Download Unit plan - Chengage

Curriculum Map for:
Time
Frame /
Content
40
days
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3-4
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MRS21/22 M4
Essential Question(s)
and
ENGAGENY Link
Final Draft
Skills
Module 4: Probability and Statistics
Common Core Standards
Sample Lesson Link,
Projects and Assessments
Topic A:Probability
Lesson 1: Chance
Experiments, Sample
Spaces, and Events
[Experimental
probability, sample
space, And/Or/Not]
Objectives: Students determine the sample
space for a chance experiment. Given a
description of a chance experiment and an event,
students identify the subset of outcomes from the
sample space corresponding to the complement of
an event. Given a description of a chance
experiment and two events, students identify the
subset of outcomes from the sample space
corresponding to the union or intersection of two
events. Students calculate the probability of
events defined in terms of unions, intersections
and complements for a simple chance experiment
with equally likely outcomes.
Lesson 2: Calculating
Probabilities of Events
Using Two-Way Tables
Objectives: Students calculate probabilities
given a two-way table of data. Students construct
a “hypothetical 1000” two-way table given
probability information. Students interpret
probabilities in context.
Lessons 3–4: Calculating
Objectives: Students construct a hypothetical
1,000 two-way table from given probability
information and use the table to calculate the
probabilities of events. Students calculate
conditional probabilities given a two-way data
table or using a hypothetical 1,000 two-way table.
Students interpret probabilities, including
conditional probabilities, in context.
Conditional Probabilities
and Evaluating
Independence Using
Two-Way Frequency
Tables
Students use a hypothetical 1,000 two-way table
to calculate probabilities of events. Students
S-IC.A.2, S-CP.A.1, S-CP.A.2, S-CP.A.3, SCP.A.4, S-CP.A.5, S-CP.B.6, S-CP.B.7
Sample Lessons
Module 4
Differentiation/ Resources/
Strategies
All Modules
Assessments Link
Regents
Mixed Reviews
calculate conditional probabilities given a twoway data table or using a hypothetical 1,000 twoway table. Students use two-way tables (data
tables or hypothetical 1,000 two-way tables) to
determine if two events are independent. Students
interpret probabilities, including conditional
probabilities, in context.
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5
5
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5
Lesson 5: Events and
Venn Diagrams
[Repeating earlier
ideas but solving with
Venn Diagrams]
Objectives: Students represent events by
shading appropriate regions in a Venn diagram.
Given a chance experiment with equally likely
outcomes, students calculate counts and
probabilities by adding/subtracting given counts
or probabilities. Students interpret probabilities in
context.
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6-7
6-7
6-7
6-7
Lessons 6–7:
Probability Rules
[Repeating earlier
ideas with formalized
rules]
Objectives: Students use the complement rule to
calculate the probability of the complement of an
event and the multiplication rule for independent
events to calculate the probability of the
intersection of two independent events. Students
recognize that two event A and B are independent
if and only if P(A and B) = P(A)P(B) and interpret
independence of two events A and B as meaning
that the conditional probability of A given B is
equal to P(A). Students use the formula for
conditional probability to calculate conditional
probabilities and interpret probabilities in context.
Students use the addition rule to calculate the
probability of a union of two events. Students
interpret probabilities in context.
Topic B: Modeling Data
Distributions.
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8
8
8
8
8
Lesson 8: Distributions
– Center, Shape, and
Spread [Mean,
Standard Deviation,
and Symmetric vs.
Skewed]
S-ID.A.4
Sample Lessons Module 4
All Modules
Assessments Link
fhhs_1
fhhs_2
fhhs_3
fhhs_4
S-IC.A.1, S-IC.B.3, S-IC.B.4, S-IC.B.6
fhhs_5
fhhs_6
Regents
Mixed Reviews
Objectives: Students describe data distributions
in terms of shape, center and variability. Students
use the mean and standard deviation to describe
center and variability for a data distribution that is
approximately symmetric.
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9
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9
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Lesson 9: Using a Curve
to Model a Data
Distribution [Normal
curve; using calculator
for Mean and Std.
Dev.]
Objectives: Students draw a smooth curve that
could be used as a model for a given data
distribution. Students recognize when it is
reasonable and when it is not reasonable to use a
normal curve as a model for a given data
distribution.
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10-11
10-11
10-11
Lessons 10–11: Normal
Distributions [Finding
z-scores and solving
problems]
Objectives: Students calculate z scores. Students
use technology and tables to estimate the area
under a normal curve. Students interpret
probabilities in context. Students use tables and
technology to estimate the area under a normal
curve. Students interpret probabilities in context.
When appropriate, students select an appropriate
normal distribution to serve as a model for a given
data distribution.
Topic C: Drawing
Conclusions Using Data
from a Sample.
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Lesson 12: Types of
Statistical Studies
[Designing a good
study/survey]
Lesson 13: Using
Sample Data to
Estimate a Population
Characteristic
[Population vs.
Sample]
Sample Lessons Module 4
All Modules
Assessments Link
fhhs_7
fhhs_8
Objectives: Students distinguish between
observational studies, surveys and experiments.
Students explain why random selection is an
important consideration in observational studies
and surveys, and why random assignment is an
important consideration in experiments. Students
recognize when it is reasonable to generalize the
results of an observational study or survey to
some larger population, and when it is reasonable
to reach a cause-and-effect conclusion about the
relationship between two variables.
Objectives: Students differentiate between a
population and a sample. Students differentiate
between a population characteristic and a sample
statistic. Students recognize statistical questions
that are answered by estimating a population
mean or population proportion.
fhhs_9
S-IC.B.3, S-IC.B.5, S-IC.B.6
fhhs_10
Regents
Mixed Reviews
14-15
14-15
14-15
14-15
16-17
16-17
16-17
16-17
16-17
18-19
18-19
18-19
18-19
Lessons 14–15:
Sampling Variability in
the Sample Proportion
Lessons 16–17: Margin
of Error when
Estimating a
Population Proportion
Lessons 18–19:
Sampling Variability in
the Sample Mean
Objectives: Students understand the term
“sampling variability” in the context of estimating
a population proportion. Students understand that
the standard deviation of the sampling distribution
of the sample proportion offers insight into the
accuracy of the sample proportion as an estimate
of the population proportion. Students understand
the term “sampling variability” in the context of
estimating a population proportion. Students
understand that the standard deviation of the
sampling distribution of the sample proportion
offers insight into the accuracy of the sample
proportion as an estimate of the population
proportion.
Objectives: Students use data from a random
sample to estimate a population proportion.
Students calculate and interpret margin of error in
context. Students know the relationship between
sample size and margin of error in the context of
estimating a population proportion. Students use
data from a random sample to estimate a
population proportion. Students calculate and
interpret margin of error in context. Students
know the relationship between sample size and
margin of error in the context of estimating a
population proportion.
Objectives: Students understand the term
“sampling variability” in the context of estimating
a population mean. Students understand that the
standard deviation of the sampling distribution of
the sample mean offers insight into the accuracy
of the sample mean as an estimate of the
population mean. Students understand the term
“sampling variability” in the context of estimating
a population mean. Students understand that the
standard deviation of the sampling distribution of
the sample mean conveys information about the
anticipated accuracy of the sample mean as an
estimate of the population mean.
Sample Lessons Module 4
All Modules
Assessments Link
fhhs_11
fhhs_12
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fhhs_14
Regents
Mixed Reviews
20-21
20-21
20-21
20-21
22
22
22
Lessons 20–21: Margin
of Error when
Estimating a
Population Mean
Lesson 22: Evaluating
Reports Based on Data
from a Sample
Objectives: Students use data from a random
sample to estimate a population mean. Students
calculate and interpret margin of error in context.
Students know the relationship between sample
size and margin of error in the context of
estimating a population mean. Students use data
from a random sample to estimate a population
mean. Students calculate and interpret margin of
error in context. Students know the relationship
between sample size and margin of error in the
context of estimating a population mean.
Objectives: Students interpret margin of error
from reports that appear in newspapers and other
media. Students critique and evaluate statements
in published reports that involve estimating a
population proportion or a population mean.
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Lesson 24: Differences
Due to Random
Assignment Alone
All Modules
Assessments Link
fhhs_15
fhhs_16
Topic D: Drawing
Conclusions Using Data
from an Experiment
Lesson 23:
Experiments and the
Role of Random
Assignment
Sample Lessons Module 4
fhhs_17
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Objectives: Given a description of a statistical
experiment, students identify the response
variable and the treatments.Students recognize the
different purposes of random selection and of
random assignment. Students recognize the
importance of random assignment in statistical
experiments.
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Objectives: Students understand that when one
group is randomly divided into two groups, the
two groups’ means will differ just by chance (a
consequence of the random division).
Students understand that when one group is
randomly divided into two groups, the distribution
of the difference in the two groups’ means can be
described in terms of shape, center, and spread.
Regents
Mixed Reviews
25-27
25-27
25-27
25-27
25-27
Lessons 25–27: Ruling
Out Chance
Objectives: Given data from a statistical
experiment with two treatments, students create a
randomization distribution. Students use a
randomization distribution to determine if there is
a significant difference between two treatments.
Given data from a statistical experiment with two
treatments, students create a randomization
distribution. Students use a randomization
distribution to determine if there is a significant
difference between two treatments. Given data
from a statistical experiment with two treatments,
students create a randomization distribution.
Students use a randomization distribution to
determine if there is a significant difference
between two treatments.
Sample Lessons Module 4
All Modules
Assessments Link
fhhs_21
28-29
28-29
28-29
28-29
28-29
Lessons 28–29:
Drawing a Conclusion
from an Experiment
Objectives: Students carry out a statistical
experiment to compare two treatments. Given
data from a statistical experiment with two
treatments, students create a randomization
distribution. Students use a randomization
distribution to determine if there is a significant
difference between two treatments.
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30
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Lesson 30: Evaluating
Reports Based on Data
from an Experiment
Objectives: Students critique and evaluate
statements in published reports that involve
determining if there is a significant difference
between two treatments in a statistical
experiment.
Regents
Mixed Reviews