Download algebra ii - Sisseton School District

UNIT 4
ALGEBRA II
TEMPLATE CREATED BY
REGION 1 ESA
UNIT 4
Algebra II Math Tool Unit 4
Algebra II Unit 4 Overview: Inferences and Conclusions from Data
In this unit, students see how the visual displays and summary statistics they learned in earlier grades relate to different
types of data and to probability distributions. They identify different ways of collecting data—including sample surveys,
experiments, and simulations—and the role that randomness and careful design play in the conclusions that can be drawn.
Note:
It is important to note that the units (or critical areas) are intended to convey coherent groupings of content. The clusters and standards within units are ordered
as they are in the Common Core State Standards, and are not intended to convey an instructional order. Considerations regarding constraints, extensions, and
connections are found in the instructional notes. The instructional notes are a critical attribute of the courses and should not be overlooked. For example, one
will see that standards such as A.CED.1 and A.CED.2 are repeated in multiple courses, yet their emphases change from one course to the next. These changes are
seen only in the instructional notes, making the notes an indispensable component of the pathways.
(All instructional notes/suggestions will be found in italics throughout this document)
Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for
Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol
Template created by Region 1 ESA
Page 2 of 13
Algebra II Math Tool Unit 4
Unit 4: Inferences and Conclusions from Data- S.ID.4
Cluster: Summarize, represent, and interpret data on a single count or measurement variable.
Standard
Instructional Notes: While students may have heard of the normal

distribution, it is unlikely that they will have prior experience using it to
make specific estimates. Build on students’ understanding of data
distributions to help them see how the normal distribution uses area
to make estimates of frequencies (which can be expressed as
probabilities). Emphasize that only some data are well described by a
normal distribution.

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.
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Standards of Mathematical Practice (SMP’s)
#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.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets


I can use the mean and standard deviation
of a set of data to fit the data to a normal
curve.
I can use the 68-95-99.7 Rule to estimate
the percent of a normal population that
falls within 1, 2, or 3 standard deviations of
the mean.
I can recognize that normal distributions
are only appropriate for unimodal and
symmetrical shapes.
I can estimate the area under a normal
curve using a calculator, table, or
spreadsheet.
Essential Questions/ Enduring Understandings
How can I communicate the properties of
a data set to illuminate its important
features?
Statisticians summarize, represent, and
interpret categorical and quantitative data in
multiple ways since one method can reveal or
create a different impression than another.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Mean, standard deviation, data set, z-score, normal distribution, 68-95-99.7 Rule. Percent,
population, unimodal, symmetric, distribution shape, area, normal curve
Page 3 of 13
Algebra II Math Tool Unit 4
Unit 4: Inferences and Conclusions from Data- S.IC.1
Cluster: Understand and evaluate random processes underlying statistical experiments.
Standard
Instructional Notes: For S.IC.2, include comparing theoretical
and empirical results to evaluate the effectiveness of a
treatment.
S.IC.1 Understand statistics as a process for making inferences
about population parameters based on a random sample from
that population.
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




Standards of Mathematical Practice (SMP’s)
#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.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets



I can define population, population
parameter, random sample, and inference.
I can explain why randomization is used to
draw a sample that represents a population
well.
I can recognize that statistics involves
drawing conclusions about a population
based on the results obtained from a
random sample of the population.
Essential Questions/ Enduring Understandings
How can a population be described when
it is so large, it would be nearly impossible
to collect all of the data?
Statisticians design experiments based on
random samples and analyze the data to
estimate the important properties of a
population and make informed judgments.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Inference, population parameter, random sample, population, statistics
Page 4 of 13
Algebra II Math Tool Unit 4
Unit 4: Inferences and Conclusions from Data- S.IC.2
Cluster: Understand and evaluate random processes underlying statistical experiments.
Standard
Instructional Notes: For S.IC.2, include comparing theoretical
and empirical results to evaluate the effectiveness of a
treatment.
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?
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
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




Standards of Mathematical Practice (SMP’s)
#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.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets
I can choose a probability model for a
problem situation.
I can conduct a simulation of the model and
determine which results are typical of the
model and which results are considered
outliers (possible but unexpected).
I can decide if the data collected is
consistent with the selected model or if
another model is required.
I can pose a question that suggests a model
and a means of collecting data and answer
my question.
Essential Questions/ Enduring Understandings
How can a population be described when
it is so large, it would be nearly impossible
to collect all of the data?
Statisticians design experiments based on
random samples and analyze the data to
estimate the important properties of a
population and make informed judgments.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Theoretical probability, experimental probability, simulation, model, event
Page 5 of 13
Algebra II Math Tool Unit 4
Unit 4: Inferences and Conclusions from Data- S.IC.3
Cluster: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Standard
Instructional Notes: In earlier grades, students are introduced to
different ways of collecting data and use graphical displays and summary
statistics to make comparisons. These ideas are revisited with a focus on how
the way in which data is collected determines the scope and nature of the
conclusions that can be drawn from that data. The concept of statistical
significance is developed informally through simulation as meaning a result
that is unlikely to have occurred solely as a result of random selection in
sampling or random assignment in an experiment. For S.IC.4 and 5, focus on
the variability of results from experiments—that is, focus on statistics as a way
of dealing with, not eliminating, inherent randomness.
S.IC.3 Recognize the purposes of and differences among
sample surveys, experiments, and observational studies;
explain how randomization relates to each.
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




Standards of Mathematical Practice (SMP’s)
#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.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets





I can define sample survey, experiment,
observational study, and randomization.
I can describe the purpose of a sample
survey, an experiment, and an
observational study.
I can describe the differences among
sample surveys, experiments, and
observational studies.
I can explain the role of randomization in
sample surveys, experiments, and
observational studies.
I can apply random sampling techniques to
draw a sample from a population.
Essential Questions/ Enduring Understandings
How can a population be described when
it is so large, it would be nearly impossible
to collect all of the data?
Statisticians design experiments based on
random samples and analyze the data to
estimate the important properties of a
population and make informed judgments.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Sample survey, experiment, observational study, randomization
Page 6 of 13
Algebra II Math Tool Unit 4
Unit 4: Inferences and Conclusions from Data- S.IC.4
Cluster: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Standard
Instructional Notes: In earlier grades, students are introduced to
different ways of collecting data and use graphical displays and summary
statistics to make comparisons. These ideas are revisited with a focus on how
the way in which data is collected determines the scope and nature of the
conclusions that can be drawn from that data. The concept of statistical
significance is developed informally through simulation as meaning a result
that is unlikely to have occurred solely as a result of random selection in
sampling or random assignment in an experiment. For S.IC.4 and 5, focus on
the variability of results from experiments—that is, focus on statistics as a way
of dealing with, not eliminating, inherent randomness.
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.








Standards of Mathematical Practice (SMP’s)
#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.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets




I can define population mean, sample mean,
population proportion, and sample proportion.
I can calculate the sample mean or proportion.
I can defend the statement, “The population
mean or proportion is close to the sample mean
or proportion when the sample is randomly
selected and large enough to represent the
population well.”
I can infer that the population mean or
proportion is equal to the sample mean or
proportion and conduct a simulation to
determine which sample results are typical of
this model and which results are considered
possible outliers (possibly, but unexpected).
Essential Questions/ Enduring Understandings
How can a population be described when
it is so large, it would be nearly impossible
to collect all of the data?
Statisticians design experiments based on
random samples and analyze the data to
estimate the important properties of a
population and make informed judgments.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Population mean, sample mean, population proportion, sample proportion, sample survey,
margin of error, simulation model, random sampling, confidence interval
Page 7 of 13
Algebra II Math Tool Unit 4
Unit 4: Inferences and Conclusions from Data- S.IC.4 continued
Cluster: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Standard
Instructional Notes: In earlier grades, students are introduced to
different ways of collecting data and use graphical displays and summary
statistics to make comparisons. These ideas are revisited with a focus on how
the way in which data is collected determines the scope and nature of the
conclusions that can be drawn from that data. The concept of statistical
significance is developed informally through simulation as meaning a result
that is unlikely to have occurred solely as a result of random selection in
sampling or random assignment in an experiment. For S.IC.4 and 5, focus on
the variability of results from experiments—that is, focus on statistics as a way
of dealing with, not eliminating, inherent randomness.
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.








Standards of Mathematical Practice (SMP’s)
#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.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets

I can choose an appropriate margin of error
for the sample mean or proportion and
create a confidence interval based on the
results of the simulation conducted.
 I can determine how often the true
population mean or proportion is within
the margin of error of each sample mean or
proportion.
 I can pose a question regarding the mean or
proportion of a population, use statistical
techniques to estimate the parameter, and
design an appropriate product to
summarize the process and report the
estimate.
Essential Questions/ Enduring Understandings
Assessment
How can a population be described when
Assessments align to suggested learning targets.
it is so large, it would be nearly impossible
Directly
Somewhat
Not
to collect all of the data?
Aligned
Aligned
Aligned
Statisticians design experiments based on
random samples and analyze the data to
estimate the important properties of a
population and make informed judgments.
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Population mean, sample mean, population proportion, sample proportion, sample survey,
margin of error, simulation model, random sampling, confidence interval
Page 8 of 13
Algebra II Math Tool Unit 4
Unit 4: Inferences and Conclusions from Data- S.IC.5
Cluster: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Standard
Instructional Notes: In earlier grades, students are introduced to
different ways of collecting data and use graphical displays and summary
statistics to make comparisons. These ideas are revisited with a focus on how
the way in which data is collected determines the scope and nature of the
conclusions that can be drawn from that data. The concept of statistical
significance is developed informally through simulation as meaning a result
that is unlikely to have occurred solely as a result of random selection in
sampling or random assignment in an experiment. For S.IC.4 and 5, focus on
the variability of results from experiments—that is, focus on statistics as a way
of dealing with, not eliminating, inherent randomness.
S.IC.5 Use data from a randomized experiment to compare
two treatments; use simulations to decide if differences
between parameters are significant.








Standards of Mathematical Practice (SMP’s)
#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.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets




I can calculate the sample mean and
standard deviation of the two treatment
groups and the difference of the means.
I can conduct a simulation for each
treatment group using the sample results as
the parameters for the distribution.
I can calculate the difference of means for
each simulation and represent those
differences in a histogram.
I can use the results of the simulation to
create a confidence interval for the
difference of means.
Essential Questions/ Enduring Understandings
How can a population be described when
it is so large, it would be nearly impossible
to collect all of the data?
Statisticians design experiments based on
random samples and analyze the data to
estimate the important properties of a
population and make informed judgments.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Sample, mean, treatment, simulation, standard deviation, histogram, extreme, parameters,
significant
Page 9 of 13
Algebra II Math Tool Unit 4
Unit 4: Inferences and Conclusions from Data- S.IC.5 continued
Cluster: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Standard
Instructional Notes: In earlier grades, students are introduced to

different ways of collecting data and use graphical displays and summary
statistics to make comparisons. These ideas are revisited with a focus on how
the way in which data is collected determines the scope and nature of the
conclusions that can be drawn from that data. The concept of statistical
significance is developed informally through simulation as meaning a result
that is unlikely to have occurred solely as a result of random selection in
sampling or random assignment in an experiment. For S.IC.4 and 5, focus on
the variability of results from experiments—that is, focus on statistics as a way
of dealing with, not eliminating, inherent randomness.

S.IC.5 Use data from a randomized experiment to compare
two treatments; use simulations to decide if differences
between parameters are significant.








Standards of Mathematical Practice (SMP’s)
#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.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets
I can use the confidence interval to
determine if the parameters are
significantly different based on the original
difference of means.
I can pose a question regarding the means
or proportions of two populations, use
statistical techniques to estimate the
difference, and design an appropriate
product to summarize the process and
report the estimate.
Essential Questions/ Enduring Understandings
How can a population be described when
it is so large, it would be nearly impossible
to collect all of the data?
Statisticians design experiments based on
random samples and analyze the data to
estimate the important properties of a
population and make informed judgments.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Sample, mean, treatment, simulation, standard deviation, histogram, extreme, parameters,
significant
Page 10 of 13
Algebra II Math Tool Unit 4
Unit 4: Inferences and Conclusions from Data- S.IC.6
Cluster: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Standard
Instructional Notes: In earlier grades, students are introduced to
different ways of collecting data and use graphical displays and summary
statistics to make comparisons. These ideas are revisited with a focus on how
the way in which data is collected determines the scope and nature of the
conclusions that can be drawn from that data. The concept of statistical
significance is developed informally through simulation as meaning a result
that is unlikely to have occurred solely as a result of random selection in
sampling or random assignment in an experiment. For S.IC.4 and 5, focus on
the variability of results from experiments—that is, focus on statistics as a way
of dealing with, not eliminating, inherent randomness.
S.IC.6 Evaluate reports based on data.








Standards of Mathematical Practice (SMP’s)
#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.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets





I can identify the variables as quantitative
or categorical.
I can describe how the data was collected.
I can indicate any biases or flaws.
I can identify inferences the author of the
report made from the sample data.
I can write or present a summary of a databased report addressing the sampling
techniques used, inferences made, and any
flaws or biases.
Essential Questions/ Enduring Understandings
How can a population be described when
it is so large, it would be nearly impossible
to collect all of the data?
Statisticians design experiments based on
random samples and analyze the data to
estimate the important properties of a
population and make informed judgments.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Report, variables, quantitative, categorical, bias, inferences
Page 11 of 13
Algebra II Math Tool Unit 4
Unit 4: Inferences and Conclusions from Data- S.MD.6
Cluster: Use probability to evaluate outcomes of decisions.
Standard
Instructional Notes: Extend to more complex probability
models. Include situations such as those involving quality
control, or diagnostic tests that yield both false positive and
false negative results.
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets


I can use probability to create a method for
making a fair decision.
I can use probability to analyze the results
of a process and decide if it resulted in a
fair decision.
S.MD.6 (+) Use probabilities to make fair decisions
(e.g., drawing by lots, using a random number generator).








Standards of Mathematical Practice (SMP’s)
#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.
Template created by Region 1 ESA
Essential Questions/ Enduring Understandings
How is probability used to make informed
decisions about uncertain events?
The rules of probability can lead to more valid
and reliable predictions about the likelihood of
an event occurring.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Sample space, probability, event, simulation, fair
Page 12 of 13
Algebra II Math Tool Unit 4
Unit 4: Inferences and Conclusions from Data- S.MD.7
Cluster: Use probability to evaluate outcomes of decisions.
Standard
Instructional Notes: Extend to more complex probability
models. Include situations such as those involving quality
control, or diagnostic tests that yield both false positive and
false negative results.
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets


I can analyze data to determine whether or
not the best decision was made.
I can analyze the available strategies,
recommend a strategy, and defend my
choice.
S.MD.7 (+) Analyze decisions and strategies using probability
concepts (e.g., product testing, medical testing, pulling a
hockey goalie at the end of a game).








Standards of Mathematical Practice (SMP’s)
#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.
Template created by Region 1 ESA
Essential Questions/ Enduring Understandings
How is probability used to make informed
decisions about uncertain events?
The rules of probability can lead to more valid
and reliable predictions about the likelihood of
an event occurring.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard
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Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Sample space, probability, event
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