1. CCGPS Mathematics Unit-by-Unit Grade Level Webinar 8 th Grade Unit 7: Solving Systems of Equations March 5, 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.

2. CCGPS Mathematics Unit-by-Unit Grade Level Webinar 8 th Grade Unit 7: Solving Systems of Equations March 5, 2013 James Pratt – jpratt@doe.k12.ga.usjpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.usbkline@doe.k12.ga.us Secondary Mathematics Specialists These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

3. Expectations and clearing up confusion Intent and focus of Unit 7 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.

4. CCGPS Mathematics Sequence for Implementation

5. CCGPS Mathematics Resources for Implementation

6. The big idea of Unit 7 Incorporating SMPs into systems of equations tasks Resources Welcome!

7.  Question: Are arithmetic sequences a part of CCGPS for 8th grade? I have not seen it in the standards (or maybe I just missed it), but it would make sense to teach it with linear functions (just like geometric sequences is a part of exponential functions topic in Coordinate algebra course) Wiki/Email Questions – Units 5-7

8.  Question: …students are exposed to y = mx + b (slope- intercept form) when graphing lines, not standard form. She said they use standard form when solving systems algebraically, so they haven’t covered how to graph lines in standard form. Can you tell us the standard associated with this or let us know what the teachers need to do with respect to graphing lines (convert from standard to slope-intercept or use x and y intercepts to get the correct graph)? Wiki/Email Questions – Units 5-7

9. MCC7.SP.1-4: Investigate patterns of association in bivariate data. Question: Am I correct that box and whisker plots are not part of the 8th grade curriculum? I think some of the teachers were confused about the difference in "box plots" and box and whisker. Wiki/Email Questions – Unit 6 Favorite Subject by Grade GradeEnglishHistoryMath/ScienceOtherTotals 7 th 38362814116 8 th 47457218182 Total858110032298

10. MCC8.EE.8: Analyze and solve pairs of simultaneous linear equations.  Question: I have teachers who are inquiring about the algebraic ways to teach systems of equations (such as substitution and elimination). Or is there more of a focus on the conceptual understanding? Wiki/Email Questions – Unit 7

11. 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.http://ccgps-task-submission-guidelines.wikispaces.com/ Career-Based Mathematics Task Challenge

12. 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

13. 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 School Brooke Kline bkline@doe.k12.ga.usbkline@doe.k12.ga.us Mathematics Program Lead Specialist Grades 6-High School James Pratt jpratt@doe.k12.ga.usjpratt@doe.k12.ga.us Elementary Mathematics Program Specialist

14. Adapted from Illustrative Mathematics 8.EE How Many Solutions?

15. Achieve: Math Works http://www.achieve.org/math-works

16. Adapted from Illustrative Mathematics 8.EE How Many Solutions?

24. What’s the big idea? Deepen previous understandings linear equations. Develop understanding of systems of equations. Standards for Mathematical Practice.

25. Coherence and Focus K-7 th  Operations with rational numbers and algebraic thinking  Graphing on the coordinate plane  Ratios and proportional reasoning  Linear Functions (8 th grade Unit 5/6) 9 th -12 th  Systems of functions (linear and quadratic)  Constraints

26. Examples & Explanations Ivan’s furnace has quit working. He calls some companies to get an estimate on labor costs to determine which company to hire. Below are the price estimates for labor from three different companies. A.$35 per hour to its customers B.$25 per hour plus a $20 service fee C.$20 per hour plus a $45 service fee For which time intervals should Ivan choose Company A, Company B, Company C? Adapted from Illustrative Mathematics 8.EE Fixing the Furnace

27. Examples & Explanations Adapted from Illustrative Mathematics 8.EE Fixing the Furnace

28. Examples & Explanations Adapted from Illustrative Mathematics 8.EE Fixing the Furnace

29. A type of pasta is made of a blend of quinoa and corn. The pasta company is not disclosing the percentage of each ingredient in the blend but we know that the quinoa in the blend contains 16.2% protein, and the corn in the blend contains 3.5% protein. Overall, each 57 gram serving of pasta contains 4 grams of protein. How much quinoa and how much corn is in one serving of the pasta? Adapted from Illustrative Mathematics 8.EE Quinoa Pasta 1 Examples & Explanations

30. Adapted from Illustrative Mathematics 8.EE Quinoa Pasta 1 Examples & Explanations

31. Adapted from Illustrative Mathematics 8.EE Quinoa Pasta 1 Examples & Explanations

32. Adapted from Illustrative Mathematics 8.EE Quinoa Pasta 1 Examples & Explanations

33. Adapted from Illustrative Mathematics 8.EE Cell Phone Plans A customer wants to know how to decide which plan will save her the most money. Determine which plan has the lowest cost given the number of text messages a customer is likely to send. A.Basic fee of $29.95 fee per month and 10 cents per text message B.Basic fee of $90.20 per month and has unlimited text messages C.Basic fee of $49.95 per month and 5 cents per text message

34. Examples & Explanations Adapted from Illustrative Mathematics 8.EE Cell Phone Plans

35. Examples & Explanations Adapted from Illustrative Mathematics 8.EE Cell Phone Plans

36. Examples & Explanations Adapted from Illustrative Mathematics 8.EE Cell Phone Plans

37. Examples & Explanations Adapted from Illustrative Mathematics 8.EE Cell Phone Plans B C A

38. Examples & Explanations Adapted from Illustrative Mathematics 8.EE Cell Phone Plans

39. Examples & Explanations Adapted from Illustrative Mathematics 8.EE Cell Phone Plans

40. Examples & Explanations Adapted from Illustrative Mathematics 8.EE Cell Phone Plans B C A

41. Examples & Explanations Adapted from Illustrative Mathematics 8.EE Cell Phone Plans A customer wants to know how to decide which plan will save her the most money. Determine which plan has the lowest cost given the number of text messages a customer is likely to send. Plan A is best for less than 400 texts Plan C is best for between 400 and 805 texts Plan B is best for over 805 texts

42. Show What We Know?

43. Feedback http://www.surveymonkey.com/s/WZKG5G2 Thank you!

44. 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.

45. Common Core Resources  SEDL videos - http://bit.ly/RwWTdc or http://bit.ly/yyhvtchttp://bit.ly/RwWTdchttp://bit.ly/yyhvtc  Illustrative Mathematics - http://www.illustrativemathematics.org/http://www.illustrativemathematics.org/  Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/http://www.ccsstoolbox.com/  Common Core Standards - http://www.corestandards.org/http://www.corestandards.org/  Tools for the Common Core Standards - http://commoncoretools.me/http://commoncoretools.me/  Phil Daro talks about the Common Core Mathematics Standards - http://bit.ly/URwOFThttp://bit.ly/URwOFT  LearnZillion - http://learnzillion.com/http://learnzillion.com/ Assessment Resources  MAP - http://www.map.mathshell.org.uk/materials/index.phphttp://www.map.mathshell.org.uk/materials/index.php  Illustrative Mathematics - http://illustrativemathematics.org/http://illustrativemathematics.org/  CCSS Toolbox: PARCC Prototyping Project - http://www.ccsstoolbox.org/http://www.ccsstoolbox.org/  PARCC - http://www.parcconline.org/http://www.parcconline.org/  Online Assessment System - http://bit.ly/OoyaK5http://bit.ly/OoyaK5 Resources

46. Professional Learning Resources  Inside Mathematics- http://www.insidemathematics.org/http://www.insidemathematics.org/  Annenberg Learner - http://www.learner.org/index.htmlhttp://www.learner.org/index.html  Edutopia – http://www.edutopia.orghttp://www.edutopia.org  Teaching Channel - http://www.teachingchannel.orghttp://www.teachingchannel.org  Ontario Ministry of Education - http://bit.ly/cGZlcehttp://bit.ly/cGZlce  Achieve - http://www.achieve.org/http://www.achieve.org/ Blogs  Dan Meyer – http://blog.mrmeyer.com/http://blog.mrmeyer.com/  Timon Piccini – http://mrpiccmath.weebly.com/3-acts.htmlhttp://mrpiccmath.weebly.com/3-acts.html  Dan Anderson – http://blog.recursiveprocess.com/tag/wcydwt/http://blog.recursiveprocess.com/tag/wcydwt/

47. 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 @GaDOEMathhttp://ccgpsmathematics6-8.wikispaces.com/https://www.georgiastandards.org/Common-Core/Pages/Math.aspx Brooke Kline Program Specialist (6 ‐ 12) bkline@doe.k12.ga.us James Pratt Program Specialist (6-12) jpratt@doe.k12.ga.us These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.