment

NA





(F) use accessible language and learn new and essential language in the process

(1) use accessible language and learn new and essential language in the process

T: 9-12

9781269614382 455b Lesson 6.6



(1) demonstrate an increasing ability to distinguish between formal and informal English

NA



(2) demonstrate an increasing knowledge of when to use [formal and informal English] commensurate with grade-level learning expectations

NA





(H) develop and expand repertoire of learning strategies such as reasoning inductively or deductively, looking for patterns in language, and analyzing sayings and expressions commensurate with grade-level learning expectations

(1) develop and expand repertoire of learning strategies

NA



(1) distinguish sounds of English with increasing ease

NA



(2) distinguish intonation patterns of English with increasing ease

NA





(B) recognize elements of the English sound system in newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters

(1) recognize elements of the English sound system in newly acquired vocabulary

NA



(1) learn new language structures heard during classroom instruction and interactions

T: 9-12

9781269614382 63b Lesson 1.1






(2) learn new expressions heard during classroom instruction and interactions

T: 9-12

9781269614382 1b Lesson P.4



(3) learn basic vocabulary heard during classroom instruction and interactions

T: 9-12S: 9-12

9781269614382 570b Lesson 8.3

9781269614382 676b Lesson 10.4






(4) learn academic vocabulary heard during classroom instruction and interactions

T: 9-12S: 9-12

9781269614382 455b Lesson 6.5



(1) monitor understanding of spoken language during classroom instruction and interactions

T: 9-12

9781269614382 319b Lesson 4.7






(2) seek clarification [of spoken language] as needed

T: 9-12S: 9-12

9781269614382 455b Lesson 6.5



(1) use visual support to enhance and confirm understanding of increasingly complex and elaborated spoken language

NA






(2) use contextual support to enhance and confirm understanding of increasingly complex and elaborated spoken language

NA



(3) use linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language

T: 9-12S: 9-12

9781269614382 570b Lesson 8.6

9781269614382 753b Lesson 11.1






(1) listen to and derive meaning from a variety of media to build and reinforce concept attainment

NA



(2) listen to and derive meaning from a variety of media to build and reinforce language attainment

NA



(1) understand the general meaning of spoken language ranging from situations in which topics are familiar to unfamiliar

NA






(2) understand the general meaning of spoken language ranging from situations in which language [is] are familiar to unfamiliar

NA



(3) understand the general meaning of spoken language ranging from situations in which contexts are familiar to unfamiliar

NA



(4) understand the main points of spoken language ranging from situations in which topics are familiar to unfamiliar

NA






(5) understand the main points of spoken language ranging from situations in which language [is] are familiar to unfamiliar

NA



(6) understand the main points of spoken language ranging from situations in which contexts are familiar to unfamiliar

NA



(7) understand the important details of spoken language ranging from situations in which topics are familiar to unfamiliar

NA






(8) understand the important details of spoken language ranging from situations in which language [is] are familiar to unfamiliar

NA



(9) understand the important details of spoken language ranging from situations in which contexts are familiar to unfamiliar

NA



(1) understand implicit ideas in increasingly complex spoken language commensurate with grade-level learning expectations

NA






(2) understand information in increasingly complex spoken language commensurate with grade-level learning expectations

NA



(1) demonstrate listening comprehension of increasingly complex spoken English by following directions commensurate with content and grade-level needs

NA



(2) demonstrate listening comprehension of increasingly complex spoken English by retelling or summarizing spoken messages commensurate with content and grade-level needs

NA






(3) demonstrate listening comprehension of increasingly complex spoken English by responding to questions and requests commensurate with content and grade-level needs

T: 9-12S: 9-12

9781269614382 319b Lesson 4.2



(4) demonstrate listening comprehension of increasingly complex spoken English by collaborating with peers commensurate with content and grade-level needs

T: 9-12

9781269614382 403b Lesson 5.1






(5) demonstrate listening comprehension of increasingly complex spoken English by taking notes commensurate with content and grade-level needs

T: 9-12S: 9-12

9781269614382 403b Lesson 5.1

9781269614382 633b Lesson 9.4


(A) practice producing sounds of newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters to pronounce English words in a manner that is increasingly comprehensible

(1) practice producing sounds of newly acquired vocabulary to pronounce English words in a manner that is increasingly comprehensible

NA






(1) expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects

NA



(2) expand and internalize initial English vocabulary by retelling simple stories and basic information represented or supported by pictures

NA






(3) expand and internalize initial English vocabulary by learning and using routine language needed for classroom communication

T: 9-12S: 9-12

9781269614382 455b Lesson 6.6

9781269614382 518b Lesson 7.3



(1) speak using a variety of grammatical structures with increasing accuracy and ease as more English is acquired

NA






(2) speak using a variety of sentence lengths with increasing accuracy and ease as more English is acquired

NA



(3) speak using a variety of sentence types with increasing accuracy and ease as more English is acquired

NA






(4) speak using a variety of connecting words with increasing accuracy and ease as more English is acquired

T: 9-12S: 9-12

9781269614382 157b Lesson 2.5

9781269614382 319b Lesson 4.89781269614382 518b Lesson 7.3



(1) speak using grade-level content area vocabulary in context to internalize new English words

T: 9-12S: 9-12

9781269614382 251b Lesson 3.3

9781269614382 455b Lesson 6.5






(2) speak using grade-level content area vocabulary in context to build academic language proficiency

T: 9-12S: 9-12

9781269614382 676b Lesson 10.4


(E) share information in cooperative learning interactions

(1) share information in cooperative learning interactions

T: 9-12S: 9-12

9781269614382 403b Lesson 5.1

9781269614382 518b Lesson 7.4






(1) ask [for] information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments

T: 9-12S: 9-12

9781269614382 251b Lesson 3.1



(2) give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments

T: 9-12S: 9-12

9781269614382 251b Lesson 3.1

9781269614382 518b Lesson 7.4






(1) express opinions ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

T: 9-12

9781269614382 63b Chapter 1 Project



(2) express ideas ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

T: 9-12

9781269614382 403b Lesson 5.6

9781269614382 570b Lesson 8.3






(3) express feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

NA



(1) narrate with increasing specificity and detail as more English is acquired

NA






(2) describe with increasing specificity and detail as more English is acquired

NA



(3) explain with increasing specificity and detail as more English is acquired

T: 9-12S: 9-12

9781269614382 403b Lesson 5.6

9781269614382 633b Lesson 9.4






(1) adapt spoken language appropriately for formal purposes

NA



(2) adapt spoken language appropriately for informal purposes

NA






(1) respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept attainment

NA



(2) respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce language attainment

N/A






(1) learn relationships between sounds and letters of the English language

NA



(2) decode (sound out) words using a combination of skills

NA





(B) recognize directionality of English reading such as left to right and top to bottom

(1) recognize directionality of English reading

NA



(1) develop basic sight vocabulary used routinely in written classroom materials

T: 9-12S: 9-12

9781269614382 518b Lesson 7.2






(2) derive meaning of environmental print

T: 9-12S: 9-12

9781269614382 570b Lesson 8.1



(3) comprehend English vocabulary used routinely in written classroom materials

T: 9-12S: 9-12

9781269614382 455b Lesson 6.1

9781269614382 633b Lesson 9.4






(4) comprehend English language structures used routinely in written classroom materials

T: 9-12S: 9-12

9781269614382 157b Lesson 2.2


(D) use prereading supports such as graphic organizers, illustrations, and pretaught topic-related vocabulary and other prereading activities to enhance comprehension of written text

(1) use prereading supports to enhance comprehension of written text

T: 9-12S: 9-12

9781269614382 1b Lesson P.5

9781269614382 570b Lesson 8.19781269614382 676b Lesson 10.2





(E) read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned

(1) read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned

T: 9-12

9781269614382 251b Lesson 3.6

9781269614382 633b Lesson 9.5



(1) use visual and contextual support to read grade-appropriate content area text

T: 9-12S: 9-12

9781269614382 455b Lesson 6.1






(2) use visual and contextual support to enhance and confirm understanding

T: 9-12S: 9-12

9781269614382 403b Lesson 5.2

9781269614382 676b Lesson 10.3



(3) use visual and contextual support to develop vocabulary needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614382 403b Lesson 5.2

9781269614382 676b Lesson 10.2






(4) use visual and contextual support to develop grasp of language structures needed to comprehend increasingly challenging language

NA



(5) use visual and contextual support to develop background knowledge needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614382 570b Lesson 8.6

9781269614382 753b Lesson 11.2






(6) use support from peers and teachers to read grade-appropriate content area text

T: 9-12S: 9-12

9781269614382 251b Lesson 3.3

9781269614382 403b Lesson 5.2



(7) use support from peers and teachers to enhance and confirm understanding

T: 9-12S: 9-12

9781269614382 63b Lesson 1.3






(8) use support from peers and teachers to develop vocabulary needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614382 403b Lesson 5.1



(9) use support from peers and teachers to develop grasp of language structures needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614382 753b Lesson 11.2






(10) use support from peers and teachers to develop background knowledge needed to comprehend increasingly challenging language

T: 9-12S: 9-12

9781269614382 1b Lesson P.2

9781269614382 753b Lesson 11.3



(1) demonstrate comprehension of increasingly complex English by participating in shared reading commensurate with content area and grade level needs

NA






(2) demonstrate comprehension of increasingly complex English by retelling or summarizing material commensurate with content area and grade level needs

T: 9-12S: 9-12

9781269614382 319b Lesson 4.8



(3) demonstrate comprehension of increasingly complex English by responding to questions commensurate with content area and grade level needs

T: 9-12S: 9-12

9781269614382 633b Lesson 9.4

9781269614382 676b Lesson 10.3






(4) demonstrate comprehension of increasingly complex English by taking notes commensurate with content area and grade level needs

T: 9-12S: 9-12

9781269614382 63b Lesson 1.3

9781269614382 633b Lesson 10.2



(1) read silently with increasing ease for longer periods

NA






(2) read silently with increasing comprehension for longer periods

NA



(1) demonstrate English comprehension by employing basic reading skills commensurate with content area needs

NA






(2) expand reading skills commensurate with content area needs

NA


(J) demonstrate English comprehension and expand reading skills by employing inferential skills such as predicting, making connections between ideas, drawing inferences and conclusions from text and graphic sources, and finding supporting text evidence commensurate with content area needs

(1) demonstrate English comprehension and expand reading skills by employing inferential skills

NA





(K) demonstrate English comprehension and expand reading skills by employing analytical skills such as evaluating written information and performing critical analyses commensurate with content area and grade level needs

(1) demonstrate English comprehension and expand reading skills by employing analytical skills

NA


(A) learn relationships between sounds and letters of the English language to represent sounds when writing in English

(1) learn relationships between sounds and letters of the English language to represent sounds when writing in English

NA






(1) write using newly acquired basic vocabulary

NA



(2) write using content-based grade-level vocabulary

NA






(1) spell familiar English words with increasing accuracy

NA



(2) employ English spelling pattern with increasing accuracy as more English is acquired

NA






(3) employ English spelling rules with increasing accuracy as more English is acquired

NA



(1) edit writing for standard grammar and usage, including subject-verb agreement commensurate with grade-level expectations as more English is acquired

NA






(2) edit writing for standard grammar and usage, including pronoun agreement, commensurate with grade-level expectations as more English is acquired

NA



(3) edit writing for standard grammar and usage, including appropriate verb tenses, commensurate with grade-level expectations as more English is acquired

NA





(E) employ increasingly complex grammatical structures in content area writing commensurate with grade level expectations such as (i) using correct verbs, tenses, and pronouns/antecedents; (ii) using possessive case (apostrophe -s) correctly; and, (iii) using negatives and contractions correctly

(1) employ increasingly complex grammatical structures in content area writing commensurate with grade level expectations

NA



(1) write using a variety of grade-appropriate sentence lengths in increasingly accurate ways as more English is acquired

NA






(2) write using a variety of grade-appropriate sentence patterns in increasingly accurate ways as more English is acquired

NA



(3) write using a variety of grade-appropriate connecting words to combine phrases, clauses, and sentences in increasingly accurate ways as more English is acquired

NA






(1) narrate with increasing specificity and detail to fulfill content area writing needs as more English is acquired

NA



(2) describe with increasing specificity and detail to fulfill content area writing needs as more English is acquired

NA






(3) explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired

NA

a correlation of precalculus - pearson · pdf filea correlation of . precalculus . graphical,...

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