Download AP Statistics - Southern Regional School District

SOUTHERN REGIONAL SCHOOL DISTRICT
MATHEMATICS CURRICULUM
Content Area: Mathematics
Course Title: Statistics Advanced Placement
Grade Level: 10, 11, 12
Unit Plan 1
Exploring Data: Observing Patterns and
Departures from Patterns
Pacing Guide
6 weeks
Unit Plan 2
Planning a Study: Deciding What
and How to Measure
Pacing Guide
2-3 weeks
Unit Plan 3
Anticipating Patterns: Producing Models
Using Probability & Simulations
Pacing Guide
9 weeks
Unit Plan 4
Statistical Inference: Confirming Models
Pacing Guide
8 weeks
Unit Plan 5
Test Review for AP Examination
Pacing Guide
3 weeks
Unit Plan 6
Real Life Statistics In Action
Pacing Guide
4 weeks
Date Revised:
December 2014
Board Approved on:
January 7, 2015
1
SOUTHERN REGIONAL SCHOOL DISTRICT
Unit Overview
Content Area: Mathematics
Unit Title: Exploring Data: Observing Patterns and Departures from Patterns
Target Course/Grade Level: Statistics Advanced Placement / 10, 11, 12
Unit Summary:
Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures
from patterns. Emphasis should be placed on interpreting information from graphical and numerical displays and
summarizing it in a clear, concise manner.
Primary interdisciplinary connections:
Infused within the unit are connections to the Common Core Standards in Mathematics and Language Arts
Literacy and the NJCCCS in Technology.
21st Century Themes:
The unit will integrate the 21st Century Life and Career stand 9.1 strands A-D. These strands include: Critical
thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership, and cross
cultural understanding and interpersonal communication.
Technology connections:
For further clarification refer to NJ Core Curriculum Content Standards at: http://www.state.nj.us/education/cccs/
Common Core Standards
Summarize, represent, and interpret data on a single count or measurement variable
S-ID.1. Represent data with plots on the real number line (dot plots, histograms, and box plots).
S-ID.2. Use statistics appropriate to the shape of the data distribution to compare center (median, mean)
and spread (interquartile range, standard deviation) of two or more different data sets.
S-ID.3. Interpret differences in shape, center, and spread in the context of the data sets, accounting for
possible effects of extreme data points (outliers).
S-ID.4. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate
population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use
calculators, spreadsheets, and tables to estimate areas under the normal curve.
Summarize, represent, and interpret data on two categorical and quantitative variables
S-ID.5. Summarize categorical data for two categories in two-way frequency tables. Interpret relative
frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize
possible associations and trends in the data.
S-ID.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are
related.
a. Fit a function to the data; use functions fitted to data to solve problems in the context of the
data. Use given functions or chooses a function suggested by the context. Emphasize linear, quadratic, and
exponential models.
b. Informally assess the fit of a function by plotting and analyzing residuals.
c. Fit a linear function for a scatter plot that suggests a linear association.
Interpret linear models
S-ID.7. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the
context of the data.
S-ID.8. Compute (using technology) and interpret the correlation coefficient of a linear fit.
S-ID.9. Distinguish between correlation and causation.
2
Unit Essential Questions
• What is the appropriate graphical display for a
set of data?
• How are the measures of center, spread and
position used to interpret graphical displays?
• What does the shape of a distribution tell about
the data?
• What assumptions can be made from data?
• How can graphical displays be manipulated to
present misleading information?
• How can data analysis be used in the areas of
science to predict future happenings?
Unit Enduring Understandings
Students will understand that…
• They can use graphs and summary statistics to analyze
data.
• Deviations in data can have a huge effect on the final
results.
• Real life applications are numerous and across many
different subjects.
Unit Objectives
Students will know…
• Graphical displays of univariate data: dotplot,
stemplot, histogram, boxplots
o Interpreting graphical displays: outliers,
clusters, gaps, shape
o Measures of center: median, mean, mode
o Measures of spread: range, interquartile
range, standard deviation
o Measures of position: quartiles, percentiles,
standardized scores (z-scores)
o Comparing distributions of univariate data
• Exploring bivariate data: scatterplots
o Analyzing patterns in scatterplots
o Correlation and linearity
o Least squares regression line
o Residual plots, outliers, influential points
o Transformations to achieve linearity:
logarithmic, power
• Exploring categorical data: frequency tables
o Marginal and joint frequencies for two-way
tables
o Conditional relative frequencies and
association
o Simpson’s Paradox
Unit Objectives
Students will be able to…
• Enter data into TI-83
• Create graphical displays with/without the TI-83
• Simulate data using the TI-83
• Interpret graphical displays
• Calculate measures of center, spread and position
with/without TI-83
• Compare distributions using shape, clusters, outliers
and measures of center, spread and position
• Identify outliers using the 1.5 x IQR method
• Calculate and graph the least squares regression line
without and with the TI-83
• Calculate the correlation coefficient without and with
the TI-83
• Graph a residual plot
• Identify influential points
• Transform data to achieve linearity using logarithmic
and power transformations
• Find articles concerning statistics in newspapers,
magazines or on web sites
• Communicate findings rather than focus on a single
answer
3
SOUTHERN REGIONAL SCHOOL DISTRICT
Evidence of Learning
Formative Assessments
For additional ideas please refer to NJ State DOE classroom application documents:
http://www.state.nj.us/education/cccs/
•
•
•
•
•
Observation
Homework
Class participation
Do Now
Notebook
Summative Assessments
For additional ideas please refer to:
http://www.state.nj.us/education/cccs/
http://www.parcconline.org/assessment-blueprints-test-specs
http://www.parcconline.org/samples/mathematics/high-school-mathematics
•
•
•
•
•
•
Chapter/Unit Test
Quizzes
Presentations
Unit Projects
Quarterlies and Final Exam
PARCC PBA and EOY Assessments
Modifications (ELLs, Special Education, Gifted and Talented)
•
•
•
•
•
•
•
Teacher tutoring
Peer tutoring
Cooperative learning groups
Modified assignments
Differentiated instruction
Native language texts and native language to English dictionary
Follow all IEP modifications/504 plan
Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources:
•
•
•
•
•
•
•
•
•
Activity-Based Statistics (ABS), Schearffer, Gnanadesikan, Watkins, Witmer, 1996
Exploring Statistics with the TI-83 (ES w/83), Burrill, Hopfensperger, Koehler, 2001
The Practice of Statistics (YMM), Daniel Yates, David Moore, George McCabe, 1999
Statistics: Decisions Through Data(DTD), David S. Moore, 1993
The Cartoon Guide to Statistics, Gonick, Smith, 1993
How to Lie with Statistics, Darrell Huff, 1954
Activities and Projects for High School Statistics Courses, Millard, Turner, 2004
Workshop Statistics (WS), Allan Rossman, J. Barr Von Oehsen, 1997
Amsco: AP Statistics, James Bohan with Beth Chance, 2000
4
SOUTHERN REGIONAL SCHOOL DISTRICT
Unit Overview
Content Area: Mathematics
Unit Title: Planning a Study: Deciding What and How to Measure
Target Course/Grade Level: Statistics Advanced Placement / 10, 11, 12
Unit Summary:
Data must be collected according to a well-developed plan if valid information on a conjecture is to be obtained.
This plan includes clarifying the question and deciding upon a method of data collection and analysis. These
methods are used every day in the areas of science, medicine, politics, etc. and are valuable to understanding the
information that is presented to society in the media.
Primary interdisciplinary connections:
Infused within the unit are connections to the Common Core Standards in Mathematics and Language Arts
Literacy and the NJCCCS in Technology.
21st Century Themes:
The unit will integrate the 21st Century Life and Career stand 9.1 strands A-D. These strands include: Critical
thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership, and cross
cultural understanding and interpersonal communication.
Technology connections:
For further clarification refer to NJ Core Curriculum Content Standards at: http://www.state.nj.us/education/cccs/
Common Core Standards
Make inferences and justify conclusions from sample surveys, experiments, and observational studies
S-IC.3. Recognize the purposes of and differences among sample surveys, experiments, and
observational studies; explain how randomization relates to each.
S-IC.4. Use data from a sample survey to estimate a population mean or proportion; develop a margin of
error through the use of simulation models for random sampling.
S-IC.5. Use data from a randomized experiment to compare two treatments; use simulations to decide if
differences between parameters are significant.
S-IC.6. Evaluate reports based on data.
5
Unit Essential Questions
• Why is it important to be concerned with the
methods of data collection?
• How is the appropriate method of collection
decided?
• How can data be collected to represent an
unbiased sample of the population?
Unit Enduring Understandings
Students will understand that…
• Setting up experiments and surveys correctly is
essential to evaluating data.
• Bias must be avoided at all costs.
• There are other acceptable methods of collecting
data besides a simple random sample.
Unit Objectives
Students will know…
• Method of Data Collection: census, sample
survey, experiment observational study.
• Planning and conducting surveys: simple
random samplings (SRS)
o Characteristics of a well-designed and
conducted survey
o Sampling error: the variation inherent in a
survey
o Sources of bias in surveys
o Stratifying to reduce variation
• Planning and conducting experiments
o Comparing experiments to observational
studies and surveys
o Confounding, control groups, placebo
effects, blinding
o Treatments, experimental units,
randomization
o Completely randomized design for two
treatments
o Randomized paired comparison design
o Replication, blocking and application of
results
Unit Objectives
Students will be able to…
• Design a survey
• Conduct a survey
• Identify sampling error and sources of bias
• Stratify a survey
• Identify differences between experiments,
observational studies and surveys
• Identify the basic principles of statistical design of
experiments: control, randomization and replication.
• Randomize an experiment
• Simulate experiments with/without the TI-83/84 and
a computer
6
SOUTHERN REGIONAL SCHOOL DISTRICT
Evidence of Learning
Formative Assessments
For additional ideas please refer to NJ State DOE classroom application documents:
http://www.state.nj.us/education/cccs/
•
•
•
•
•
Observation
Homework
Class participation
Do Now
Notebook
Summative Assessments
For additional ideas please refer to:
http://www.state.nj.us/education/cccs/
http://www.parcconline.org/assessment-blueprints-test-specs
http://www.parcconline.org/samples/mathematics/high-school-mathematics
•
•
•
•
•
•
Chapter/Unit Test
Quizzes
Presentations
Unit Projects
Quarterlies and Final Exam
PARCC PBA and EOY Assessments
Modifications (ELLs, Special Education, Gifted and Talented)
•
•
•
•
•
•
•
Teacher tutoring
Peer tutoring
Cooperative learning groups
Modified assignments
Differentiated instruction
Native language texts and native language to English dictionary
Follow all IEP modifications/504 plan
Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources:
•
•
•
•
•
•
•
•
•
Activity-Based Statistics (ABS), Schearffer, Gnanadesikan, Watkins, Witmer, 1996
Exploring Statistics with the TI-83 (ES w/83), Burrill, Hopfensperger, Koehler, 2001
The Practice of Statistics (YMM), Daniel Yates, David Moore, George McCabe, 1999
Statistics: Decisions Through Data(DTD), David S. Moore, 1993
The Cartoon Guide to Statistics, Gonick, Smith, 1993
How to Lie with Statistics, Darrell Huff, 1954
Activities and Projects for High School Statistics Courses, Millard, Turner, 2004
Workshop Statistics (WS), Allan Rossman, J. Barr Von Oehsen, 1997
Amsco: AP Statistics, James Bohan with Beth Chance, 2000
7
SOUTHERN REGIONAL SCHOOL DISTRICT
Unit Overview
Content Area: Mathematics
Unit Title: Anticipating Patterns: Producing Models Using Probability & Simulations
Target Course/Grade Level: Statistics Advanced Placement / 10, 11, 12
Unit Summary:
Probability is the tool used for anticipating what the distribution of data should look like under a given model.
Primary interdisciplinary connections:
Infused within the unit are connections to the Common Core Standards in Mathematics and Language Arts
Literacy and the NJCCCS in Technology.
21st Century Themes:
The unit will integrate the 21st Century Life and Career stand 9.1 strands A-D. These strands include: Critical
thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership, and cross
cultural understanding and interpersonal communication.
Technology connections:
For further clarification refer to NJ Core Curriculum Content Standards at: http://www.state.nj.us/education/cccs/
Common Core Standards
Understand independence and conditional probability and use them to interpret data
S-CP.1. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or
categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
S-CP.2. Understand that two events A and B are independent if the probability of A and B occurring
together is the product of their probabilities, and uses this characterization to determine if they are independent.
S-CP.3. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret
independence of A and B as saying that the conditional probability of A given B is the same as the probability of A,
and the conditional probability of B given A is the same as the probability of B.
S-CP.4. Construct and interpret two-way frequency tables of data when two categories are associated with
each object being classified. Use the two-way table as a sample space to decide if events are independent and to
approximate conditional probabilities. For example, collect data from a random sample of students in your school
on their favorite subject among math, science, and English. Estimate the probability that a randomly selected
student from your school will favor science given that the student is in tenth grade. Do the same for other subjects
and compare the results.
S-CP.5. Recognize and explain the concepts of conditional probability and independence in everyday
language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker
with the chance of being a smoker if you have lung cancer.
Use the rules of probability to compute probabilities of compound events in a uniform probability model
S-CP.6. Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A,
and interpret the answer in terms of the model.
S-CP.7. Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in
terms of the model.
S-CP.8. (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) =
P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
S-CP.9. (+) Use permutations and combinations to compute probabilities of compound events and solve
problems.
8
Unit Essential Questions
• How is probability used to simulate events and
to predict future happenings?
• How is probability used to anticipate what a
distribution should look like?
• What are the benefits of simulating events
opposed to gathering real data?
Unit Enduring Understandings
Students will understand that…
• Patterns only appear in the long run.
• Probability is used in many real life situations
including games of chance.
• Simulations help predict how an event will play out in
the future.
• Experimental and theoretical probabilities are not the
same.
Unit Objectives
Students will know…
•
Probability as relative frequency
o Law of Large Numbers” concept
o Complement, addition and multiplication
rules, conditional probabilities,
independence
o Discrete random variables and their
probability distributions
o Geometric and Binomial Probability
Distributions
o Simulation of probability distributions
including binomial and geometric
o Mean and standard deviation of a random
variable
•
Combining independent random variables
o Independence vs. dependence
o Mean and standard deviation for sums and
differences of independent random variables
•
Normal distribution
o Properties of the normal distribution
o Using table of the normal distribution
o The normal distribution as a model for
measurements
•
Simulating sampling distributions: sample
proportion and sample mean (10 days)
o Central Limit Theorem
o Sampling distribution of a difference
between two independent sample
proportions and two independent sample
means.
Unit Objectives
Students will be able to…
• Calculate probability using the complement, addition
and multiplication rules.
• Construct a tree diagram and a Venn diagram
• Calculate conditional probability.
• Using geometric areas to find probabilities of events
• Differentiate between discrete and continuous random
variables.
• Calculate the mean and variance of a random variable.
• Use the rules for the sum and difference of random
variable.
• Find the probabilities of events using the standard
normal distribution curve.
• Use the “Law of Large Numbers” and simulation
methods to approximate the mean of a distribution.
• Identify a random variable as binomial or geometric
and determine its probabilities using the TI-83 and the
formula.
• Construct probability distribution tables and histograms
for binomial and geometric.
• Construct cumulative probability distribution tables
and histograms for binomial and geometric.
• Calculate means and standard deviations of binomial
and geometric random variables.
• Identify the properties of the normal distribution.
• Recognize the fact of sampling variability.
• Interpret a sampling distribution vs. a sampling
proportion vs. a sampling mean.
• Describe the bias and variability of a statistic with the
mean and standard deviation of its sampling
distribution or its sample proportion or its sample
mean.
• Apply the Central Limit Theorem.
• Use normal approximations to calculate sample
proportion or sample mean probabilities.
9
SOUTHERN REGIONAL SCHOOL DISTRICT
Evidence of Learning
Formative Assessments
For additional ideas please refer to NJ State DOE classroom application documents:
http://www.state.nj.us/education/cccs/
•
•
•
•
•
Observation
Homework
Class participation
Do Now
Notebook
Summative Assessments
For additional ideas please refer to:
http://www.state.nj.us/education/cccs/
http://www.parcconline.org/assessment-blueprints-test-specs
http://www.parcconline.org/samples/mathematics/high-school-mathematics
•
•
•
•
•
•
Chapter/Unit Test
Quizzes
Presentations
Unit Projects
Quarterlies and Final Exam
PARCC PBA and EOY Assessments
Modifications (ELLs, Special Education, Gifted and Talented)
•
•
•
•
•
•
•
Teacher tutoring
Peer tutoring
Cooperative learning groups
Modified assignments
Differentiated instruction
Native language texts and native language to English dictionary
Follow all IEP modifications/504 plan
Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources:
•
•
•
•
•
•
•
•
•
Activity-Based Statistics (ABS), Schearffer, Gnanadesikan, Watkins, Witmer, 1996
Exploring Statistics with the TI-83 (ES w/83), Burrill, Hopfensperger, Koehler, 2001
The Practice of Statistics (YMM), Daniel Yates, David Moore, George McCabe, 1999
Statistics: Decisions Through Data(DTD), David S. Moore, 1993
The Cartoon Guide to Statistics, Gonick, Smith, 1993
How to Lie with Statistics, Darrell Huff, 1954
Activities and Projects for High School Statistics Courses, Millard, Turner, 2004
Workshop Statistics (WS), Allan Rossman, J. Barr Von Oehsen, 1997
Amsco: AP Statistics, James Bohan with Beth Chance, 2000
10
SOUTHERN REGIONAL SCHOOL DISTRICT
Unit Overview
Content Area: Mathematics
Unit Title: Statistical Inference: Confirming Models
Target Course/Grade Level: Statistics Advanced Placement / 10, 11, 12
Unit Summary:
Statistical inference guides the selection of appropriate models, draws conclusions about a population based on a
sample and analyzes how certain you are in those conclusions.
Primary interdisciplinary connections:
Infused within the unit are connections to the Common Core Standards in Mathematics and Language Arts
Literacy and the NJCCCS in Technology.
21st Century Themes:
The unit will integrate the 21st Century Life and Career stand 9.1 strands A-D. These strands include: Critical
thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership, and cross
cultural understanding and interpersonal communication.
Technology connections:
For further clarification refer to NJ Core Curriculum Content Standards at: http://www.state.nj.us/education/cccs/
Common Core Standards
Understand and evaluate random processes underlying statistical experiments
S-IC.1. Understand statistics as a process for making inferences about population parameters based on a
random sample from that population.
S-IC.2. Decide if a specified model is consistent with results from a given data-generating process, e.g.,
using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of
5 tails in a row cause you to question the model?
Make inferences and justify conclusions from sample surveys, experiments, and observational studies
S-IC.3. Recognize the purposes of and differences among sample surveys, experiments, and observational
studies; explain how randomization relates to each.
S-IC.4. Use data from a sample survey to estimate a population mean or proportion; develop a margin of
error through the use of simulation models for random sampling.
S-IC.5. Use data from a randomized experiment to compare two treatments; use simulations to decide if
differences between parameters are significant.
S-IC.6. Evaluate reports based on data.
11
Unit Essential Questions
• How much evidence do you need to gather
before you are able to make a reasonable
conjecture?
• Is it reasonable to think that different people
require different amounts of convincing?
• How is statistical inference used to draw
conclusions from data?
• How is probability used to express the strength
of our conclusions?
• How are confidence intervals and significance
tests used in scientific experiments?
Unit Enduring Understandings
Students will understand that…
• Inference leads to many real life decisions involving
medical experiments, quality control, etc.
• Estimation should be given as a confidence interval and
not as a single number.
• Bias and how a sample is gather or an experiment run
is very important when performing a significance test
or creating a confidence interval.
Unit Objectives
Students will know…
• Confidence Intervals:
o Large sample confidence intervals for a
proportion and for a difference of two
proportions.
o Large sample confidence intervals for a
mean and for a difference of two means
(unpaired and paired).
• Tests of significance: null and alternative
hypotheses, p-values, one- and two-sided tests
o Large sample test for proportion and for a
difference of two proportions.
o Large sample test for a mean and for a
difference of two means (unpaired and
paired)
o Chi-square test for goodness of fit,
homogeneity of proportions and
independence.
o Type I Error, Type II Error and Power of a
Significance Test
• Normally distributed data
o t-distribution
o Single sample t procedures.
o Two sample (independent and matched
pairs) t procedures
o Inference for slope of least squares line.
Unit Objectives
Students will be able to…
• Explain in non-technical language the meaning of
statements of confidence in statistical reports
• Calculate confidence intervals
• Find the sample size required to obtain a confidence
interval with a specified margin of error
• State null and alternative hypotheses in a testing
situation
• Explain in non-technical language the meaning of the
P-value
• Calculate the z statistic and the P-value for one- and
two-sided tests
• Recognize when a problem requires inference about a
mean or comparing two means
• Recognize from the design of a study when onesample, matched pairs or two-sample procedures are
needed
• Carry out a t test for the hypothesis of a population
mean for one- and two-samples
• Perform confidence intervals and tests of significance
on matched pairs data
• Recognize when a problem requires inference about a
proportion or comparing two proportions
• Use a z procedure to give a confidence interval and
significance test for a population proportion either onesample or two-sample
• Calculate and analyzing Type I, Type II and Error of
significance test.
• Calculate expected courts for each category in a
distribution, the chi-squared statistic and the P-value
stating null and alternative hypotheses in for a
difference between two distributions
• Interpret Chi-square tests for independence
• Calculate the confidence interval about a regression
slope and perform a linear regression t-distribution
significance test on the slope of a regression line.
12
•
•
•
13
Use the TI-83/84 for confidence intervals and
significance tests.
Analyze computer output for intervals and tests.
State the correct conditions (assumptions) to carry out a
test or interval.
SOUTHERN REGIONAL SCHOOL DISTRICT
Evidence of Learning
Formative Assessments
For additional ideas please refer to NJ State DOE classroom application documents:
http://www.state.nj.us/education/cccs/
•
•
•
•
•
Observation
Homework
Class participation
Do Now
Notebook
Summative Assessments
For additional ideas please refer to:
http://www.state.nj.us/education/cccs/
http://www.parcconline.org/assessment-blueprints-test-specs
http://www.parcconline.org/samples/mathematics/high-school-mathematics
•
•
•
•
•
•
Chapter/Unit Test
Quizzes
Presentations
Unit Projects
Quarterlies and Final Exam
PARCC PBA and EOY Assessments
Modifications (ELLs, Special Education, Gifted and Talented)
•
•
•
•
•
•
•
Teacher tutoring
Peer tutoring
Cooperative learning groups
Modified assignments
Differentiated instruction
Native language texts and native language to English dictionary
Follow all IEP modifications/504 plan
Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources:
•
•
•
•
•
•
•
•
•
Activity-Based Statistics (ABS), Schearffer, Gnanadesikan, Watkins, Witmer, 1996
Exploring Statistics with the TI-83 (ES w/83), Burrill, Hopfensperger, Koehler, 2001
The Practice of Statistics (YMM), Daniel Yates, David Moore, George McCabe, 1999
Statistics: Decisions Through Data(DTD), David S. Moore, 1993
The Cartoon Guide to Statistics, Gonick, Smith, 1993
How to Lie with Statistics, Darrell Huff, 1954
Activities and Projects for High School Statistics Courses, Millard, Turner, 2004
Workshop Statistics (WS), Allan Rossman, J. Barr Von Oehsen, 1997
Amsco: AP Statistics, James Bohan with Beth Chance, 2000
14
SOUTHERN REGIONAL SCHOOL DISTRICT
Unit Overview
Content Area: Mathematics
Unit Title: Test Review for AP Examination
Target Course/Grade Level: Statistics Advanced Placement / 10, 11, 12
Unit Summary:
Students may receive college credit for a 3 or better on the AP examination. Being prepared for the test is
essential to success. Students must know the format of the test and what types of questions they might encounter.
Primary interdisciplinary connections:
Infused within the unit are connections to the Common Core Standards in Mathematics and Language Arts
Literacy and the NJCCCS in Technology.
21st Century Themes:
The unit will integrate the 21st Century Life and Career stand 9.1 strands A-D. These strands include: Critical
thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership, and cross
cultural understanding and interpersonal communication.
Technology connections:
For further clarification refer to NJ Core Curriculum Content Standards at: http://www.state.nj.us/education/cccs/
Common Core Standards
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
15
Unit Essential Questions
• What is the best way to prepare for the AP
examination?
• Why is review so important?
• How well must I communicate my ideas to
score well on the exam?
Unit Enduring Understandings
Students will understand that…
• The AP Test is comprised of forty multiple choice
questions and six free response questions.
• They must show their reasoning on the free response
questions.
Unit Objectives
Students will know…
• See all previous units.
Unit Objectives
Students will be able to…
• Evaluate when and when not to use the calculator.
• Know when to “guess” on multiple-choice questions.
• Recognize extraneous information in a question.
• Communicate your statistical knowledge on the freeresponse questions.
• Check assumptions.
• Clearly identify variables when using a formula,
writing it down then substituting.
• Identify which tests to use in what parts of the problem.
• Realize there might not be one correct answer.
• Know how to score a free response answer using an
official AP rubric.
16
SOUTHERN REGIONAL SCHOOL DISTRICT
Evidence of Learning
Formative Assessments
For additional ideas please refer to NJ State DOE classroom application documents:
http://www.state.nj.us/education/cccs/
•
•
•
•
•
Observation
Homework
Class participation
Do Now
Notebook
Summative Assessments
For additional ideas please refer to:
http://www.state.nj.us/education/cccs/
http://www.parcconline.org/assessment-blueprints-test-specs
http://www.parcconline.org/samples/mathematics/high-school-mathematics
•
•
•
•
•
•
Chapter/Unit Test
Quizzes
Presentations
Unit Projects
Quarterlies and Final Exam
PARCC PBA and EOY Assessments
Modifications (ELLs, Special Education, Gifted and Talented)
•
•
•
•
•
•
•
Teacher tutoring
Peer tutoring
Cooperative learning groups
Modified assignments
Differentiated instruction
Native language texts and native language to English dictionary
Follow all IEP modifications/504 plan
Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources:
•
•
•
•
•
•
•
•
•
Activity-Based Statistics (ABS), Schearffer, Gnanadesikan, Watkins, Witmer, 1996
Exploring Statistics with the TI-83 (ES w/83), Burrill, Hopfensperger, Koehler, 2001
The Practice of Statistics (YMM), Daniel Yates, David Moore, George McCabe, 1999
Statistics: Decisions Through Data(DTD), David S. Moore, 1993
The Cartoon Guide to Statistics, Gonick, Smith, 1993
How to Lie with Statistics, Darrell Huff, 1954
Activities and Projects for High School Statistics Courses, Millard, Turner, 2004
Workshop Statistics (WS), Allan Rossman, J. Barr Von Oehsen, 1997
Amsco: AP Statistics, James Bohan with Beth Chance, 2000
17
SOUTHERN REGIONAL SCHOOL DISTRICT
Unit Overview
Content Area: Mathematics
Unit Title: Real Life Statistics in Action
Target Course/Grade Level: Statistics Advanced Placement / 10, 11, 12
Unit Summary:
Students have to know how to put all the skills they have learned throughout the year together to see the value of
statistics in everyday decisions. Their final product will be a true comprehensive product that will show them the
importance of their year of study.
Primary interdisciplinary connections:
Infused within the unit are connections to the Common Core Standards in Mathematics and Language Arts
Literacy and the NJCCCS in Technology.
21st Century Themes:
The unit will integrate the 21st Century Life and Career stand 9.1 strands A-D. These strands include: Critical
thinking and problem solving, creativity and innovation, collaboration, teamwork and leadership, and cross
cultural understanding and interpersonal communication.
Technology connections:
For further clarification refer to NJ Core Curriculum Content Standards at: http://www.state.nj.us/education/cccs/
Common Core Standards
Make inferences and justify conclusions from sample surveys, experiments, and observational studies
S-IC.3. Recognize the purposes of and differences among sample surveys, experiments, and
observational studies; explain how randomization relates to each.
S-IC.4. Use data from a sample survey to estimate a population mean or proportion; develop a margin of
error through the use of simulation models for random sampling.
S-IC.5. Use data from a randomized experiment to compare two treatments; use simulations to decide if
differences between parameters are significant.
S-IC.6. Evaluate reports based on data.
18
Unit Essential Questions
• How do statistics affect everyday decisions in
our world?
Unit Enduring Understandings
Students will understand that…
• Statistics have every day practical uses and to be
statistically literate is valuable in their future
endeavors.
Unit Objectives
Students will know…
• See all previous units
Unit Objectives
Students will be able to…
• Use all skills from previous units in a comprehensive
manner.
• Organize an experiment to collect data from fellow
students on personal taste preferences.
• Analyze the results of experiment using a significance
test and confidence interval.
• Write a conclusion on findings and difficulties with
experiment.
• Create a multimedia presentation to present findings.
• Work cooperatively with group members.
19
SOUTHERN REGIONAL SCHOOL DISTRICT
Evidence of Learning
Formative Assessments
For additional ideas please refer to NJ State DOE classroom application documents:
http://www.state.nj.us/education/cccs/
•
•
•
•
•
Observation
Homework
Class participation
Do Now
Notebook
Summative Assessments
For additional ideas please refer to:
http://www.state.nj.us/education/cccs/
http://www.parcconline.org/assessment-blueprints-test-specs
http://www.parcconline.org/samples/mathematics/high-school-mathematics
•
•
•
•
•
•
Chapter/Unit Test
Quizzes
Presentations
Unit Projects
Quarterlies and Final Exam
PARCC PBA and EOY Assessments
Modifications (ELLs, Special Education, Gifted and Talented)
•
•
•
•
•
•
•
Teacher tutoring
Peer tutoring
Cooperative learning groups
Modified assignments
Differentiated instruction
Native language texts and native language to English dictionary
Follow all IEP modifications/504 plan
Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources:
•
•
•
•
•
•
•
•
•
Activity-Based Statistics (ABS), Schearffer, Gnanadesikan, Watkins, Witmer, 1996
Exploring Statistics with the TI-83 (ES w/83), Burrill, Hopfensperger, Koehler, 2001
The Practice of Statistics (YMM), Daniel Yates, David Moore, George McCabe, 1999
Statistics: Decisions Through Data(DTD), David S. Moore, 1993
The Cartoon Guide to Statistics, Gonick, Smith, 1993
How to Lie with Statistics, Darrell Huff, 1954
Activities and Projects for High School Statistics Courses, Millard, Turner, 2004
Workshop Statistics (WS), Allan Rossman, J. Barr Von Oehsen, 1997
Amsco: AP Statistics, James Bohan with Beth Chance, 2000
20