Download Aug29_800amAGBAAUnit5

CCGPS Mathematics
Unit-by-Unit Grade Level Webinar
Accelerated Analytic Geometry B/Advanced Algebra
Unit 5: Inferences and Conclusions from Data
August 29, 2013
Session will be begin at 8:00 am
While you are waiting, please do the following:
Configure your microphone and speakers by going to:
Tools – Audio – Audio setup wizard
Document downloads:
When you are prompted to download a document, please choose or create the
folder to which the document should be saved, so that you may retrieve it later.
CCGPS Mathematics
Unit-by-Unit Grade Level Webinar
Accelerated Analytic Geometry B/Advanced Algebra
Unit 5: Inferences and Conclusions from Data
August 29, 2013
James Pratt – [email protected]
Brooke Kline – [email protected]
Secondary Mathematics Specialists
These materials are for nonprofit educational purposes
only. Any other use may constitute copyright infringement.
Welcome!
• The big idea of Unit 5
•Incorporating SMPs into applications of statistics
• Resources
Wiki/Email Questions
• What is different about S.ID.2 in this course and when
it was addressed in Accelerated Coordinate
Algebra/Analytic Geometry A?
Wiki/Email Questions
• What is different about S.ID.2 in this course and when
it was addressed in Accelerated Coordinate
Algebra/Analytic Geometry A?
The difference is using Standard Deviation as a
measure of spread as opposed to Absolute Mean
Deviation.
From a class containing 12 girls
and 10 boys, three students are to
be selected to serve on a school
advisory panel. Which of the
following is the best sampling
method, among the four, if you want
the school panel to represent a fair
and representative view of the
opinions of your class?
Adapted from Illustrative Mathematics S-IC School Advisory Panel
1. Select the first three names on the class roll.
2. Select the first three student who volunteer.
3. Place the names of the 22 students in a hat, mix
them thoroughly, and select three names from the
mix.
4. Select the first three students who show up for
class tomorrow.
Adapted from Illustrative Mathematics S-IC School Advisory Panel
What’s the big idea?
•
•
•
Summarize, represent, and
interpret data on a single count or
measurement variable
Understand and evaluate random
processes underlying statistical
experiments
Make inferences and justify
conclusions from sample surveys,
experiments, and observational
studies.
What’s the big idea?
Standards for Mathematical Practice
What’s the big idea?
• SMP 1 – Make sense of problems
and persevere in solving them
• SMP 2 – Reason abstractly and
quantitatively
• SMP 3 – Construct viable
arguments and critique the
reasoning of others
• SMP 4 – Model with mathematics
• SMP 5 – Use appropriate tools
http://blog.mrmeyer.com/
strategically
http://bit.ly/17QDmw9
http://www.schooltube.com/video/81f35b2779ef8d4727fd/
http://www.youtube.com/watch?v=jRMVjHjYB6w
Coherence and Focus
• K-9th
Develop understanding of statistical
variability
Summarize and describe distributions
Use random sampling to draw inferences
about a population and comparative
inferences about two populations
Summarize, represent and interpret data
on a single count or measurement variable
(No standard deviation)
• 11th-12th
 Evaluate outcomes of decisions
Examples & Explanations
Automobile manufactures have to design the driver’s seat area
so that both tall and short adults can sit comfortably, reach all
the controls and pedals, and see through the windshield.
Suppose a new car is designed so that these conditions are
met for people from 58 inches to 76 inches tall.
The heights of adult men in the US are approximately normally
distributed with a mean of 70 inches and a standard deviation
of 3 inches. Heights of adult women are approximately normally
distributed with a mean of 64.5 inches and a standard deviation
of 2.5 inches.
Adapted from Illustrative Mathematics S-ID.4 Do You Fit In This Car?
Examples & Explanations
Automobile manufactures have to design the driver’s seat area so that both tall and short
adults can sit comfortably, reach all the controls and pedals, and see through the
windshield. Suppose a new car is designed so that these conditions are met for people
from 58 inches to 76 inches tall.
The heights of adult men in the US are approximately normally distributed with a mean of
70 inches and a standard deviation of 3 inches. Heights of adult women are
approximately normally distributed with a mean of 64.5 inches and a standard deviation
of 2.5 inches.
What percentage of US men will not be accommodated by the car?
What percentage of US women will not be accommodated by the car?
Adapted from Illustrative Mathematics S-ID.4 Do You Fit In This Car?
Examples & Explanations
Automobile manufactures have to design the driver’s seat area so that both tall and short
adults can sit comfortably, reach all the controls and pedals, and see through the
windshield. Suppose a new car is designed so that these conditions are met for people
from 58 inches to 76 inches tall.
The heights of adult men in the US are approximately normally distributed with a mean of
70 inches and a standard deviation of 3 inches. Heights of adult women are
approximately normally distributed with a mean of 64.5 inches and a standard deviation
of 2.5 inches.
What percentage of US men will not be accommodated by the car?
What percentage of US women will not be accommodated by the car?
Adapted from Illustrative Mathematics S-ID.4 Do You Fit In This Car?
Examples & Explanations
Suppose a new car is designed so that these conditions are met for people from 58
inches to 76 inches tall.
The heights of adult men in the US are approximately normally distributed with a mean of
70 inches and a standard deviation of 3 inches.
What percentage of US men will not be accommodated by the car?
For men, we want the percentage of the normal distribution with mean 70
and standard deviation 3 that is above 76 inches or below 58 inches.
76−70 6
=3=2
3
standard deviations above the mean and
standard deviations below the mean.
Adapted from Illustrative Mathematics S-ID.4 Do You Fit In This Car?
70−58
3
=
12
=4
3
Examples & Explanations
For men, we want the percentage of the normal distribution with mean 70
and standard deviation 3 that is above 76 inches or below 58 inches.
76−70 6
=3=2
3
standard deviations above the mean and
standard deviations below the mean.
Adapted from Illustrative Mathematics S-ID.4 Do You Fit In This Car?
70−58
3
=
12
=4
3
Examples & Explanations
For men, we want the percentage of the normal distribution with mean 70
and standard deviation 3 that is above 76 inches or below 58 inches.
76−70 6
=3=2
3
standard deviations above the mean and
standard deviations below the mean.
1 − 0.9772 = 0.0228
So, about 2.3% of adult men won’t fit in this car.
Adapted from Illustrative Mathematics S-ID.4 Do You Fit In This Car?
70−58
3
=
12
=4
3
Examples & Explanations
Suppose a new car is designed so that these conditions are met for people from 58
inches to 76 inches tall.
Heights of adult women are approximately normally distributed with a mean of 64.5
inches and a standard deviation of 2.5 inches.
What percentage of US women will not be accommodated by the car?
For women, we want the percentage of the normal distribution with mean
64.5 and standard deviation 2.5 that is above 76 inches or below 58
inches.
76−64.5 11.5
=
= 4.6 standard
2.5
2.5
6.5
= 2.6 standard deviations
2.5
deviations above the mean and 64.5−58
=
2.5
below the mean.
Adapted from Illustrative Mathematics S-ID.4 Do You Fit In This Car?
Examples & Explanations
For women, we want the percentage of the normal distribution with mean
64.5 and standard deviation 2.5 that is above 76 inches or below 58
inches.
76−64.5 11.5
= 2.5 = 4.6
2.5
standard
deviations above the mean
and 64.5−58
=
2.5
6.5
= 2.6
2.5
standard deviations below
the mean.
Adapted from Illustrative Mathematics S-ID.4 Do You Fit In This Car?
Examples & Explanations
For women, we want the percentage of the normal distribution with mean
64.5 and standard deviation 2.5 that is above 76 inches or below 58
inches.
76−64.5 11.5
= 2.5 = 4.6
2.5
standard
deviations above the mean
and 64.5−58
=
2.5
6.5
= 2.6
2.5
standard deviations below
the mean.
The area is 0.00466, so that about
0.5% of adult women will not fit in this car.
Adapted from Illustrative Mathematics S-ID.4 Do You Fit In This Car?
Examples & Explanations
In 1978, researchers Premack and Woodruff published a study
in Science magazine, reporting an experiment where an adult
chimpanzee named Sarah was shown videotapes of eight
different scenarios of a human being faced with a problem.
After being shown each videotape, she was presented with two
photographs, one of which depicted a possible solution to the
problem. In the experiment, Sarah picked the photograph with
the correct solution seven times out of eight.
Adapted from Illustrative Mathematics S-IC Sarah the Chimpanzee
Examples & Explanations
In 1978, researchers Premack and Woodruff published a study in Science
magazine, reporting an experiment where an adult chimpanzee named
Sarah was shown videotapes of eight different scenarios of a human
being faced with a problem. After being shown each videotape, she was
presented with two photographs, one of which depicted a possible
solution to the problem. In the experiment, Sarah picked the photograph
with the correct solution seven times out of eight.
Does the outcome of Premack and Woodruff’s experiment
provide evidence that Sarah was recognizing correct solutions,
and not just randomly guessing? Explain.
Adapted from Illustrative Mathematics S-IC Sarah the Chimpanzee
Examples & Explanations
Does the outcome of Premack and Woodruff’s experiment provide
evidence that Sarah was recognizing correct solutions, and not just
randomly guessing? Explain.
Using a coin flip simulator you can see that 7 or more
successes out of 8 trials rarely happens by pure chance.
Adapted from Illustrative Mathematics S-IC Sarah the Chimpanzee
Examples & Explanations
A bank has placed 1,500 marbles in a very large, clear jar near
the customer entrance. Since the bank’s logo’s colors are blue
and white, some of the 1,500 marbles are blue and the rest are
white. In order to enter the contest, a customer must fill in an
entry form with his/her estimate for the percentage of blue
marbles in the jar. The entry form says the following:
I think that 1 out of every _________ marbles in this jar is blue.
(Fill in the blank with a “2”, “3”, “4”, “5”, or “6”.)
Adapted from Illustrative Mathematics S-IC The Marble Jar
Examples & Explanations
A bank has placed 1,500 marbles in a very large, clear jar near the customer entrance.
Since the bank’s logo’s colors are blue and white, some of the 1,500 marbles are blue
and the rest are white. In order to enter the contest, a customer must fill in an entry form
with his/her estimate for the percentage of blue marbles in the jar. The entry form says
the following:
I think that 1 out of every _________ marbles in this jar is blue.
(Fill in the blank with a “2”, “3”, “4”, “5”, or “6”.)
Without counting all the marbles, how would you determine the
proportion of blue marbles in the jar?
Adapted from Illustrative Mathematics S-IC The Marble Jar
1. Select the first three names on the
class roll.
2. Select the first three student who
volunteer.
3. Place the names of the 22 students
in a hat, mix them thoroughly, and
select three names from the mix.
4. Select the first three students who
show up for class tomorrow.
Adapted from Illustrative Mathematics S-IC School Advisory Panel
Assessment – Released Items
We have posted a set of released […] EOCT items to the GaDOE
website. In addition to the item booklet itself, you will find commentary and
field test performance data. […] The items are posted on the EOCT
webpage, under the link 'EOCT Resources.' A direct link to this webpage is
provided below. Please scroll down the page and look under the heading
'Other Documents and Resources.' […]
http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Pages/EOCTResources.aspx
~ Dr. Melissa Fincher, Associate Superintendent for Assessment and Accountability
(excerpt from an email sent to K-12 Assessment Directors from Dr. Fincher)
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
 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/
 Common Core Standards - http://www.corestandards.org/
 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

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/
• Blogs
 Dan Meyer – http://blog.mrmeyer.com/
 Robert Kaplinsky - http://robertkaplinsky.com/
• Books
 Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8
Resources
http://robertkaplinsky.com/
Feedback
http://www.surveymonkey.com/s/WZKG5G2
James Pratt – [email protected]
Brooke Kline – [email protected]
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)
[email protected]
James Pratt
Program Specialist (6-12)
[email protected]
These materials are for nonprofit educational purposes only.
Any other use may constitute copyright infringement.