Precalculus Enhanced with Graphing Utilities Texas Edition

A Correlation of

Precalculus Enhanced with Graphing Utilities

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: 9781269614092 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.

9781269614092

(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: Enhanced with Graphing Utilities, 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 9781269614092 75 Example 4

Activity 9781269614092 17 Problem 110



(ii) apply mathematics to problems arising in society

Instruction 9781269614092 296 Example 10




(iii) apply mathematics to problems arising in the workplace Instruction 9781269614092 99-100 Example 4



(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 9781269614092 131-132 Example 2

Activity 9781269614092 870 Problem III Surveys






(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




(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





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








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

Instruction 9781269614092 104 Section 1




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





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

Instruction 9781269614092 10 “Procedures That Result in Equivalent Equations”







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





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


Activity 9781269614092 A30 Problem 138


(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 9781269614092 233 Example 6







(ii) communicate mathematical ideas using multiple representations, including diagrams as appropriate Instruction 9781269614092 161 Example 2

Activity 9781269614092 165 Problem 9Activity 9781269614092 517 Problem 59

Instruction 9781269614092 162-163 Example 4Instruction 9781269614092 509 Example 2



(iii) communicate mathematical ideas using multiple representations, including graphs as appropriate Instruction 9781269614092 281-282 Example 9




(iv) communicate mathematical ideas using multiple representations, including language as appropriate Instruction 9781269614092 513 Example 8







(v) communicate mathematical reasoning using multiple representations, including symbols as appropriate Instruction 9781269614092 233 Example 6




(vi) communicate mathematical reasoning using multiple representations, including diagrams as appropriate Instruction 9781269614092 161 Example 2

Activity 9781269614092 166 Problem 15Review 9781269614092 631 Problem 60

Instruction 9781269614092 162-163 Example 4Instruction 9781269614092 509 Example 2



(vii) communicate mathematical reasoning using multiple representations, including graphs as appropriate Instruction 9781269614092 281-282 Example 9

Activity 9781269614092 127 Problem 5-6






(viii) communicate mathematical reasoning using multiple representations, including language as appropriate Instruction 9781269614092 440 The Inverse Sine Function




(ix) communicate [mathematical ideas'] implications using multiple representations, including symbols as appropriate Instruction 9781269614092 333-334 Example 5




(x) communicate [mathematical ideas'] implications using multiple representations, including diagrams as appropriate Instruction 9781269614092 319-320 Example 2

Activity 9781269614092 326-327 Problem 75






(xi) communicate [mathematical ideas'] implications using multiple representations, including graphs as appropriate Instruction 9781269614092 281-282 Example 9




(xii) communicate [mathematical ideas'] implications using multiple representations, including language as appropriate Instruction 9781269614092 440 Statement 4

Activity 9781269614092 79 Problem 37(d)



(xiii) communicate [mathematical reasoning's] implications using multiple representations, including symbols as appropriate Instruction 9781269614092 296 Example 10







(xiv) communicate [mathematical reasoning's] implications using multiple representations, including diagrams as appropriate Instruction 9781269614092 319-320 Example 2




(xv) communicate [mathematical reasoning's] implications using multiple representations, including graphs as appropriate Instruction 9781269614092 73 Example 2

Activity 9781269614092 56 Problem 6(d)Activity 9781269614092 78-79 Problems 29, 36, 37

Instruction 9781269614092 75 Example 4Instruction 9781269614092 281-282 Example 9



(xvi) communicate [mathematical reasoning's] implications using multiple representations, including language as appropriate Instruction 9781269614092 440 Statement 4



(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 9781269614092 281-282 Example 9




(iv) use representations to organize mathematical ideas





(v) use representations to record mathematical ideas








(vi) use representations to communicate mathematical ideas Instruction 9781269614092 281-282 Example 9



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

(i) analyze mathematical relationships to connect mathematical ideas Instruction 9781269614092 544-545 Section 1




(ii) analyze mathematical relationships to communicate mathematical ideas Instruction 9781269614092 162-163 Example 4



(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








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





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

Instruction 9781269614092 259 Section 1 last paragraph




(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 9781269614092 514-515 Example 10







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


Activity 9781269614092 352 Problem 16c

(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

Instruction 9781269614092 251 Section 1 PRiew




(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




(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




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

(i) describe symmetry of graphs of even functions








(ii) describe symmetry of graphs of odd functions


Activity 9781269614092 89-90 Problem 25(d)


(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 9781269614092 262 Example 4




(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 9781269614092 182 Exploration




(vi) graph trigonometric functions








(vii) graph inverse trigonometric functions

Instruction 9781269614092 440-441 TheInverse Sine Function

Activity 9781269614092 458 Problems 82, 83, 84



(viii) graph piecewise defined functions, including step functions

Instruction 9781269614092 98 Graph Piecewise-defined 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





(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

Instruction 9781269614092 922-924 Examples 13, 14, 15

Activity 9781269614092 918 Problems 8 and 9Activity 9781269614092 925 Problem 11



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





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

Instruction 9781269614092 913-915 Examples 6 and 7

Activity 9781269614092 226 Problem 57; Activity 9781269614092 915 Problems 5 and 6






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


Review 9781269614092 352 Problem 9



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


Activity 9781269614092 196 Problem 109, 110, 111



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








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

Instruction 9781269614092 909-910 Examples 2




(xv) graph functions, including exponential transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614092 280 Example 6




(xvi) graph functions, including exponential transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614092 339 Example 1

Review 9781269614092 350 Problem 57






(xvii) graph functions, including logarithmic transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614092 310-311 Example 1




(xviii) graph functions, including logarithmic transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614092 291 Graph Logarithmic Functions




(xix) graph functions, including sine transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614092 404 Example 4







(xx) graph functions, including sine transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614092 921 Example 12

Activity 9781269614092 411 Problems 87, 88, 89, 90



(xxi) graph functions, including cosine transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614092 406-407 Example 7




(xxii) graph functions, including cosine transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614092 922 Example 13

Activity 9781269614092 925 Problems 11-13






(xxiii) graph functions, including rational transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614092 218 Example 3




(xxiv) graph functions, including rational transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614092 218 Example 3




(xxv) graph functions, including polynomial transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614092 183 Example 3







(xxvi) graph functions, including polynomial transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614092 192 Example 11




(xxvii) graph functions, including power transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614092 183 Example 3




(xxviii) graph functions, including power transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614092 910-911 Example 3







(xxix) graph functions, including exponential transformations, including f(x) + d , for specific values of d, in mathematical problems Instruction 9781269614092 278 Example 5




(xxx) graph functions, including exponential transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614092 916 Example 8




(xxxi) graph functions, including logarithmic transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614092 291 Example Graphing Logarithmic Functions







(xxxii) graph functions, including logarithmic transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614092 917 Example 9




(xxxiii) graph functions, including sine transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614092 920 Example 11




(xxxiv) graph functions, including sine transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614092 921 Example 12







(xxxv) graph functions, including cosine transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614092 406 Example 7




(xxxvi) graph functions, including cosine transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614092 924 Example 15

Activity 9781269614092 925 Problems 12 and 13



(xxxvii) graph functions, including rational transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614092 218 Example 3







(xxxviii) graph functions, including rational transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614092 233 Example 6




(xxxix) graph functions, including polynomial transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614092 108 Example 3




(xl) graph functions, including polynomial transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614092 909-910 Example 2







(xli) graph functions, including power transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614092 182 Example 2




(xlii) graph functions, including power transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614092 909-910 Example 2




(xliii) graph functions, including exponential transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614092 281 Example 7







(xliv) graph functions, including exponential transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614092 916 Example 8




(xlv) graph functions, including logarithmic transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614092 292-293 Example 6




(xlvi) graph functions, including logarithmic transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614092 918 Example 10







(xlvii) graph functions, including sine transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614092 428 Example 5




(xlviii) graph functions, including sine transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614092 425-426 Example 3




(xlix) graph functions, including cosine transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614092 423 Example 2







(l) graph functions, including cosine transformations, including f(x - c), for specific values of c , in real-world problems Instruction 9781269614092 923 Example 14




(li) graph functions, including rational transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614092 218 Example 3




(lii) graph functions, including rational transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614092 913-914 Example 6

Activity 9781269614092 115 Problem 88(b)






(liii) graph functions, including polynomial transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614092 149 Example 1




(liv) graph functions, including polynomial transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614092 192-193 Example 11




(lv) graph functions, including power transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614092 182-183 Examples 2.3







(lvi) graph functions, including power transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614092 911-912 Example 4




(lvii) graph functions, including exponential transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614092 280 Example 6




(lviii) graph functions, including exponential transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614092 281-282 Example 9







(lix) graph functions, including logarithmic transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614092 292-293 Example 6




(lx) graph functions, including logarithmic transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614092 330 Example 3




(lxi) graph functions, including sine transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614092 404-405 Example 5







(lxii) graph functions, including sine transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614092 404-405 Example 5




(lxiii) graph functions, including cosine transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614092 406-407 Example 7




(lxiv) graph functions, including cosine transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614092 922 Example 13







(lxv) graph functions, including rational transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614092 110 Example 5

Activity 9781269614092 225 #34, 35, 36, 39, 41, 42



(lxvi) graph functions, including rational transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614092 233 Example 6(b)

Activity 9781269614092 235 Problems 50, 51



(lxvii) graph functions, including polynomial transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614092 189-190 Example 9







(lxviii) graph functions, including polynomial transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614092 192-193 Example 11




(lxix) graph functions, including power transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614092 909 Example 1




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

Instruction 9781269614092 910-911 Example 3(b)

Activity 9781269614092 115 Problem 88Activity 9781269614092 913 Problem 3(b)





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

(i) graph arcsin x





(ii) graph arccos x





(iii) describe the limitations on the domain

Instruction 9781269614092 445 Figure 13 * bottom of page






(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





(ii) determine the key features of logarithmic functions








(iii) determine the key features of rational functions





(iv) determine the key features of polynomial functions


Review 9781269614092 352 Problem 11






(v) determine the key features of power functions





(vi) determine the key features of trigonometric functions








(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





(x) analyze the key features of logarithmic functions








(xi) analyze the key features of rational functions





(xii) analyze the key features of polynomial functions


Review 9781269614092 352 Problem 11






(xiii) analyze the key features of power functions





(xiv) analyze the key features of trigonometric functions








(xv) analyze the key features of inverse trigonometric functions





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

Instruction 9781269614092 97-98 Greatest Integer Function






(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 9781269614092 275-277 Example 3, 4

Activity 9781269614092 285 93, 94



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


Activity 9781269614092 286 106



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

Instruction 9781269614092 291 “Graph Logarithmic Functions” section







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

Instruction 9781269614092 917 Example 9(b)




(v) analyze end behavior of functions, including rational functions, using infinity notation to communicate this characteristic in mathematical problems Instruction 9781269614092 221 Example 5




(vi) analyze end behavior of functions, including rational functions, using infinity notation to communicate this characteristic in real-world problems Instruction 9781269614092 912 Example 5







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

Instruction 9781269614092 187-188 End Behavior




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

Instruction 9781269614092 193 Immediately following Example 11




(ix) analyze end behavior of functions, including power functions, using infinity notation to communicate this characteristic in mathematical problems Instruction 9781269614092 181-182 Explorations







(x) analyze end behavior of functions, including power functions, using infinity notation to communicate this characteristic in real-world problems Instruction 9781269614092 910-911 Example 3(a)

Activity 9781269614092 913 Problem 3(a)



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





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








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

Instruction 9781269614092 291 “Graph Logarithmic Functions”

Activity 9781269614092 299 111, 112



(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 9781269614092 221-222 Example 5







(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 9781269614092 188 Figure 12




(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 9781269614092 181-182 Explorations




(xx) describe end behavior of functions, including power functions, using infinity notation to communicate this characteristic in real-world problems Instruction 9781269614092 910-911 Example 3



(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 9781269614092 223 Example 7




(iii) analyze the behavior of the function around the asymptotes, including vertical asymptotes Instruction 9781269614092 227-228 Example 1




(iv) analyze the behavior of the function around the asymptotes, including oblique asymptotes Instruction 9781269614092 229 Example 2






(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 9781269614092 231-232 Example 4



(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 9781269614092 886 Section 2







(ii) describe the right-sided behavior of the graph of a function around discontinuities Instruction 9781269614092 886 Section 2



(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 9781269614092 279 Section 3




(ii) analyze situations modeled by functions, including logarithmic functions, to solve real-world problems Instruction 9781269614092 332 Section 4







(iii) analyze situations modeled by functions, including rational functions, to solve real-world problems Instruction 9781269614092 912 Example 5




(iv) analyze situations modeled by functions, including polynomial functions, to solve real-world problems Instruction 9781269614092 192-193 Example 11




(v) analyze situations modeled by functions, including power functions, to solve real-world problems Instruction 9781269614092 910-911 Example 3






(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 9781269614092 399-400 Example 1




(ii) develop a sinusoidal function that models a situation in real-world problems Instruction 9781269614092 427-428 Example 4




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

Instruction 9781269614092 402 Sinusoidal Graphs







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


Activity 9781269614092 412 Problem 91Activity 9781269614092 430 Problems 33, 35


(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


Assessment 9781269614092 436 Problem 10



(ii) relate them in mathematical problems


Review 9781269614092 434 Problem 7






(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




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

(i) convert parametric equations into rectangular relations Instruction 9781269614092 687-688 Example 4




(ii) convert rectangular relations into parametric equations Instruction 9781269614092 692 Example 8






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

(i) use parametric equations to model mathematical problems Instruction 9781269614092 691 Example 7




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





(iii) use parametric equations to solve mathematical problems Instruction 9781269614092 688-699 Section 4




(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 9781269614092 566 Example 8



(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


Activity 9781269614092 635 ”Assess Your Understanding” Problems 1-4


(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 9781269614092 636 Definition



(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

Instruction 9781269614092 918-920 “Connecting the Unit Circle with the Graphs of the Sine and Cosine Functions”



(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 9781269614092 372 Example 2



(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 9781269614092 360 Example 4







(ii) find the measure of reference angles

Instruction 9781269614092 378 Above Example 10




(iii) find the measure of angles in standard position

Instruction 9781269614092 356 Degrees



(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 9781269614092 378 Example 11







(iii) solve problems involving trigonometric ratios in real-world problems Instruction 9781269614092 376-377 Example 8



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

(i) use trigonometry in mathematical, including directional bearing Instruction 9781269614092 515 Example 12




(ii) use trigonometry in real-world problems, including directional bearing Instruction 9781269614092 515 Example 11

Review 9781269614092 554 Problem 36


(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 9781269614092 601 Example 9






(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 9781269614092 595 Example 1




(iv) represent the multiplication of a vector by a scalar symbolically Instruction 9781269614092 616 Example 4






(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





(iii) apply multiplication of a vector by a scalar in mathematical problems Instruction 9781269614092 598 Example 4

Review 9781269614092 630 Problem 34



(iv) apply multiplication of a vector by a scalar in real-world problems Instruction 9781269614092 611 Example 7





(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





(ii) evaluate geometric series, when possible, written in sigma notation Instruction 9781269614092 822 Example 7



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

(i) represent arithmetic sequences using recursive formulas Instruction 9781269614092 814 Example 5




(ii) represent geometric sequences using recursive formulas Instruction 9781269614092 819-820 Example 4






(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 9781269614092 813 Example 4




(ii) calculate the n th term of an arithmetic series in real-world problems Instruction 9781269614092 815-816 Example 8




(iii) calculate the n th partial sum of an arithmetic series in mathematical problems Instruction 9781269614092 815 Example 6




(iv) calculate the n th partial sum of an arithmetic series in real-world problems Instruction 9781269614092 815-816 Example 8






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

(i) represent arithmetic series using sigma notation





(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









(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 9781269614092 306-307 Example 8



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

(i) generate logarithmic equations in mathematical problems Instruction 9781269614092 323 Example 7







(ii) generate logarithmic equations in real-world problems Instruction 9781269614092 323 Example 7




(iii) solve logarithmic equations in mathematical problems Instruction 9781269614092 311 Example 2




(iv) solve logarithmic equations in real-world problems Instruction 9781269614092 323 Example 7



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

(i) generate exponential equations in mathematical problems Instruction 9781269614092 330 Example 3







(ii) generate exponential equations in real-world problems Instruction 9781269614092 331-332 Example 4




(iii) solve exponential equations in mathematical problems Instruction 9781269614092 313 Example 5




(iv) solve exponential equations in real-world problems Instruction 9781269614092 323 Example 6



(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




(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 9781269614092 239-240 Example 4




(ii) write the solution set of the rational inequality in interval notation in mathematical problems Instruction 9781269614092 239-240 Example 4







(iii) write the solution set of the rational inequality in interval notation in real-world problems Instruction 9781269614092 914-915 Example 7

Activity 9781269614092 242-243 Problems 77-81


(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 9781269614092 471 Example 2




(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 9781269614092 479 Example 3




(ii) generate trigonometric equations in real-world problems Instruction 9781269614092 512-513 Examples 7 and 8

Activity 9781269614092 497 Problem 100(a)Activity 9781269614092 518 Problem 67



(iii) solve trigonometric equations in mathematical problems Instruction 9781269614092 484 Example 12




(iv) solve trigonometric equations in real-world problems Instruction 9781269614092 491-492 Example 5



Page 86 of 273 Pearson Education, Inc., publishing as Prentice Hall: 9781269614092 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: Enhanced with Graphing Utilities, Texas Edition9781269614092

(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 9781269614375 161 Example 2




(ii) apply mathematics to problems arising in society





(iii) apply mathematics to problems arising in the workplace Instruction 9781269614375 330-331 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








(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





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





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








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


Activity 9781269614375 114 Problem 74 (e, f)



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





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


Activity 9781269614375 A30 Problem 142






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





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


Activity 9781269614375 165 Problem #11



(i) communicate mathematical ideas using multiple representations, including symbols as appropriate Instruction 9781269614375 161 Example 2







(ii) communicate mathematical ideas using multiple representations, including diagrams as appropriate Instruction 9781269614375 513 Example 8

Activity 9781269614375 632 Chapter Project 1-4



(iii) communicate mathematical ideas using multiple representations, including graphs as appropriate Instruction 9781269614375 427-428 Example 4




(iv) communicate mathematical ideas using multiple representations, including language as appropriate Instruction 9781269614375 440 The Inverse Sine Function







(v) communicate mathematical reasoning using multiple representations, including symbols as appropriate Instruction 9781269614375 803 Example 8




(vi) communicate mathematical reasoning using multiple representations, including diagrams as appropriate Instruction 9781269614375 140-141 Example 1




(vii) communicate mathematical reasoning using multiple representations, including graphs as appropriate Instruction 9781269614375 427-428 Example 4







(viii) communicate mathematical reasoning using multiple representations, including language as appropriate Instruction 9781269614375 333-334 Example 5




(ix) communicate [mathematical ideas'] implications using multiple representations, including symbols as appropriate Instruction 9781269614375 321 Example 4




(x) communicate [mathematical ideas'] implications using multiple representations, including diagrams as appropriate Instruction 9781269614375 163-164 Example 5







(xi) communicate [mathematical ideas'] implications using multiple representations, including graphs as appropriate Instruction 9781269614375 281-282 Example 9

Activity 9781269614375 337 Problem 26(b-d)



(xii) communicate [mathematical ideas'] implications using multiple representations, including language as appropriate Instruction 9781269614375 333-334 Example 5




(xiii) communicate [mathematical reasoning's] implications using multiple representations, including symbols as appropriate Instruction 9781269614375 321 Example 4







(xiv) communicate [mathematical reasoning's] implications using multiple representations, including diagrams as appropriate Instruction 9781269614375 163-164 Example 5




(xv) communicate [mathematical reasoning's] implications using multiple representations, including graphs as appropriate Instruction 9781269614375 73-74 Example 2

Activity 9781269614375 78-79 Problems 29, 36, 37, 79Instruction 9781269614375 75 Example 4



(xvi) communicate [mathematical reasoning's] implications using multiple representations, including language as appropriate Instruction 9781269614375 333-334 Example 5




(i) create representations to organize mathematical ideas








(ii) create representations to record mathematical ideas





(iii) create representations to communicate mathematical ideas Instruction 9781269614375 427-428 Example 4




(iv) use representations to organize mathematical ideas





(v) use representations to record mathematical ideas








(vi) use representations to communicate mathematical ideas Instruction 9781269614375 427-428 Example 4




(i) analyze mathematical relationships to connect mathematical ideas Instruction 9781269614375 159-160 Example 1




(ii) analyze mathematical relationships to communicate mathematical ideas Instruction 9781269614375 161-162 Example 3




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








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





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

Instruction 9781269614375 143 Example 4 last paragraph




(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 9781269614375 514-515 Example 10







(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

Instruction 9781269614375 251 Section 1 PRiew




(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 9781269614375 259 Definition Section 1



(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


Activity 9781269614375 89-90 Problem 25(d)



(i) determine an inverse function, when it exists, for a given function over its domain or a subset of its domain Instruction 9781269614375 262 Example 4




(ii) represent the inverse using multiple representations








(i) graph exponential functions





(ii) graph logarithmic functions

Instruction 9781269614375 291 Graph Logarithmic Functions




(iii) graph rational functions








(iv) graph polynomial functions





(v) graph power functions


Activity 9781269614375 194 33



(vi) graph trigonometric functions








(vii) graph inverse trigonometric functions

Instruction 9781269614375 445 The Inverse Cosine Function

Activity 9781269614375 458 Problems 82, 83, 84



(viii) graph piecewise defined functions, including step functions

Instruction 9781269614375 98 Example Graph Piecewise-defined Functions




(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





(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

Instruction 9781269614375 400 The Graph of the Cosine Function







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

Instruction 9781269614375 922-924 Examples 13, 14, 15

Activity 9781269614375 918 Problems 8 and 9Activity 9781269614375 925 Problem 11



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





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

Instruction 9781269614375 913-915 Examples 6 and 7

Activity 9781269614375 226 Problem 58Activity 9781269614375 915 Problems 5 and 6






(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 9781269614375 280 Example 6




(xvi) graph functions, including exponential transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614375 339 Example 1

Review 9781269614375 342 Problem 2






(xvii) graph functions, including logarithmic transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614375 293-294 Example 7




(xviii) graph functions, including logarithmic transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614375 292 Example 6

Review 9781269614375 335 Problem 1



(xix) graph functions, including sine transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614375 404-405 Example 5







(xx) graph functions, including sine transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614375 921 Example 12

Activity 9781269614375 411 Problems 87, 88, 89, 90



(xxi) graph functions, including cosine transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614375 406-407 Example 7




(xxii) graph functions, including cosine transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614375 922 Example 13







(xxiii) graph functions, including rational transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614375 218 Example 3




(xxiv) graph functions, including rational transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614375 218 Example 3




(xxv) graph functions, including polynomial transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614375 182 Example 2







(xxvi) graph functions, including polynomial transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614375 192 Example 11




(xxvii) graph functions, including power transformations, including af(x) , for specific values of a , in mathematical problems Instruction 9781269614375 183 Example 3




(xxviii) graph functions, including power transformations, including af(x) , for specific values of a , in real-world problems Instruction 9781269614375 910-911 Example 3







(xxix) graph functions, including exponential transformations, including f(x) + d , for specific values of d, in mathematical problems Instruction 9781269614375 278 Example 5




(xxx) graph functions, including exponential transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614375 916 Example 8




(xxxi) graph functions, including logarithmic transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614375 292 Example 6







(xxxii) graph functions, including logarithmic transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614375 917 Example 9




(xxxiii) graph functions, including sine transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614375 920 Example 11




(xxxiv) graph functions, including sine transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614375 921 Example 12







(xxxv) graph functions, including cosine transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614375 406 Example 7




(xxxvi) graph functions, including cosine transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614375 924 Example 15




(xxxvii) graph functions, including rational transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614375 218 Example 3







(xxxviii) graph functions, including rational transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614375 233 Example 6




(xxxix) graph functions, including polynomial transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614375 106 Example 2




(xl) graph functions, including polynomial transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614375 909-910 Example 2







(xli) graph functions, including power transformations, including f(x) + d , for specific values of d , in mathematical problems Instruction 9781269614375 182 Example 2




(xlii) graph functions, including power transformations, including f(x) + d , for specific values of d , in real-world problems Instruction 9781269614375 909-910 Example 2




(xliii) graph functions, including exponential transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614375 280 Example 6

Review 9781269614375 352 Problem 12(a)






(xliv) graph functions, including exponential transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614375 916 Example 8




(xlv) graph functions, including logarithmic transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614375 293-294 Example 7




(xlvi) graph functions, including logarithmic transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614375 918 Example 10







(xlvii) graph functions, including sine transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614375 428 Example 5




(xlviii) graph functions, including sine transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614375 425-426 Example 3




(xlix) graph functions, including cosine transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614375 423 Example 2







(l) graph functions, including cosine transformations, including f(x - c), for specific values of c , in real-world problems Instruction 9781269614375 923 Example 14




(li) graph functions, including rational transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614375 218 Example 3




(lii) graph functions, including rational transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614375 913-914 Example 6

Activity 9781269614375 115 Problem 88(b)






(liii) graph functions, including polynomial transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614375 183 Example 3




(liv) graph functions, including polynomial transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614375 192-193 Example 11




(lv) graph functions, including power transformations, including f(x - c) , for specific values of c , in mathematical problems Instruction 9781269614375 182-183 Example 3







(lvi) graph functions, including power transformations, including f(x - c) , for specific values of c , in real-world problems Instruction 9781269614375 911-912 Example 4




(lvii) graph functions, including exponential transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614375 313 Example 5




(lviii) graph functions, including exponential transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614375 281-282 Example 9







(lix) graph functions, including logarithmic transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614375 291 Graph Logarithmic Functions




(lx) graph functions, including logarithmic transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614375 328 Example 1




(lxi) graph functions, including sine transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614375 404-405 Example 5







(lxii) graph functions, including sine transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614375 404-405 Example 5




(lxiii) graph functions, including cosine transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614375 406-407 Example 7




(lxiv) graph functions, including cosine transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614375 922 Example 13







(lxv) graph functions, including rational transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614375 110 Example 5

Activity 9781269614375 225 Problems 34-36, 39, 41, 42



(lxvi) graph functions, including rational transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614375 233 Example 6(b)




(lxvii) graph functions, including polynomial transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614375 189-190 Example 9







(lxviii) graph functions, including polynomial transformations, including f(bx) for specific values of b , in real-world problems Instruction 9781269614375 192-193 Example 11




(lxix) graph functions, including power transformations, including f(bx) for specific values of b , in mathematical problems Instruction 9781269614375 909 Example 1




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

Instruction 9781269614375 910-911 Example 3(b)

Activity 9781269614375 115 Problem 88Activity 9781269614375 913 Problem 3(b)






(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 9781269614375 297 Summary







(iii) determine the key features of rational functions





(iv) determine the key features of polynomial functions








(v) determine the key features of power functions





(vi) determine the key features of trigonometric functions








(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





(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








(xv) analyze the key features of inverse trigonometric functions





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

Instruction 9781269614375 97-98 Greatest Integer Function







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


Activity 9781269614375 285 93, 94



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


Activity 9781269614375 286 106



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

Instruction 9781269614375 291 “Graph Logarithmic Functions” section







(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 9781269614375 219 Figure35




(vi) analyze end behavior of functions, including rational functions, using infinity notation to communicate this characteristic in real-world problems Instruction 9781269614375 912 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 9781269614375 181-182 Explorations







(x) analyze end behavior of functions, including power functions, using infinity notation to communicate this characteristic in real-world problems Instruction 9781269614375 910-911 Example 3(a)




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





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








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

Instruction 9781269614375 291 “Graph Logarithmic Functions”

Activity 9781269614375 299 111, 112



(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 9781269614375 219 Figure 35







(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 9781269614375 187 End Behavior




(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 9781269614375 181-182 Explorations




(xx) describe end behavior of functions, including power functions, using infinity notation to communicate this characteristic in real-world problems Instruction 9781269614375 910-911 Example 3




(i) analyze characteristics of rational functions








(ii) analyze the behavior of the function around the asymptotes, including horizontal asymptotes Instruction 9781269614375 221-222 Example 5




(iii) analyze the behavior of the function around the asymptotes, including vertical asymptotes Instruction 9781269614375 230 Example 3




(iv) analyze the behavior of the function around the asymptotes, including oblique asymptotes Instruction 9781269614375 222 Example 6







(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 9781269614375 231-232 Example 4




(i) describe the left-sided behavior of the graph of a function around discontinuities Instruction 9781269614375 888 Example 3







(ii) describe the right-sided behavior of the graph of a function around discontinuities Instruction 9781269614375 888 Section 3




(i) analyze situations modeled by functions, including exponential functions, to solve real-world problems Instruction 9781269614375 281-282 Example 9




(ii) analyze situations modeled by functions, including logarithmic functions, to solve real-world problems Instruction 9781269614375 333-334 Example 5







(iii) analyze situations modeled by functions, including rational functions, to solve real-world problems Instruction 9781269614375 912 Example 5




(iv) analyze situations modeled by functions, including polynomial functions, to solve real-world problems Instruction 9781269614375 192-193 Example 11




(v) analyze situations modeled by functions, including power functions, to solve real-world problems Instruction 9781269614375 910-911 Example 3







(i) develop a sinusoidal function that models a situation in mathematical problems Instruction 9781269614375 400 Example 2




(ii) develop a sinusoidal function that models a situation in real-world problems Instruction 9781269614375 427-428 Example 4




(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 9781269614375 687 Example 3




(ii) convert rectangular relations into parametric equations Instruction 9781269614375 691 Example 7







(i) use parametric equations to model mathematical problems Instruction 9781269614375 692 Example 8




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


Activity 9781269614375 690-691 Problem 57(a)



(iii) use parametric equations to solve mathematical problems Instruction 9781269614375 691 Section 5




(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 9781269614375 577 Example 10




(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


Activity 9781269614375 635 “Assess Your Understanding" Problems 1-4


(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 9781269614375 646 Definition




(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

Instruction 9781269614375 918-920 “Connecting the Unit Circle with the Graphs of the Sine and Cosine Functions”



(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 9781269614375 371 Definition




(i) represent angles in radians or degrees based on the concept of rotation Instruction 9781269614375 359-360 Example 3







(ii) find the measure of reference angles

Instruction 9781269614375 378 Above Example 10




(iii) find the measure of angles in standard position

Instruction 9781269614375 356 Degrees




(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 9781269614375 378 Example 11







(iii) solve problems involving trigonometric ratios in real-world problems Instruction 9781269614375 376-377 Example 8




(i) use trigonometry in mathematical, including directional bearing Instruction 9781269614375 515 Example 11




(ii) use trigonometry in real-world problems, including directional bearing Instruction 9781269614375 515 Example 12




(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 9781269614375 600-601 Example 8







(i) represent the addition of vectors geometrically

Instruction 9781269614375 594 Adding Vectors Geometrically




(ii) represent the addition of vectors symbolically





(iii) represent the multiplication of a vector by a scalar geometrically Instruction 9781269614375 594 Multiplying Vectors by Numbers Geometrically




(iv) represent the multiplication of a vector by a scalar symbolically Instruction 9781269614375 598 Example 4







(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 9781269614375 598 Example 4

Review 9781269614375 631 Problem 60



(iv) apply multiplication of a vector by a scalar in real-world problems Instruction 9781269614375 611 Example 7







(i) evaluate finite sums written in sigma notation





(ii) evaluate geometric series, when possible, written in sigma notation Instruction 9781269614375 822 Example 8

Review 9781269614375 838 Problem 16



(i) represent arithmetic sequences using recursive formulas Instruction 9781269614375 814 Example 5

Review 9781269614375 838 Problem 20



(ii) represent geometric sequences using recursive formulas Instruction 9781269614375 819-820 Example 4







(i) calculate the n th term of an arithmetic series in mathematical problems Instruction 9781269614375 813 Example 4




(ii) calculate the n th term of an arithmetic series in real-world problems Instruction 9781269614375 815-816 Example 8




(iii) calculate the n th partial sum of an arithmetic series in mathematical problems Instruction 9781269614375 815 Example 7

Review 9781269614375 838 Problem 13



(iv) calculate the n th partial sum of an arithmetic series in real-world problems Instruction 9781269614375 815-816 Example 8

Review 9781269614375 839 Problem 37






(i) represent arithmetic series using sigma notation





(ii) represent geometric series using sigma notation






(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




(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 9781269614375 304 Example 5

Review 9781269614375 349 Problem 26



(i) generate logarithmic equations in mathematical problems Instruction 9781269614375 323 Example 7

Review 9781269614375 350 Problem 50






(ii) generate logarithmic equations in real-world problems Instruction 9781269614375 323 Example 7

Review 9781269614375 350 Problem 50



(iii) solve logarithmic equations in mathematical problems Instruction 9781269614375 310-311 Example 1




(iv) solve logarithmic equations in real-world problems Instruction 9781269614375 323 Example 7




(i) generate exponential equations in mathematical problems Instruction 9781269614375 330 Example 3







(ii) generate exponential equations in real-world problems Instruction 9781269614375 321 Example 3




(iii) solve exponential equations in mathematical problems Instruction 9781269614375 312-313 Example 4




(iv) solve exponential equations in real-world problems Instruction 9781269614375 321 Example 3




(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





(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 9781269614375 239 Example 3




(ii) write the solution set of the rational inequality in interval notation in mathematical problems Instruction 9781269614375 239 Example 3







(iii) write the solution set of the rational inequality in interval notation in real-world problems Instruction 9781269614375 914-915 Example 7

Activity 9781269614375 242-243 Problems 77-81



(i) use trigonometric identities for cosine to simplify trigonometric expressions Instruction 9781269614375 470 Example 1




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








(i) generate trigonometric equations in mathematical problems Instruction 9781269614375 477 Example 1




(ii) generate trigonometric equations in real-world problems Instruction 9781269614375 512-513 Examples 7 and 8

Activity 9781269614375 497 Problem 100(a)Activity 9781269614375 518 Problem 67



(iii) solve trigonometric equations in mathematical problems Instruction 9781269614375 483 Example 11




(iv) solve trigonometric equations in real-world problems Instruction 9781269614375 491-492 Example 5



Page 171 of 273 Pearson Education, Inc., publishing as Prentice Hall: 9781269614092 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

9781269614092 30 Lesson 1.4

9781269614092 169 Lesson 3.59781269614092 387 Lesson 6.39781269614092 488 Lesson 7.6

9781269614092

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: Enhanced with Graphing Utilities, Texas Edition






(2) use prior experiences to understand meanings in English

T: 9-12S: 9-12

9781269614092 48 Lesson 1.5

9781269614092 640 Lesson 10.2


(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

9781269614092 211 Lesson 4.3

9781269614092 500 Lesson 7.79781269614092 802 Lesson 12.1


(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

9781269614092 289 Lesson 5.4

9781269614092 508 Lesson 8.19781269614092 749 Lesson 11.4



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

T: 9-12S: 9-12

9781269614092 318 Lesson 5.7

9781269614092 508 Lesson 8.19781269614092 749 Lesson 11.4





(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

9781269614092 179 Lesson 4.1

9781269614092 618 Lesson 9.6





(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

9781269614092 685 Lesson 10.7




9781269614092 802 Lesson 12.19781269614092 843 Lesson 13.1


(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

9781269614092 105 Lesson 2.5

9781269614092 440 Lesson 7.19781269614092 833 Lesson 12.5






(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

9781269614092 546 Lesson 8.5

9781269614092 849 Lesson 13.2




(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

9781269614092 218 Lesson 4.4

9781269614092 526 Lesson 8.29781269614092 827 Lesson 12.4





(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

9781269614092 253 Lesson 5.1

9781269614092 777 Lesson 11.79781269614092 863 Lesson 13.3





(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

9781269614092 7 Lesson 1.1

9781269614092 560 Lesson 9.19781269614092 770 Lesson 11.6



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

T: 9-12S: 9-12

9781269614092 61 Lesson 2.1

9781269614092 355 Lesson 6.19781269614092 813 Lesson 12.2





(E) share information in cooperative learning interactions

(1) share information in cooperative learning interactions

T: 9-12S: 9-12

9781269614092 203 Lesson 4.2

9781269614092 405 Lesson 6.49781269614092 891 Lesson 14.4


(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

9781269614092 266 Lesson 5.2

9781269614092 588 Lesson 9.39781269614092 882 Lesson 14.2






(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

9781269614092 18 Lesson 1.2

9781269614092 460 Lesson 7.39781269614092 872 Lesson 14.1


(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

9781269614092 95 Lesson 2.4

9781269614092 573 Lesson 9.29781269614092 884 Lesson 14.3


(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

9781269614092 476 Lesson 7.5

9781269614092 635 Lesson 10.19781269614092 818 Lesson 12.3



(2) derive meaning of environmental print

T: 9-12S: 9-12

9781269614092 789 Lesson 11.8






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

T: 9-12S: 9-12

9781269614092 142 Lesson 3.2

9781269614092 470 Lesson 7.49781269614092 902 Lesson 14.5



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

T: 9-12S: 9-12

9781269614092 73 Lesson 2.2

9781269614092 310 Lesson 5.69781269614092 902 Lesson 14.5





(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

9781269614092 148 Lesson 3.3

9781269614092 413 Lesson 6.5


(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

9781269614092 233 Lesson 4.5

9781269614092 455 Lesson 7.2



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

T: 9-12S: 9-12

9781269614092 26 Lesson 1.3

9781269614092 373 Lesson 6.2






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

T: 9-12S: 9-12

9781269614092 86 Lesson 2.3

9781269614092 607 Lesson 9.59781269614092 657 Lesson 10.4



(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

9781269614092 455 Lesson 7.2



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

T: 9-12S: 9-12

9781269614092 26 Lesson 1.3

9781269614092 117 Lesson 2.69781269614092 594 Lesson 9.4






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

T: 9-12S: 9-12

9781269614092 240 Lesson 4.6

9781269614092 533 Lesson 8.3



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

T: 9-12S: 9-12

9781269614092 169 Lesson 3.5

9781269614092 625 Lesson 9.7






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

T: 9-12S: 9-12

9781269614092 133 Lesson 3.1

9781269614092 678 Lesson 10.69781269614092 732 Lesson 11.3



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

T: 9-12S: 9-12

9781269614092 340 Lesson 5.9

9781269614092 704 Lesson 11.1





(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

9781269614092 161 Lesson 3.4

9781269614092 424 Lesson 6.6






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

T: 9-12S: 9-12

9781269614092 278 Lesson 5.3

9781269614092 647 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

9781269614092 302 Lesson 5.5

9781269614092 671 Lesson 10.59781269614092 758 Lesson 11.5





(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: 9781269614092 ELPS: Teacher Material





(1) use prior knowledge to understand meanings in English

T: 9-12S: 9-12

9781269614375 57b Lesson 2.3

9781269614092

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: Enhanced with Graphing Utilities, Texas Edition






(2) use prior experiences to understand meanings in English

T: 9-12S: 9-12

9781269614375 797b Lesson 12.4

9781269614375 842b Lesson 13.3



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

T: 9-12

9781269614375 250b Lesson 5.7



(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

9781269614375 250b Lesson 5.4



(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

9781269614375 702b Lesson 11.4

9781269614375 871b Lesson 14.1



(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

9781269614375 1b Lesson 1.2






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

T: 9-12

9781269614375 250b Lesson 5.2



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

T: 9-12S: 9-12

9781269614375 57b Lesson 2.5






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

T: 9-12S: 9-12

9781269614375 57b Lesson 2.1



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

T: 9-12

9781269614375 797b Lesson 12.3

9781269614375 871b Lesson 14.1






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

T: 9-12S: 9-12

9781269614375 797b Lesson 12.3

9781269614375 871b Lesson 14.1



(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

9781269614375 354b Lesson 6.2






(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

9781269614375 178b Lesson 4.2

9781269614375 842b Lesson 13.2



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

T: 9-12

9781269614375 842b Lesson 13.2






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

T: 9-12S: 9-12

9781269614375 797b Lesson 12.3

9781269614375 842b Lesson 13.2


(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

9781269614375 1b Lesson 1.4



(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

9781269614375 559b Lesson 9.1



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

T: 9-12S: 9-12

9781269614375 439b Lesson 7.4






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

T: 9-12S: 9-12

9781269614375 507b Lesson 8.1


(E) share information in cooperative learning interactions

(1) share information in cooperative learning interactions

T: 9-12S: 9-12

9781269614375 1b Lesson 1.5

9781269614375 559b Lesson 9.49781269614375 634b Lesson 10.4






(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

9781269614375 439b Lesson 7.1



(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

9781269614375 842b Lesson 13.3






(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

9781269614375 1b Lesson 1.5



(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

9781269614375 178b Lesson 4.4

9781269614375 634b Lesson 10.4






(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

9781269614375 507b Lesson 8.2






(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

9781269614375 178b Lesson 4.1






(2) derive meaning of environmental print

T: 9-12S: 9-12

9781269614375 702b Lesson 11.7

9781269614375 842b Lesson 13.1



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

T: 9-12S: 9-12

9781269614375 129b Lesson 3.1






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

T: 9-12S: 9-12

9781269614375 439b Lesson 7.6


(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

9781269614375 842b Lesson 13.1





(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

9781269614375 559b Lesson 9.2

9781269614375 871b Lesson 14.3



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

T: 9-12S: 9-12

9781269614375 57b Lesson 2.5






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

T: 9-12S: 9-12

9781269614375 1b Lesson 1.4

9781269614375 634b Lesson 10.2



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

T: 9-12S: 9-12

9781269614375 871b Lesson 14.3






(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

9781269614375 129b Lesson 3.4

9781269614375 797b Lesson 12.1






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

T: 9-12S: 9-12

9781269614375 507b Lesson 8.5



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

T: 9-12S: 9-12

9781269614375 129b Lesson 3.3

9781269614375 797b Lesson 12.4






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

T: 9-12S: 9-12

9781269614375 559b Lesson 9.2

9781269614375 871b Lesson 14.4



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

T: 9-12S: 9-12

9781269614375 359b Lesson 6.6






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

T: 9-12S: 9-12

9781269614375 702b Lesson 11.1



(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

9781269614375 634b Lesson 10.3

9781269614375 797b Lesson 12.4



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

T: 9-12S: 9-12

9781269614375 1b Lesson 1.2






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

T: 9-12S: 9-12

9781269614375 354b Lesson 6.3



(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

Precalculus Enhanced with Graphing Utilities Texas Edition

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