CCGPS Mathematics Unit-by-Unit Grade Level Webinar 7 th Grade Unit 6: Probability February 28, 2013 Session will be begin at 8:00 am While you are waiting,

CCGPS MathematicsUnit-by-Unit Grade Level Webinar

7th GradeUnit 6: Probability

February 28, 2013

Session will be begin at 8:00 amWhile you are waiting, please do the following:

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CCGPS MathematicsUnit-by-Unit Grade Level Webinar

7th GradeUnit 6: Probability

February 28, 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]


Expectations and clearing up confusion

• Intent and focus of Unit 6 webinar.• Framework tasks.• GPB sessions on Georgiastandards.org.• Standards for Mathematical Practice. • Resources. • http://ccgpsmathematics6-8.wikispaces.com/• CCGPS is taught and assessed from 2012-2013 and beyond.

http://ccgpsmathematics9-10.wikispaces.com/

CCGPS Mathematics Sequence for Implementation

CCGPS Mathematics Resources for Implementation

• The big idea of Unit 6• Incorporating SMPs into probability tasks• Resources

Welcome!

• Question: ...So, should I be teaching box and whisker plots, scatter plots, dot plots. I did notice on the 6th grade standards it lists box plots (I teach 6th grade math too). Is a box plot the same as a box and whisker plot? I just feel like I should be teaching box and whisker plots when I teach measures of variability. I just feel like I am missing something when I look at these standards. Any help would be appreciated.

Wiki/Email Questions – Unit 4

• MCC7.G.2: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Question: Does the 7th grade teacher need to teach

geometric constructions as they did under GPS?


• MCC7.G.5: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

• Question: I have a question about the task “I Have a Secret Angle” in the Grade 7 Unit 5 frameworks which indicates that it addresses content standard 7.G.5. Should students know the sum of the interior angles of a triangle by this point? The two problems in this task would require that they know this information. Standard 8.G.5 is the first time I see a reference to the sum of the interior angles of a triangle in Common Core. Have I overlooked something in an earlier grade?


• MCC7.G.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prismsQuestion: …However, in the Unit 5 the Three Little Pig Builders –

House B task includes students working with the volume and surface area of a cylinder. My co-workers and I are confused on whether we need to include cylinders and cones in our teaching of this standard or not. Can you please shed a little light on this standard for us?


As part of the continuing implementation of CCGPS, the current CCGPS mathematics frameworks and units are being reviewed, revised, and augmented. The Georgia Department of Education is seeking qualified math educators to become part of the 2013 CCGPS Mathematics Resource Revision Team which will assist in this critical process.

The scope of the CCGPS Mathematics Resource Revision Team work will include, but is not limited to:• evaluating newly submitted tasks • assessing the need for additional tasks• assessing the order of current units and tasks• editing of current units and tasks • creating additional tasks to address gaps, if necessary

2013 Resource Revision Team

All work will be completed collaboratively with support structures provided by the Georgia Department of Education Mathematics Team.

All work is to be completed at the Georgia Department of Education, June 3rd-June 6, and June 10-13, 2013.

Team members will be compensated for contracted work in the amount of $2000 and travel expenses will be reimbursed.

If you are interested in becoming a part of the CCGPS Mathematics Resource Revision Team, please respond to the appropriate Georgia Department of Education contact below by March 1, 2013. In your response, please indicate grade level interest, why you would like to be part of this team, related experience, and the contact information for two references.

2013 Resource Revision Team

Grades 6-High SchoolBrooke Kline [email protected] Program Lead Specialist

Grades 6-High SchoolJames Pratt [email protected] Mathematics Program Specialist



As part of the continuing implementation of CCGPS in the year 2013 - 2014, the current GADOE mathematics frameworks and units are being reviewed, revised, and augmented. We are offering an opportunity for educators to assist in this critical process.

The challenge: Create a career-based mathematics task using guidelines provided to supplement and/or address gaps in the existing CCGPS frameworks units.

If your task is selected for addition to a unit, you will receive a $200 honorarium per task. All work is to be original using support structures provided by the Georgia Department of Education Mathematics Team.

If you are interested in participating in this challenge, please view the task creation guidelines at http://ccgps-task-submission-guidelines.wikispaces.com/, and get started! Task submission period begins now and closes May 1, 2013. We look forward to seeing your tasks.

Career-Based Mathematics Task Challenge

http://ccgps-task-submission-guidelines.wikispaces.com/

As part of the continuing implementation of CCGPS in the year 2013 - 2014, the current GADOE mathematics units are being augmented. We would like your assistance with this critical process.

Student work samples are a vital component of the frameworks which only you can provide. If you have been using the GADOE frameworks and have student work which you would be willing to share, please send it our way. We will remove any identifiers, and include selected student work samples in the revised frameworks which are slated to be released July 1, 2013. If your student work sample is selected for inclusion we will notify you of its placement in the units via email.

Request for Student Sample Work

Submission guidelines: Attach the work sample(s) to an email in any format. Whatever works for you, works for us. Indicate the grade level, unit, and task in the body of your email, and on the work sample in the upper left corner.You may cover any student/school identifiers if you wish, and we will do the same if any remain. Send the email with student work attached to the appropriate team member below. To be considered for inclusion, work samples must be submitted by May 17, 2013. We look forward to seeing your students’ work.

Request for Student Sample Work

Grades 6-High SchoolBrooke Kline [email protected] Program Lead Specialist

Grades 6-High SchoolJames Pratt [email protected] Mathematics Program Specialist



Look at the shirt you are wearing today, and determine how many buttons it has. Then complete the following table for all of the members of your class.

Activate your Brain

Adapted from Illustrative Mathematics 7.SP.7a How Many Buttons

No Buttons

One or TwoButtons

Three or FourButtons

More Than Four Buttons

Male

Female

Achieve: Math Works

http://www.achieve.org/math-works

Look at the shirt you are wearing today, and determine how many buttons it has. Then complete the following table for all of the members of your class.

Activate your Brain


No Buttons

One or TwoButtons



Male

Female

Suppose each student writes their name on an index card, and one card is selected randomly.

What is the probability that the student whose card is selected is wearing a shirt with no buttons?

Activate your Brain


No Buttons

One or TwoButtons



Male p q r s

Female t u v w


What is the probability that the student whose card is selected is wearing a shirt with no buttons?

Activate your Brain


No Buttons

One or TwoButtons



Male p q r s

Female t u v w


What is the probability that the student whose card is selected is female is wearing a shirt with two or fewer buttons?

Activate your Brain


No Buttons

One or TwoButtons



Male p q r s

Female t u v w


What is the probability that the student whose card is selected is female is wearing a shirt with two or fewer buttons?

Activate your Brain


No Buttons

One or TwoButtons



Male p q r s

Female t u v w

What’s the big idea?•Develop understanding of probability.•Develop understanding of probability models.•Deepen understanding of organization and representation of data.•Standards for Mathematical Practice.

What’s the big idea?Unit 6: Probability

New Content• Probability of a chance event – came from

6th grade• Predicting frequency based on probability –

came from 6th grade• Determine basic probability from probability

models – came from 8th grade• Find the probability of compound events –

came from 8th grade

Coherence and Focus• K-6th

Categorical data Measurement and data Data organization

• 8th-12th Independence Conditional Probability Probability formulas Expected Value

Examples & ExplanationsMake a list of all the different possible outcomes that might be observed when two dice are rolled.

Adapted from Illustrative Mathematics 7.SP Rolling Dice



(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)


What proportion of the 36 possible outcomes result in at least one six?


(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)




(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)




(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)


Suppose you were able to roll the two dice many thousands of times. What proportion of the time would you expect to roll at least one six?



Suppose you were able to roll the two dice many thousands of times. What proportion of the time would you expect to roll at least one six?


Examples & Explanations

SEDL Video for 7.SP.7a

http://secc.sedl.org/common_core_videos/grade.php?action=view&id=754




Adapted from Illustrative Mathematics 7.SP Waiting Times

Suppose each box of a popular brand of cereal contains a pen as a prize. The pens come in four colors, blue, red, green and yellow. Each color of pen is equally likely to appear in any box of cereal. Design and carry out a simulation to help you answer the following question.

What is the probability of having to buy at least five boxes of cereal to get a blue pen? What is the mean number of boxes you would have to buy to get a blue pen if you repeated the process many times?



Suppose each box of a popular brand of cereal contains a pen as a prize. The pens come in four colors, blue, red, green and yellow. Each color of pen is equally likely to appear in any box of cereal. Design and carry out a simulation to help you answer the following question.

If each color of pen is equally likely to appear in any box, the chance of getting a blue pen in any one box is ¼.

Using four colored tiles (blue, red, green and yellow) do random draws to determine how many draws required to get a blue.



Using four colored tiles (blue, red, green and yellow) I randomly drew until getting a blue recording the outcomes.

R,B]G,R,R,Y,R,G,Y,G,G,B]B]R,G,B]R,B]B]B]G,G,R,B]R,R,G,G,R,R,R,R,Y,Y,Y,R,B]



Using four colored tiles (blue, red, green and yellow) I randomly drew until getting a blue recording the outcomes. Then record the wait time to get a blue.R,B] →2G,R,R,Y,R,G,Y,G,G,B] →10B] →1R,G,B] →3R,B] →2B] →1B] →1G,G,R,B] →4R,R,G,G,R,R,R,R,Y,Y,Y,R,B] →13



Using four colored tiles (blue, red, green and yellow) I randomly drew until getting a blue recording the outcomes. Then record the wait time to get a blue.R,B] →2G,R,R,Y,R,G,Y,G,G,B] →10B] →1R,G,B] →3R,B] →2B] →1B] →1G,G,R,B] →4R,R,G,G,R,R,R,R,Y,Y,Y,R,B] →13

1 2 3 4 5 6 7 8 9 10 11 12 130

5

10

15

20

25

30

35

Wait Times

Waiting times to get a blue pen

Freq

uenc

y of

Wai

t Tim

e




Probability of having to purchase at least 5 boxesto get a blue pen.

1 2 3 4 5 6 7 8 9 10 11 12 130

5

10

15

20

25

30

35

Wait Times


Freq

uenc

y of

Wai

t Tim

e




Probability of having to purchase at least 5 boxesto get a blue pen.

1 2 3 4 5 6 7 8 9 10 11 12 13

0

5

10

15

20

25

30

35

Wait Times


Freq

uenc

y of

Wai

t Tim

e




Mean number of boxes you would have to buy to get a blue pen.

1 2 3 4 5 6 7 8 9 10 11 12 130

5

10

15

20

25

30

35

Wait Times


Freq

uenc

y of

Wai

t Tim

e




Mean number of boxes you would have to buy to get a blue pen.

1 2 3 4 5 6 7 8 9 10 11 12 130

5

10

15

20

25

30

35

Wait Times


Freq

uenc

y of

Wai

t Tim

e

3.26

Show What We Know?

Feedback

http://www.surveymonkey.com/s/WZKG5G2Thank you!

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

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.

• Common Core Resources SEDL videos - http://bit.ly/RwWTdc or http://bit.ly/yyhvtc Illustrative Mathematics - http://www.illustrativemathematics.org/ 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/ Phil Daro talks about the Common Core Mathematics Standards - http://bit.ly/URwOFT 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/ 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.ccsstoolbox.com/

http://www.corestandards.org/

http://commoncoretools.me/

http://bit.ly/URwOFT

http://learnzillion.com/

http://learnzillion.com/

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

http://illustrativemathematics.org/

http://www.ccsstoolbox.org/

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/ Timon Piccini – http://mrpiccmath.weebly.com/3-acts.html Dan Anderson – http://blog.recursiveprocess.com/tag/wcydwt/

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://blog.mrmeyer.com/

http://mrpiccmath.weebly.com/3-acts.html

http://blog.recursiveprocess.com/tag/wcydwt/

Thank You! Please visit http://ccgpsmathematics6-8.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 6-8 Mathematics email listserve.Follow on Twitter!

Follow @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://ccgpsmathematics9-10.wikispaces.com/

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



Documents

CCGPS Mathematics Unit-by-Unit Grade Level Webinar 7 th Grade Unit 6: Probability February 28, 2013 Session will be begin at 8:00 am While you are waiting,