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Williamsport Area School District Mathematics Grade(s): 12 Course Title: Statistics Unit Unit Title 1 Introduction to Statistics Duration (Days) 15 Descriptive Statistics 26 Probability 17 Discrete Probability Distributions 26 Normal Probability Distributions 23 6 Confidence Intervals 20 7 Hypothesis Testing with One Sample 22 CA College Algebra Review (Between Unit 3 and 4) 15 2 3 4 5 Statistics Williamsport Area School District Unit 1: Introduction to Statistics Days: 15 Big Idea: Look at a sample and make inferences about a population. Unit Essential Question: What is the difference between a population and a sample? How can we take a representative sample? Concept Concept Title 1.1 1.2 1.3 An Overview of Statistics Data Classification Data Collection and Experimental Design Duration (Days) 2 2 11 Statistics Concept 1.1 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District An Overview of Statistics What is the difference between a population and a sample? data, statistics, population, sample, parameter, statistic, descriptive statistics, inferential statistics Descriptor Days 1.1.A Distinguish between a population and a sample. 0.5 1.1.B Distinguish between a parameter and a statistic. 1.1.C Determine the difference between descriptive and inferential statistics. 0.5 1 Resources: Assessment Sources: Whiteboard Practice Color Cards Exit Ticket Homework Quiz 1.1-1.2 Unit Assessment Notes: Page 3 Statistics Concept 1.2 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Data Classification What is the difference between qualitative and quantitative data? qualitative data, quantitative data Descriptor 1.1.A Distinguish between qualitative and quantitative data. Resources: Fast Food Data Assignment Assessment Sources: Color Cards Exit Ticket Quiz 1.1-1.2 Unit Assessment Fast Food Data Assignment connects lessons 1.2 and 1.3. Additional day for review/quiz. Notes: Days 1 Page 4 Statistics Concept 1.3 Lesson Essential Question(s): Vocabulary: Learning Goals: Resources: Assessment Sources: Notes: Williamsport Area School District Data Collection and Experimental Design How did the creators of Scrabble decide how many of each letter to include in their game? observational study, experiment, treatment, control group, experimental units, placebo, simulation, survey, confounding variable, blinding, doubleblind experiment, randomization, completely randomized design, blocks, randomized block design, matched-pairs design, sample size, replication, census, sampling, sampling error, random sample, simple random sample, stratified sample, cluster sample, systematic sample, convenience sample Descriptor Days 1.1.A Collect data through an observational study, and 1 experiment, a simulation, or a survey. 1.1.B Generate Random Numbers 2 1.1.C Create a sample using random sampling, cluster sampling, systematic sampling, stratified sampling, and convenience sampling. 4 1.1.D Design a statistical study. 2 Countries in the UN Activity Generating Random Numbers Activity Redesigning Scrabble Activity Coke vs. Pepsi or Regular vs. Diet Soda Activities Milgram’s Obedience Experiment Activity Whiteboard Practice Exit Ticket Homework Unit Assessment Two additional days for review and test. Page 5 Statistics Williamsport Area School District Unit 2: Descriptive Statistics Days: 26 Big Idea: Display data using frequency tables, pie charts, bar graphs, dot plots, stem-and-leaf plots, and box and whisker plots. Describe the data sets using measures of center and spread. Unit Essential Question: How can we represent and describe a data set? Concept Concept Title 2.1 2.2 2.3 2.4 2.5 Frequency Distributions and Their Graphs More Graphs and Displays Measures of Central Tendency Measures of Variation Measures of Position Duration (Days) 4 7 4 5 6 Statistics Concept 2.1 Lesson Essential Question(s): Vocabulary: Learning Goals: Resources: Assessment Sources: Williamsport Area School District Frequency Distributions and Their Graphs How can I create a graph of a frequency distribution? center, variability, shape, frequency distribution, classes, intervals, frequency, midpoint, relative frequency, cumulative frequency, frequency histogram, class boundaries. Relative frequency histogram, cumulative frequency histogram, ogive Descriptor Days 2.1.A Construct a frequency table, frequency histogram, 4 polygon, relative frequency histogram, and a cumulative frequency histogram. Book Notes 2.1 Olympic Medal Count Frequency Table Frequency Histograms (N-gram) Activity Frequency Graphs P-M-I Quiz 2.1-2.2 Homework Unit Assessment Notes: Page 7 Statistics Concept 2.2 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District More Graphs and Displays How can I display data? Stem-and-leaf plot, stem, leaf, dot plot, pie chart, Pareto chart, paired data sets, scatter plot, time series, time series chart Descriptor Days 2.2.A Graph and interpret stem-and-leaf plots, dot plots, pie 5 charts, Pareto charts, and scatter plots. 2.2.B Use a graphing calculator to create a histogram. Resources: Graphs and Displays Jigsaw Activity Assessment Sources: Presentations Quiz 2.1-2.2 Homework Unit Assessment One Extra day for quiz. Notes: 1 Page 8 Statistics Concept 2.3 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Measures of Central Tendency How can we describe the center of a data set? measure of central tendency, median, mode, bimodal, outlier, gaps, weighted mean, mean of a frequency distribution, symmetric, uniform, rectangular, skewed left, negatively skewed, skewed right, positively skewed Descriptor Days 2.3.A Find the mean, median, and mode of a population and 3 sample. 2.3.B Describe the shape of a distribution. Resources: Creating Data Sets Activity Assessment Sources: KWL Chart Exit Ticket Quiz 2.3-2.4 Homework Unit Assessment 1 Notes: Page 9 Statistics Concept 2.4 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Measures of Variation How can we quantify the quality of guesses? range, deviation, sum of squares, population variance, population standard deviation, sample variance, sample standard deviation, empirical rule Descriptor Days 2.4.A Determine how far predicted values are from actual 3 values. 2.4.B Describe the variation of a data set. Resources: Guessing Ages Activity Assessment Sources: Group Presentations Exit Ticket Quiz 2.3-2.4 Homework Unit Assessment 2 Notes: Page 10 Statistics Concept 2.5 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Measures of Position Where does your height fall in comparison to others? fractiles, quartiles, first quartile, second quartile, third quartile, box-andwhisker plot, five-number summary, percentiles, standard score, z-score Descriptor Days 2.5.A Construct and analyze box-and-whisker plots. 1 2.5.B Describe the position of a data point using quartiles. 1 2.5.C Describe the position of a data point using percentiles. 1 2.5.D Describe the position of a data point using a standard score. 1 Resources: Percentile and Z-Score of Heights Activity Assessment Sources: Whiteboard Practice Exit Ticket Homework Unit Assessment Two additional days for review and unit test. Notes: Page 11 Statistics Williamsport Area School District Unit 3: Probability Days: 17 Big Idea: Solve simple probability, compound probability, and counting problems. Unit Essential Question: How can we find the probability of simple and compound events? How can we find the number of possible arrangements with and without regard to order? Concept Concept Title 3.1 3.2 Basic Concepts of Probability and Counting Conditional Probability and the Multiplication Rule The Addition Rule Additional Topics in Probability and Counting 3.3 3.4 Duration (Days) 2 6 3 6 Page 12 Statistics Concept 3.1 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Basic Concepts of Probability and Counting What is the difference between theoretical and experimental probability? Probability experiment, outcome, sample space, event, simple event, classical probability, theoretical probability, empirical probability, statistical probability, law of large numbers, subjective probability, complement of event E Descriptor Days 3.1.A Find the probability of a simple event. 1 3.1.B Resources: Assessment Sources: Describe and find the probability of the compliment of an event. Dice Activity (Theoretical vs. Experimental Probability) 1 Exit Ticket Homework Unit Assessment Notes: Page 13 Statistics Concept 3.2 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Conditional Probability and the Multiplication Rule What is the probability that an honest person fails a lie detector test? conditional probability, independent, dependent, multiplication rule Descriptor Days 3.2.A Find the probability that an event will occur given that 4 another event already occurred. 3.2.B Resources: Assessment Sources: Determine whether an event is independent or dependent. Lie Detectors/Colored Dots Activity Water and Soda Probabilities Activity Color Cards Exit Ticket Quiz 3.2 Homework Unit Assessment 2 Notes: Page 14 Statistics Concept 3.3 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District The Addition Rule How much information do we need to determine how many students are female or blue is their favorite color? mutually exclusive, addition rule, Descriptor Days 3.3.A Determine whether two event are mutually exclusive 1 or not mutually exclusive. 3.3.B Find the probability of mutually exclusive events. Resources: Favorite Color Probability Activity Assessment Sources: Color Cards Exit Ticket Homework Unit Assessment 2 Notes: Page 15 Statistics Concept 3.4 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Additional Topics in Probability and Counting What is the probability of winning Powerball? permutation, factorial, permutation of n objects taken r at a time, distinguishable permutations, combination, combinations of n objects taken r at a time Descriptor Days 3.4.A Find the number of ways several objects can be 2 arranged or grouped. 3.4.B Resources: Assessment Sources: Notes: Use counting principles to find probabilities. 2 Powerball Activity (Part I) Monty Hall Problem Probability Games Find Someone Who Can… Exit Ticket Homework Unit Assessment Two additional days for review and unit assessment. Monty Hall Problem and Probability Games were used right before winter break. Power Activity (Part II) is in Unit 4. Page 16 Statistics Williamsport Area School District Unit 4: Discrete Probability Distributions Days: 26 Big Idea: Solve probability problems using the binomial, geometric, and Poisson distributions. Unit Essential Question: What are probability distributions and how can we use them? Concept Concept Title 4.1 4.2 4.3 Probability Distributions Binomial Distributions More Discrete Probability Distributions Duration (Days) 10 8 8 Page 17 Statistics Concept 4.1 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Probability Distributions What is a probability distribution? random variable, discrete continuous, discrete probability distribution, expected value Descriptor Days 4.1.A Distinguish between discrete random variables and 2 continuous random variables. 4.1.B Resources: Assessment Sources: Find the mean, variance, standard deviation, and expected value of a probability distribution. Probability Distribution with Two Dice Powerball Expected Value Deal or No Deal Expected Value Exit Tickets 8 Notes: Page 18 Statistics Concept 4.2 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Binomial Distributions What is the binomial probability distribution? binomial experiment, binomial probability distribution, Descriptor 4.2.A Determine if a probability experiment is a binomial experiment. 4.2.B Find binomial probabilities. 4.2.C Resources: Assessment Sources: Find the mean, variance, and standard deviation of a binomial probability distribution Baseball Binomial Activity Days 2 5 1 Clicker Practice Exit Tickets Quiz 4.2 Notes: Page 19 Statistics Concept 4.3 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District More Discrete Probability Distributions What are the geometric and Poisson probability disributions? geometric distribution, Poisson distribution Descriptor 4.3.A Find probabilities using the geometric distribution. 4.3.B Resources: Assessment Sources: Notes: Find probabilities using the Poisson distribution. Days 4 2 Geometric Baseball Activity Golden Ticket Clicker Practice Exit Tickets Word-Wall Matching Unit Assessment Two additional days for unit review and assessment Page 20 Statistics Williamsport Area School District Unit 5: Normal Probability Distributions Days: 23 Big Idea: Use the normal distribution solve probability problems. Unit Essential Question: How can we apply the normal distribution to probability problems? What is a sampling distribution and how can we use it? Concept Concept Title 5.1 Introduction to Normal Distributions and the Standard normal Distribution Normal Distributions: Finding Probabilities Normal Distributions: Finding Values Sampling Distributions and the Central Limit Theorem Normal Approximations to Binomial Distributions 5.2 5.3 5.4 5.5 Duration (Days) 4 4 3 5 7 Page 21 Statistics Concept 5.1 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Introduction to Normal Distributions and the Standard Normal Distribution How can I find the area under the standard normal curve? continuous probability distributions, normal distribution, normal curve, probability density function, standard normal distribution, Descriptor Days 5.1.A Interpret graphs of normal probability distributions. 1 5.1.B Find areas under the standard normal curve. Resources: Mind Map Assessment Sources: Clicker Practice Exit Tickets Quiz 5.1 3 Notes: Page 22 Statistics Concept 5.2 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Normal Distributions: Finding Probabilities How can I find probabilities using the normal distribution? 5.2.A Resources: Assessment Sources: Descriptor Find probabilities for normal distributed variables. Days 4 Height Activity Mind Map Exit Ticket Quiz 5.2 Notes: Page 23 Statistics Concept 5.3 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Normal Distributions: Finding Values How can I find the data value that corresponds to a given probability? x-value 5.3.A Descriptor Find a z-score given the area under the normal curve. 5.3.B Transform a z-score to an x-value. 5.3.C Resources: Assessment Sources: Find a specific data value of a normal distribution given the probability. Airplane Seat Pitch Activity Mind Maps Clicker Practice Exit Tickets Days 1 1 1 Notes: Page 24 Statistics Concept 5.4 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Sampling Distributions and the Central Limit Theorem What is a sampling distribution? Sampling distribution, sampling distribution of sample means, standard error of the mean, Central Limit Theorem Descriptor Days 5.4.A Find sampling distributions and verify their properties. 2 5.4.B Resources: Assessment Sources: Use the Central Limit Theorem to find the probability of a sample mean. Sampling Number Activity Mind Maps Clicker Practice Exit Tickets Quiz 5.4 3 Notes: Page 25 Statistics Concept 5.5 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Normal Approximations to Binomial Distributions How can I approximate binomial probabilities with the normal distribution? continuity correction 5.5.A Descriptor Decide when a normal distribution can approximate a binomial distribution. 5.5.B Find continuity corrections. 5.5.C Resources: Assessment Sources: Notes: Use normal distribution to approximate binomial probabilities. Mind Maps Days 1 1 3 Clicker Practice Exit Tickets Quiz 5.5 Unit Assessment Three extra days for unit review and assessment. Page 26 Statistics Williamsport Area School District Unit 6: Confidence Intervals Days: Big Idea: Find the margin of error in a sample and construct confidence intervals for parameters. Unit Essential Question: How can we estimate a population parameter using sample statistics? Concept Concept Title 6.1 Confidence Intervals for the Mean (Large Samples) Confidence Intervals for the Mean (Small Samples) Confidence Intervals for Population Proportions 6.2 6.3 Duration (Days) 6 6 6 Page 27 Statistics Concept 6.1 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Confidence Intervals for the Mean (Large Samples) point estimate, interval estimate, level of confidence, sampling error, margin of error, confidence interval, Descriptor Days 6.1.A Find a point estimate and a margin of error. 2 6.1.B Construct and interpret a confidence interval for the population mean with a large sample. 2 6.1.C Determine the minimum sample size required when estimated a population mean. 2 Resources: Assessment Sources: Add Notes: Page 28 Statistics Concept 6.2 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Confidence Intervals for the Mean (Small Samples) t-distribution, degrees of freedom, Descriptor 6.2.A Interpret and use the t-distribution. 6.2.B Construct and interpret a confidence interval for the population mean with a small sample. Days 3 3 Resources: Assessment Sources: Add Notes: Page 29 Statistics Concept 6.3 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Confidence Intervals for Population Proportions population proportion Descriptor Find a point estimate for a population proportion. Days 2 6.3.B Construct and Interpret a confidence interval for a population proportion. 2 6.3.C Determine the minimum sample size required when estimating a population proportion. 2 6.3.A Resources: Assessment Sources: Add Notes: ‘ Page 30 Statistics Williamsport Area School District Unit 7: Hypothesis Testing with One Sample Days: Big Idea: Unit Essential Question: How can we test a claim about a parameter? Concept Concept Title 7.1 7.2 Introduction to Hypothesis Testing Hypothesis Testing for the Mean (Large Samples) Hypothesis Testing for the Mean (Small Samples) Hypothesis Testing for Proportions 7.3 7.4 Duration (Days) 9 4 4 3 Page 31 Statistics Concept 7.1 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Introduction to Hypothesis Testing Statistical hypothesis, null hypothesis, alternative hypothesis, type I error, type II error, level of significance, test statistic, P-value, left-tailed test, right-tailed test, two-tailed test Descriptor Days 7.1.A Introduction to hypothesis testing. 1 7.1.B State a null and alternative hypothesis 1 7.1.C Identify and interpret Type I and Type II error. 1 7.1.D Determine whether to use a one-tailed or a two-tailed statistical test. 1 7.1.E Calculate the P-value of a statistical test. 3 7.1.F Make and interpret a decision based on the results of a statistical test. 1 7.1.G Write a claim for a hypothesis test. 1 Resources: Assessment Sources: Add Notes: Page 32 Statistics Concept 7.2 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Hypothesis Testing for the Mean (Large Samples) z-test for a mean, test statistic, standardized test statistic, rejection region, critical value, Descriptor Days 7.2.A Find and interpret a P-value for a test about a 2 population mean. 7.2B Find and interpret critical values and rejection regions. 2 Resources: Assessment Sources: Add Notes: Page 33 Statistics Concept 7.3 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Hypothesis Testing for the Mean (Small Samples) t-test for a mean, test statistic, standardized test statistic Descriptor 7.3.A Find critical values using the t-distribution. 7.3.B Use a t-test to perform a test about a population mean. Days 2 2 Resources: Assessment Sources: Add Notes: Page 34 Statistics Concept 7.4 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Hypothesis Testing for Proportions z-test for a proportion, test statistic, standardized test statistic, Descriptor 7.4.A Perform a z-test for a population proportion. Days 3 Resources: Assessment Sources: Add Notes: Page 35 Statistics Williamsport Area School District Additional Information: Include College Algebra Review Unit after Unit 3. Students will work in small groups and be responsible for organizing resources on a specific algebra topic. This is intended as a review of key algebra concepts prior to students taking college placement exams. (Approximately 15 days) Page 36