Download S-ID.2. Use statistics appropriate to the shape of the data distribution

1
MATH CURRICULUM MAP
Park East High School
Instructor: Brady
Course: Statistics I
Unit
(Number
of Days)
Central
tendency
with outliers
and variables
(11)
Knowledge/Content
Central tendency with outliers:
baseball salaries
The effect of outliers on a graph,
shape of a graph, mean and median
Accuracy of measure of central
tendency when there are outliers
Applications: baseball salaries,
income by education level,
colleges, and politicians
Modality
Nominal and quantitative variables
Relationships between variables:
independent and dependent,
correlational, no relationship
Scales
Teach study skill: consolidating
notes
Assessments
Transferrable Skills
Homework:
central tendency
letter
Study skills
Homework:
voter registration
Recall factual
information
Homework:
consolidate unit
1 notes
Homework:
unit 1 review
problem set
Exam: central
tendency with
outliers and
variables
(matching
column, multiple
choice,
calculations and
short answer)
Self-reflection
Big Ideas
Averages reported by
colleges, politicians,
and other
organizations should
be looked at with a
critical eye.
Sometimes they
intentionally or
unintentionally report
biased averages due to
the presence of
outliers
Common Core Standards
STATISTICS AND PROBABILITY
Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a
single count or measurement variable
 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).
2
Unit
(Number of
Days)
Sampling
bias
(13)
Knowledge/Content
Assessments
Transferrable Skills
Big Ideas
Common Core Standards
Sample survey vs. census, sample
vs. population, parameter vs.
statistic
Homework:
article on
sampling bias
with questions
Study skills
Surveys and polls
(including election
polls) should be
viewed with a critical
eye. They sometimes
include bias or errors
due to sampling
methods, survey
methods, errors in
sampling, and/or poor
question wording.
STATISTICS AND PROBABILITY
Sampling methods: random,
voluntary response, convenience
The difference between race and
ethnicity
Errors in sampling: non-response,
undercoverage, response error,
processing errors
Survey methods: group
administration, mail, internet,
telephone, face-to-face, focus group
How question wording can lead to
sampling error
Homework:
Dewey defeats
Truman article
with questions
Homework:
consolidate unit
2 notes
Homework:
unit 2 review
problem set
The impact of question wording on
poll results
Project:
census letter
Identifying the problems with
question wording in real polls
Exam: sampling
bias (matching
column, multiple
choice,
calculations and
short answer)
Identifying biased sampling
methods and sampling errors
Teach study skill mnemonic
devices: association
Formulation and
justification of
hypotheses
Identify bias
Recall factual
information
Think critically
The difference
between race and
ethnicity explains why
Hispanic is not
considered a race.
Interpreting Categorical and Quantitative Data
Make inferences and justify conclusions from
sample surveys, experiments, and observational
studies
 S-IC.3. Recognize the purposes of 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.
Making Inferences and Justifying Conclusions
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.
MODELING
 Relating population statistics to individual
predictions.
3
Unit
(Number of
Days)
Variability
and
hypothesis
testing
(16)
Knowledge/Content
Assessments
Transferrable Skills
Big Ideas
Common Core Standards
Advantages/disadvantages of types
of variability (range and
variance/standard deviation)
Homework:
marking period 1
course reflection
Study skills
STATISTICS AND PROBABILITY
Homework:
calculating
standard
deviation
Multiple
methodologies
An ideal investment
in the stock market
would have a high
mean and a low
standard deviation.
Homework:
decision matrices
Analysis of data
Standard deviation application:
interpreting class test scores
Standard deviation application:
stock market
Calculating SS, variance, and
standard deviation
Writing research questions, H0, and
H1
Deciding whether to accept or reject
H0
Type I/II error and decision chart
Decision chart application to jury
trials and famous court cases
Evaluating which type of error is
worse in various real world contexts
Selecting a significance test
Teach study skill: elimination
quizzing in pairs
Homework:
consolidate unit
3 notes
Homework:
unit 3 review
problem set
Exam: variability
and hypothesis
testing (matching
column, multiple
choice,
calculations and
short answer)
Cooperative learning
Use of technology
Formulation and
justification of
hypotheses
Interpretation of
results and
development of
theories
Interpretation of
graphs
Perform multi-step
calculations
Recall factual
information
Think critically
An appropriate
standard for decision
making should be
used to balance the
possibility of Type I
and Type II errors. In
court cases, the
balance is between
convicting the
innocent or letting the
guilty go free. In
research, it’s between
concluding there is a
significant
relationship when
there actually is not
one and failing to
identify a significant
relationship that
actually does exist.
For example, it could
be between
distributing a false
cure and failing to
distribute a true cure,
or operating when a
patient does not need
it and failing to
operate when a
patient actually does
need it.
Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a
single count or measurement variable
 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.
MODELING
 Relating population statistics to individual
predictions.
4
Unit
(Number
of Days)
Correlation
(16)
Knowledge/Content
Assessments
Transferrable Skills
Big Ideas
Common Core Standards
Creating a scatter plot and
application activity
Homework:
read sample
research paper
and answer
questions
Use of technology (TI84 PLUS graphing
calculator)
Correlation does not
imply causation.
STATISTICS AND PROBABILITY
Homework:
select variables
and run prestudy
Formulation and
justification of
hypotheses
Identifying the strength and
direction of a correlation
Analysis of data
Testing the significance of r
Calculating r by hand using real
world data sets
Calculating r on the TI-84 PLUS
using real world data sets
Formulating a hypothesis and
reason
Homework:
consolidate unit
4 notes
Interpretation of
results and
development of
theories
Evaluating significance
Formulating an interpretation and
theory
Homework:
unit 4 review
problem set
Errors in interpreting r (correlation
does not imply causation,
curvilinear relationships, and
restricted range)
Project:
formal study
group
Exam #4:
correlation
(matching
column, multiple
choice,
calculations and
short answer)
Oral expression of and
defense of ideas
Conduct original
research
Distinguish between
correlation and
causation
Identify bias
Perform multi-step
calculations
Recall factual
information
Think critically
Questions about the
relationship between
two quantitative
variables can be
answered via a survey
and correlation
analysis.
Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on two
categorical and quantitative variables
 S-ID.6. Represent data on two quantitative
variables on a scatter plot, and describe how the
variables are related
Interpret linear models
 S-ID.8. Compute (using technology) and
interpret the correlation coefficient of a linear
fit.
 S-ID.9. Distinguish between correlation and
causation.
Make inferences and justify conclusions from
sample surveys, experiments, and observational
studies
 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.6. Evaluate reports based on data.
Making Inferences and Justifying Conclusions
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.
MODELING
 Relating population statistics to individual
predictions.
5
Unit
(Number of
Days)
Correlation
Research
(20)
Knowledge/Content
Assessments
Transferrable Skills
Big Ideas
Common Core Standards
Problems with survey questions
Homework:
weekly checkpoints on
research project
progress
Study skills
STATISTICS AND PROBABILITY
Project:
correlation
research
Identify bias
Questions about the
relationship between
two quantitative
variables can be
answered via a survey
and correlation
analysis.
Workshop survey questions /
research design
Choose two quantitative variables
Create survey
Title page
Table of contents
Peer edit
Revision
Time management
Introduction
Think critically
Administer survey
Use of technology (TI84 PLUS graphing
calculator and
Microsoft Excel)
Data analysis
Create scatter plot in Excel
Results
Method
Discussion
Abstract
Peer edit
Presentation planning guide
Presentations
Analysis of data
Methodology for
conducting and
formally writing up
research.
Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on two
categorical and quantitative variables
 S-ID.6. Represent data on two quantitative
variables on a scatter plot, and describe how the
variables are related
Interpret linear models
 S-ID.8. Compute (using technology) and
interpret the correlation coefficient of a linear
fit.
 S-ID.9. Distinguish between correlation and
causation.
Make inferences and justify conclusions from
sample surveys, experiments, and observational
studies
 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.
Making Inferences and Justifying Conclusions
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.
MODELING
 Relating population statistics to individual
predictions.
6
Unit
Knowledge/Content
Assessments
Transferrable Skills
Big Ideas
Common Core Standards
(Number
of Days)
Final Exam
Review
CUNY placement test background
information
Homework:
consolidate
semester notes
Study skills
Study stills are
particularly important
tools for the recall
large quantities of
information on a
cumulative exam.
All of the above
(8)
Finals review
Homework:
semester review
with mnemonic
devices
Final Exam
(matching
column, multiple
choice,
calculations,
short answer and
self-reflection
essay)
Self-reflection
Recall factual
information
7
MATH CURRICULUM MAP
Park East High School
Instructor: Brady
Course: Statistics II
Unit
(Number
of Days)
Data ethics
(12)
Knowledge/Content
Assessments
Ethics: ethical/unethical, deception,
confederate, debriefing, costbenefit analysis
Homework:
Heinz dilemma
and MyersBriggs Typology
Indicator
IRB: minimal risk, costs/benefits
Stanford Prison experiment
Milgram obedience experiment
Informed consent: little Albert
experiment
Confidentiality, anonymity, and
privacy
Bystander effect
Placebo effect, clinical trials
(article: sham surgeries)
When are clinical trials unethical?:
Tuskegee syphilis study
Five ways a study can be unethical:
Kohlberg chart: interpretations of
responses to the Heinz dilemma
Homework:
Tuskegee
syphilis study
and design a
clinical trial
Homework:
consolidate unit
1 notes
Homework:
unit 1 review
problem set
Exam: data
ethics (matching
column, multiple
choice,
calculations and
short answer)
Transferrable Skills
Learn material
independently from a
textbook
Recall factual
information
Big Ideas
Decision making via
cost-benefit analysis
Apply ethics to
dilemmas
Common Core Standards
STATISTICS AND PROBABILITY
Interpreting Categorical and Quantitative Data
Make inferences and justify conclusions from
sample surveys, experiments, and observational
studies
 S-IC.6. Evaluate reports based on data.
8
Unit
(Number
of Days)
The normal
curve and
standard
scores
(10)
Knowledge/Content
The normal curve: curving tests
Calculations based on the normal
curve
Percentiles
Z scores given mean and standard
deviation
T scores given mean and standard
deviation
SAT scores given mean and SD
Converting raw scores to z, t, and
SAT scores
Assessments
Transferrable Skills
Homework:
curving policies
Recall factual
information
Homework:
the normal curve
and standard
scores
Represent data in
multiple ways
Homework:
resume
Compare individual
performance to group
performance
Analysis of data
Homework:
resume edits and
post high school
plans
Homework:
consolidate Unit
2 notes
Homework:
unit 2 review
problem set
Project:
tackle the
textbook
Exam #2: the
normal curve and
standard scores
(matching
column, multiple
choice,
calculations and
short answer)
Big Ideas
Curving is a
comparative form of
grading that can help
or hurt a score.
Common Core Standards
STATISTICS AND PROBABILITY
Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a
single count or measurement variable
 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.
9
Unit
Knowledge/Content
Assessments
Transferrable Skills
Big Ideas
Common Core Standards
(Number
of Days)
Chi square
and
reliability /
validity
Applying the normal curve to Park
East PSAT data
Homework:
chi square tables
Multiple
methodologies
STATISTICS AND PROBABILITY
Homework:
consolidate unit
3 notes
Use of technology (TI84 PLUS graphing
calculator)
Questions about the
relationship between
two nominal variables
can be answered via a
survey and a chi
square test.
Homework:
unit 3 review
problem set
Analysis of data
(15)
Chi square by hand with real world
data sets
Chi square 2x2 shortcut with real
world data sets
Chi square on the TI-84 plus with
real world data sets
Reliability and validity
Percent variance
Predictive validity
Project:
chi square:
gender vs. race
Exam: chi square
reliability /
validity
(matching
column, multiple
choice,
calculations and
short answer)
Formulation and
justification of
hypotheses
Interpretation of
results and
development of
theories
Identify bias
Perform multi-step
calculations
Read and interpret
journal articles
Recall factual
information
Think critically
The difference
between reliability and
validity.
Interpreting Categorical and Quantitative Data
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.
Make inferences and justify conclusions from
sample surveys, experiments, and observational
studies
 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.6. Evaluate reports based on data.
Making Inferences and Justifying Conclusions
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.
MODELING
 Relating population statistics to individual
predictions.
10
Unit
(Number
of Days)
t-test
(10)
Knowledge/Content
Assessments
Transferrable Skills
Big Ideas
Common Core Standards
Selecting a significance test and
writing H0
Homework:
selecting a
significance test
Multiple
methodologies
Questions about the
relationship between a
quantitative variable
and a nominal variable
with two levels can be
answered via a survey
and a t-test.
STATISTICS AND PROBABILITY
t test given n, mean, and s
Calculating t test with raw data by
hand
t-test with hypothesis, reason,
significance, interpretation and
theory
t test on the TI-84 PLUS with real
world data sets
t test activity in partners on the TI84 PLUS
Homework:
stereotype
brainstorm
Use of technology (TI84 PLUS graphing
calculator)
Analysis of data
Homework:
consolidate unit
4 notes
Homework:
unit 4 review
problem set
Exam: t-test
(matching
column, multiple
choice,
calculations and
short answer)
Formulation and
justification of
hypotheses
Interpretation of
results and
development of
theories
Identify bias
Perform multi-step
calculations
Recall factual
information
Think critically
Interpreting Categorical and Quantitative Data
Make inferences and justify conclusions from
sample surveys, experiments, and observational
studies
 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.6. Evaluate reports based on data.
Making Inferences and Justifying Conclusions
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.
MODELING
 Relating population statistics to individual
predictions.
11
Unit
(Number
of Days)
CUNY
Placement
Test
Review
(7)
Knowledge/Content
Assessments
Transferrable Skills
Big Ideas
Common Core Standards
How to choose a college math class
Homework:
CUNY
placement
diagnostic tests
Use of technology
(Microsoft Windows
calculator)
College classes in a
catalog can be
distinguished by
course number (a
lower number means
lower level) and
course description.
ALGEBRA
Arithmetic/pre-algebra
Algebra
Creating Equations
Create equations that describe numbers or
relationships.
 A-CED.1. Create equations and inequalities in
one variable and use them to solve problems.
Include equations arising from linear and
quadratic functions, and simple rational and
exponential functions.
Reasoning with Equations and Inequalities
Understand solving equations as a process of
reasoning and explain the reasoning.
 A-REI.2. Solve simple rational and radical
equations in one variable, and give examples
showing how extraneous solutions may arise.
Solve equations and inequalities in one variable.
 A-REI.3. Solve linear equations and inequalities
in one variable, including equations with
coefficients represented by letters.
Solve systems of equations.
 A-REI.6. Solve systems of linear equations
exactly and approximately (e.g., with graphs),
focusing on pairs of linear equations in two
variables.
Seeing Structure in Expressions
Write expressions in equivalent forms to solve
problems.
 A-SSE.3. Choose and produce an equivalent
form of an expression to reveal and explain
properties of the quantity represented by the
expression.
a. Factor a quadratic expression to reveal
the zeros of the function it defines.
12
Unit
Knowledge/Content
Assessments
Transferrable Skills
Big Ideas
Common Core Standards
(Number
of Days)
Chi square
research
Workshop survey questions /
research design
Homework:
weekly checkpoints on
research project
progress
Use of technology
(TI-84 PLUS
graphing calculator
and Microsoft Excel)
Questions about the
relationship between
two nominal variables
can be answered via a
survey and a chi
square test.
STATISTICS AND PROBABILITY
(19)
Choose 2 nominal variables
Create survey
Title page
Table of contents
Introduction
Analysis of data
Project:
chi square
stereotype
research
Formulation and
justification of
hypotheses
Administer survey
Data analysis
Write results
Method
Table
Discussion
Abstract
Interpretation of
results and
development of
theories
Oral expression and
defense of ideas
Conduct original
research
Presentation planning guide
Peer edit
Peer edit
Presentations
Revision
Methodology for
conducting and
formally writing up
research
Interpreting Categorical and Quantitative Data
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.
Make inferences and justify conclusions from
sample surveys, experiments, and observational
studies
 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.
Making Inferences and Justifying Conclusions
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.
Identify bias
Time management
Think critically
MODELING
 Relating population statistics to individual
predictions.
13
Unit
(Number
of Days)
Final Exam
Review
Knowledge/Content
Assessments
Transferrable Skills
Big Ideas
Common Core Standards
Finals review
Homework:
consolidate
semester notes
Self-reflection
Study stills are
particularly important
tools for the recall
large quantities of
information on a
cumulative exam.
All of the above
(6)
Homework:
semester review
with mnemonic
devices
Final exam
(matching
column, multiple
choice,
calculations,
short answer and
self-reflection
essay)
Recall factual
information