GLEN RIDGE PUBLIC SCHOOLS

Curriculum Guide

Course Title: AP STATISTICS

Subject: Mathematics

Grade Level: 9 – 12

Department/School: Mathematics/High School

Duration: Full Year

Number of Credits: 5

Prerequisite: Algebra II with a grade of “B+” or better, teacher

recommendation, and completion of summer

assignment

Elective or Required: Elective

Author: Catherine McCarthy

Date Submitted: Summer 2007

COURSE DESCRIPTION

AP Statistics is a full year course intended for students who have successfully completed Algebra II with a minimum grade of 85%. It is an introductory, non-calculus based course in statistics. The purpose of the course is to introduce and develop strategies for collecting, organizing, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes:

1. Exploring Data: Observing patterns and departures from patterns
2. Planning a Study: Deciding what and how to measure
3. Anticipating Patterns: Producing models using probability and simulation
4. Statistical Inference: Confirming models.

This course is designed to cover those topics necessary for success on the College Board AP Statistics Exam.

COURSE GOALS: In AP Statistics, students are expected to learn to:

• Produce convincing oral and written statistical arguments, using appropriate terminology, in a variety of applied settings
• Determine when and how to use technology to aid them in solving statistical problems
• Use graphical and numerical techniques to study patterns and departures from patterns in the exploration and analysis of data
• Collect and produce data according to statistically well designed methods in order to determine valid conjectures and conclusions
• Use methods of probability analysis to anticipate and conjecture what a distribution of data should look like using appropriate model structures
• Use statistical inference to guide them in selecting appropriate models and thereby draw conclusions from data
• Become informed and critical consumers when presented with statistical results.

Teaching materials for this course include a primary textbook, The Practice of Statistics (3^rd edition), by Yates, Moore, and Starnes, W.H. Freeman & Co., 2008, supplemental texts, (see list at end of curriculum) classroom lectures, power point presentations, lab assignments and activities, AP binder of past AP Statistics free-response questions, newspaper and journal articles, videos, and the World Wide Web. Preliminary summer activities will include outside reading from a suggested list of books, writing a reaction paper to chosen reading, and/or outlining preliminary chapter from text. Students are required to keep a personal journal in which they collect and review articles and/or graphical displays pertinent to the topics studied over the course of the year. These journals will be collected and graded twice per marking period. Throughout the course of the year, tests and quizzes will include practice AP multiple choice and free response questions. Projects and lab write-ups will be graded in the manner of the AP testing rubrics. The course midterm and final exams will simulate the AP testing situation. Students are expected to provide their own TI-83/TI-83+/TI-84 graphing calculator for use in class, at home and on the AP exam. Students will use their graphing calculators extensively throughout the course and the teacher will use a graphing calculator with an overhead display as well as a projection unit for class demonstrations. Throughout the primary text, students are provided with instruction and practice on the statistical capabilities of their calculator. Students also have access to the computer software Fathom, and are further provided examples of computer printouts from other software packages such as Minitab, Data Desk, etc.

GLEN RIDGE PUBLIC SCHOOLS

MATHEMATICS MISSION STATEMENT

Mathematics and Computer Science are an integral part of our lives. Students must be actively involved in their mathematics education with problem solving being an essential part of the curriculum. The mathematics and computer science curricula should emphasize thinking skills through a balance of computation, intuition, common sense, logic, analysis and technology. Students will be engaged and challenged in a student- centered learning environment that is developmentally appropriate. Students will communicate mathematical ideas effectively by applying hands-on manipulatives, basic computational skills, mathematical models, and technology in order to solve practical problems.

New Jersey Mathematics Standards

The Mathematics Standards consist of five statements, which describe what is essential to excellent mathematics education, and present a view of mathematics teaching and learning that integrates the processes of mathematical activity, the content of mathematics, and the learning environment in the classroom. The following standards were adopted by the New Jersey State Board of Education.

This course will cover the following Core Curriculum Standards:

Descriptive Statement:  Numbers and arithmetic operations are what most of the general public think about when they think of mathematics; and, even though other areas like geometry, algebra, and data analysis have become increasingly important in recent years, numbers and operations remain at the heart of mathematical teaching and learning.  Facility with numbers, the ability to choose the appropriate types of numbers and the appropriate operations for a given situation, and the ability to perform those operations as well as to estimate their results, are all skills that are essential for modern day life.

Number Sense

Numerical Operations

Estimation

Descriptive Statement:  Spatial sense is an intuitive feel for shape and space. Geometry and measurement both involve describing the shapes we see all around us in art, nature, and the things we make.  Spatial sense, geometric modeling, and measurement can help us to describe and interpret our physical environment and to solve problems. 

Geometric Properties

Transforming Shapes

Coordinate Geometry

Units of Measurement

Measuring Geometric Objects

Descriptive Statement: Algebra is a symbolic language used to express mathematical relationships.  Students need to understand how quantities are related to one another, and how algebra can be used to concisely express and analyze those relationships.  Modern technology provides tools for supplementing the traditional focus on algebraic procedures, such as solving equations, with a more visual perspective, with graphs of equations displayed on a screen.  Students can then focus on understanding the relationship between the equation and the graph, and on what the graph represents in a real-life situation. 

Patterns

Functions and Relationships

Modeling

Procedures

Descriptive Statement:  Data analysis, probability, and discrete mathematics are important interrelated areas of applied mathematics.  Each provides students with powerful mathematical perspectives on everyday phenomena and with important examples of how mathematics is used in the modern world.  Two important areas of discrete mathematics are addressed in this standard; a third area, iteration and recursion, is addressed in Standard 4.3 (Patterns and Algebra).

Data Analysis

Probability

Discrete Mathematics – Systematic Listing and Counting

Discrete Mathematics – Vertex-edge Graphs and Algorithms

Descriptive Statement:  The mathematical processes described here highlight ways of acquiring and using the content knowledge and skills delineated in the first four mathematics standards.

Problem Solving Reasoning

Communication Representations

Connections Technology

Curriculum Description

UNIT I: WHAT IS STATISTICS

CCCS: 4.1, 4.3, 4.4, 4.5

Objectives:

The students will be able to:

1. Recognize whether a study is an experiment, a survey, or an observational study that is not a survey.

2. Determine the best method for producing data to answer a specific question: experiment, survey, or other observational study.

3. Locate available data on the Internet to help answer a question of interest.

4. Identify the individuals and variables in a set of data.

5. Classify each variable as categorical or quantitative.

6. Identify the units in which each quantitative variable is measured.

7. Answer key questions – who, what, when, where, how, and by whom? – about a given set of data.

8. Construct a bar graph of the distribution of a categorical variable.

9. Interpret bar graphs.

10. Construct a dotplot of the distribution of a quantitative variable.

11. Describe patterns observed in a dotplot.

Approximate duration: 3 days

Activities:

- Move-up day – How Many Licks to Get to the Middle of a Tootsie Pop?

- Summer assignment – Students will choose a book from a suggested list and read and write a brief reaction paper.

UNIT II: EXPLORING DATA

CCCS: 4.1, 4.3, 4.4, 4.5

Objectives:

The students will be able to:

1. Construct stem and leaf plots of the distribution of a quantitative variable.

2. Construct a histogram of the distribution of a quantitative variable.

3. Construct and interpret an ogive of a set of quantitative variable.

4. Observe the overall pattern and deviations from the pattern.

5. Characterize the shape of a stem and leaf plot, dotplot, or histogram.

6. Determine numerical measures of center and spread for a given distribution: mean, standard deviation, five number summary.

7. Determine which measures of center and spread are more appropriate for a given distribution.

8. Recognize and determine outliers.

9. Understand the effects of outliers

10. Construct time plot of data.

11. Recognize strong trends or other patterns in a time plot.

12. Calculate the mean of a set of observations.

13. Determine the median of a set of observations.

14. Understand that the median is more resistant than the mean.

15. Recognize the effects of the skewness of a data distribution on the mean.

16. Define and calculate five-number summary, IQR, and outliers.

17. Construct a boxplot with and without calculator.

18. Use a calculator or software to calculate the standard deviation for a set of observations.

19. Use TI-83 menu to determine univariate data statistics.

20. Determine the effect of a linear transformation on measures of center and spread.

21. Calculate new measures of center and spread on transformed data.

22. Construct side-by-side bar graphs to compare distributions of categorical data.

23. Construct back-to-back stem and leaf plots and side-by-side boxplots to compare distributions of quantitative variables.

24. Write narrative comparisons of the shape, center, spread, and outliers for two or more quantitative distributions.

Approximate duration: 15 days

Activities:

(See Platinum Binder and Text)

- HOW BIG IS THE USA?

- THE GAME OF GREED

- CASE STUDY: NIELSEN RATINGS

Short project:

- GOT FRIENDS?

AP free response exam questions - 2000 # 3, 2001 # 1, 2002 # 1, 2000B # 5, 2004 # 1

UNIT III: DESCRIBING LOCATION IN A DISTRIBUTION

CCCS: 4.1, 4.3, 4.4, 4.5

Objectives:

The students will be able to:

1. Determine the standardized value (z score) of an observation.

2. Interpret z-scores in context.

3. Use percentiles to locate individual values within distributions of data.

4. Apply Chebyshev’s inequality to a given distribution of data.

5. Understand the concept that areas under a density curve represent proportions of all observations and that the total area under a density curve is 1.

6. Approximately locate the median and the mean on a density curve.

7. Understand and recognize that the mean and median both lie at the center of a symmetric density curve.

8. Recognize the effect on the relationship between the mean and the median of a skewed density curve.

9. Recognize the shape of the Normal curve.

10. Estimate the mean and standard deviation from a density curve.

11. Develop and apply the Empirical Rule to state what percent of the observations from a Normal distribution within 1, 2, or 3 standard deviations away from the mean.

12. Use the standard Normal distribution to determine the proportion of values in a specified range.

13. Use z-scores to standardize non-standard Normal distributions.

14. Calculate probabilities using the Normal distribution using either table or calculator.

15. Determine a z-score from a percentile.

16. Given that a variable has a Normal distribution with stated mean and standard deviation, use table and calculator to find the value of the observation having a stated proportion of values to the left or to the right of it.

17. Solve problems involving the Normal distribution.

18. Be familiar with Normal Distribution functions of the TI-83.

19. Plot histogram, stem and leaf plot, and/or boxplot to determine if a distribution is bell-shaped.

20. Construct and interpret Normal probability plots on the calculator.

Approximate duration: 9 days

Activities:

- DO YOU SUDOKU? ,

- NORMAL CURVE APPLET

- Video: AGAINST ALL ODDS PROGRAM # 4 & 5

- AP free response – 1999 #4, 2002 # 3A, 2003 # 3AB, 2004B # 3AB

UNIT IV: EXAMINING RELATIONSHIPS

CCCS: 4.1, 4.3, 4.4, 4.5

Objectives:

The students will be able to:

1. Recognize whether a variable is categorical or quantitative.

2. Identify the explanatory and response variables in situations where one variable explains or influences another.

3. Construct a scatterplot to display the relationship between two quantitative variables with and without the use of a calculator.

4. Describe the direction, form, and strength of the overall pattern of a scatterplot.

5.