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HIGH SCHOOL MATHEMATICS PACING GUIDE
June 2011
PROBABILITY AND STATISTICS WITH APPLICATIONSCourse 1210300
Text: Understanding Basic Statistics; Fifth EditionBrase/Brase
Chapter 1: GETTING STARTED WEEKS 1-3
Days Section Topic Benchmarks Vocabulary DW Test Items #s
2 1-1 What is Statistics
MA.912.S.1.1MA.912.S.1.2
Statistics, individual, variable, quantitative variable, qualitative variable, population data, sample data, parameter, statistic, levels of measurement: nominal, ordinal, integral, ratio
104916
2 1-2 Random Samples MA.912.S.2.1MA.912.S.2.2MA.912.S.2.3
Simple random sample, simulation, sampling techniques: random, stratified, systematic, cluster, multi-stage, convenient, sampling frame, under-coverage, sampling error, non-sampling error
2 1-3 Introduction to Experimental Design
MA.912.S.2.1MA.912.S.2.2MA.912.S.2.3
Census, sample, observational study, experiment, placebo effect, block, control group, randomization, replication, double-blind, voluntary response, lurking variable
104989
8 SAT Prep, Labs, Review, and Testing
14 Total Days
Chapter 2: ORGANIZING DATA WEEKS 4-6
Days Section Topic Benchmarks Vocabulary DW Test Items #s
2 2-1Frequency Distributions, Histograms and Related Topics
MA.912.S.3.1MA.912.S.3.2
Frequency, frequency distribution, class: width, lower limit, upper limit, frequency, midpoint, end boundaries, histogram, distribution: symmetrical, uniform, bimodal, skewness, outlier, dotplot
104918, 104981, 104986, 104987, 131496, 131502131454, 131456, 131469, 131471, 131480, 131517, 131519, 131523, 131524, 131526, 131689, 131690, 131691
2 2-2 Bar Graphs, Circle Graphs, and Time Series Graphs
MA.912.S.3.1MA.912.S.3.2 Bar graph, pareto chart, pie chart, time-series graph
2 2-3 Stem-and-Leaf Displays MA.912.S.3.1MA.912.S.3.2
Exploratory data analysis (EDA), stem, leaf, stem and leaf display, back-to-back stem plot
9 SAT Prep, Labs, Review, and Testing
15 Total Days
NOTE: SAT TEST 10/1
Chapter 3: AVERAGES AND VARIATION WEEKS 7-9
Days Section Topic Benchmarks Vocabulary DW test items #s
2 3-1Measures of Central Tendency: Mode, Median, and Mean
MA.912.S.3.3MA.912.S.3.8
Average, mode, median, mean, x-bar, µ, ∑, resistant measure, trimmed mean, weighted average
104982, 104983, 104984, 104985, 131443, 131445, 131447, 131481, 131695, 131699, 105764, 105765, 105278, 105279, 105622, 105621, 1315102 3-2
Measures of Variation MA.912.S.3.4MA.912.S.3.6
Range, sum of squares, sample standard deviation, sample variance, population standard deviation, population size, coefficient of variation, mean of grouped data, standard deviation of grouped data
2 3-3 Percentiles and Box-and-Whisker Plots
MA.912.S.3.5MA.912.S.3.9
Percentile, quartile, interquartile range, 5-number summary, box and whisker plot
131450, 131482
9 SAT Prep, Labs, Review, and Testing
15 Total Days
Chapter 4: CORRELATION AND REGRESSION WEEKS 10-13
Days Section Topic Benchmarks Vocabulary DW test item #s
3 4-1 Scatter Diagrams and Linear Correlation
MA.912.S.3.1MA.912.S.3.2MA.912.S.3.7
Paired data values, explanatory variable, response variable, scatter diagram, sample correlation coefficient, perfect linear correlation
105737
3 4-2Linear Regression and the Coefficient of Determination
MA.912.S.4.5MA.912.S.5.8MA.912.S.5.9
Least squares line, slope, interpolation, extrapolation, explained variation, unexplained variation, coefficient of determination, residual, residual plot
12 SAT Prep, Labs, Review, and Testing
18 Total Days
NOTE: SAT TEST 11/5
Chapter 5: ELEMENTARY PROBABILITY THEORY WEEKS 14-17
Days Section Topic Benchmarks Vocabulary DW test item #s
2 5-1 What is Probability
MA.912.P.2.1MA.912.P.2.2
Probability of A, P(A), relative frequency, law of large numbers, equally likely outcomes, statistical experiments, simple event, sample space, complement of event A
105049, 105075, 105076, 105079, 105131, 105132, 131709, 131710, 105764, 105623, 105628, 105130, 105133, 105210, 131702, 131704, 131705, 131707
25-2 Some Probability Rules-
Compound Events
MA.912.P.2.1MA.912.P.2.2MA.912.P.1.1MA.912.P.2.3
Independent and dependent events, A|B, conditional probability, multiplication rules A and B, mutually exclusive events, addition rules A or B
2 5-3 Tree Diagrams and Counting Techniques
MA.912.P.1.1MA.912.P.1.2
Multiplication rule of counting, tree diagram, permutation rule, combination rule
12SAT Prep, Labs, Review, and Testing
18 Total Days
NOTE: SAT TEST 12/3
WEEKS 18-19 SEMESTER REVIEW & EXAM
FIRST SEMESTER DAYSCOURSE CONTENT & INSTRUCTION 78FINAL PREP & EXAM 7FLEX DAYS 3TOTAL 93
Chapter 6: THE BINOMIAL PROBABILITY DISTRIBUTION AND RELATED TOPICS WEEKS 20-22
Days Section Topic Benchmark Vocabulary DW test item #s
2 6-1Introduction to Random Variables and Probability Distributions
MA.912.P.3.1
Discrete random variable, continuous random variable, population parameters, mean µ of a probability distribution, standard deviation σ of a probability distribution, expected value µ
26-2 Binomial Probabilities MA.912.P.3.1
Binomial experiment, independent trial, successes and failures in a binomial experiment
26-3 Additional Properties of
the Binomial Distribution MA.912.P.3.2
Mean for binomial distribution, standard deviation for the binomial distribution, binomial distribution
7
SAT Prep, Labs, Review, and Testing
13 Total Days
NOTE: SAT TEST 1/28
Chapter 7: NORMAL CURVES AND SAMPLING DISTRIBUTIONS WEEKS 23-26
Days Section Topic Benchmarks Vocabulary DW test item #s
2 7-1 Graphs of Normal Probability Distributions
MA.912.S.3.6MA.912.P.3.3MA.912.P.3.4
Normal distribution, normal curve, upward cup, downward cup, symmetry of the normal curve, empirical rule
2 7-2Standard Units and Areas Under the Standard Normal Distribution
MA.912.S.3.5MA.912.S.3.6MA.912.P.3.3MA.912.P.3.4
z-score, standard units, standard normal distribution, raw score X, area under the standard normal curve
105738, 105739, 105766, 105621, 105622
2 7-3 Areas Under Any Normal Curve
MA.912.S.3.6MA.912.P.3.3MA.912.P.3.4
Areas under any normal curve, normality indicator
1 7-4 Sampling DistributionsMA.912.S.3.6MA.912.P.3.3MA.912.P.3.4
Population parameter, statistics, sampling distribution
1 7-5 The Central Limit TheoremMA.912.S.3.6MA.912.P.3.3MA.912.P.3.4
Standard error of the mean, central limit theorem
2 7-6 Normal Approximation to the Binomial Distribution
Normal approximation to the binomial distribution, continuity correction
9 SAT Prep, Labs, Review, and Testing
19 Total Days
Chapter 8: ESTIMATION WEEKS 27-29
Days Section Topic Benchmarks Vocabulary DW test item #s
2 8-1 Estimating μ When σ Is Known
MA.912.S.4.2MA.912.S.4.3MA.912.S.4.4MA.912.S.5.1
Maximal margin of error, confidence level, critical values, point estimate, confidence interval, confidence for µ, sample size
2 8-2 Estimating μ When σ Is Unknown
MA.912.S.4.1MA.912.S.4.2MA.912.S.4.3MA.912.S.4.4MA.912.S.5.1
Student t-variable, degrees of freedom, critical t-value
2 8-3 Estimating р in the Binomial Distribution
MA.912.S.4.1MA.912.S.4.3MA.912.S.5.1
Point estimate for p, confidence interval for p, margin of error, sample size
8 SAT Prep, Labs, Review, and Testing
14 Total Days
NOTE: SAT TEST 3/10
Chapter 9: HYPOTHESIS TESTING WEEKS 30-33 (WEEK 32 RESERVED FOR FCAT)Days Section Topic Benchmarks Vocabulary DW test item #s
2 9-1 Introduction to Statistical Tests
MA.912.S.5.2MA.912.S.5.3MA.912.S.5.4
Hypothesis testing, hypotheses, null hypothesis, alternate hypothesis, right-tail, left-tail, two-tailed test, sample test for statistic, P-value, statistical significance, Type I error, Type II error
3 9-2 Testing the Mean μMA.912.S.5.3MA.912.S.5.5MA.912.S.5.6
Degrees of freedom, critical region, critical value
3 9-3 Testing a Proportion рMA.912.S.5.3MA.912.S.5.5MA.912.S.5.6
7 SAT Prep, Labs, Review, and Testing
15 Total Days
Chapter 10: INFERENCES ABOUT DIFFERENCES WEEKS 34-37Days Section Topic Benchmarks Vocabulary DW test item #s
3 10-1 Tests Involving Paired Differences (Dependent Samples)
MA.912.S.5.3MA.912.S.5.5MA.912.S.5.6
Dependent samples, data pairs, difference of means for data pairs
3 10-2 Inferences About the Difference of Two Means μ1 – μ2
MA.912.S.5.3MA.912.S.5.5MA.912.S.5.6
Independent samples, degrees of freedom for testing two means, pooled standard deviation
3 10-3 Inferences About the Difference of Two Proportions р1 – р2
MA.912.S.5.3MA.912.S.5.5MA.912.S.5.6
Pooled estimate of the proportion
11 SAT Prep, Labs, Review, and Testing
20 Total Days
NOTE: SAT TEST 5/5 & 6/2
Chapter 11: ADDITIONAL TOPICS USING INFERENCE (OPTIONAL)Section Topic Vocabulary DW test item #s
11-1 Chi-Square: Tests of Independence and Homogeneity
Independence test, chi-square distribution, degrees of freedom, contingency table with cells, row total, column total, expected frequency, observed frequency, homogeneity test
11-2 Chi-Square: Goodness of Fit
Goodness-of-fit tests
11-3 Testing a Single Variance or Standard Deviation
Hypotheses tests
11-4 Inferences for Correlation and Regression
Population correlation coefficient, population slope of the least-squares line, standard error of estimate, confidence interval for y
SECOND SEMESTER DAYSCOURSE CONTENT & INSTRUCTION 77FCAT 5FINAL PREP & EXAM 6FLEX DAYS 5TOTAL 93
ESSENTIAL QUESTIONS
Chapter 1 GETTING STARTED Why is statistics important? What is the nature of data? How can you draw a random sample? What are the other sampling techniques? How can you design ways to collect data?
Chapter 2 ORGANIZING DATA What are histograms? When are they used? What are common distribution shapes? How can you select graphs appropriate for given data sets? How can you quickly order data and, at the same time, reveal the distribution shape?
Chapter 3 AVERAGES AND VARIATION What are commonly used measures of central tendency? What do they tell you? How do variance and standard deviation measure data spread? Why is this important? How do you make a box-and-whisker plot, and what does it tell you about the spread of the data?
Chapter 4 CORRELATION AND REGRESSION How can you use a scatter diagram to visually estimate the degree of linear correlation of two random variables? How do you compute the correlation coefficient and what does it tell you about the strength of the linear relationship between two random variables? What is the least-squares criterion? How do you find the equation of the least-squares line? What is the coefficient of determination, and what does it tell you about the explained variation of y in a random sample of data pairs (x,y) ?
Chapter 5 ELEMENTARY PROBABILITY THEORY Why would anyone study probability? Hint: Most big issues in life involve uncertainty. What are the basic definitions and rules of probability? What are counting techniques, trees, permutations, and combinations?
Chapter 6 THE BINOMIAL PROBABILITY DISTRIBUTION AND RELATED TOPICS What is a random variable? How do you compute µ and σ for a discrete random variable? How can you use the binomial probability distribution to compute the probability of r successes? How do you compute µ and σ for the binomial distribution?
Chapter 7 NORMAL CURVES AND SAMPLING DISTRIBUTIONS What are some characteristics of a normal distribution? What does the empirical rule tell you about data spread about the mean? Can you compare apples and oranges? What is a standard normal distribution? What is a standard z score? How do you convert any normal distribution to a standard normal distribution?
How do you find probabilities of “standardized events”? What is a probability sampling distribution? How do sampling distributions help us make good decisions based on incomplete information? All probability distributions average out to be normal distributions as the sample size increases. How can we take advantage of this in our study of sampling
distributions? Under certain conditions, the binomial can evolve into the normal distribution. How can we apply this concept in the real world?
Chapter 8 ESTIMATION How do you estimate the expected value of a random variable? What assumptions are needed? How much confidence should be placed in such estimates? How do you select the size of a sample? What famous statistician worked for Guinness brewing company in Ireland? What has this to do with constructing estimates from sample data? How do you estimate the proportion p of successes in a binomial experiment? How does the normal approximation fit into this process?
Chapter 9 HYPOTHESIS TESTING When you must act on incomplete (sample) information, how do you decide whether to accept or reject a proposal? What is the P-value of a statistical test? What does this measurement have to do with performance reliability? How do you construct statistical test for µ? Does it make a difference whether σ is known or unknown? How do you construct statistical tests for the proportion p of successes in a binomial experiment?
Chapter 10 INFERENCES ABOUT DIFFERENCES What are the statistical advantages of paired data values? How do we construct statistical tests? How do we compare means from two independent populations when we know σ for each population? What if we want to compare means from two independent populations, but we do not know σ for each population? How do we use sample data to compare proportions from two independent populations?
Chapter 11 (Optional) ADDITIONAL TOPICS USING INFERENCE How do you decide if random variables are dependent or independent? How do you decide if different populations share the same proportions of specified characteristics? How do you decide if two distributions are not only dependent, but actually the same distribution? How do you construct tests for σ ? How do you test a correlation coefficient? What is the standard error of estimate? How do you compute it, and where is it used? How do you compute confidence intervals for a least-squares prediction? The slope of the least-squares line represents rate of growth. How can you determine if the rate of growth is statistically significant?
TEACHER RESOURCES: (ctrl-click to follow link)
http://www.cengage.com/statistics/Brase/UBS5e http://studyisland.com/ Introduction to Probability. By Charles M. Grinstead and J. Laurie Snell http://www.findingdulcinea.com/guides/Education/High-School-Statistics.pg_00.html#00
Learning Probability Theory via Tutorial Dialogues Probability Theory: The Logic of Science. By E.T. Jaynes Probability Tutorials. Advanced probability, measure theory. By Noel Vaillant. A Short Introduction to Probability. By Dr. Dirk P. Kroese. Virtual Laboratories in Probability and Statistics. Provides interactive resources for students and teachers. Cut the Knot. Probability puzzles. Java Demos for Probability and Statistics. Primoridal Soup Kitchen. Cellular automata.
Probability by Surprise. Teaching by paradox. Graphics and animations developed for teaching intro probability. Susan Holmes, Stanford University. Chance. A wealth of material to teach a Chance course. Laurie Snell, Dartmouth College.
Math Forum - Probability and Statistics. Links to teaching resources for K-12 and college level courses. Swarthmore College. Mathematical Atlas: Probability theory and stochastic processes Non-technical books relating to probability (thanks to David Aldous) Planet. Probabilistic Learning Activities Network. Probability Central. A nicely designed site for learning basic probability. Probability Computer Projects with Mathematica Probability and Statistics. Lots of links to interesting probability problems Talk Stats Forums A discussion forum for probability and statistics enthusiasts. Get free probability and statistics help or just hang out and talk. 10% Assumption for Inference Is That an Assumption or a Condition? Why Do We Pool for the Two-Proportion z-Test? On Power National Council of Teachers of Mathematics Mathematical Association of America American Statistical Association WinStats StatCrunch Graphing Calculator Simulations Simplified The Satterthwaite Formula for Degrees of Freedom in the Two-Sample t-Test (.pdf/198KB) Teach AP Statistics Next Year! Lesson Study: A PCMI Experience The Mathematical Puzzles of Benjamin Banneker One Chancey in a Million Women and Mathematics: Stereotypes, Identity, and Achievement Calculations Aren't Enough! In a World of Data, Statistics Counts
Life as an "Acorn": My Experience as a First-Time AP Statistics Reader The AP Reading Experience Women's History: Women in Mathematics Engaging the Intuition in Statistics to Motivate AP Statistics Web Guide Preparing to Teach Statistics So Much Data, So Little Time Coke Versus Pepsi: An Introductory Test of Significance Planning and Conducting a Study (.pdf/980KB) Sampling Distributions Special Focus—MLB data (.xls/192KB) Why Variances Add -- And Why It Matters Three Calculator Simulation Activities Random Variables vs. Algebraic Variables Is It Normal? A First Look at Significance and the p-value Through Simulation http://www.wku.edu/~neal/probability/prob.html Provides interesting problems occurring in probability. This page includes "Monte Carlo Approximation of
Pi", "The Mystery of the Three Cards", "The Birthday Problem", "The Gambling Boundary Problem", and others. http://www.maths.uq.oz.au/~pkp/probweb/probweb.html Contains a collection of pages with the following headings: Probability links, Abstracts, Listservers,
Newsgroups, People, Jobs, Journals, Software, Books, Conferences, Publishers and Miscellaneous. http://lrs.ed.uiuc.edu/students/mcornell/cerealbox/index.html Website for a cooperative classroom project for grades K- 9. Students from five countries and 19
of the U. S. states participated in this project. http://www.intergalact.com/threedoor/threedoor.html Includes a simulation of the "Three Door Puzzle" of probability. Students can play an interactive game as
often as they wish. http://forum.swarthmore.edu/probstat/probstat.lessons.html Provides unit course materials and lesson plans, problems and puzzles, and reference materials. http://forum.swarthmore.edu/probstat/probstat.software.html Contains publicly available software and online publishers for probability and statistics. http://forum.swarthmore.edu/probstat/probstat.projects.html Provides fun and challenging activities for students.