· Web viewUnit 5 will have students begin a formal investigation into statistical inference. The unit will begin with some work involving sampling distribution models and the central

District OverviewThe mathematics curriculum provides sequential and comprehensive K-12 instruction in a collaborative, student-centered learning environment that fosters critical thinking, creativity, skillful problem-solving, and effective communication in order to enable all students to adapt to an ever-changing, global society and increase college and career readiness. An emphasis has been placed on conceptual understanding, higher-order thinking, and problem solving skills to prepare students for 21st century careers. This is further embedded through the integrated use of technology into daily lessons. Instruction focuses on meaningful development of mathematical ideas at each grade level where students are given the opportunity to explore, engage, and take risks with content as they build and expand their knowledge and understanding of mathematics. Students will experience mathematics as a coherent and useful subject within the context of real-life situations. In all, the curriculum aims to reach high standards while encouraging curiosity and building confidence in a collaborative atmosphere.

Advanced Placement Statisitcs Course DescriptionAP Statistics will introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students will be exposed to four broad conceptual themes: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. AP Statistics is the equivalent of a one-semester, introductory, non-calculus based college course in statistics.

AP Statistics Units: Unit 1: Exploring and Understanding Data Unit 2: Exploring Relationships Between Variables Unit 3: Gathering Data Unit 4: Randomness and Probability Unit 5: From the Data at Hand to the World at Large Unit 6: Learning About the World Unit 7: Inference When Variables Are Related

Subject: Mathematics

Course:AP Statistics

Suggested Timeline: 5 weeks

Unit Title: Exploring and Understanding DataUnit Overview/Essential Understanding: Unit 1 covers data displays and summaries. Students will recognize some of the material from previous math classes, but there will be an emphasis on statistical thinking. While there will be many new terms defined and examples provided, there will also be discussions as to why methods presented are used, and what the students can hope to learn from them. The concepts in this unit will lay the groundwork for many of the lessons that are explored throughout the entire course.Unit Objectives: At the end of this unit, students will have a strong understanding of and be able to independently work with:

Data Displaying and describing categorical data Displaying and summarizing quantitative data Understanding and comparing distributions The standard deviation as a ruler and the normal model

Focus Standards Addressed in this Unit: CC.2.4.HS.B.1 – Summarize, represent, and interpret data on a single count or measurement variable

Important Standards Addressed in this Unit:N/AMisconceptions:

Difficulties choosing the most appropriate graph or chart to display data Choosing the correct methods for summarizing shape, center, and spread of a distribution Trying to apply a normal model to a distribution that is not unimodal or symmetric

Concepts/Content: Data Sample Population Categorical Quantitative Frequency distribution Contingency table Independence Simpson’s paradox

Competencies/Skills: Identify the Who, What, When,

Where, Why, and How of data Choose an appropriate display for

categorical data Summarize the distribution of a

categorical variable with a frequency table

Display the distribution of a categorical variable with a bar

Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos

Histogram Stem-and-leaf plot Dotplot Shape Center Spread Skewed Outlier 5-number summary Variance Standard deviation Boxplot Timeplot Shifting Rescaling Normal model Parameter Statistic z-score

chart or pie chart Make and examine a contingency

table Identify an appropriate display for

any quantitative variable Discuss shape, center, and spread

of the distribution of a variable Compute mean, median, and

standard deviation Describe any anomalies revealed

by the display of a variable Select suitable displays and

methods for comparing groups Create and use histograms to

display quantitative data Understand how shifting and

rescaling effects a variable Determine if a variable is normally

distributed Use z-scores and the normal

model appropriatelyAssessments:

informal questioning in-class formative assessments review of homework periodic quizzes unit test

Interdisciplinary Connections:N/A

Additional Resources: Stats: Modeling the World textbook USA TestPrep




Unit Title:

Exploring Relationships Between VariablesUnit Overview/Essential Understanding: Unit 2 expands on the idea of considering a second variable for exploration. The students will discuss relationships between two quantitative variables through the introduction of scatter plots, correlation, and regression. A heavy emphasis will be on the use of technology (graphing calculator) to enhance the students’ abilities to investigate and discover important concepts throughout the unit. The unit concludes with a discussion of data re-expression as a way to straighten relationships between variables.Unit Objectives: At the end of this unit, students will have a strong understanding of and be able to independently work with:

Scatter plots, association, and correlation Linear regression Regression wisdom Re-expressing data

Focus Standards Addressed in this Unit: CC.2.4.HS.B.2 – Summarize, represent, and interpret data on two categorical and quantitative variables


Confusing the ideas of correlation and causation Trying to apply linear regression ideas to a relationship that is not straight Misunderstanding how outliers and lurking variables affect data

Concepts/Content: Scatter plot Association Outlier Correlation coefficient Response and explanatory Linear model Residual Least squares Regression Slope intercept Leverage Influential point Lurking variable

Competencies/Skills: Make a scatter plot by hand and

with technology Compute and interpret the

correlation of two variables Describe the direction, form, and

strength of a scatter plot Find and use a regression

equation from the summary statistics and correlation

Use a linear model to predict a value of y for a given x

Compute and display the residuals for data values


Re-expression Ladder of powers

Look for high leverage, large residual, and influential points on a scatter plot

Discuss possible lurking variables Use diagnostic information as part

of a report of a regression Re-express data to improve

symmetry and linearity of data Reverse common re-expressions

when finding a predicted valueAssessments:

informal questioning in-class formative assessments review of homework periodic quizzes unit test






Unit Title: Gathering DataUnit Overview/Essential Understanding:

In Unit 3 the students will investigate where data come from and how to appropriately gather data. They will learn that randomness is essential in the gathering of data for statistical inference, as well as the effects that bias has on analyzing data. The paths that follow the discussion of data gathering lead naturally to probability and inference.Unit Objectives: At the end of this unit, students will have a strong understanding of and be able to independently work with:

Understanding randomness Sample surveys Experiments and observational studies

Focus Standards Addressed in this Unit: CC.2.4.HS.B.4 – Recognize and evaluate random processes underlying statistical experiments


Adopting strategies that model outcome chances inaccurately Creating poor sampling designs and allowing preventable bias to affect our results Misunderstanding how confounding variables affect data

Concepts/Content: Random Simulation Component Trial Response variable Survey Bias Census Representative Simple random sample Sampling frame Sampling variability Stratified sample Cluster sample Systematic Multistage sample Observational study

Competencies/Skills: Recognize random outcomes in a

real-world situation Perform, describe, and interpret a

simulation based on randomness Draw conclusions about questions

being investigated Know the basic concepts and

terminology of sampling Recognize population parameters Understand the value of

randomization as a defense against bias

Draw a random sample from a master list of a population

Report possible sources of bias in sampling methods

Know the basic principles of


Experiment Factor Level Treatment Experimental units Statistically significant Control group Blinding Placebo Blocking Matching Confounding

experimental design Design a completely randomized

experiment or observational study Use blocking and/or blinding to

reduce variation and bias Use graphical displays to compare

responses for different treatment groups

Report statistical significance of the results from an experiment or observational study

Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test






Unit Title: Randomness and ProbabilityUnit Overview/Essential Understanding: In Unit 4 the students will be introduced to the formal concepts of probability and distribution. The beginning of the unit will lay the foundations for probability and discuss how it works through conditional probabilities and tree diagrams. Later on in the unit, the students will work with random variables and probability models—these will contribute greatly to their understanding of statistical inference.Unit Objectives:

At the end of this unit, students will have a strong understanding of and be able to independently work with: Moving from randomness to probability Probability rules Random variables Probability models

Focus Standards Addressed in this Unit: CC.2.4.HS.B.7 – Apply the rules of probability to compute probabilities of compound events in a uniform probability model


General confusion between the concepts of disjoint and independent Misunderstandings about which probability rule should be applied in certain situations Inaccurate creation of a probability model for a random variable Confusing the geometric and binomial models

Concepts/Content: Trial Outcome Law of large numbers Probability Complement Disjoint Addition rules Independence Multiplication rules Conditional probability Tree diagram Discrete random variable Continuous random variable Probability model Expected value Bernoulli trials Geometric probability model Binomial probability model 10% condition

Competencies/Skills: Recognize random outcomes in a

real-world situation Recognize when events are

disjoint and independent Apply the addition and

multiplication rules Use the complement rule to make

calculations simpler Understand the concept of

conditional probability Find probabilities of compound

events in a two-way table Make and use a tree diagram to

understand conditional probabilities and reverse conditioning

Find the probability model for a random variable

Find the mean, variance, and


Success/failure condition standard deviation of a random variable

Determine the effects that adding/multiplying a constant and adding or subtract two independent variables has

Tell if a situation involves Bernoulli trials

Know the conditions for using geometric, binomial, and normal models

Use the normal model to approximate binomial probability







Unit Title: From the Data at Hand to the World at LargeUnit Overview/Essential Understanding: Unit 5 will have students begin a formal investigation into statistical inference. The unit will begin with some work involving sampling distribution models and the central limit theorem. Eventually, the students will work on the construction and interpretation of confidence intervals and hypothesis tests for proportions. An emphasis is placed on satisfying necessary assumptions and conditions, as well as the use of specific language and a very detailed procedure.Unit Objectives: At the end of this unit, students will have a strong understanding of and be able to independently work with:

Sampling distribution models

Confidence intervals for proportions Testing hypotheses about proportions More about tests and intervals Comparing two proportions

Focus Standards Addressed in this Unit: CC.2.4.HS.B.6 – Use the concepts of independence and conditional probability to interpret data


Accidentally thinking that all samples from a population will have the same characteristics Common violations of required assumptions and conditions Difficulties with constructing an accurate conclusion for confidence intervals and hypothesis tests Misinterpretations of the practical results of type I and type II errors in inference

Concepts/Content: Sampling distribution model Sampling variability/error Central limit theorem Standard error Confidence interval Margin of error Critical value Hypothesis test Null hypothesis Alternative hypothesis P-value Alpha level Statistically significant Type I error Type II error Power Effect size Pooling

Competencies/Skills: Demonstrate a sampling

distribution model by simulation Use a sampling distribution model

to make statements about the distribution of a proportion or mean under repeated sampling

Understand the central limit theorem

Construct and interpret a one-proportion z-interval

Understand the balance between precision and certainty in a confidence interval

Write accurate null and alternative hypotheses

Choose accurately between a one- and two-sided test

Perform and interpret a one-proportion z-test

Interpret the meaning of a P-value


Understand the relationship between hypothesis tests and confidence intervals

Identify and interpret the different types of errors that can occur in hypothesis testing

Create and interpret confidence intervals and hypothesis tests for two proportions







Unit Title: Learning About the WorldUnit Overview/Essential Understanding: Unit 6 will have the students continuing their work with confidence intervals and hypothesis testing, however this time the emphasis will be on means rather than proportions. The main procedures used will exactly the same with only slight adjustments to some of the assumptions and conditions. During this unit, it is expected that students will approach a mastery level of their understanding of statistical inference.Unit Objectives: At the end of this unit, students will have a strong understanding of and be able to independently work with:

Inferences about means Comparing means Paired samples and blocks

Focus Standards Addressed in this Unit: CC.2.4.HS.B.5 – Make inferences and justify conclusions based on sample surveys, experiments, and observational studies


Confusion between inference for proportions and means Difficulty understanding how outliers affect data samples Confusion between working with independent groups and paired groups

Concepts/Content: Student’s t-model One-sample t-test One-sample t-interval Two-sample t-test Two-sample t-interval Pooling Paired data Paired t-test Paired t-interval

Competencies/Skills: Compute and interpret hypothesis

tests and confidence intervals for the population mean

Know how to examine data for violations of conditions and assumptions

Write accurate conclusions for confidence intervals and hypothesis tests in context

Recognize when a pooled-t procedure might be appropriate

Recognize situations to do inference on the difference between the means of two groups

Recognize whether the design that compares two groups is paired

Perform and interpret intervals and tests for both independent groups and paired groups



Interdisciplinary Connections: Additional Resources:

N/A Stats: Modeling the World textbook USA TestPrep




Unit Title: Inferences When Variables Are RelatedUnit Overview/Essential Understanding: Unit 7 will have the students look forward as well as backward applying just about everything that has been learned so far in this course. The main theme of this unit is understanding and modeling relationships between variables. Students will look at categorical data with Chi-square models. The final lesson of this unit involves regression models for statistical inference.Unit Objectives: At the end of this unit, students will have a strong understanding of and be able to independently work with:

Comparing counts Inferences for regression

Focus Standards Addressed in this Unit: CC.2.4.HS.B.3 –Analyze linear models to make interpretations based on the data

Important Standards Addressed in this Unit:N/A

Misconceptions: Choosing the correct Chi-square method to use for each situation Common mistakes occur with some of the uses of technology in this unit Need for a complete refresh of many concepts relating to linear regression

Concepts/Content: Chi-square model Cell Chi-square statistic Test of goodness-of-fit Test of homogeneity Test of independence Component Standardized residual Two-way table Conditions for inference in

regression Residual standard deviation t-test for the regression slope Confident interval for the

regression slope Beta (B)

Competencies/Skills: Recognize the appropriate Chi-

square test to use in a given situation

Understand how degrees of freedom work in a chi-square test

Display and interpret counts in a two-way table

Examine the standardized residuals

Interpret the results of a chi-square test

Check all of the assumptions and conditions for inferences relating to regression

Examine data and a scatter plot of y vs. x

Test the standard hypothesis that the true regression slope is zero and interpret the results

Find and interpret a confidence interval for the slope of a regression



Interdisciplinary Connections: Additional Resources:

N/A Stats: Modeling the World textbook USA TestPrep

Documents

· Web viewUnit 5 will have students begin a formal investigation into statistical inference. The unit will begin with some work involving sampling distribution models and the central