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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
7E
Big Idea(s)
Unit 5: Statistics and Probability
• Use random sampling to draw inferences about a population.
What enduring understandings are
essential for application to new
situations within or beyond this
content?
• Draw informal comparative inferences about two populations.
Essential Question(s)
What questions will provoke and
sustain student engagement while
focusing learning?
• Investigate chance processes and develop, use, and evaluate
probability models.
Why is random sampling important when collecting data?
Why is it necessary to compare information about two populations?
How can data collection assist in making predictions about an event?
How can a model help me solve a probability or statistical problem?
Enduring Standard(s)
Which standards provide
endurance beyond the course,
leverage across multiple
disciplines, and readiness for the
next level?
Enduring Understandings
• Understand that statistics can be used to gain information about a
population by examining a sample of the population; generalizations
about a population from a sample are valid only if the sample is
representative of that population.
• Understand that random sampling tends to produce representative
samples and support valid inferences.
• Use data from a random sample to draw inferences about a
population with an unknown characteristic of interest.
• Generate multiple samples (or simulated samples) of the same size
to gauge the variation in estimates or predictions.
• Informally assess the degree of visual overlap of two numerical data
distributions with similar variability, measuring the difference between
the centers by expressing it as a multiple of a measure of variability.
• Use measures of center and measures of variability for numerical
data from random samples to draw informal comparative inferences
about two populations.
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them. Students
make sense of probability situations by creating visual, tabular and
symbolic models to represent the situations. They persevere through
approximating probabilities and refining approximations based upon
data.
*2. Reason abstractly and quantitatively. Students’ reason about the
numerical values used to represent probabilities as values between 0
and 1.
*3. Construct viable arguments and critique the reasoning of others.
Students approximate probabilities and create probability models and
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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
explain reasoning for their approximations. They also question each
other about the representations they create to represent probabilities.
*4. Model with mathematics. Students model real world populations
using mathematical probability representations that are algebraic,
tabular or graphic.
5. Use appropriate tools strategically. Students select and use
technological, graphic or real-world contexts to model and simulate
probabilities.
6. Attend to precision. Students use precise language and calculations
to represent probabilities in mathematical and real-world contexts.
7. Look for and make use of structure. Students recognize that
probability can be represented in tables, visual models, or as a rational
number.
8. Look for express regularity in repeated reasoning. Students use
repeated reasoning when approximating probabilities. They refine
their approximations based upon experiences with data.
Standards for Mathematical Content
Use random sampling to draw inferences about a population.
7.SP.A.1 Understand that statistics can be used to gain information
about a population by examining a sample of the population;
generalizations about a population from a sample are valid only if the
sample is representative of that population. Understand that random
sampling tends to produce representative samples and support valid
inferences.
7.SP.A.2 Use data from a random sample to draw inferences about a
population with an unknown characteristic of interest. Generate
multiple samples (or simulated samples) of the same size to gauge the
variation in estimates or predictions. For example, estimate the mean
word length in a book by randomly sampling words from the book;
predict the winner of a school election based on randomly sampled
survey.
Draw informal comparative inferences about two populations.
7.SP.B.3 Informally assess the degree of visual overlap of two numerical
data distributions with similar variabilities, measuring the difference
between the centers by expressing it as a multiple of a measure of
variability. For example, the mean height of players on the basketball
team is 10 cm greater than the mean height of players on the soccer
team, about twice the variability (mean absolute deviation) on either
team; on a dot plot, the separation between the two distributions of
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District Curriculum Map for Mathematics: Grade 7
heights is noticeable.
7.SP.B.4 Use measures of center and measures of variability for
numerical data from random samples to draw informal comparative
inferences about two populations. For example, decide whether the
words in a chapter of a seventh-grade science book are generally
longer than the words in a chapter of a fourth-grade science book.
Investigate chance processes and develop, use, and evaluate
probability models.
7.SP.C.5 Understand that the probability of a chance event is a
number between 0 and 1 that expresses the likelihood of the event
occurring. Larger numbers indicate greater likelihood. A probability
near 0 indicates an unlikely event, a probability around 1/2 indicates
an event that is neither unlikely nor likely, and a probability near 1
indicates a likely event.
7.SP.C.6 Approximate the probability of a chance event by collecting
data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative
frequency given the probability. For example, when rolling a number
cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times,
but probably not exactly 200 times.
7.SP.C.7 Develop a probability model and use it to find probabilities of
events. Compare probabilities from a model to observed frequencies;
if the agreement is not good, explain possible sources of the
discrepancy.
7.SP.C.8 Find probabilities of compound events using organized lists,
tables, tree diagrams, and simulation.
Supporting Standard(s)
Which related standards will be
incorporated to support and
enhance the enduring standards?
Curriculum and Instruction
Investigate chance processes and develop, use, and evaluate
probability models.
7.SP.C.7
a. Develop a uniform probability model by assigning equal probability
to all outcomes, and use the model to determine probabilities of
events. For example, if a student is selected at random from a class,
find the probability that Jane will be selected and the probability that
a girl will be selected.
b. Develop a probability model (which may not be uniform) by
observing frequencies in data generated from a chance process. For
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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
Instructional Outcomes
What must students learn by the
end of the unit?
Curriculum and Instruction
example, find the approximate probability that a spinning penny will
land heads up or that a tossed paper cup will land open-end down.
Do the outcomes for the spinning penny appear to be equally likely
based on the observed frequencies?
7.SP.C.8
a. Understand that, just as with simple events, the probability of a
compound event is the fraction of outcomes in the sample space
for which the compound event occurs.
b. Represent sample spaces for compound events using methods
such as organized lists, tables and tree diagrams. For an event
described in everyday language (e.g., “rolling double sixes”),
identify the outcomes in the sample space which compose the
event.
c. Design and use a simulation to generate frequencies for compound
events. For example, use random digits as a simulation tool to
approximate the answer to the question: If 40% of donors have type A
blood, what is the probability that it will take at least 4 donors to find
one with type A blood?
I can…
 I can use statistics to gain information about a population by
examining a sample of the population.

I can determine if a sample is representative of a population.

I can define random sample.

I can represent a population through random sampling.

I can use data to draw inferences.

I can generate multiple samples of the same size to gauge the
variation in predictions.

I can find mean, median, and mode for a set of numerical
data.

I can identify measures of variation including upper quartile,
lower quartile, upper extreme-maximum, lower extrememinimum, range, interquartile range, and mean absolute
deviation.

I can create box-and-whisker plots, line plots, and dot plots.

I can compare two sets of data on a graph.
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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7

I can compare two sets of data using the measures of central
tendency.

I can use the measures of center and measures of variability to
make informal comparative inferences about two populations.

I can express probability as a number between 0 and 1.

I can define when two events are equally likely to occur.

I can describe a probability as being more or less likely to occur.

I can determine the relative frequency (experimental
probability) of an event.

I can determine when the relative frequency of an event
closely represents the theoretical probability of the event.

I can make predictions based on theoretical probability.

I can develop a probability model and find probability of
events.

I can develop a probability model with equal probability for all
outcomes.

I can determine experimental probability based on observed
frequencies.

I can identify differences between theoretical and
experimental probabilities and explain possible reasons for
them.
I can develop a probability model with unequal probability for
all outcomes.
Students who demonstrate understanding can…
 Use random sampling to draw inferences about a population.
 Draw informal comparative inferences about two populations.
 Investigate chance processes and develop, use, and evaluate
probability models.

Performance Expectations
What must students be able to do
by the end of the unit to
demonstrate their mastery of the
instructional outcomes?
Essential Vocabulary
What vocabulary must students
know to understand and
communicate effectively about
Curriculum and Instruction
Essential Vocabulary –
bivariate data - Involves two variables. Bivariate data deals with
causes or relationships. The major purpose of bivariate data analysis is
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District Curriculum Map for Mathematics: Grade 7
this content?
to explain.
box plot - A method of visually displaying a distribution of data values
by using the median, quartiles, and extremes of the data set. A box
shows the middle 50% of the data.
chance event - Anything that happens suddenly or by chance without
an apparent cause; ex: Winning the lottery.
clusters - Small group or bunch of something resulting from a "natural"
grouping evident in a data set.
combination - A selection in which order is not important.
compound event - An event whose probability of occurrence
depends upon the probability of occurrence of two or more
independent events. An event that consists of two or more events that
are not mutually exclusive.
data display - An organized way to display data EX: tables, charts,
tally tables, pictographs, bar graphs, circle graphs, line plots, Venn
Diagrams.
data distribution - Shape of a probability distribution. It most often
arises in questions of finding an appropriate distribution to use to
model the statistical properties of a population, given a sample from
that population.
data set - Numeric information usually gathered for analysis.
dependent variable - Variable dependent on another variable: the
independent variable.
dot plot - A method of visually displaying a distribution of data values
where each data value is shown as a dot or mark above a number
line. Also known as a line plot.
first quartile - For a data set with median M, the first quartile is the
median of the data values less than M. EX: For the data set {1, 3, 6, 7,
10, 12, 14, 15, 22, 120}, the first quartile is 6.
frequency - The number of times a particular item appears in a data
set.
gaps - Space between objects or points.
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District Curriculum Map for Mathematics: Grade 7
independent variable - A variable that stands alone and isn't change
by the other variables you are trying to measure.
inference – The process of drawing conclusions from data that are
subject to random variation, for example, observational errors or
sampling variation; systems of procedures that can be used to draw
conclusions from datasets arising from systems affected by random
variation.
interquartile range - A measure of variation in a set of numerical data,
the interquartile range is the distance between the first and third
quartiles of the data set. EX: For the data set {1, 3, 6, 7, 10, 12, 14, 15,
22, 120}, the interquartile range is 15 - 6 = 9.
line plot - A method of visually displaying a distribution of data values
where each data value is shown as a dot or mark above a number
line. Also known as a dot plot.
maximum value - The highest/largest value of a given set of data.
mean - A measure of center in a set of numerical data, computed by
adding the values in a list and then dividing by the number of values in
the list. EX: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean
is 21.
mean absolute deviation - The average of the distance of a set of
numbers from the mean of the set.
measure of center - A calculation resulting in a central value for a set
of data; a mean, median, or mode.
measure of variance - A measurement that describes how values vary
with a single value.
median - The middle value in a set of data when the data is ordered
from the greatest to least; EX: The median of 13,7,6,4,2,2,1 is 4.
modeling - The process of choosing and using appropriate
mathematics and statistics to analyze empirical situations, to
understand them better, and to improve decisions.
observed frequency - The number of measurements in an interval of a
frequency distribution.
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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
outcome - In probability, a possible result of an experiment.
outliers - extreme data points.
permutation - A way to arrange things in which order is important.
population - The total sample space for a set of data.
probability - A number between 0 and 1 used to quantify likelihood for
processes that have uncertain outcomes (such as tossing a coin,
selecting a person at random from a group of people, tossing a ball at
a target, or testing for a medical condition).
probability distribution – The set of possible values of a random
variable with a probability assigned to each.
probability model - A probability model is used to assign probabilities
to outcomes of a chance process by examining the nature of the
process. The set of all outcomes is called the sample space, and their
probabilities sum to 1. See also: uniform probability model.
random sample - A sample in which every element in the population
has an equal chance of being selected.
range - The difference between the biggest number and the smallest
number in a set of data; EX: The range of 13,7,6,5,4,2,2,1, is 12 (13-1 =
12.
sample space - In a probability model for a random process, a list of
the individual outcomes that are to be considered.
scale - The numerical system used to define the axis on a graph or a
line on a data display.
scatter plot - A graph in the coordinate plane representing a set of
bivariate data. For example, the heights and weights of a group of
people could be displaced on a scatter plot.
simulation - A way of acting out a problem by creating a situation like
one in the real world.
statistical thinking - A mode of thinking that include both logical and
analytical reasoning.
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District Curriculum Map for Mathematics: Grade 7
theoretical probability - The probability/likelihood of an event
happening based upon mathematical calculations: P(event) =
Number of favorable outcomes / total number of possible outcomes.
third quartile - For a set of data with median M, the third quartile is the
median of the data values greater than M. Example: For the data set
{2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the third quartile is 15.
Supporting Vocabulary
experimental probability
quartile
Common Core Glossary
http://www.corestandards.org/Math/Content/mathematicsglossary/glossary
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Subject and Grade Level
Unit Title
Summative Assessment of
Learning
Mathematics 7E
Unit 5: Statistics and Probability
In what way will students meet the
performance expectations to
demonstrate mastery of the
standards?
Instructional Outcomes
How will the instructional outcomes
be sequenced into a
progression of learning?
Learning Activities
What well-designed progression of
learning tasks will intellectually
engage students
in challenging content?
Formal Formative Assessments
What is the evidence to show
students have learned the lesson
objective and are progressing
toward mastery of the instructional
outcomes?
Integration Standards
What standards from other
disciplines will enrich the learning
experiences for the students?
Resources
What resources will be utilized to
enhance student learning?
Connected Math Project Module: Samples and Populations
Additional resources are hyperlinked under “Topic/Resources” on
the Long Range Plan sheet.
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