ccgps mathematics unit-by-unit grade level webinar accelerated analytic geometry b/advanced algebra...

CCGPS MathematicsUnit-by-Unit Grade Level Webinar

Accelerated Analytic Geometry B/Advanced AlgebraUnit 5: Inferences and Conclusions from Data

August 29, 2013

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CCGPS MathematicsUnit-by-Unit Grade Level Webinar

Accelerated Analytic Geometry B/Advanced AlgebraUnit 5: Inferences and Conclusions from Data

August 29, 2013

James Pratt – [email protected] Kline – [email protected] Mathematics Specialists

These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

mailto:[email protected]


• The big idea of Unit 5•Incorporating SMPs into applications of statistics• Resources

Welcome!

• 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.

Wiki/Email Questions

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?

Activate your Brain

Adapted from Illustrative Mathematics S-IC School Advisory Panel

Activate your Brain

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.


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

strategically http://blog.mrmeyer.com/http://bit.ly/17QDmw9

http://www.schooltube.com/video/81f35b2779ef8d4727fd/http://www.youtube.com/watch?v=jRMVjHjYB6w

http://blog.mrmeyer.com/


http://bit.ly/17QDmw9

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 variabilitySummarize and describe distributionsUse random sampling to draw inferences about a population and comparative inferences about two populationsSummarize, represent and interpret data on a single count or measurement variable (No standard deviation)

• 11th-12th Evaluate outcomes of decisions

Examples & ExplanationsAutomobile 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 & ExplanationsAutomobile 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?


Examples & ExplanationsSuppose 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.

standard deviations above the mean and standard deviations below the mean.


Examples & ExplanationsFor 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.



Examples & ExplanationsFor 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.


So, about 2.3% of adult men won’t fit in this car.


Examples & ExplanationsSuppose 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.



Examples & ExplanationsFor 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.

standard deviations above the mean

and standard deviations below the mean.


Examples & ExplanationsFor 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.

standard deviations above the mean

and standard deviations below the mean.The area is 0.00466, so that about0.5% of adult women will not 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 & ExplanationsIn 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.


Examples & ExplanationsDoes 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.


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 & ExplanationsA 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.

Activate your Brain


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/EOCT-Resources.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 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

http://bit.ly/RwWTdc

http://bit.ly/yyhvtc

http://www.illustrativemathematics.org/

http://www.mathematicsvisionproject.org/index.html

http://www.mathematicsvisionproject.org/index.html

http://www.ccsstoolbox.com/

http://www.corestandards.org/

http://commoncoretools.me/

http://learnzillion.com/

http://learnzillion.com/

http://www.map.mathshell.org.uk/materials/index.php

http://illustrativemathematics.org/

http://www.ccsstoolbox.org/

http://www.smarterbalanced.org/smarter-balanced-assessments/

http://www.parcconline.org/

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

http://www.insidemathematics.org/

http://www.learner.org/index.html

http://www.edutopia.org/

http://www.teachingchannel.org/

http://bit.ly/cGZlce

http://www.achieve.org/

http://www.achieve.org/


http://robertkaplinsky.com/


Resources




Feedbackhttp://www.surveymonkey.com/s/WZKG5G2

James Pratt – [email protected] Brooke Kline – [email protected]

http://www.surveymonkey.com/s/WZKG5G2

http://www.surveymonkey.com/s/WZKG5G2



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 KlineProgram Specialist (6‐12)

[email protected]

James PrattProgram Specialist (6-12)

[email protected]

These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

http://ccgpsmathematics9-12.wikispaces.com/

https://www.georgiastandards.org/Common-Core/Pages/Math.aspx



ccgps mathematics unit-by-unit grade level webinar accelerated analytic geometry b/advanced algebra...

Documents

big idea of unit

comparative inferences

school panel

class tomorrow

class roll

mathematics specialists

single count

ccgps mathematicsunit