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.
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CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Analytic Geometry B/Advanced Algebra Unit 5: Inferences and Conclusions from Data August.
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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
Session will be begin at 8:00 amWhile 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 MathematicsUnit-by-Unit Grade Level Webinar
Accelerated Analytic Geometry B/Advanced AlgebraUnit 5: Inferences and Conclusions from Data
• 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.
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
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?
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?
Adapted from Illustrative Mathematics S-ID.4 Do You 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.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.
Adapted from Illustrative Mathematics S-ID.4 Do You Fit In This Car?
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.
standard deviations above the mean and standard deviations below the mean.
Adapted from Illustrative Mathematics S-ID.4 Do You Fit In This Car?
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.
standard deviations above the mean and standard deviations below the mean.
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?
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.
standard deviations above the mean and standard deviations below the mean.
Adapted from Illustrative Mathematics S-ID.4 Do You Fit In This Car?
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.
Adapted from Illustrative Mathematics S-ID.4 Do You Fit In This Car?
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.
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 & 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.
Adapted from Illustrative Mathematics S-IC Sarah the Chimpanzee
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.
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 & 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
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.' […]
~ Dr. Melissa Fincher, Associate Superintendent for Assessment and Accountability(excerpt from an email sent to K-12 Assessment Directors from Dr. Fincher)
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/