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, 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 7 th Grade Unit 6: Probability February 28, 2013 James Pratt – Brooke Kline – Secondary Mathematics Specialists These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

Expectations and clearing up confusion Intent and focus of Unit 6 webinar. Framework tasks. GPB sessions on Georgiastandards.org. Standards for Mathematical Practice. Resources. CCGPS is taught and assessed from and beyond.

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 6 th grade standards it lists box plots (I teach 6 th 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/ 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 7 th grade teacher need to teach geometric constructions as they did under GPS? Wiki/ Questions – Unit 5

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? Wiki/ Questions – Unit 5

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 prisms  Question: …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? Wiki/ Questions – Unit 5

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, 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, 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 Resource Revision Team Grades 6-High School Brooke Kline Mathematics Program Lead Specialist Grades 6-High School James Pratt Secondary Mathematics Program Specialist

As part of the continuing implementation of CCGPS in the year , 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 and get started! Task submission period begins now and closes May 1, We look forward to seeing your tasks. Career-Based Mathematics Task Challenge

As part of the continuing implementation of CCGPS in the year , 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, If your student work sample is selected for inclusion we will notify you of its placement in the units via . Request for Student Sample Work

Submission guidelines : Attach the work sample(s) to an in any format. Whatever works for you, works for us. Indicate the grade level, unit, and task in the body of your , 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 with student work attached to the appropriate team member below. To be considered for inclusion, work samples must be submitted by May 17, We look forward to seeing your students’ work. Request for Student Sample Work Grades 6-High School Brooke Kline Mathematics Program Lead Specialist Grades 6-High School James Pratt Elementary 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. Adapted from Illustrative Mathematics 7.SP.7a How Many Buttons No Buttons One or Two Buttons Three or Four Buttons More Than Four Buttons Male Female

Achieve: 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. Adapted from Illustrative Mathematics 7.SP.7a How Many Buttons No Buttons One or Two Buttons Three or Four Buttons More Than Four Buttons 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? Adapted from Illustrative Mathematics 7.SP.7a How Many Buttons No Buttons One or Two Buttons Three or Four Buttons More Than Four Buttons Male pqrs Female tuvw

Adapted from Illustrative Mathematics 7.SP.7a How Many Buttons No Buttons One or Two Buttons Three or Four Buttons More Than Four Buttons Male pqrs Female tuvw

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 female is wearing a shirt with two or fewer buttons? Adapted from Illustrative Mathematics 7.SP.7a How Many Buttons No Buttons One or Two Buttons Three or Four Buttons More Than Four Buttons Male pqrs Female tuvw

Adapted from Illustrative Mathematics 7.SP.7a How Many Buttons No Buttons One or Two Buttons Three or Four Buttons More Than Four Buttons Male pqrs Female tuvw

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 6 th grade Predicting frequency based on probability – came from 6 th grade Determine basic probability from probability models – came from 8 th grade Find the probability of compound events – came from 8 th grade

Coherence and Focus K-6 th  Categorical data  Measurement and data  Data organization 8 th -12 th  Independence  Conditional Probability  Probability formulas  Expected Value

Examples & Explanations Make 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

Examples & Explanations Make 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)

Examples & Explanations Make a list of all the different possible outcomes that might be observed when two dice are rolled. What proportion of the 36 possible outcomes result in at least one six? 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)

Examples & Explanations Make a list of all the different possible outcomes that might be observed when two dice are rolled. What proportion of the 36 possible outcomes result in at least one six? 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)

Examples & Explanations 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)

Examples & Explanations Make a list of all the different possible outcomes that might be observed when two dice are rolled. 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? Adapted from Illustrative Mathematics 7.SP Rolling Dice

Examples & Explanations Adapted from Illustrative Mathematics 7.SP Rolling Dice

Examples & Explanations SEDL Video for 7.SP.7a

Examples & Explanations 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?

Examples & Explanations 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. 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.

Examples & Explanations Adapted from Illustrative Mathematics 7.SP Waiting Times 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] G,G,R,B] R,R,G,G,R,R,R,R,Y,Y,Y,R,B]

Examples & Explanations Adapted from Illustrative Mathematics 7.SP Waiting Times 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] →2 G,R,R,Y,R,G,Y,G,G,B] →10 B] →1 R,G,B] →3 R,B] →2 B] →1 G,G,R,B] →4 R,R,G,G,R,R,R,R,Y,Y,Y,R,B] →13

Examples & Explanations Adapted from Illustrative Mathematics 7.SP Waiting Times 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] →2 G,R,R,Y,R,G,Y,G,G,B] →10 B] →1 R,G,B] →3 R,B] →2 B] →1 G,G,R,B] →4 R,R,G,G,R,R,R,R,Y,Y,Y,R,B] →13

Examples & Explanations Adapted from Illustrative Mathematics 7.SP Waiting Times 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? Probability of having to purchase at least 5 boxes to get a blue pen.

Examples & Explanations Adapted from Illustrative Mathematics 7.SP Waiting Times

Examples & Explanations Adapted from Illustrative Mathematics 7.SP Waiting Times 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? Mean number of boxes you would have to buy to get a blue pen.

Examples & Explanations Adapted from Illustrative Mathematics 7.SP Waiting Times 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? Mean number of boxes you would have to buy to get a blue pen.

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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 - or  Illustrative Mathematics -  Dana Center's CCSS Toolbox -  Common Core Standards -  Tools for the Common Core Standards -  Phil Daro talks about the Common Core Mathematics Standards -  LearnZillion - Assessment Resources  MAP -  Illustrative Mathematics -  CCSS Toolbox: PARCC Prototyping Project -  PARCC -  Online Assessment System - Resources

Professional Learning Resources  Inside Mathematics-  Annenberg Learner -  Edutopia –  Teaching Channel -  Ontario Ministry of Education -  Achieve - Blogs  Dan Meyer –  Timon Piccini –  Dan Anderson –

Thank You! Please visit to share your feedback, ask questions, and share your ideas and resources! Please visit to join the 6-8 Mathematics listserve. Follow on Twitter! Brooke Kline Program Specialist (6 ‐ 12) James Pratt Program Specialist (6-12) These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.