Grade 7
Unit 3
Table of Contents
Probability and Expected Value
Section
Page Number
Unit Description
Unit Standards
Unit Essential Questions
Unit Proficiencies (Learning Targets)
Unit Vocabulary and Language Support
Sample Unit Calendar and Possible Supporting Materials
Student Proficiencies Handout
Unit Assessments and Rubric/Commentary
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This Unit Developed by: Althea Beam, Robert Shearer, and Brad
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Grade 7
Content Unit 3
Unit Title:
Stage 1
Unit
Description:
Standards:
Dates of Unit:
____________
(5 weeks)
Probability and Expected Value
Identify Desired Results
Students will develop an understanding of probability and use it to predict and calculate various events.
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7.SP.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.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and
observing its long-run 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.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.
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 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.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
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
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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?
Essential
Questions:
Standard
Proficiencies
(Learning Targets)
1. How is the probability of an event useful in problem solving?
2. How does experimental probability compare to theoretical probability?
7.SP.5
I can calculate the probability
of an event as a number
between 0 and 1.
7.SP.6
I can find the
experimental
probability of an event
and compare it to its
theoretical
probability.
7.SP.7
I can develop a
uniform probability
model and use it to
find the probability of
an event.
a) I can analyze a
probability model
and justify why it
is uniform or
explain the
discrepancy if it is
not.
b) I can develop a
probability model
by observing the
frequencies in
data produced by
a chance process.
7.SP.8
I can describe a
compound event and
identify the fraction of
outcomes in the
sample space for
which it occurs.
a) I can find the
probability of
compound events
using organized lists,
tree diagrams, tables,
and analyze the
outcomes.
b) I can design and
use a simulation to
generate frequencies
for compound events.
I can predict the
relative frequency of
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This Unit Developed by: Althea Beam, Robert Shearer, and Brad Agenbroad (June, 2014)
an event based on its
theoretical
probability.
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Stage 2
Determine Assessment Evidence
Academic Language (What language will students need to sound like experts?)
Academic Vocabulary:
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Stage 3
Plan Learning Experiences and Instruction
Pacing Calendar
Proficiency
Materials
Time Allotment
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NUMBER SENSE
PROFICIENCIES
Name ______________________________
Date ________________________ Period _____
My Proficiency Assessment Scores
Proficiency #1 – “I can find the greatest common factor of two
whole numbers up to 100.”
Proficiency #2 – “I can find the least common multiple using two
numbers up to 12.”
Proficiency #3 – “I can use the distributive property.”
Proficiency #4 – “I can divide multi-digit decimals numbers
using long division.”
Proficiency #5 – “I can add multi-digit decimals.”
Proficiency #6 – “I can subtract multi-digit decimals.”
Proficiency #7 – “I can multiply multi-digit decimals.”
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Proficiency #8 – “I can divide multi-digit decimals.”
Proficiency #9 – “I can use positive and negative numbers to
describe quantities.”
Proficiency #10 – “I can use positive and negative numbers to
describe real life situations .”
Proficiency #11 – “I can explain the meaning of zero in real life
situations.”
Proficiency #12 – “I can find the mean of a set of numbers.”
Proficiency #13 – “I can find the median of a set of numbers .”
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Proficiency #14 – “I can find the mode of a set of numbers .”
Proficiency #15 – “I can find the range of a numbers .”
Proficiency #16 – “I can understand and use mathematical
vocabulary .”
Data set, event,
frequency,
probability,
experimental probability
theoretical probability,
relative
frequency,
tree diagram
variability,,
relative frequency
Probability Model
Observe
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Proficiency Assessment…
Name _________________________________
Date _______________________ Period ____
Proficiency # – “I can ….”
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Proficiency
Score
4
Percentage
3
83%
2
67%
1
50%
100%
Description
WOW!
I have shown proficiency and deeper understanding by:
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You got it 
I have shown proficiency by:
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Help is needed
I have shown partial understanding by:
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Uh-oh…
I have not yet shown my understanding of the math.
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This Unit Developed by: Althea Beam, Robert Shearer, and Brad
Agenbroad (June, 2014)