VIEWS: 1 PAGES: 8 POSTED ON: 5/18/2012
APS DISTRICT HIGH SCHOOL MATHEMATICS CURRICULUM FRAMEWORK Course Title: AP Statistics Course Number: 38022 Department: Mathematics ADS Number: 20604133 Prerequisites: Successful completion of Algebra II Length of Course: One Year Credit/PRI Area: .50 per Semester/Mathematics or elective Grade Level(s): 11 - 12 Important Notes: It is not required, but strongly recommended, that the student purchase a TI83+ graphing calculator. The Advanced Placement Statistics course is a basic introduction to statistics. The AP title is an indication that the course may be preparation for the AP exam but taking the exam is wholly optional. COURSE DESCRIPTION: Advanced Placement Statistics introduces the student to the major concepts and tools for collecting, analyzing, and drawing conclusions from data using these four broad themes: 1. Exploration: Observing patterns and departure from patterns 2. Study design 3. Producing models using probability theory and simulation 4. Statistical inference This course uses an interactive data collection approach using the text and lessons as resources and addresses the standards presented by the National Council of Teachers of mathematics (NCTM). The student applies his/her knowledge of algebra and geometry to linear transformation of data, conducting surveys, and analyzing the results. The student builds his/her own studies using both proper and improper data analysis techniques, critiques studies conducted by other students and entitles, and makes suggested improvements. References in parenthesis following each performance standard align with the State of New Mexico Mathematics Standards (NM) and the Albuquerque Public Schools (APS) Mathematics Standards. AP STATISTICS 14.1.8 Albuquerque Public 03/04 STRATEGIES: The “Illustrations” column in the Program of Studies provides exemplars of the standards, strategies, and best practices suggested by Mathematics departments in the Albuquerque Public Schools (APS). ASSESSMENTS: The “Illustrations” column also incorporates a variety of assessments and “check for” items suggested by the mathematics departments in APS. Assessments include: teacher evaluations of statistical studies using rubrics, short answer essay tests, homework assignments, AP exam, and criterion quizzes. SUGGESTED TEXTBOOKS AND INSTRUCTIONAL MATERIALS: Until new adoptions: Larsen Farber Elementary Statistics Cartoon Guide to Statistics Harper Perennial 1993 JMP Start Statistics Software Fathom Software At mathematics adoption: Introduction to Statistics and Data Analysis Peck Olsen Devore Statistics for the Utterly Confused McGraw Hill 2000 SUGGESTED TITLES/AUTHORS WEB SITES: Approved by HSCA: AP STATISTICS 14.2.8 Albuquerque Public 03/04 STRAND I: GLOBAL MATHEMATICAL PROCESSES CONTENT STANDARD: The student understands and uses mathematical processes. BENCHMARK: The student uses problem solving, reasoning and proof, communication, connections, and representations, as appropriate, in all mathematical experiences. GRADE PERFORMANCE STANDARDS ILLUSTRATIONS 11 – 12 Note: Illustrations include suggested activities for attaining each performance standard. A check () refers to a key feature to look for while assessing student performance. 1. Develops resourcefulness and perseverance in problem solving in 1, 4-10. The student, working in teams, plans and conducts product studies mathematics and other disciplines (NM-4D; APS-1.1). that have long time duration. Using this study, he/she discusses how the 2. Recognizes when to use previously learned strategies to solve new statistics were analyzed, how he/she arrived at the conclusions, and problems (NM-1C, 3B; APS-I.2). presents the studies to the class and to the corporations involved in the 3. Develops and uses strategies to solve given problems (NM-1C,1E, 3B; studies. Other class members critique each other’s work. APS-I-2). all required components 4. Monitors, discusses, and reflects on the processes of mathematical team work/peer support problem solving (NM-1A, 2A; APS-I.4). effective communication 5. Works in teams to share ideas, to develop and coordinate group problem-solving techniques approaches to problems, and to communicate findings analysis (NM-2B; APS-I.8). 6. Communicates mathematical thinking coherently and clearly to others 2, 3. The student utilizes Algebra II mathematics (matrices) to analyze (NM-2B, 2C; APS-I-9). data and presents solutions to the class. 7. Analyzes and evaluates mathematical thinking and strategies of others new problem-solving strategies (NM-2D; APS-I.10). relevance 8. Relates applications to mathematical language in various modalities clarity and comprehension in communication (NM-2B, 2C, 2C; APS-I.11). 9. Identifies and connects functions with real-world applications (NM-4E, 12D; APS-I.12). 10. Recognizes and applies mathematics in contexts outside the mathematics course (NM-6B; APS-I.15). AP STATISTICS 14.3.8 Albuquerque Public 03/04 STRAND II: NUMBER SENSE AND OPERATIONS CONTENT STANDARD: The student demonstrates number sense through experiences with meaningful mathematical problems tht focus on number meaning, number relationships, place value, relative effect of operations, and multiple representations to communicate sound mathematical thinking. BENCHMARK: The student understands rational, real, and complex numbers, and uses a variety of means, including technology, to solve problems in these number systems. GRADE PERFORMANCE STANDARDS ILLUSTRATIONS 11 - 12 Note: Although successful completion of Algebra II is required for this course, review and remediation of algebraic concepts has to take place on a regular basis for the student to accomplish performance tasks required by this course. 1. Develops a deeper understanding of very large and very small numbers 1, 2. The student uses statistical software to construct graphs and to analyze (NM-5B; APS-II.1). variance (e.g., determination of a “p” value – the smallest significance level at which something is statistically significant). 2. Uses graphical representations to model numerical relationships use of technology (NM-2C, 5D, 12B; APS-II.4). process graphical representation accuracy 3. Applies ratios, proportions, and percents in more complex mathematical 3-5, 7. The student uses the correct methodology (e.g., matrices, probability situations (NM-5C; APS-II.11). distribution) to calculate standard deviation, measures of central tendency, variance, and confidence intervals for his/her individual study, provided 4. Evaluates relationships between key components in a problem situation studies or teacher-selected studies using equations, matrices, factorials, and (NM-4B, 4C, 6D; APS-II.11). linear regression. 5. Develops fluency in operations with real numbers and matrices using accuracy mental computation, paper and pencil, or technology (NM-2D, 4D, 13A; correct equations for data APS-II.3 Late HS). comprehension of “p” value 6. Develops a fundamental understanding of sequences and series 6. The student uses factorials to computer complex probability outcomes (NM-3H; APS-II.6 Late HS). (e.g., odds of winning the Powerball). accuracy 7. Solves an application involving optimization (NM-13G; APS-II.7 LHS). formulas AP STATISTICS 14.4.8 Albuquerque Public 03/04 STRAND III: DATA ANALYSIS, STATISTICS, AND PROBABILITY CONTENT STANDARD: The student identifies patterns and special features of data and events of chance through experiences with meaningful mathemeatical problems that Focus on comparing, predicting, representing data, and making decisions to communicate mathematical understanding. BENCHMARK: The student understands the characteristics of a well designed study, describes the difference between studies, and uses a variety of ways to interpret data. The student computes basic statistics and evaluates published statistics and representations of data. The student simulates probability situations and computes and interprets simple probability cases. GRADE PERFORMANCE STANDARDS ILLUSTRATIONS 11 - 12 1. Creates histograms, box plots, and scatter plots and uses them to display 1-3, 6, 9, 11, 12. Using the data from the last boy’s high school basketball data (NM-10A; APS IV.1). game, the student creates charts and tables with regression lines to illustrate shooting percentages, correlation of time vs. shooting 2. Computes mean, median, mode, and identifies the merit of each percentage, from three-pointers, field goals, and free throws. The (NM-10C, 10F; APS-IV.2). student finds the measures of central tendencies (e.g., mean, median, mode, interquartile range, skew) for each. 3. Identifies and uses statistical terms (NM-10B-D, 10F; APS-IV.3). calculations completion of all tasks neatness of graphs and tables matching of data to tables and graphs 4. Defines sampling and recognizes its role (NM-10D; APS-IV.4). 4, 5, 10, 14. Using student’s individual studies and studies from other sources, the student differentiates between proper sampling techniques and sampling 5. Constructs and draws inferences from charts, tables, and graphs techniques that have bias in them. (NM-10A; APS-IV.5). recognition of bias recognition of proper statistical techniques 6. Writes an equation of best-fit using a set of data points, and makes logical inferences predictions based on the graph (NM-10B; APS-IV.6). 7. Uses simulations to create and interpret discrete probability distributions 7, 8, 13, 15-17. The student observes a teacher demonstration (ten students at a (NM-11 A; APS-IV.7). time) of Black Jack hands (without gambling) using four decks of cards. He/she interprets probability distributions, probability of compound events, 8. Computes the probability of a compound event (NM-11D; APS-IV.8). fundamental counting principle, and predicts the probability of a particular setoff cards coming up next and the independence of those events. 9. Explains the differences among various kinds of studies and which types ability to calculate the probability of the next card of inferences can be legitimately be drawn from each (NM-10A; prediction of the probability of the succession of cards APS-IV.1 Late HS). understanding of probability principles 10. Recognizes the characteristics of well designed studies including the role of randomness (NM-10E; APS-IV.2 LHS). AP STATISTICS 14.5.8 Albuquerque Public 03/04 GRADE PERFORMANCE STANDARDS ILLUSTRATIONS 11 - 12 11. Analyzes the effects of data transformations on measures of central tendency and variability (NM-10C, 10 F; APS-IV.3 LHS). 12. For bivariate measurement data, creates and displays a scatter plot, describes its shape, and determines the regression of the coefficients (NM-10A, 10B; APS-IV.4 LHS). 13. Uses simulations to explore the variability of sample statistics from a known population and to construct sampling distributions (NM-11A; APS-IV.5 LHS). 14. Evaluates published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of the conclusions (NM-10E; APS-IV.6 LHS). STRAND IV: PATTERNS, FUNCTIONS, AND ALGEBRAIC CONCEPTS CONTENT STANDARD: The student demonstrates an understanding of algebraic skills and concepts through experiences with meaningful mathematical problems that focus on discovering, describing, modeling, and generalizing patterns and functions, representing and analyzing relationships, and finding and supporting solutions. AP STATISTICS 14.6.8 Albuquerque Public 03/04 BENCHMARK: The student represents patterns with relations and functions, investigates rates of change, and symbolically manipulates numbers. GRADE PERFORMANCE STANDARDS ILLUSTRATIONS 11 - 12 1. Explains the meanings of and uses common algebraic symbols 1-17. The student, through the construction of his study (teacher-approved), (NM-13D, APS-V.7). creates his own real-life word problem that incorporates statistical 2. Identifies and uses algebraic terms such as variable, exponent, factor formulas, variables, exponents, matrices, polynomials, radicals, rational term, and function (NM-13D; APS-V.8). expressions, order of operations, and graphical representations of data, 3. Uses order of operations and the commutative, associative, and including regression analysis. The student solves his own problem and distributive axioms to simplify expressions (NM-4A, 13A; APS-V.9). submits the results. 4. Translates a real-life problem into an expression, equation, inequality, or variety of concepts matrix as the first step (NM-13A; APS-V.11). solution 5. Graphs linear equations and inequalities from given equations and from critical thinking, problem-solving skills symbolic reasoning in the context of applied settings or presented data accuracy (NM-12B, 13B; APS-V.12). visuals 6. Applies the laws of exponents with integers to perform operations on use of technology expressions (NM-5B, 13A; APS-V.14). reasonableness of conclusions 7. Adds, subtracts, multiplies, and divides polynomials with monomial presence of all required components divisors using concrete objects, pictorial representation, and algebraic manipulation (NM-2C, 4A; APS-V.15). 8. Simplifies radicals and numerical radicands and estimates their value both mentally and with a calculator (NM-5A; APS-V.18). 9. Finds the sum, difference, product, and quotient of rational expressions with monomial and polynomial numerators and denominators (NM-13A; APS-V.20). 10. Solves equations involving rational expressions with monomial and polynomial numerators and denominators (NM-13C; APS-V.21). 11. Solves word problems involving algebraic functions using appropriate units, unit analysis, and precision (NM-1C, E, 9B, 12D; APS-V.22). 12. Analyzes functions of one variable by investigating rates of change, intercepts, zero’s asymptotes, maximum/minimum, and local/ global behavior (NM-12E, 13G; APS-V.2 LHS). 13. Creates systems of equations in two or three variables and solves them by using the following algebraic processes; graphing by hand as well as graphing with calculators, using algebraic methods such as linear combination and substitution, applying basic matrix operations, and inverse matrix properties (NM-13B, 13E; APS-V.5 LHS). AP STATISTICS 14.7.8 Albuquerque Public 03/04 GRADE PERFORMANCE STANDARDS ILLUSTRATIONS 11 - 12 14. Describes a real-life problem or event algebraically and graphically using various functions including linear, exponential power, rational square, square root, cube and cube root (NM-12 A-C; APS-V.7 LHS). 15. Validates the reasonableness of conclusions (NM-3C; APS-V.9 LHS). 16. Identifies linear, quadratic, polynomial, logarithmic, and exponential functions from graphs (NM-12A, 12C, 13B; APS-V.10 LHS). 17. Applies the laws of exponents with real numbers to perform operations on expressions (NM-5B, 13A, 13D; APS-V.16 LHS). AP STATISTICS 14.8.8 Albuquerque Public 03/04