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Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Date: November 10, 2009 ET

Topic: 1. Exploring and Understanding Days: 19 Subject Area(s): Grade(s):

Key Learning: The student will describe, display, and summarize data in a variety of ways based on the type of variables and data that is under analysis.

Unit Essential Question(s): How do we describe, display, and summarize data?

Concept: Concept: Concept: Data Displaying and Displaying and Describing Categorical Summarizing Data Quantitative Data

2.6.11.F, M11.E.4.1.1 M11.E.1.1.1, M11.E.2.1.1, M11.E.1.1.2, M11.E. 2.1.2

Lesson Essential Question(s): Lesson Essential Question(s): Lesson Essential Question(s): What do we need to know How do we display and describe How do we display and summarize about the data in order to analyze it? categorical data? (A) quantitative data? (A) (A)

Vocabulary: Vocabulary: Vocabulary: The W's, Context, Data, Data Table, Table, Proportion, Distribution, , Relative Cases, Sample, Population, Variables, Percentage, Relative Frequency Table, Frequency Histogram, Stem-and-Leaf Units, , Distribution, Area Principle, Bar , Display, Dotplot, , Unimodal, Quantitative Variable Relative Frequency , Pie Bimodal, Multimodal, Uniform, Chart, , Marginal Symmetric, Skewed, Tails, Outliers, Distribution, Conditional Distribution, Center, , Spread, , Independent Variables, Segmented Quartiles, Lower Quartile, Upper Bar Chart, Simpson's Paradox Quartile, , , Five-number Summary, , Resistant, ,

Concept: Concept: Concept: Understanding and The Standard Deviation Comparing Distributions as a Ruler and the Normal M11.E.2.1.3, M11.E.1.1.2, M11.E.1.1.1 Model 2.6.11.I

Lesson Essential Question(s): Lesson Essential Question(s): Lesson Essential Question(s): How do we compare distributions? (A) How do we use the normal model and standard deviation as a ruler? (A) How and why do we transform data? (ET)

Vocabulary: Vocabulary: Vocabulary: Boxplot, Far Outlier, Transform Data, Standardized Values, Z-scores, Normal Re-express Data Model, Parameter, , Standard Normal model, Assumptions, Conditions, 66-95-99.7 Rule, Normal Percentiles

Page 1 of 2 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 1. Exploring and Understanding Data Days: 19 Subject Area(s): Grade(s):

Additional Information:

Attached Document(s):

Page 2 of 2 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 1. Exploring and Understanding Data Days: 19 Subject Area(s): Grade(s):

Concept: Data The W's - Context - Data - Data Table - Cases - Sample - Population - Variables - Units - Categorical Variable - Quantitative Variable -

Concept: Displaying and Describing Categorical Data Frequency Table - Proportion - Percentage - Relative Frequency Table - Distribution - Area Principle - Bar Chart - Relative Frequency Bar Chart - - Contingency Table - Marginal Distribution - Conditional Distribution - Independent Variables - Segmented Bar Chart - Simpson's Paradox -

Page 1 of 2 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 1. Exploring and Understanding Data Days: 19 Subject Area(s): Grade(s):

Concept: Displaying and Summarizing Quantitative Data Distribution - Histogram - Relative Frequency Histogram - Stem-and-Leaf Display - Dotplot - Mode - Unimodal - Bimodal - Multimodal - Uniform - Symmetric - Skewed - Tails - Outliers - Center - Median - Spread - Range - Quartiles - Lower Quartile - Upper Quartile - Interquartile Range - Percentiles - Five-number Summary - Mean - Resistant - Standard Deviation - Variance -

Concept: Understanding and Comparing Distributions Boxplot - Far Outlier - Transform Data - Re-express Data -

Concept: The Standard Deviation as a Ruler and the Normal Model Standardized Values - Z-scores - Normal Model - Parameter - Statistic - Standard Normal model - Assumptions - Conditions - 66-95-99.7 Rule - Normal Percentiles -

Page 2 of 2 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 2. Exploring Relationships Between Variables Days: 21 Subject Area(s): Grade(s):

Key Learning: The student will determine the association and correlation of the data in the scatterplot, and explain what it tells us about the data. The student will also graph scatterplots, calculate regression lines and equations, find residuals and make residual plots, and transform data to find a better linear fit. The student will use this information to make predictions and evaluate the accuracy of the model.

Unit Essential Question(s): How do we use scatterplots, regression lines and equations, residuals, and data transformations to make predictions and evaluate the model's accuracy?

Concept: Concept: Concept: Scatterplots, Association, Regression Wisdom and Correlation 2.5.11.B, M11.E.4.2.1, 2.6.11.C, 2.8.11.L, 2.2.11.C, 2.2.11.F, 2.5.11.C, 2.5.11.D

2.2.11.C, 2.2.11.F, 2.8.11.K 2.8.11.K, 2.6.11.D, 2.2.11.F, M11.E.4.2.2, 2.8.11.M, M11.E.4.1.1

Lesson Essential Question(s): Lesson Essential Question(s): Lesson Essential Question(s): How do we determine the association How do we determine the regression How do we calculate and plot residuals and correlation of a scatterplot? (A) line of a scatterplot and use it to make and determine the validity of the initial predictions? (A) model? (A)

Vocabulary: Vocabulary: Vocabulary: Explanatory Variable, Response Line, Line of Best Fit, Extrapolation, Leverage, Influential Variable, Correlation, Lurking Variable, Regression Line, Residual, Regression Point, Lurking Variable, Outlier Scatterplot, Association to the Mean, Slope, Intercept

Concept: Concept: Concept: Re-expressing Data: Get It Straight!

2.5.11.C, 2.1.11.A, 2.2.11.F, 2.5.11.D

Lesson Essential Question(s): Lesson Essential Question(s): Lesson Essential Question(s): How and why do we re-express data? (A)

Vocabulary: Vocabulary: Vocabulary: Re-expression, Ladder of Powers

Additional Information:

Attached Document(s):

Page 1 of 1 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 2. Exploring Relationships Between Variables Days: 21 Subject Area(s): Grade(s):

Concept: Scatterplots, Association, and Correlation Explanatory Variable - Response Variable - Correlation - Lurking Variable - Scatterplot - Association -

Concept: Linear Regression Least Squares Line - Line of Best Fit - Regression Line - Residual - Regression to the Mean - Slope - Intercept -

Concept: Regression Wisdom Extrapolation - Leverage - Influential Point - Lurking Variable - Outlier -

Concept: Re-expressing Data: Get It Straight! Re-expression - Ladder of Powers -

Page 1 of 1 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 3. Gathering Data Days: 15 Subject Area(s): Grade(s):

Key Learning: The student will use the principles of random and experimental design to conduct unbiased , and determine if a cause- and-effect relationship exists.

Unit Essential Question(s): How do we use the principles of random sampling and experimental design to conduct unbiased experiments that can allow us to reach cause-and-effect conclusions?

Concept: Concept: Concept: Understanding Sample Surveys Experiments and 2.6.11.E, 2.6.11.H Observational Studies

2.6.11.B 2.6.11.G, 2.6.11.A, 2.7.11.B, 2.7.11.C

Lesson Essential Question(s): Lesson Essential Question(s): Lesson Essential Question(s): How do we perform a simulation and How do we conduct sampling so that How are observational studies useful? report its results? (A) the sample and the data obtained is (A) representative of the population? (A) How do we design and conduct unbiased experiments? (ET)

Vocabulary: Vocabulary: Vocabulary: Random Numbers, Trial, Component, Population, Sample, Sample Surveys, Observational Studies, Retrospective Response Variable, Simulation Biased, Randomizing, Sample Size, Study, Prospective Study, , , Parameter, Statistic, , Factor, Subjects Representative, Simple Random (or Participants), Experimental Unit, Sample, Sampling Frame, Sampling Levels, Treatment, Control, Variability, Strata, Stratified Random Randomize, Replicate, Block, Sampling, , Variable, Statistically Significant, , Systematic Control Group, Blinding, Single-blind, Sampling, Pilot, Voluntary Response Double-blind, Placebo, Placebo Effect, Bias, Convenience Sampling, Blocks, Randomized Block Design, Undercoverage, Nonresponse Bias, , Confounded, Completely Response Bias Randomized Design

Additional Information:

Attached Document(s):

Page 1 of 1 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 3. Gathering Data Days: 15 Subject Area(s): Grade(s):

Concept: Understanding Randomness Random Numbers - Trial - Component - Response Variable - Simulation -

Concept: Sample Surveys Population - Sample - Sample Surveys - Biased - Randomizing - Sample Size - Census - Parameter - Statistic - Representative - Simple Random Sample - Sampling Frame - Sampling Variability - Strata - Stratified Random Sampling - Cluster Sampling - Multistage Sampling - Systematic Sampling - Pilot - Voluntary Response Bias - Convenience Sampling - Undercoverage - Nonresponse Bias - Response Bias -

Page 1 of 2 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 3. Gathering Data Days: 15 Subject Area(s): Grade(s):

Concept: Experiments and Observational Studies Observational Studies - Retrospective Study - Prospective Study - Experiment - Random Assignment - Factor - Subjects (or Participants) - Experimental Unit - Levels - Treatment - Control - Randomize - Replicate - Block - Blocking Variable - Statistically Significant - Control Group - Blinding - Single-blind - Double-blind - Placebo - Placebo Effect - Blocks - Randomized Block Design - Matching - Confounded - Completely Randomized Design -

Page 2 of 2 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 4. Randomness and Probability Days: 17 Subject Area(s): Grade(s):

Key Learning: The student will use basic probability rules to determine the probability of an event. There are several probability models for a that describe the theoretical distribution of outcomes.

Unit Essential Question(s): How do we determine the probability of an event using basic probability rules, and how do we use probability models to describe the theoretical distribution of outcomes?

Concept: Concept: Concept: From Randomness to Probability Rules! Random Variables Probability M11.E.3.1.1, M11.E.4.1.2 2.5.11.C, 2.5.11.B, M11.E.4.1.2, M11.E.4.1.1,

2.7.11.A, M11.E.3.1.2, M11.E.3.2.1, M11.E.4.1.2, 2.6.11.A 2.7.11.D

Lesson Essential Question(s): Lesson Essential Question(s): Lesson Essential Question(s): How do we combine probabilities of How do we use the General Addition How do we determine the expected outcomes to find probabilities of more Rule and the General Multiplication value and the standard deviation of a complex events? (A) Rule? (A) discrete random variable? (A)

How do we calculate conditional How and why do we add ? probability? (A) (ET)

How do we determine independence? (ET)

Vocabulary: Vocabulary: Vocabulary: Random Phenomenon, Trial, Outcome, Conditional Probability, Independence, Random Variable, Discrete Random Event, Sample Space, Independent, Tree Variable, Continuous Random Variable, Probability, Empirical Probability, Probability Model, Expected Value, Theoretical Probability, Personal Standard Deviation, Variance Probability, Complement, Disjoint (Mutually Exclusive)

Page 1 of 2 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 4. Randomness and Probability Days: 17 Subject Area(s): Grade(s):

Concept: Concept: Concept: Probability Models

2.6.11.I, M11.E.4.1.1, 2.2.11.F, 2.5.11.B, 2.5.11.C

Lesson Essential Question(s): Lesson Essential Question(s): Lesson Essential Question(s): How and when do we use the Geometric probability model? (A)

How and when do we use a Binomial probability model? (A)

How and when do we use a Normal probability model to approximate a Binomial model? (ET)

Vocabulary: Vocabulary: Vocabulary: Bernoulli Trials, Geometric Probability Model, Binomial Probability Model, 10% Condition, Success/Failure Condition

Additional Information:

Attached Document(s):

Page 2 of 2 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 4. Randomness and Probability Days: 17 Subject Area(s): Grade(s):

Concept: From Randomness to Probability Random Phenomenon - Trial - Outcome - Event - Sample Space - Independent - Probability - Empirical Probability - Theoretical Probability - Personal Probability - Complement - Disjoint (Mutually Exclusive) -

Concept: Probability Rules! Conditional Probability - Independence - Tree Diagram -

Concept: Random Variables Random Variable - Discrete Random Variable - Continuous Random Variable - Probability Model - Expected Value - Standard Deviation - Variance -

Concept: Probability Models Bernoulli Trials - Geometric Probability Model - Binomial Probability Model - 10% Condition - Success/Failure Condition -

Page 1 of 1 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 5. From the Data at Hand to the World at Large Days: 17 Subject Area(s): Grade(s):

Key Learning: The student will find confidence intervals for both one and two proportions and perform hypothesis tests for both one and two proportions. Results will be analyzed for significance and errors.

Unit Essential Question(s): How do we find confidence intervals for both one and two proportions and perform hypothesis tests for both one or two proportions?

Concept: Concept: Concept: Confidence Intervals for Testing Hypotheses Models Proportions About Proportions

2.2.11.D 2.5.11.D, 2.5.11.B, 2.5.11.C 2.5.11.D, 2.5.11.B, 2.5.11.C, 2.7.11.D

Lesson Essential Question(s): Lesson Essential Question(s): Lesson Essential Question(s): How do we use the Central Limit How do we construct confidence How do we perform one and two tailed Theorem? (A) intervals for proportions? (A) hypothesis tests? (A)

How do we determine if the assumptions and conditions are met before constructing a ? (ET)

How do we calculate the margin of error? (A)

Vocabulary: Vocabulary: Vocabulary: Sampling Distribution, Sampling , Confidence Interval, Null Hypothesis, Alternative Distribution Model, Sampling Error, One-proportion Z-interval, Margin of Hypothesis, P-value, One-proportion Z- Sampling Variability, Central Limit Error, Critical Value test, One-sided Alternative, Two-sided Theorem Alternative

Page 1 of 2 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 5. From the Data at Hand to the World at Large Days: 17 Subject Area(s): Grade(s):

Concept: Concept: Concept: More About Tests and Comparing Two Intervals (Type I and Proportions Type II Errors) 2.5.11.D, 2.5.11.B, 2.5.11.C, 2.7.11.D 2.2.11.D

Lesson Essential Question(s): Lesson Essential Question(s): Lesson Essential Question(s): What is the differance between a How do we find a confidence interval Confidence Interval and a Hypothesis for two proportions? (A) Test? (A) How do we perform a hypothesis test How can we determine whether a Type for two proportions? (A) I or Type II error has occurred, and how can we reduce the chance of What is the difference in the either happening? (ET) procedure, conditions, and results when comparing a two-proportion confidence interval and a two- proportion hypothesis test? (ET)

Vocabulary: Vocabulary: Vocabulary: Statistically Significant, Alpha Level, Two-proportion Z-interval, Pooling, Significance Level, Type I Error, Type II Two-proportion Z-test Error, Power,

Additional Information:

Attached Document(s):

Page 2 of 2 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 5. From the Data at Hand to the World at Large Days: 17 Subject Area(s): Grade(s):

Concept: Sampling Distribution Models Sampling Distribution - Sampling Distribution Model - Sampling Error - Sampling Variability - -

Concept: Confidence Intervals for Proportions Standard Error - Confidence Interval - One-proportion Z-interval - Margin of Error - Critical Value -

Concept: Testing Hypotheses About Proportions Null Hypothesis - - P-value - One-proportion Z-test - One-sided Alternative - Two-sided Alternative -

Concept: More About Tests and Intervals (Type I and Type II Errors) Statistically Significant - Alpha Level - Significance Level - Type I Error - Type II Error - Power - Effect Size -

Concept: Comparing Two Proportions Two-proportion Z-interval - Pooling - Two-proportion Z-test -

Page 1 of 1 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 6. Learning About the World Days: 10 Subject Area(s): Grade(s):

Key Learning: The student will construct confidence intervals and generate hypothesis tests for . These methods will also be used to compare the difference of two means and to analyze paired data.

Unit Essential Question(s): How do we construct confidence intervals and generate hypothesis tests for means, to compare the difference of two means, and to analyze paired data?

Concept: Concept: Concept: Inferences About Means Comparing Means Paired Samples and 2.6.11.A, M11.E.4.1.2, 2.2.11.F, 2.5.11.B, 2.5.11.C, 2.6.11.A, M11.E.4.1.2, 2.2.11.F, 2.5.11.B, 2.5.11.C, Blocks

2.7.11.D 2.7.11.D 2.6.11.A, M11.E.4.1.2, 2.2.11.F, 2.5.11.B, 2.5.11.C, 2.7.11.D

Lesson Essential Question(s): Lesson Essential Question(s): Lesson Essential Question(s): How do we construct a confidence How do we construct confidence How do test hypotheses and generate interval for means and conduct a intervals and conduct hypothesis tests confidence intervals to look at pairwise hypothesis test for means? (A) to compare the difference between differences? (A) two means? (A) How do we determine whether to use independent t-procedures or paired t- methods when analyzing paired data? (ET)

Vocabulary: Vocabulary: Vocabulary: Degrees of Freedom, One-sample t- Two-sample T-interval, Two-sample T- Paired Data, Paired T-test, Paired T- Interval for the Mean, One-Sample t- test, Two-sample T-interval for the Confidence Interval Test for the Mean Difference Between Means, Two- sample T-test for the Difference Between Means, Pooled T-test

Additional Information:

Attached Document(s):

Page 1 of 1 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 6. Learning About the World Days: 10 Subject Area(s): Grade(s):

Concept: Inferences About Means Degrees of Freedom - One-sample t-Interval for the Mean - One-Sample t-Test for the Mean -

Concept: Comparing Means Two-sample T-interval - Two-sample T-test - Two-sample T-interval for the Difference Between Means - Two-sample T-test for the Difference Between Means - Pooled T-test -

Concept: Paired Samples and Blocks Paired Data - Paired T-test - Paired T-Confidence Interval -

Page 1 of 1 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 7. Inference When Variables Are Related Days: 12 Subject Area(s): Grade(s):

Key Learning: The student will conduct tests of concerning distributions of counts and about association between variables. The results will be used to answer questions about means, proportions, distributions, and associations.

Unit Essential Question(s): How do we conduct tests of statistical inference concerning distributions of counts and about association between variables, and use the results to answer questions about means, proportions, distributions, and associations?

Concept: Concept: Concept: Comparing Counts Inferences for Regression

2.2.11.F, 2.5.11.C 2.2.11.F, 2.5.11.C

Lesson Essential Question(s): Lesson Essential Question(s): Lesson Essential Question(s): How do we conduct chi-square tests How do we check the assumptions and for goodness-of-fit? (A) conditions before continuing with an inference procedure? (A) How do we conduct chi-square tests of homogeneity? (A) How do we test the hypothesis about the slope? (A) How do we conduct chi-square tests of independence? (A) How do we create and interpret a confidence interval for the true slope? How do we use standardized (A) residuals? (ET)

Vocabulary: Vocabulary: Vocabulary: Goodness-of-fit, Chi-Square Statistic, Residual Standard Deviation, T-test for Chi-Square Model, Chi-Square Test for the Regression Slope, Confidence Goodness-of-fit, Chi-Square Test of Interval for the Regression Slope (), Homogeneity, Chi-Square Test for Independence, Contingency Table, Standardized Residual, Cell, Chi- Square Component

Additional Information:

Attached Document(s):

Page 1 of 1 Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - AP Statistics Date: November 10, 2009 ET

Topic: 7. Inference When Variables Are Related Days: 12 Subject Area(s): Grade(s):

Concept: Comparing Counts Goodness-of-fit - Chi-Square Statistic - Chi-Square Model - Chi-Square Test for Goodness-of-fit - Chi-Square Test of Homogeneity - Chi-Square Test for Independence - Contingency Table - Standardized Residual - Cell - Chi-Square Component -

Concept: Inferences for Regression Residual Standard Deviation - T-test for the Regression Slope - Confidence Interval for the Regression Slope () - -

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