Prentice Hall Stats: Modeling the World, 3rd Edition 2010 C O R R E L A T E D T O West Virginia 21st Century Mathematics Content Standards and Objectives for Probability and Statistics
PUBLISHER: Pearson Education, Inc., publishing as Prentice Hall SUBJECT: Mathematics SPECIFIC GRADE: 9-12 COURSE: Probability and Statistics TITLE: Stats: Modeling the World, 3rd Edition COPYRIGHT DATE: 2010 SE ISBN: 0-13-135958-4 TE ISBN: 0-13-135959-2 GENERIC EVALUATION CRITERIA 2010-2015 Mathematics Probability and Statistics 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 Probability and Statistics (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 SE/TE: 135-142, 217-222, 244-252, 405-410, 523-528, 609-616, 683-682 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 Appendix B Guide to Statistical Software Pages A3-A24 See Appendix F TI Tips A100 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 Probability and Statistics (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 Instructor s Resource CD included Appendix A Guide to Statistical Software Pages A3-A24 www. aw.com/bock Math XL for school StatCrunch 4. Multimedia 1. offer appropriate multimedia (e.g., software, audio, visual, internet access) materials. 2. provide a website which provides links to relevant sites as well as lesson plans, student activities and parent resources. 4
SE/TE: 14-15, 65, 86, 94, 117-119, 155, 235-235, 262, 287, 371-372, 392, 448-449, 568, 638 3. Integrate technology seamlessly when appropriate to model mathematical situations, analyze data, calculate results, and solve problems. B. Scientifically-Based Research Strategies SE/TE: 36-37, 68-70, 93-95, 162-165, 212-213, 238, 263-264, 285-286, 308-311, 336-338, 381-383, 490-491, SE/TE: 30, 52, 107, 153, 183, 227, 273, 333, 399, 445, 488, 538, 598-599, 632 SE/TE: 31-33, 85, 110-111, 114-115, 178-180, 228-230, 260-262, 298-299, 358-359, 370-371, 376-377, 395-396, 425-426, 591-593, 622-623 SE/TE: 30, 52, 107, 153, 183, 227, 273, 333, 399, 445, 488, 538, 598-599, 632 SE/TE: 68, 92, 127, 162, 189, 211-212, 238, 263, 285, 336, 360, 381, 430, 517, 577 SE/TE: 22-24, 26-27, 30-33, 47-49, 64-65, 81-86, 146-150, 223-226 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. 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. 5
Power Point Lecture Slides Video Lectures See pages xiv-xv 7. Present varied teaching models with emphasis on differentiated instruction in content, process, and product. 6
C. Critical Thinking SE/TE: 30-31, 63-64, 110-111, 154-155, 228-230, 260-262, 297-299, 333-335, 376-377, 418-419, 467-468, 538-540, 629-630 SE/TE: 33, 65, 211-212, 236, 283-284, 308, 335-336, 359, 429-430, 451, 474, 496-497, 549-550 SE/TE: 26-27, 56-58, 106-107, 178-179, 205-206, 259-260, 275-276, 327, 391-392, 447-448, 531-532 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 SE/TE: 13, 21, 31, 33, 65-68, 295-296, 399 SE/TE: 2-6 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). 2. address habits of mind activities (e.g., literacy skills, interpersonal communications, problem solving and self-directional skills). E. Classroom Management JUST CHECKING features in most chapters Companion DVD 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). 7
Instructor s Resource CD Companion DVD 3. provide suggestions for differentiated instruction (e.g., practice activities, learning stations, assessment, lesson plans). 8
F. Instructional Materials Companion DVD ActivStats Instructor s Resource CD Instructor s Resource CD Instructor s Resource CD Math XL for schools Instructor s Resource CD Power Point Lecture Slides Video Lecture Series See pages xiv-xv Math XL for schools Resource CD included Math XL for schools Instructor s Resource CD Power Point Lecture Slides Video Lecture Series See pages xiv-xv 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. 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. 9
Companion DVD ActivStats 10. Spiral previously taught skills and strategies with new content. 10
G. Assessment TestGen CD See page xiv Instructor s Resource CD See page xiv TestGen CD See page xiv TestGen CD See page xiv Companion DVD Companion DVD Companion DVD TestGen CD See page xiv 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. 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. 11
H. Process Standards JUST CHECKING feature in Most chapters SE/TE: 30-31, 63-64, 110-111, 154-155, 260-262, 333-335, 418-419, 467-468, 538-540 SE/TE: 30-31, 63-64, 110-111, 154-155, 260-262, 333-335, 418-419, 467-468, 538-540 SE/TE: 68, 130, 162, 189, 212, 238, 263, 285, 309, 336, 381, 430, 474, 517, 537, 669-670 SE/TE: 20-21, 23-27, 30-33, 44-46, 50, 65, 205-206, 228-230 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. 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. 12
SPECIFIC EVALUATION CRITERIA Mathematics Probability and Statistics Probability and Statistics is one of the most important branches of the mathematical sciences. Knowledge of these topics is critical to decision-making and to the analysis of data. Using concepts of probability and statistics, individuals are able to predict the likelihood of an event occurring, organize and evaluate data, and identify the significance of statements. Connections between content and applications to the real-world will be emphasized. Graphing utilities such as calculators and computers will be used to enhance student learning and to aid in the solution of practical problems. Prerequisites for this course are successful completion of Algebra II and Geometry. 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 5: Data Analysis and Probability Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them, select and use appropriate statistical methods to analyze data, develop and evaluate inferences and predictions that are based on models, and apply and demonstrate an understanding of basic concepts of probability. 13
(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 utilize interactive software, websites, applets, graphing calculators, and manipulatives through out each criteria as they A. Data Analysis and Probability SE/TE: 326, 329-331 SE/TE: 20-21, 23-27, 30-33, 44-46, 50, 65, 114-115, 205-206, 228-230 SE/TE: 354-355, 297-299, 304-305, 359 SE/TE: 326, 328-331, 334-335, 347-348 1. distinguish between experimental and theoretical probability through investigation and exploration. 2. using a real-world problem solving investigation, create and interpret data using various methods of displaying circle graphs, histograms, and frequency curves; make predictions, include information concerning outliers, present and justify results. 3. Use investigations to develop conjectures and procedures necessary to determine possible outcomes using tree diagrams and the counting principles of permutations and combinations. 4. express the chances of events occurring either in terms of a probability or odds. 14
SE/TE: 105-106, 111-115, 117-121, 123-125 SE/TE: 49-50, 52-53, 58-60, 114-115, 545, 561-564, 569-572 SE/TE: 54-57, 60-64, 105-107, 114-115, 369-372, 423-425 SE/TE: 105-107, 111-113, 119-120, 542-546, 574-575, 591, Chapter 29 Companion DVD SE/TE: 269-270, 273-277, 282-284, 452, 549-550 SE/TE: 467-468, 471-473, 487-490,542-546, 574-575, Chapter 29 Companion DVD 5. use the normal distribution and the binomial distribution including Pascal's triangle, to determine probability of events. 6. analyze data given or collected through experimentations and presented in a variety of formats (charts, tables, and graphs) using measures of central tendency (mean, median, and mode) from data presented in a variety of forms such as charts, tables, and graphs. 7. interpret and calculate measures of dispersions (range and standard deviation) from data presented in a variety of forms such as charts, tables and graphs or from data created through experimentation. 8. analyze individual performances in terms of percentiles, z- scores, and t- scores. 9. analyze the role of sampling, randomness, bias, and sample size in data collection and interpretation. 10. identify real life situations that involve statistical concepts including a t-test, make a hypothesis as to the outcome; develop, justify, and implement a method to collect, organize and analyze data; generalize the results to make a conclusion, compare the hypothesis and the conclusion; present the project using predictive and analytic tools (with and without technology). 15
SE/TE: 152-154, 156-158, 160-161, 171, 173 SE/TE: 621-625, 629-630, 633-636, 638-639, 642 SE/TE: 172-173, 176-180, 185-187, 200-204, 650-653, 655-659, 661-665 Chapter 28 Companion DVD 11. determine the correlation values for given data or for data generated by students and use the results to describe the association of the variables within the given data. Identify whether this association is systematic or predictable. 12. calculate the Chi-Square values for a given population. 13. perform a regression analysis on a set of data, either given or created through experimentation, and use the results to predict specific values of a variable. Identify the regression equation. 14. perform an analysis of variance (ANOVA) and interpret the results. 16