Prentice Hall Mathematics, Algebra 2 Foundations 2011 Algebra II C O R R E L A T E D T O West Virginia 21st Century Mathematics Content Standards and Objectives for Algebra II
PUBLISHER: Pearson Education, Inc., publishing as Prentice Hall SUBJECT: Mathematics SPECIFIC GRADE: 10-12 COURSE: Algebra II TITLE: Prentice Hall Mathematics, Algebra 2, The Foundations Series COPYRIGHT DATE: 2011 SE ISBN: 0133696588 TE ISBN: 0785469249 GENERIC EVALUATION CRITERIA 2010-2015 Mathematics Algebra II R-E-S-P-O-N-S-E Yes No N/A CRITERIA NOTES x I. INTER-ETHNIC The instructional material meets the requirements of inter-ethnic: concepts, content and illustrations, as set by West Virginia Board of Education Policy (Adopted December 1970). x II. EQUAL OPPORTUNITY The instructional material meets the requirements of equal opportunity: concept, content, illustration, heritage, roles contributions, experiences and achievements of males and females in American and other cultures, as set by West Virginia Board of Education Policy (Adopted May 1975). 1
INSTRUCTIONAL MATERIALS ADOPTION: 21 st CENTURY LEARNING EVALUATION CRITERIA GENERAL EVALUATION CRITERIA 2010-2015 Mathematics Algebra II (Vendor/Publisher) SPECIFIC LOCATION OF CONTENT WITHIN PRODUCT (IMR Committee) Responses I=In-depth A=Adequate M=Minimal N=Nonexistent I A M N In addition to alignment of Content Standards and Objectives (CSOs), materials must also clearly connect to Learning for the 21 st Century which includes opportunities for students to develop A. Learning Skills Addressed throughout the text. Sample citations follow: SE/TE: 4-6, 53, 64-67, 110, 135, 184-188, 192, 269, 281, 361-364, 368, 451, 462-466, 508, 565-568, 572, 622, 641-646, 674, 686-692, 698, 725, 760, 809, 858-860 Thinking and Problem-Solving Skills/ Rigor and Depth of Content Content is presented in a way that deepens student understanding through engagement in meaningful, challenging mathematics that builds on prior knowledge and promotes connections among mathematical concepts. Thinking and Problem-Solving Skills /Development of Conceptual Understanding Learning opportunities require students to develop their own viable mathematical understandings and help them build connections between mathematical ideas. Information and Communication Skills/Mathematical Language Appropriately introduce and reinforce in multiple ways all necessary terms and symbols. Personal and Work Place Productivity Skills 2
B. 21 st Century Tools See PowerAlgebra.com, the digital environment for Prentice Hall High School Mathematics, for videos, audios, dynamic activities and math tools, the Pearson Video Challenge, and more. Also cited throughout the text; see especially My Math Video, Dynamic Activities, and Concept Bytes. Sample citations follow: SE/TE: 3, 63-64, 121, 145, 162, 164, 175, 203, 212, 231, 255, 291, 379, 443, 461, 488-489, 499, 507, 519, 583, 633, 685, 771, 780, 848 Also see www.pearsonsuccess net.com. Problem-solving tools (such as spreadsheets, decision support, design tools) Communication, information processing and research tools (such as word processing, e-mail, groupware, presentation, Web development, Internet search tools) Personal development and productivity tools (such as e-learning, time management/calendar, collaboration tools) 3
INSTRUCTIONAL MATERIALS ADOPTION: 21 st Century Learning EVALUATION CRITERIA The general evaluation criteria apply to each grade level and are to be evaluated for each grade level unless otherwise specified. These criteria consist of information critical to the development of all grade levels. In reading the general evaluation criteria and subsequent specific grade level criteria, e.g. means examples of and i.e. means that each of those items must be addressed. Eighty percent of the combined general and specific criteria must be met with I (In-depth) or A (Adequate) in order to be recommended. 2010-2015 Mathematics Algebra II (Vendor/Publisher) SPECIFIC LOCATION OF CONTENT WITHIN PRODUCT (IMR Committee) Responses I=In-depth A=Adequate M=Minimal N=Nonexistent I A M N For student mastery of content standards and objectives, the instructional materials will provide students with the opportunity to 4. Multimedia See PowerAlgebra.com, the digital environment for Prentice Hall High School Mathematics, for videos, audios, dynamic activities and math tools, the Pearson Video Challenge, and more. Dynamic Activities are cited at point of use throughout the text. SE/TE: 39, 121, 227, 243, 255, 260, 444, 463, 470, 521, 592, 649, 723, 745, 848, 666, 695 1. offer appropriate multimedia (e.g., software, audio, visual, internet access) materials. 4
See PowerAlgebra.com, a digital environment with videos, audios, dynamic activities and math tools, the Pearson Video Challenge, and more. 2. provide a website which provides links to relevant sites as well as lesson plans, student activities and parent resources. 5
Technology is integrated throughout the text; see especially Concept Bytes, Dynamic Activities, and graphing calculator Problems. SE/TE: 64, 121, 162, 164, 175, 212, 231, 255, 291, 294, 305-306, 342, 353-356, 404, 443, 488-489, 499, 507, 640, 650, 780, 848 see especially Solve Its and Pull It All Together. SE/TE: 11, 53, 88, 154, 176, 192, 227, 347, 368, 417, 451, 508, 555, 572, 607, 622, 674, 760, 772, 809 See Pull It All Together Sample citations: SE/TE: 53, 135, 192, 281, 368, 451, 508, 572, 622, 674, 760, 809 see especially Writing exercises and Solve Its. SE/TE: 7, 25, 38, 79, 107, 149, 152, 156, 205, 207, 210, 313, 343, 373, 441, 486, 558, 571, 605, 641, 648, 652, 657-658, 666, 689, 698, 702, 725, 758, 778, 825, 836, 846, 861 see especially Reasoning exercises and Got Its, and Know/Need/Plan and Think/Write Problems. SE/TE: 4, 6, 20, 66, 115, 158, 170, 217, 232, 302, 384, 418, 434, 499-500, 524, 557, 594, 602, 616, 635, 643, 712, 726, 783, 804, 838 3. Integrate technology seamlessly when appropriate to model mathematical situations, analyze data, calculate results, and solve problems. B. Scientifically-Based Research Strategies 1. Consistently require students to link prior knowledge to new information to construct their own viable understandings of mathematical ideas. 2. Consistently provide opportunities for students to solve complex problems that have multiple entry points and the possibility of multiple solution processes. 3. Consistently provide opportunities for students to communicate their mathematical thinking processes to others orally, in writing, or pictorially. 4. Routinely require students to develop and defend mathematical conjectures, arguments, reasoning and proof. 6
See Concept Bytes and Solve Its. SE/TE: 11, 26, 121, 162, 176, 251, 252, 318, 332, 346, 387, 426, 491, 508, 584, 607, 711 Addressed throughout the text. SE/TE: 4-6, 64-67, 146-147, 244, 261, 363, 407, 428, 476, 688 Addressed throughout the Teacher Edition. See Lesson Resource on Teacher Edition pages A and B after every lesson. 5. Provide opportunities for the students to be involved in investigations that enable them to make connections among mathematical ideas. 6. Expect students to develop multiple representations of the mathematics in order to depict reasoning used to explain real world phenomena or solutions to relevant problems and move fluently between those representations. 7. Present varied teaching models with emphasis on differentiated instruction in content, process, and product. 7
C. Critical Thinking see especially Reasoning exercises and Got Its. Sample citations: SE/TE: 6, 39-40, 66, 109, 126, 158, 165, 170, 217, 229, 232, 267, 302, 344, 384, 424, 434, 499, 506, 524, 577, 594, 597, 602, 627, 635, 640, 712, 741, 783, 807, 838-839 see especially Solve Its and Error Analysis exercises. Sample citations: SE/TE: 11, 32, 79, 121, 152, 162, 214, 220, 316, 332, 424, 426, 491, 496, 520, 562, 584, 597, 607, 662, 711, 738, 861 Addressed throughout the text. SE/TE: 28, 65, 147, 208, 217, 355, 396, 419, 438, 466, 567, 595, 644, 652, 661, 700, 794, 825 1. emphasize questioning models to promote higher order thinking skills based on depth of knowledge. 2. Consistently require students to discuss mathematics with each other and with the teacher, make arguments, conjecture and reason, and justify/clarify their ideas in writing and orally in precise mathematical symbols and language. 3. Present real world application that is current, engaging, integrated throughout the instruction, and promotes and develops critical thinking. D. Life Skills see especially Solve Its and the Pearson Video Challenge at PowerAlgebra.com. Sample citations: SE/TE: 3, 19, 57, 63, 128, 154, 182, 291, 379, 426, 431, 453, 477, 609, 685, 781, 799 1. address life skills (e.g., reading road maps, using reference tools, researching, reading a newspaper, using want ads, completing an application, applying the interview process and goal setting). 8
see especially Tips for Success and Think/Plan margin notes. SE/TE: 58, 104, 140, 198, 228, 286, 374, 390, 456, 514, 523, 578, 628, 642, 680, 740, 766, 824 2. address habits of mind activities (e.g., literacy skills, interpersonal communications, problem solving and self-directional skills). E. Classroom Management see certain Solve Its and Concept Bytes. SE/TE: 18, 33, 128, 162, 175-176, 251-252, 279-280, 318, 332, 346, 387, 426, 443, 584, 592, 711, 744 see My Math Video, and certain Solve Its and Concept Bytes. SE/TE: 3, 18, 63, 128, 175-176, 203, 291, 379, 395, 443, 461, 519, 583, 633, 685, 771-772 see Lesson Resource pages at the end of each lesson in the TE. TE: 24A, 120A, 191A, 225A, 317A, 401A, 479A, 546A, 598A, 648A, 710A, 798A 1. include opportunities for large group, small group, and independent learning. 2. Consistently require students to explore mathematical ideas, individually and collaboratively, while integrating the process standards (see Section I of this rubric). 3. provide suggestions for differentiated instruction (e.g., practice activities, learning stations, assessment, lesson plans). 9
F. Instructional Materials see each lesson, the WV standards listed at the front of the text, and the All-In-One Teacher Resource. see especially Open-Ended exercises and Problems that are done using two different methods. SE/TE: 4-9, 24, 55, 146-147, 210, 339, 363, 407, 428, 455, 476, 553, 584-590, 612, 624, 688, 750, 846 see Teacher Support in each lesson of the TE, and the Focus Questions found throughout the SE. Sample citations follow: SE: 14-15, 90, 159, 229, 272, 315, 364, 419, 447, 544, 611, 646, 749, 776, 838 See All-in-One Teaching Resources. see Lesson Resource pages at the end of each lesson in the Teacher s Edition. Sample citations: TE: 24A, 120A, 191A, 225A, 317A, 401A, 479A, 546A, 598A, 648A, 710A, 798A 1. Are organized according to WV content standards or other increments that allow students to investigate and explore major mathematical ideas; provide a variety of lessons, activities, and projects from which to choose; and emphasize connections between mathematical ideas. 2. Consistently integrate tasks that engage students and invite them to speculate and hypothesize, are open-ended, and require them to determine appropriate strategies. 3. Provide teachers with guiding questions to aid students development of mathematical discourse to further mathematical understanding. 4. Provide additional resources that are organized in a way that is easy to access and use. 5. Include various instructional models to address varied learning styles of students. 10
see Lesson Resource pages at the end of each lesson in the Teacher s Edition. Sample citations: TE: 24A, 120A, 191A, 225A, 317A, 401A, 479A, 546A, 598A, 648A, 710A, 798A See All-in-One Teaching Resources. The Process Standards are integrated throughout the text with appropriate teacher support. See Section H of this document. Addressed throughout the TE; see especially the Math Background at the start of each chapter and the Lesson Opener at the start of each lesson. TE: 3A-B, 4, 63A-B, 64, 145A-B, 146, 203A-B, 204, 291A-B, 292, 379A-B, 380, 461A-B, 462, 519A- B, 520, 583A-B, 584, 633A-B, 634, 685A-B, 686, 771A-B, 772, 823 see especially Solve Its, Get Ready, Mixed Reviews, and Cumulative Test Prep. Sample citations: SE/TE: 1, 11, 32, 53, 58-61, 88, 109, 140-143, 153-154, 176, 192, 198-201, 225, 227, 286-289, 326, 347, 368, 374-377, 417, 442, 451, 456-459, 487, 508, 514-517, 555, 564, 572, 578-581, 598, 607, 622, 628-631, 665, 674, 680-683, 751, 760, 766-769, 772, 779, 809, 847 6. Provide extensive and varied opportunities to differentiate individual needs for skill-building. 7. Provide supplemental materials for intervention and enrichment. 8. Provide teachers with support to properly integrate the process standards using the available resources. 9. Include a teacher resource that builds content knowledge for the teacher. 10. Spiral previously taught skills and strategies with new content. 11
See the Cumulative Test Preps at the end of each chapter and the WV Progress Monitoring Assessment resource. Sample citations: SE/TE: 58-60, 140-142, 198-200, 286-288, 374-376, 456-458, 514-516, 578-580, 628-630, 680-682, 766-768, 814-821 see especially Pull It All Together (and the rubric on page 53), Solve Its, Short and Extended Response questions, and the Pearson Video Challenge at PowerAlgebra.com. SE/TE: 3, 19, 57, 60, 63, 109, 128, 135, 142, 154, 182, 200, 281, 288, 291, 376, 379, 426, 431, 451, 453, 458, 469, 477, 516, 580, 609, 622, 630, 682, 685, 760, 768, 781, 799, 816, 821, 827, 857 TE: 53 See West Virginia Progress Monitoring Assessments. see especially Pull It All Together, Solve Its, Short and Extended Response questions, and the Pearson Video Challenge at PowerAlgebra.com. Sample citations: SE/TE: 3, 19, 57, 60, 63, 109, 128, 135, 142, 154, 182, 200, 281, 288, 291, 376, 379, 426, 431, 451, 453, 458, 469, 477, 516, 580, 609, G. Assessment 1. provide assessment formats commensurate with WV assessment programs (e.g., WESTEST, NAEP, State Writing Assessment, informal assessments, PLAN, EXPLORE, ACT and SAT). 2. provide opportunities for assessment based on performance-based measures, open-ended questioning, portfolio evaluation, rubrics and multimedia simulations. 3. provide benchmark and ongoing progress monitoring. 4. provide rubric-based differentiated assessment. 12
622, 630, 682, 685, 760, 768, 781, 799, 816, 821, 827, 857 TE: 53 In the digital environment at Power.Algebra.com, SuccessTracker provides teachers with the capabilities to manage and interpret data for students, classes, and beyond along with remediation options for students based on performance in the various assessments offered. see the Chapter Reviews, especially Connecting Big Ideas. See the self-quiz for each lesson at PowerAlgebra.com. Sample citations: SE/TE: 54, 136, 193, 282, 369, 452, 509, 573, 623, 675, 761, 810, 863 see especially Get Ready, Got Its, Lesson Checks, and Chapter Tests. Also see Performance Task in All-In-One Teaching Resources. SE/TE: 1, 36-37, 57, 61, 101, 112, 117, 139, 143, 158-159, 197, 201, 205, 229, 240, 285, 289, 316, 320, 330, 373, 377, 403-404, 415, 455, 459, 492, 501, 513, 517, 535, 540, 577, 581, 604, 608, 627, 631, 645-646, 679, 683, 721, 733-735, 765, 769, 813, 854, 860 see especially Cumulative Test Prep, Pull It All Together, and the Performance Task in All-In-One Teaching Resources. Sample 5. provide an electronic system for managing assessment data to facilitate the implementation of tiered instruction 6. integrate student self-assessment for and of learning by providing tools and organizers that are linked to clearly identified learning goals. 7. Integrate formal and informal means of assessment in the materials for diagnostic, formative, and summative purposes. 8. include various types of assessments: performance tasks, multiple choice, short answer, and free response. 13
citations: SE/TE: 53, 58-60, 121, 140-142, 192, 198-200, 281, 286-288, 368, 374-376, 451, 456-458, 508, 514-516, 572, 578-580, 622, 628-630, 674, 680-682, 760, 766-768, 809, 814-821 14
H. Process Standards see especially Challenge exercises and Pull It All Together features. SE/TE: 53, 121, 192, 226, 278-281, 368, 451, 508, 572, 622, 640, 674, 760, 809 see especially Solve Its, Writing exercises, and Error Analysis exercises. SE/TE: 11, 22, 24, 32, 79, 107-108, 121, 152, 162, 214, 220, 223-224, 316, 332, 424, 426, 474, 491, 496, 502, 507, 520, 562, 584, 597, 607, 638, 662, 711, 738, 787, 839, 861 see especially Solve It; Lesson Check; Think and Plan callouts for each example Problem. SE/TE: 4, 6, 20, 34, 66-67, 104-105, 115, 158, 170, 187, 213, 217, 228, 232, 296, 302, 324, 384, 388, 397-398, 418, 434, 493-494, 499-500, 524, 542, 550, 557, 566, 594, 602, 608-609, 616, 635, 643, 712, 726, 739, 783, 804, 829, 838 Addressed throughout the text. SE/TE: 28, 49, 65, 147, 208, 217, 323, 355, 396, 419, 438, 466, 524, 536, 567, 595, 644, 652, 661, 700, 794, 825 1. Problem Solving: Provide frequent opportunities for students to formulate, grapple with, and solve complex problems that require a significant amount of effort and have multiple viable solution paths. 2. Communication: Routinely challenge students to communicate their thinking to others orally, in writing, and/or pictorially, using precise mathematical language. 3. Reasoning and Proof: Provide frequent opportunities for students to complete mathematical investigations with and without technology; develop conjectures, mathematical arguments and proofs to confirm those conjectures. 4. Connections with Mathematics: Consistently establish connections, and provide opportunities for students to establish connections, among mathematical concepts and their real-world applications. 15
Addressed throughout the text. SE/TE: 5-6, 64-67, 146-147, 244, 261, 279-280, 363, 407, 428, 476, 566-568, 688, 842, 854 5. Representations: Provide frequent opportunities for students to develop multiple representations of the mathematics in order to depict reasoning used to explain real world phenomena or solutions to relevant problems and move fluently between those representations. 16
SPECIFIC EVALUATION CRITERIA Mathematics Algebra II Algebra II objectives emphasize the use of investigation to more advanced functions, using them to solve real-world problems. Focus is on multiple representations to develop conjectures, testing and justifying validity. Calculators, computers, and interactive utilities are an integral part of instruction. The West Virginia Standards for 21st Century Learning include the following components: 21st Century Content Standards and Objectives and 21st Century Learning Skills and Technology Tools. All West Virginia teachers are responsible for classroom instruction that integrates learning skills, technology tools and content standards and objectives. Standard 2: Algebra Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of patterns, relations and functions, represent and analyze mathematical situations and structures using algebraic symbols, use mathematical models to represent and understand quantitative relationships, and analyze change in various contexts. 17
(Vendor/Publisher) SPECIFIC LOCATION OF CONTENT WITHIN PRODUCT (IMR Committee) Responses I=In-depth A=Adequate M=Minimal N=Nonexistent I A M N For student mastery of content standards and objectives, the instructional materials will A. Algebra SE/TE: 81-97, 99-101 SE/TE: 300-312 SE/TE: 212-225, 227-236 SE/TE: 268-278, 284-285 1. Provide a variety of opportunities to determine equations of lines including parallel, perpendicular, vertical and horizontal lines, and compare and contrast the properties of these equations. 2. Provide a variety of examples and exercises to factor higher order polynomials by applying various methods including factoring by grouping and the sum and difference of two cubes. 3. Provide a variety of opportunities to analyze and describe the relationship between the factored form and the graphical representation. 4. Provide a variety of examples and exercises to define complex numbers, simplify powers of i, perform basic operations with complex numbers, and give answers as complex numbers in simplest form. 18
SE/TE: 383-386, 402-410, 413-415, 417-424, 5. Provide a variety of examples and exercises to simplify expressions involving radicals and fractional exponents, convert between the two forms, and solve equations containing radicals and exponents. SE/TE: 243-277, 283-285 6. Provide a variety of examples and exercises to solve quadratic equations over the set of complex numbers: apply the techniques of factoring, completing the square, and the quadratic formula; use the discriminate to determine the number and nature of the roots; identify the maxima and minima. SE/TE: 268-278 7. Provide a variety of opportunities to use words, graphs, tables, and equations to generate and analyze solutions to practical problems that involve quadratic equations over the set of complex numbers. SE/TE: 184-191, 196-197, 772-788, 804-807, 811-813 8. Consistently develop and use the appropriate field properties of matrices by adding, subtracting, and multiplying; solve a system of linear equations using matrices; and apply skills toward solving practical problems. SE/TE: 64-73, 98, 101, 426-443, 453-455 9. Provide a variety of examples and exercises that define a function and find its zeros; express the domain and range using interval notation; find the inverse of a function; find the value of a function for a given element in its domain; and perform basic operations on functions including composition of functions. 19
SE/TE: 81-97, 103-134, 204-210, 361-367, 444-450, 462-463, 470-475, 530-537 SE/TE: 81-97, 103-134, 204-210, 292-308, 361-367, 444-450, 462-463, 470-475, 530-537 SE/TE: 279-280, 814 SE/TE: 162-175, 195, 197 SE/TE:74-80, 99, 101, 520-528 SE/TE: 634-639, 640, 641-648, 649-656, 657, 658-665, 666-673, 676-679 10. Consistently provide a variety of opportunities to analyze families of functions and their transformations; recognize linear, quadratic, radical, absolute value, step, piece-wise, and exponential functions. 11. Consistently engage students in the opportunities to analyze connections among words, graphs, tables and equations when solving practical problems with and without technology around family of functions. 12. Provide a variety of examples and exercises that solve quadratic inequalities, graph their solution sets, and express solutions using interval notation. 13. Provide a variety of opportunities to solve and graph the solution set of systems of linear inequalities in two variables by finding the maximum or minimum values of a function over the feasible region using linear programming techniques. 14. Provide a variety of examples and exercises to solve practical problems involving direct, inverse and joint variation. 15. Provide a variety of examples and exercises to analyze the conic sections; identify and sketch the graphs of a parabola, circle, ellipse, and hyperbola and convert between graphs and equations. 20
SE/TE: 43-52, 56-57, 131 16. Provide a variety of opportunities to solve absolute value inequalities graphically, numerically and algebraically and express the solution set in interval notation. SE/TE: 480-487, 490, 491-497, 498-506, 507, 511-513 17. Provide a variety of opportunities that define a logarithmic function, transform between exponential and logarithmic forms, apply the basic properties of logarithms to simplify or expand an expression. SE/TE: 220-236, 238-240, 242-267, 283-285 18. Appropriately introduce and reinforce the necessary experience that identify a real life situation that exhibits characteristics of change that can be modeled by a quadratic equations; pose a questions; make a hypothesis as to the answer; develop, justify, and implement a method to collect, organize and analyze related data; extend the nature of collected, discrete data to that of a continuous function that describes the known data set; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project numerically, analytically, graphically and verbally using the predictive and analytic tools of algebra (with and without technology). 21
SE/TE: 584-606, 624-625 19. Provide opportunities that engage students in the opportunities to describe and illustrate how patterns and sequences are used to develop recursive and closed form equations; analyze and describe characteristics of each form. 22