Standard

Essential Question

Bloom’s Taxonomy Activities

Vocabulary

Pacing

S.ID.1 Represent data with plots on the
real number line (dot plots, histograms, and box plots).

What are the qualities of each of the
following types of graphs and when should they be used? (dot plots,
histograms, box plots)

Conduct an informal survey about
issues relevant to you and express your results in dot plots, histograms, and
box plots.

Data points
Dot plots
Histograms
Box plots

3 days

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.

Why could the centers be different when
considering data?
What is the benefit of determining the
interquartile range?

Differentiate when to consider the
median of a set of data and the mean value of a set of data.
Analyze a given set of data by
gathering statistics on measures of central tendency, interquartile range,
and standard deviation.

Data distribution
Measures of central tendency
Mean
Median
Mode
Spread
Interquartile range
Standard deviation

3 days

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).

How could outlier information skew the
results of a data set?

Consider data with outliers and
support when to include extreme data points and when not to.

Center
Outliers
Extreme data points

3 days

S.ID.4 Use
the mean and standard deviation of a data set to fit in 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.

How would
the U.S. Census use standard deviation when considering population?

Choose a
population set to research; Go to the U.S. Census information site; compare
the data from the 2000 census with the 2010 census; display your results in a
method of your choosing

Mean
Standard
deviation
Normal
distribution
Population

3 days

S.ID.5 Summarize categorical data for
two categories in twoway 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.

How are joint, marginal, and relative
frequencies determined when looking at a twoway frequency table?
What methods could be used to summarize
large amounts of data?

 Compare the data presented in a
twoway frequency table
 Evaluate the information in two
similar contingency tables using measures of central tendency.

Categorical data
Twoway frequency table
Contingency table
Relative frequency
Joint frequency
Marginal frequency
Conditional frequency
Trend

3 days

S.ID.6 Represent data on two
quantitative variables on a scatter plot, and describe how the variables are
related.

How does a line of best fit assist in
interpreting the data displayed on a scatter plot?

Design and conduct a study which
includes two variables.
Create a visual representation of your
results including a scatter plot, line of best fit, and description of the
data.

Positive correlation
Negative correlation
No correlation

3 days

S.ID.6a Fit a function to the data; use
functions fitted to data to solve problems in the context of the data. Use given functions or choose a function
suggested by the context. Emphasize linear, quadratic, and exponential
models.

How are graphing calculators and
certain programs available on the internet useful in determining the function
which best fits the data?

 Formulate a line of best fit given
data presented in a table or in a graph.
Analyze the line of best fit to
determine qualities of the data.

Line of best fit

3 days

S.ID.6b Informally assess the fit of a
function by plotting and analyzing residuals.

How are residuals useful in determining
the accuracy of a line of best fit?

Analyze a line of best using residuals
to determine the accuracy of the function.

Residuals

3 days

S.ID.6c Fit a linear function for a
scatter plot that suggest a linear association.

What is true about the scatter plots
above and below a fitted linear function?

Support the visual determination of
the correlation of a set of data with its computed correlation coefficient.

Correlation coefficient

3 days

S.ID.7 Interpret the slope (rate of change) and
the intercept (constant term) of a linear model in the context of the data.

What information can be determined when
considering the equation of a function?

Analyze the equation of a line of best
fit to determine the rate of change and intercept.

Slope
Rate of change
Intercept

3 days

S.ID.8 Compute (using technology) and interpret
the correlation coefficient of a linear fit.

How could technology be utilized to
provide information pertaining to the qualities of a line of best fit?

Experiment with different equations to
determine the relationship between the correlation coefficient and the graph.

Correlation coefficient

3 days

S.ID.9 Distinguish between correlation and
causation.

How does correlation differ from causation?
If it is determined that one variable
causes another variable, what is also implied?

Evaluate the usage of the term
causation to determine if it is an accurate representation of the data

Causation
Correlation

3 days

Standard

Essential Question

Bloom’s Taxonomy Activities

Vocabulary

Pacing

S.IC.1
Understand statistics as a process for making inferences about population
parameters based on a random sample from that population.

Why do most
polls include a (+/) number?

View the
U.S. Census page on Center of Population, (http://2010.census.gov/2010census/data/centerofpopulation.php) investigate why the center
moved over the years

Statistics
Inference
Random
sample

2 days

S.IC.2
Decide if a specified model is consistent with results from a given
datagenerating process, e.g., using simulation. For example, a model says a spinning coin falls head up with a
probability 0.5. Would a result of 5 tails in a row cause you to question the
model?

What role
does statistics play in market research?

From Common
Core: a model says a spinning coin falls head up with a probability 0.5.
Would a result of 5 tails in a row cause you to question the model?
Create your
own model.

Model
Datagenerating
process

2 days

S.IC.3
Recognize the purposes of and differences among sample surveys, experiments,
and observational studies; explain how randomization relates to each.

How does the
television industry utilize sample surveys in developing programming?

Create a
Venn Diagram to compare and contrast: Sample surveys, experiments, and
observational studies

Sample
surveys
Experiments
Observational
studies
Randomization

3 days

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.

How does
margin of error affect the possible outcome of voting results?

Using the
internet research margin of error and political race; find an example when a
poll could not predict an upcoming election; create a PowerPoint slide
displaying your results

Population
mean
Population
proportion
Margin of
error

3 days

S.IC.5 Use
data from a randomized experiment to compare two treatments; use simulations
to decide if differences between parameters are significant.

What is the
quality of a randomized study in regard to validity and reliability?

Conduct a
study of a topic of your choosing using 1) randomized approach and 2)
targeted approach. How are your results different than if you used a targeted
sample of the population? Display your results in a method of your choosing

Data
Randomized
experiment
Parameters
Significance
Validity
Reliability

3 days

S.IC.6
Evaluate reports based on data.

How does the
medical industry utilize pilot studies in the development of new
pharmaceuticals and treatments?

Choose a
product you are interested in purchasing on the internet with no less than 45
comments from other consumers; Conduct an analysis of the comments on the
product, write a conclusion, and display your results

Pilot study

3 days

Standard

Essential Question

Bloom’s Taxonomy Activities

Vocabulary

Pacing

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”).

Why are
subsets relevant to areas beyond mathematics?

Create and
solve a word problem which uses unions and intersections of sets.

Set
Subset
Union
Intersection
Sample
space
Outcomes

1 day

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 the probabilities, and
use this characterization to determine if they are independent

How can one
check if two events are independent of each other?

Compare and
contrast the probabilities of two events to determine if the events are
independent.

Independent
Probabilities

1 day

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 B given A is the same as the probability of B.

In what
areas are conditional probabilities relative to everyday life?

Create a
Venn Diagram and determine the probabilities of each occurrence.

Conditional
probability
Venn
diagram

1 day

S.CP.4 Construct and interpret twoway frequency tables of data when two
categories are associated with each object being classified. Use the twoway
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.

How are
frequency tables used to foresee possible election results?

From Common
Core:
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.

Frequency
Table

1 day

S.CP.5
Recognize and explain in 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.

How do
meteorologists utilize probability to forecast weather?

From Common
Core:
Compare the
chance of having lung cancer if you are a smoker with the chance of being a
smoker if you have lung cancer.

Conditional
probability
Independence
of events

1 day

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.

How does
ratio relate to conditional probability?

Complete the
following problem from Dartmouth College and create a similar problem: one
finds that in a population of 100,000 females, 89.835% can expect to live to
age 60, while 57.062% can expect to live to age 80. Given that a woman is 60,
what is the probability that she lives
to age 80?

Conditional
probability
Outcomes

1 day

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

What is the
connection between intersection, union, and the Addition Rule?

Using a deck
of cards, create a worksheet which requires the use of addition rule. Share
your worksheet with your peers.

Addition
rule
Probability
Venn
Diagram

1 day

S.CP.8 (+)
Apply the general Multiplication Rule in a uniform probability model, P(A and
B) = P(A)P(BǀA) = P(B)P(AǀB), and interpret the
answer in terms of the model.

How does the
multiplication rule relate to independent and dependent events?

Using a bag
of candy, create a worksheet utilizing the Multiplication Rule with seven
examples of picking candy in a particular order.

Multiplication
Rule

1 day

S.CP.9 (+)
Use permutations and combinations to compute probabilities of compound events
and solve problems.

What is the
difference between a permutation and a combination?

Develop a
worksheet in which your peers must determine if the question requires a
permutation or a combination.

Permutations
Combinations

1 day

Standard

Essential Question

Bloom’s Taxonomy Activities

Vocabulary

Pacing

Smd1


Smd2


Smd3


Smd4


Smd5


S.MD.6 (+)
Use probabilities to make fair decisions (e.g., drawing by lots, using a
random number generator).

When would
it be appropriate to use a random number generator?

Explore the
random calculators available on random.org and write a one paragraph
reflection on any three tools.
Utilize an
online Bingo caller to play Bingo as a class (http://www.bingoadvantage.com/online/bingo_caller.cfm)
Evaluate how
this method is different than if a Bingo tumbler was used or if numbers were
chosen from cards off a table

Random
number generator

1 day

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).

How does
probability relate to drugefficacy in patients?

Choose a
form of testing which relates to probability. Read two articles related to
your form of testing; write a onepage summary of your findings.
and choose a
sports team to follow for the entire unit. Given the team’s current status,
make a hypothesis as to the team’s success over a month. Track the team each
week and create a graph of the changes; at the end of the study, review your
hypothesis and adjust it for the remainder of the season

Strategies

1 day

Statistics & Probability
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