CCGPS Mathematics
Unit-by-Unit Grade Level Webinar
Analytic Geometry
Unit 7: Applications of Probability
November 12, 2013
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CCGPS Mathematics
Unit-by-Unit Grade Level Webinar
Analytic Geometry
Unit 7: Applications of Probability
November 12, 2013
James Pratt – jpratt@doe.k12.ga.us
Brooke Kline – bkline@doe.k12.ga.us
Secondary Mathematics Specialists
These materials are for nonprofit educational purposes
only. Any other use may constitute copyright infringement.
Welcome!
• The big idea of Unit 7
• Incorporating SMPs into applications of probability
• Resources
Wiki/Email Questions
 Question: In the Middle School and Coordinate Algebra Unit
Frameworks, I noticed they have included both Formative
Assessment Lessons (FAL) and Short Cycle Tasks (SCT) from
the Mathematics Assessment Project. Why do the Analytic
Geometry Unit Frameworks only contain FALs?
http://map.mathshell.org/materials/index.php
Wiki/Email Questions
Formative Assessment Lesson (FAL)/Classroom Challenges
http://map.mathshell.org/materials/index.php
Wiki/Email Questions
Short Cycle Task (SCT)/Assessment Tasks (Novice,
Apprentice, Expert)
http://map.mathshell.org/materials/index.php
Analytic Geometry Short Cycle Tasks
Unit 1 – Hopewell Geometry, Floor Pattern
Unit 2 – Pythagorean Triplets, Triangular Frameworks
Unit 3 – Circles in Triangles, A Golden Crown, Bestsize
Cans, Funsize Cans, Propane Tanks
Unit 4 – The Real Number System, Cross Totals, Arithmetic
with Polynomial and Rational Expressions
Unit 5 – Sidewalk Stones, Patchwork, Table Tiles, Building
Functions, Functions, Reasoning with Equations &
Inequalities, Seeing Structure in Expressions
Unit 6 – no short cycle tasks included in the unit
Unit 7 – no short cycle tasks included in the unit
Unit 5: Parent Graphs Revisited Task
Teacher Edition –
page 98
• All four functions are
neither odd nor even.
S.CP.1
Using the Venn diagram, determine
the following sets.
• 𝐴∩𝐵
• 𝐴′
• 𝐴′ ∪ 𝐵′
• 𝐴∩𝐵
{Jane, George}
• 𝐴′
{Andy, Teresa, Randy}
• 𝐴′ ∪ 𝐵′
{Torri, Tony, Tom, Sandi, Andy, Teresa, Randy}
What’s the big idea?
• Understand independence and
conditional probability and use
them to interpret data
• Use the rules of probability to
compute probabilities of
compound events in a uniform
probability model
What’s the big idea?
Standards for Mathematical Practice
What’s the big idea?
Standards for Mathematical Practice
• Dan Meyer
• Robert Kaplinsky
• Teaching
Channel
• Illustrative
Mathematics
• Expeditionary
Learning
• MAP
Coherence and Focus
• K-9th
 Basic probability (no formulas)
 Probability models
 Two way tables
• 11th-12th
 Multiplication Rule for Probability
 Making decisions based on probability
Examples & Explanations
Suppose that today there is a 60% chance of rain, a
15% chance of lightning, and a 20% chance of
lightning if it’s raining. What is the chance of both rain
and lightning today?
Adapted from Illustrative Mathematics S-CP Rain and Lightning
Examples & Explanations
Suppose that today there is a 60% chance of rain, a
15% chance of lightning, and a 20% chance of
lightning if it’s raining. What is the chance of both rain
and lightning today?
P(rain) = .6
P(lightning) = .15
P(lightning | rain) = .2
Adapted from Illustrative Mathematics S-CP Rain and Lightning
Examples & Explanations
Suppose that today there is a 60% chance of rain, a
15% chance of lightning, and a 20% chance of
lightning if it’s raining. What is the chance of both rain
and lightning today?
P(rain) = .6
P(lightning) = .15
P(lightning | rain) = .2
Need to determine
P(lightning and rain)
Adapted from Illustrative Mathematics S-CP Rain and Lightning
Examples & Explanations
Suppose that today there is a 60% chance of rain, a
15% chance of lightning, and a 20% chance of
lightning if it’s raining. What is the chance of both rain
and lightning today?
P(rain) = .6
P(lightning) = .15
P(lightning | rain) = .2
P(lightning and rain)/P(rain) =
P(lightning | rain)
Adapted from Illustrative Mathematics S-CP Rain and Lightning
Examples & Explanations
Suppose that today there is a 60% chance of rain, a
15% chance of lightning, and a 20% chance of
lightning if it’s raining. What is the chance of both rain
and lightning today?
P(rain) = .6
P(lightning) = .15
P(lightning | rain) = .2
P(lightning and rain)/.6 = .2
P(lightning and rain) = .12
There is a 12% chance of
both rain and lightning today.
Adapted from Illustrative Mathematics S-CP Rain and Lightning
Examples & Explanations
On April 15, 1912, the Titanic struck an iceberg and rapidly sank with
only 710 of her 2,204 passengers and crew surviving. Some believe that
the rescue procedures favored the wealthier first class passengers.
Data on survival of passengers are summarized in the table below. We
will use this data to investigate the validity of such claims. (Data source:
http://www.encyclopedia-titanica.org/titanic-statistics.html)
Survived
Did not survive Total
First class passengers
201
123
324
Second class passengers
118
166
284
Third class passengers
181
528
709
Total
500
817
1317
Adapted from Illustrative Mathematics – S-CP The Titanic 1
Examples & Explanations
Survived
Did not survive Total
First class passengers
201
123
324
Second class passengers
118
166
284
Third class passengers
181
528
709
Total
500
817
1317
If one of the passengers is randomly selected, what is the
probability that this passenger was in first class and survived?
If one of the passengers is randomly selected from the first
class passengers, what is the probability that this passenger
survived?
Adapted from Illustrative Mathematics – S-CP The Titanic 1
Examples & Explanations
Survived
Did not survive Total
First class passengers
201
123
324
Second class passengers
118
166
284
Third class passengers
181
528
709
Total
500
817
1317
If one of the passengers is randomly selected, what is the
probability that this passenger was in first class and survived?
Adapted from Illustrative Mathematics – S-CP The Titanic 1
Examples & Explanations
Survived
Did not survive Total
First class passengers
201
123
324
Second class passengers
118
166
284
Third class passengers
181
528
709
Total
500
817
1317
If one of the passengers is randomly selected, what is the
probability that this passenger was in first class and survived?
201
1317 ≈ .153
Adapted from Illustrative Mathematics – S-CP The Titanic 1
Examples & Explanations
Survived
Did not survive Total
First class passengers
201
123
324
Second class passengers
118
166
284
Third class passengers
181
528
709
Total
500
817
1317
If one of the passengers is randomly selected from the first
class passengers, what is the probability that this passenger
survived?
Adapted from Illustrative Mathematics – S-CP The Titanic 1
Examples & Explanations
Survived
Did not survive Total
First class passengers
201
123
324
Second class passengers
118
166
284
Third class passengers
181
528
709
Total
500
817
1317
If one of the passengers is randomly selected from the first
class passengers, what is the probability that this passenger
survived?
201
324 ≈ .620
Adapted from Illustrative Mathematics – S-CP The Titanic 1
Examples & Explanations
Survived
Did not survive Total
First class passengers
201
123
324
Second class passengers
118
166
284
Third class passengers
181
528
709
Total
500
817
1317
Are the events “passenger survived” and “passenger was in
first class” independent events? Support your answer using
appropriate probability calculations.
Adapted from Illustrative Mathematics – S-CP The Titanic 2
Examples & Explanations
Survived
Did not survive Total
First class passengers
201
123
324
Second class passengers
118
166
284
Third class passengers
181
528
709
Total
500
817
1317
Are the events “passenger survived” and “passenger was in
first class” independent events? Support your answer using
appropriate probability calculations.
Two events A and B are independent if P(A|B) = P(A)
Adapted from Illustrative Mathematics – S-CP The Titanic 2
Examples & Explanations
Survived
Did not survive Total
First class passengers
201
123
324
Second class passengers
118
166
284
Third class passengers
181
528
709
Total
500
817
1317
P(survived | first class) = 201 324 ≈ .620
P(survived) = 500 1317 ≈ .380
Adapted from Illustrative Mathematics – S-CP The Titanic 2
Examples & Explanations
Survived
Did not survive Total
First class passengers
201
123
324
Second class passengers
118
166
284
Third class passengers
181
528
709
Total
500
817
1317
P(survived | first class) = 201 324 ≈ .620
P(survived) = 500 1317 ≈ .380
Since .620 ≠ .380 the two events are not independent.
Adapted from Illustrative Mathematics – S-CP The Titanic 2
Analytic Geometry EOCT Released Items
Released Items: Housed in the
Assessment Division of GADOE
http://www.gadoe.org/Curriculum-Instruction-andAssessment/Assessment/Documents/Analytic%20Geometry%
20Released%20Items%20Booklet%20Revised%208-2713.pdf
Released Items Commentary: Housed
in the Assessment Division of GADOE
http://www.gadoe.org/Curriculum-Instruction-andAssessment/Assessment/Documents/Analytic%20Geometry%2
0Released%20Items%20-%20Commentary%20Revised%20827-13.pdf
There are 18 released items and commentary about each item available for
Analytic Geometry
Analytic Geometry EOCT Released Items
Analytic Geometry Released Item #18
Data on AG Released Item #18
Unit 7 Frameworks
The following tasks in Unit 7 are related to this
released item:
•
•
•
•
The Conditions are Right
The Land of Independence
False Positives
Are You Positive
EOCT Study Guide
http://www.gadoe.org/Curriculum-Instruction-andAssessment/Assessment/Documents/EOCT%20Anal
ytic%20Geometry%20Study%20Guide%20FINAL%2
08.27.13.pdf
EOCT Study Guide
http://www.gadoe.org/Curriculum-Instruction-andAssessment/Assessment/Documents/EOCT%20Anal
ytic%20Geometry%20Study%20Guide%20FINAL%2
08.27.13.pdf
Resource List
The following list is provided as a
sample of available resources and
is for informational purposes only.
It is your responsibility to
investigate them to determine
their value and appropriateness
for your district. GaDOE does not
endorse or recommend the
purchase of or use of any
particular resource.
• CCGPS Resources
Resources
 Georgia Virtual Learning - http://www.gavirtuallearning.org/Resources.aspx
SEDL videos - http://bit.ly/RwWTdc or http://bit.ly/yyhvtc
 Illustrative Mathematics - http://www.illustrativemathematics.org/
 Mathematics Vision Project - http://www.mathematicsvisionproject.org/index.html
 Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/
Tools for the Common Core Standards - http://commoncoretools.me/
 LearnZillion - http://learnzillion.com/
• Assessment Resources
 MAP - http://www.map.mathshell.org.uk/materials/index.php
 Illustrative Mathematics - http://illustrativemathematics.org/
 CCSS Toolbox: PARCC Prototyping Project - http://www.ccsstoolbox.org/
 Smarter Balanced - http://www.smarterbalanced.org/smarter-balanced-assessments/
 PARCC - http://www.parcconline.org/
Online Assessment System - http://bit.ly/OoyaK5
LearnZillion Revised
http://learnzillion.com/lessons?utf8=%E2%9C%93&query=&commit=Go
• A more “user friendly” version of the Learnzillion lessons
support learning new strategies, sharing with parents, helping
absent students.
LearnZillion Revised
http://learnzillion.com/lessons?utf8=%E2%9C%93&query=&commit=Go
LearnZillion Revised
http://learnzillion.com/lessons?utf8=%E2%9C%93&query=&commit=Go
LearnZillion Revised
http://learnzillion.com/lessons?utf8=%E2%9C%93&query=&commit=Go
LearnZillion Revised
http://learnzillion.com/lessons?utf8=%E2%9C%93&query=&commit=Go
LearnZillion Revised
http://learnzillion.com/lessons?utf8=%E2%9C%93&query=&commit=Go
LearnZillion Revised
http://learnzillion.com/lessons?utf8=%E2%9C%93&query=&commit=Go
LearnZillion Revised
http://learnzillion.com/lessons?utf8=%E2%9C%93&query=&commit=Go
Resources
• Professional Learning Resources
 Inside Mathematics- http://www.insidemathematics.org/
 Annenberg Learner - http://www.learner.org/index.html
 Edutopia – http://www.edutopia.org
 Teaching Channel - http://www.teachingchannel.org
 Ontario Ministry of Education - http://bit.ly/cGZlce
Achieve - http://www.achieve.org/
 Expeditionary Learning: Center for Student Work - http://elschools.org/student-work
• Blogs
 Dan Meyer – http://blog.mrmeyer.com/
 Robert Kaplinsky - http://robertkaplinsky.com/
• Books
 Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8
Feedback
http://www.surveymonkey.com/s/WZKG5G2
James Pratt – jpratt@doe.k12.ga.us
Brooke Kline – bkline@doe.k12.ga.us
Thank You!
Please visit http://ccgpsmathematics9-10.wikispaces.com/ to share your feedback, ask
questions, and share your ideas and resources!
Please visit https://www.georgiastandards.org/Common-Core/Pages/Math.aspx
to join the 9-12 Mathematics email listserve.
Follow us on Twitter
@GaDOEMath
Brooke Kline
Program Specialist (6‐12)
bkline@doe.k12.ga.us
James Pratt
Program Specialist (6-12)
jpratt@doe.k12.ga.us
These materials are for nonprofit educational purposes only.
Any other use may constitute copyright infringement.