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7.SP.8
2012
Domain: Statistics & Probability
Cluster: Investigate chance processes and develop, use, and evaluate probability models.
Standards: 7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulations:
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?
Essential Questions
 Can you always predict
the outcome of an event?
 Does something in
theory always match
reality?
 What does it mean when
events are interconnected?
Content Statements
Students will be able to:
 Find the probability of
an event by performing
an experiment.
 Approximate the
Enduring Understandings
Students will understand that:
 Determine where the
probability of an event lies.
 Students will develop an
understanding of theoretical
probability.
 Students will develop an
understanding of experimental
probability.
 Students will explore the
differences between dependent
and independent events.
 Can use sample space to
compare the number of
Activities, Investigation, and Student Experiences
Activity:
 Students use tree diagrams, frequency tables, and
organized lists, and simulations to determine the
probability of compound events.

Instruct students to generate a survey, compile, and
display the data. Then interpret their results.

Relative frequency is the observed proportion of
successful event, expressed as the value calculated by
dividing the number of times an event occurs by the total
number of times an experiment is carried out.
Example:
 How many ways could the 3 students, Amy, Brenda, and
Carla, come in 1st, 2nd and 3rd place?
Solution:
Making an organized list will identify that there are 6 ways for
the students to win a race
7.SP.8
probability by collecting
data
 Predict the approximate
relative frequency given
the probability
favorable outcomes to the total
number of outcomes and
determine the probability of
the compound events
 Design and utilize a simulation
to predict the probability of a
compound event
Assessments
Problem Task
Create a tree diagram for illustrating the outcomes for a car that
has two or four doors and is red, black, or silver. Create
questions that can be answered based on the diagram.
Skill-based Task
What is the probability of a family with five children having
exactly two boys?
Performance Assessment Tasks:
Fair Game?
Problems of the Month:
Friends you can count on
Got your Number
Fair Games
2012
A, B, C
A, C, B
B, C, A
B, A, C
C, A, B
C, B, A

If you toss a coin three times, what is the probability of
flipping at least 2 heads?
Activity:
 Students can collect data using physical objects or
graphing calculator or web-based simulations. Students
can perform experiments multiple times, pool data with
other groups, or increase the number of trials in a
simulation to look at the long-run relative frequencies.
Activity:
 Students create another scenario with a different ratio of
marbles in the bag and make a conjecture about the
outcome of 50 marble pulls with replacement. (An
example would be 3 green marbles, 6 blue marbles, 3
blue marbles.)
Example:
 Students conduct a bag pull experiment. A bag contains
5 marbles. There is one red marble, two blue marbles
and two purple marbles. Students will draw one marble
without replacement and then draw another. What is the
sample space for this situation? Explain how you
determined the sample space and how you will use it to
find the probability of drawing one blue marble followed
by another blue marble.
7.SP.8
2012
(Adapted from Connecticut State Department Mathematics Standards
for Practice)
(www.sde.ct.gov/.../grade_7_illustrated_practices_pacing_guide
_units...)
Example:
 Show all possible arrangements of the letters in the word
FRED using a tree diagram. If each of the letters is on a
tile and drawn at random, what is the probability that you
will draw the letters F-R-E-D in that order? What is the
probability that your “word” will have an F as the first
letter.
(Adapted from Connecticut State Department Mathematics Standards
for Practice)
(www.sde.ct.gov/.../grade_7_illustrated_practices_pacing_guide
_units...)
Equipment Needed:

Interactive Whiteboard

Calculator

Computer

Marbles
Online Activities:
 Marble Mania
 Random Drawing Tool
 Waiting Times
 Mathematics relevant to our world today
 Websites specific to 7.SP.8a
 Websites specific to 7.SP.8b
 Websites specific to 7.SP.8c
Teacher Resources:

http://www.ncpublicschools.org/docs/acre/standards/com
mon-core-tools/unpacking/math/7th.pdf

http://www.schools.utah.gov/CURR/mathsec/Core/7thGrade-Core/7SP3.aspx
7.SP.8

Coins
2012

http://insidemathematics.org/index.php/7th-grade

http://www.khanacademy.org/math/probability

7.sp.8 | Search Results | Yummy Math

http://ccssmath.org/?page_id=675

CCSS Investigation 5: Variability