BERKELEY HEIGHTS PUBLIC SCHOOLS BERKELEY HEIGHTS, NEW JERSEY GOVERNOR LIVINGSTON HIGH SCHOOL MATHEMATICS DEPARTMENT AP STATISTICS AND DISCRETE MATHEMATICS #MAY1230 Curriculum Guide September 2010 Mrs. Judith Rattner, Superintendent Mrs. Patricia Qualshie, Assistant Superintendent Mrs. Susan Rembetsy, District Supervisor Developed by: Steve Hess This curriculum may be modified through varying techniques, strategies, and materials, as per an individual student’s Individualized Education Plan (IEP) Approved by the Berkeley Heights Board of Education at the regular meeting held on 10/28/10 . TABLE OF CONTENTS Page Vision Statement ............................................................................................................ 1 Mission Statement ......................................................................................................... 2 Course Proficiencies ....................................................................................................... 3 Course Objectives ............................................................................................... 3 Student Proficiencies .......................................................................................... 6 Methods of Evaluation ........................................................................................ 8 Course Outline/Student Objectives ................................................................................ 9 Vocabulary for AP Statistics/Discrete Math .................................................................... 14 Resources/Activities Guide ............................................................................................. 15 Suggested Materials ....................................................................................................... 17 Resources for Students ....................................................................................... 17 Resources for Teacher ......................................................................................... 17 VISION STATEMENT AP Statistics and Discrete Math is a college level course that includes the content covered by the College Board AP Statistics Exam and selected topics from discrete mathematics. The text being used was written for high school students who are at an advanced reading level. The objective of the course is to provide students with a non‐calculus introduction to statistical literacy, by presenting the tools for collecting, analyzing, and drawing conclusions from data. The themes of the course are exploring data, by observing patterns and departures from patterns, planning a study and deciding how to collect and measure data, anticipating patterns by using probability theory and simulation, and statistical inference analysis to confirm models. The course is practical. It does not deal in‐depth with numerous mathematical proofs, although some formality will exist. Most of what is covered is done through an intuitive and logical approach. This offering will provide an added opportunity for students to strengthen their quantitative reasoning abilities. The AP Statistics portion of the course is designed around the use of technology. Graphing calculators are used extensively. The computer will be used to handle larger data sets. The course will develop marketable skills through the use of data analysis and interpretation. Students will also frequently work in groups, which will help develop their communications and teamwork skills. Effective communication, using the language of mathematics, is essential for all math courses and will be emphasized throughout this course. The development of mathematical definitions, notations, terminology, syntax, and logic will be imbedded in the course studies. Students will also be required to interpret statistical measures in the context of the problem and be able to clearly discuss the reasonableness of conclusions that can be formed from specific data sets. Five (5) credits are given for passing this full year course. Standards from the New Jersey Core Curriculum Content Standards for Mathematics have been integrated throughout the curriculum. Berkeley Heights Public Schools 1 MISSION STATEMENT This course provides an opportunity for students to learn the principles of statistical analysis and how to apply them to a wide variety of real world situations, from the social sciences, business, biology, and other fields. The students will also explore a variety of discrete math topics, which will expand their problem‐solving skills and expose them to a number of math fields, which have not been covered in‐depth, in previous courses. Through both the statistics and discrete math topics, the students will become familiar with a variety of problem‐solving strategies and develop an understanding of the applications of math to many other fields. The students will also learn to use mathematical language to communicate ideas through the use of model, diagrams, and symbols. The students will be able to build mathematics models to represent specific information provided in real world situations. Technology will be integrated throughout the instruction of the course, and will be used to expand the problem‐solving capabilities of the students. The students will be held responsible for individual work while also being expected to function productively in a cooperative learning environment. The prerequisites for AP Statistics and Discrete Math are a B+ or better average in Math Analysis, or a B average or better in Math Analysis Honors with a teacher recommendation. Five (5.0) credits will be earned for successful completion of this full year course. National and state standards are integrated throughout the curriculum. Berkeley Heights Public Schools 2 COURSE PROFICIENCIES COURSE OBJECTIVES 1. Display univariate data with graphs, including histograms, stemplots, and box and whisker plots, and describe data through center, shape, and spread. (4.4/12A5) 2. Apply and analyze the normal distribution and use the normal probability plot to assess whether a dataset is approximately normal. (4.4/12A5) 3. Analyze form, directions, and strength of relationships in bivariate scatterplots. (4.4/12A5; 4.5/12B4) 4. Understand and apply correlation and discuss cause‐and‐effect relationships versus causation. (4.4/12A2,5; 4.5/12B4) 5. Use regression, including ordinary least squares, nonlinear models, and multi‐variate regression to analyze bivariate relationships. (4.4/12A4; 4.5/12F3) 6. Explore categorical data through frequency tables, bar charts, and two‐way tables, including marginal, joint, and conditional frequencies. (4.4/12A2) 7. Distinguish between census, survey, observational study, and experiment and understand most appropriate applications for each. (4.4/12A6) 8. Understand the role of randomization, simple random sample, stratified random sample, cluster sampling, and multi‐stage sampling. (4.4/12A1) 9. Recognize and anticipate sources of bias, including selection bias, response bias, non‐ response bias, convenience sampling, voluntary response bias, undercoverage, lurking variables, confounding, and common response relationships. (4.4/12A1) 10. Use three principles of experimental design – comparison of treatments, randomization, and replication. (4.4/12A2‐3) 11. Investigate random phenomena through simulation using a random number table and a graphing calculator (4.5/12A1‐3, F3‐4) 12. Estimate probabilities and predict outcomes from real world investigation, using Venn diagrams, decision trees, and conditional probability. (4.4/12B1,4‐6; 4.5/12A2‐6) Berkeley Heights Public Schools 3 COURSE PROFICIENCIES (continued) 13. Create and interpret discrete and continuous probability distributions and understand their application. (4.4/12B5; 4.5/12C4) 14. Use and interpret the mean and standard deviation for sums and differences of independent random variables. (4.4/12A5, B1) 15. Create sampling distributions and calculate their statistics for proportions and means, determine their variability based upon same size, and apply the Central Limit Theorem. (4.4/B6, C6) 16. Estimate confidence intervals for sample means and proportions, and calculate the necessary sample size to achieve a desired margin or error. (4.4/12A2,5) 17. Design and interpret hypothesis tests for statistical significance for proportions and means, choose an appropriate significance level, and explore the trade‐off between Type 1, Type II error and Power of test. (4.4/12A2,5; 4.5/12B2, C4) 18. Use Chi‐Square Goodness of Fit Test and inference for two‐way tables. (4.4/12A2,5; 4.5/12B2) 19. Create confidence intervals and hypothesis tests for the slope of a least‐squares regression model. (4.4/12A2,4,5) 20. Formulate a statistical hypothesis, design an appropriate statistical experiment, conduct the experiment, and interpret and communicate the results. (4.4/12A3; 4.5/12B1‐2,4) 21. Use formal symbolic logic notation to analyze statements, to build truth tables, and to compare expressions for logical equivalence. (4.2/12A4; 4.5/12B4, D1‐6) 22. Explore problems related to scheduling and conflict, network design, and management science using graph theory including vertex coloring, Euler paths and circuits, Hamilton circuits, and critical path analysis. (4.4/12D1; 4.5/12A1‐6, C3‐4, D2,4, E1,3) 23. Apply the tools of game theory, including payoff matrices, extensive forms, and the concept of Nash Equilibrium to explore how several agents may act strategically and predictably in a competitive or cooperative situation. (4.5/12A1‐5,