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DURHAM PUBLIC SCHOOLS 2013-2014
UNIT 6 PLAN FOR 7TH GRADE MATHEMATICS
Unit Overview:
Instructional Time: 3 weeks
Quarter
One
Two
Three
Four
Grade Level: 7th Grade
Unit Theme: Probability
Depth of Knowledge: Level 1, Level 2, Level 3, Level 4
Unit Summary: This unit will develop meaning of an unlikely, likely, and equally likely event. Students will conduct experiments, collect data,
draw conclusions, compare and contrast experimental and theoretical probabilities. Throughout the unit, students will learn about simple events
and compound events by analyzing sample space, organized lists, tables, tree diagrams, and simulations. The content will be delivered using
student-friendly knowledge and will apply to events that happen in the world around them.
Critical Area of Concentration: Critical Area #X (6-12 MATH ONLY):
North Carolina Informational Technology Essential Standards:
7.TT.1.2 Use appropriate technology tools and other resources to organize information (e.g., graphic organizers, databases, spreadsheets, and
desktop publisher).
7.TT.1.3 Use appropriate technology tools and other resources to design products to share information with others (e.g. multimedia presentations,
Web 2.0 tools, graphics, podcasts, and audio files).
7.RP.1.2 Implement an independent research process activity that is student selected.
Learning Targets:
Common Core State Standards
 I can understand that probability is expressed as a number
Investigate chance processes and develop, use, and evaluate
between 0 and 1
probability models.

I can understand that a random event with a probability of ½ is
7. SP.5 Understand that the probability of a chance event is a number
equally likely to happen
between 0 and 1 that expresses the likelihood of the event occurring.
 I can understand that as probability moves closer to 1 it is
Larger numbers indicate greater likelihood. A probability near 0
increasingly likely to happen
indicates an unlikely event, a probability around 1/2 indicates an event

I can understand that as probability moves closer to 0 it is
that is neither unlikely nor likely, and a probability near 1 indicates a
decreasingly likely to happen
likely event.
 I can draw conclusions to determine that a greater likelihood
occurs as the number of favorable outcomes approaches the
total number of outcomes
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 ovserved frequencies: if
the agreement is not good, explain possible sources of the discrepancy.
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

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 events 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.

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
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

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I can determine relative frequency (experimental probability)
is the number of times an outcome occurs divided by the total
number of times the experiment is completed
I can determine the relationship between experimental and
theoretical probabilities by using the law of large numbers
I can predict the relative frequency (experimental probability)
of an event based on the (theoretical) probability
I can use models to determine the probability of events
I can recognize uniform (equally likely) probability
I can develop a uniform probability model and use it to
determine the probability of each outcome/event
I can use models to determine the probability of events
I can develop a probability model (which may not be uniform)
by observing frequencies in data generated from a change
process
I can analyze a probability model and justify why it is uniform or
explain the discrepancy if it is not
I can determine that the probability of a compound event is the
fraction of outcomes in the sample space for which the
compound event occurs
I can identify the outcomes in the sample space for an everyday
event
I can define and describe a compound event
I can find probabilities of compound events using organized
lists, tree diagrams, etc. and analyze the outcomes
I can choose the appropriate method such as organized lists,
tables and tree diagrams to represent sample spaces for
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?


compound events
I can define simulation
I can design and use a simulation to generate frequencies for
compound events
Essential Question(s):
 Can you use previous events to make a prediction about what will happen tomorrow?
 How will the likeliness of an event affect the outcome?
 When would it be beneficial to know all of the choices that you have?
 How do you determine your chances of winning a game?
Enduring Understanding(s):
 The essentials of probability are used everyday in life, and investigating the likeliness of an event will help students make informed
decisions in real world situations.
.
Vocabulary:
Probability
Simple Event
Tree Diagram
Fundamental
Counting Principle
Frequency
Compound Event
Experimental
Theoretical
Probability
Probability
Interdisciplinary Connections (Standards would be listed):
W.8.5: English Language Arts (Use CCSS ELA if it is a Math Unit)
XXX: Science (http://www.dpi.state.nc.us/acre/standards/new-standards/)
XXX: Math (Use CCSS Math if it is an ELA Unit )
XXX: Social Studies (http://www.dpi.state.nc.us/acre/standards/new-standards/)
Evidence of Learning (Formative Assessment):
 Teacher Observation
 Exit Slips
 Small Quizzes
Summative Assessment:
 Teacher-made Test
 Chance Encounters: Real-World Simulation Game

Durham Public Schools’ Small Goal Assessment
Unit Implementation:
Unlikely, Likely, Equally Likely, Relative Frequency (CCSS 7.SP.5)
a. Introduce key vocabulary (word wall, flashcards, graphic organizers, foldable, etc)
b. How Likely Is It?: 1.1 Flipping for Breakfast
c. How Likely Is It?: 1.2 Analyzing Events
d. How Likely Is It?: 2.1 Tossing Marshmallows
e. How Likely Is It?: 2.2 Pondering Possible and Probable
f. Chance Encounters: Lessons from Phase One
Unlikely, Likely, Equally Likely, Relative Frequency (CCSS 7.SP.6)
a. Introduce key vocabulary (word wall, flashcards, graphic organizers, foldable, etc)
b. How Likely Is It?: Bargaining for a Better Bedtime
c. Recall information about Statistics from 7.SP.1-4
d. Compare and contrast frequency and relative frequency
e. Connection between relative frequency and probability (the total relative frequencies should total 1)
f. Chance Encounters: Lessons from Phase Two
Experimental Probability vs. Theoretical Probability (CCSS 7.SP.7.a, 7.SP.7.b)
a. Introduce key vocabulary (word wall, flashcards, graphic organizers, foldable, etc)
b. How Likely Is It?: 4.1 Predicting to Win
c. How Likely Is It?: 4.2 Drawing More Blocks
d. How Likely Is It?: 4.3 Wining the Bonus Prize
e. How Likely Is It?: 5.1 Roller Derby
f. How Likely Is It?: 6.1 Scratching Spots
g. Chance Encounters: Lessons from Phase Three
Simple and Compound Events/Sample Space (CCSS 7.SP.8.a, 7.SP.8.b, 7.SP.8.c)
a. Introduce key vocabulary (word wall, flashcards, graphic organizers, foldable, etc)
b. Simple Events: probability of one or more events that are unrelated
c. Compound Events: probability of one or more related events (with replacement, and without)
Supportive Unit Resources: (Please note that these are resources that can be used to supplement instruction before or during a lesson.)
Scaffolding Option 1:
Intervention
Instructional
Activities:
Scaffolding Option 2:
Maintenance
(CCSS 7.SP.8.a)
(CCSS 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8)
Manipulatives: Create actual trees using construction
paper. Have the students use the branches to find the
sample space.
Test Prep: Complete Sample EOG
questions or parallel test questions.
Scaffolding Option 3:
Extension
(CCSS 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8)
Chance Encounters: Real-World Simulation Game:
Design, build, and create a simulation game using the
knowledge gained from the probability unit.
Letter to Roger: Roger is a new student in Ms. Smith’s
math class. While Roger is a relatively bright student, at his
previous school, he had never studied probability. Your
assignment is to write to Roger and give him a foundation
to help him study probability. You are being asked to define
and give examples for each of the vocabulary words for
this unit. Organize your letter so that it is easy to
understand.
Prior knowledge: Review changing fractions to
decimals to percents (with and without a calculator)
Technology Integration: This website has several probability games: http://www.free-training-tutorial.com/probability-games.html
Multimedia
Activities:
(CCSS 7.SP.5)
Remediation of Basic Probability Skills
http://www.ixl.com/math/grade-3/certain-probableunlikely-impossible
(CCSS 7.SP.7.a)
Virtual Probability Fair
http://www.mrnussbaum.com/probfair.htm
XXXXXXX
Independent Events
http://www.bbc.co.uk/education/mathsfile/shockwave/g
ames/fish.html
Independent and Dependent Events
http://www.math-play.com/ProbabilityGame.html
(CCSS 7.SP.5)
Probability Game (written as fractions, decimals and
percents)
http://www.bbc.co.uk/schools/ks2bitesize/maths/data/probabili
ty/play.shtml