1. CCGPS Mathematics 6 th Grade Update Webinar Unit 3: Expressions October 11, 2013 James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.usjpratt@doe.k12.ga.usbkline@doe.k12.ga.us Secondary Mathematics Specialists Microphone and speakers can be configured by going to: Tools – Audio – Audio setup wizard These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

2. What are update webinars? Update on the work of the 2013 Resource Revision Team  Overall revisions  Unit 3 revisions Addressing areas which teachers have found to be more challenging Resources

3. 2013 6 th Grade Resource Revision Team

4. 6 th Grade Math Resource Revision Team Tonya Burt- Lincoln County Middle School Anne Miller Gay – MS Math Coach, Camden County Beverly Harvey- Ebenezer MS, Effingham County Janet Kennedy – Kittredge Magnet School, Dekalb County Ashley Powell – Marietta 6 th Grade Academy, Marietta City

5. 6 th Grade Math Resource Revision Team Webinar Guide Comprehensive Course Guide Tonya Burt Unit 3 SMP’s, Strategies and Misconceptions – Janet Kennedy Unit 3 changes – Beverly Harvey FALs for Unit 3 (General information for FALs along with specific information on the one FAL in this unit). – Anne Gay

6. 6 th Grade Comprehensive Course Overview  Located on the 6-8 math section of www.georgiastandards.org www.georgiastandards.org  Designed to provide clarification of CCGPS Mathematics Standards  Organized to link together many sources of information pertinent to CCGPS 6 th Grade Math

7. Direct Link to Page Select the Comprehensive Course Guide

8. Flipbooks  Bold words will provide access to the Common Core Flipbooks  The Flipbooks offer clarification  Very Large File (slow loading) Direct link to Flipbook

9. Content Domain Flipbook Resources Active links to standard resources

10. Other Sections of Interest Unit Descriptions Webinar Information Assessment Resources and Instructional Support Resources Internet Resources Curriculum Map

11. Correction to Unit 1 Teachers Edition The highlighted statement below seems a little confusing. A better way to say this is: “ How many one-fourths equal 7/2?” We hope this clears this up.

12. Tasks Unit 3

13. Standards for Mathematical Practice, Strategies Misconceptions Unit 3 Specific Standards for Mathematical Practice A step was taken by the team to incorporate in each unit specific Standards for Mathematical Practice. Instead of listing the eight general SMPs repeatedly throughout the units, we chose the standards that were most relevant with terminology specific to the task. Below are the relevant Standards for Mathematical Practice for the task: Exponents. 3. Construct viable arguments and critique the reasoning of others. Students construct and critique arguments regarding the equivalence of expressions and the use of variable expressions to represent real-world situations. 6. Attend to precision. Students use the mathematical language with relation to exponents. 7. Look for and make use of structure. Students use the table to organize and compare base, exponent, exponential forms, standard from, and value.

14. Standards for Mathematical Practice, Strategies and Misconceptions Unit 3

15. Standards for Mathematical Practice, Strategies and Misconceptions Unit 3 MISCONCEPTIONS 1. The mnemonic PEMDAS can mislead students into thinking that addition must comes before subtraction and multiplication must come before division. 2. Students fail to see juxtaposition (side by side) as indicating multiplication. For example, evaluating 3x as 35 when x = 5 instead of 3 times 5 = 15. Also, students may rewrite 8 – 2a as 6a. 3. Students also miss the understood “1” in front of a lone variable like a or x or p. For example, not realizing that 4a + a is 5a. 4. Many of the misconceptions when dealing with expressions stem from the misunderstanding/reading of the expression. For example, knowing the operations that are being referenced with notation like x 3, 4x, 3(x + 2y) is critical. The fact that x 3 means (x)(x)(x) which is x times x times x, not 3x or 3 times x; 4x means 4 times x or x + x + x + x, not forty-something.

16. Task Changes Unit 3

17. Tasks - unchanged  Rules for Exponents  Conjectures about Properties  Are we Equal?

18. Writing Expressions  Added to address EE.2a

19. Update Tasks  Writing and Evaluating Expressions  Added some items  Culminating Task: Sweet Tooth Chocolate Shop  Reworked to be more relevant  Exponents  Removed prime factor tree

20.  FALS Formative Assessment Lessons Developed by the MARS, Shell Center To Inform Instruction 2/3 into a unit Preferably not graded

21. 2 Types of FALs Specific to Unit 3  Called “Classroom Challenges” in the new revision by Shell. GaDOE will continue to refer to this type of informing activity as Formative Assessment Lessons  Concept Development FALs  Problem Solving FALS  Unit 3 contains 6 th Grade’s first Concept Development FAL

22. Concept Development FALs  Intended to assess and develop understanding of fundamental concepts  Feedback given after collaborative task but before post-assessment  Students may be grouped based on common misconceptions from pre- assessment

23. Laws of Arithmetic  http://map.mathshell.org.uk/materials/ download.php?fileid=1358

24. 6 th Grade FAL in Unit 3

25. Laws of Arithmetic  Addresses 6EE and 6G (uses area model, which students should be familiar with)  SMPs: 1, 5, 7  Pre-assessment  about 2 days before the task (15 minutes: Expressions and Areas)  Students shouldn’t worry if they can’t do everything on the pre-assessment  80-minute lesson  Some whole class examples, then cards of expressions and area models to match  15 minute Post-assessment  Expressions and Areas (revisited)

26. Laws of Arithmetic  Following the pre-assessment, the teacher should note problems seen in student work.  There is also a page of “Common Issues” included to provide commonly found misconceptions and problems you might see. Use these, add to them, whatever helps diagnose and address YOUR students’ needs.

27. FALs are accessible at the MAP website http://map.mathshell.org.uk/materials/index.php http://map.mathshell.org.uk/materials/index.php

28. Training is Available  The Mathematics Specialists at the RESAS offer training in using the FALS, Short Cycle Tasks, and other resources from the Mathematics Design Collaborative.

29. Things to Remember  Use the Wiki to share information with other teachers and to ask questions.  This is a living document. Please share anything you may have to enhance this or any unit. The Wiki is the teacher community page to share anything you have.  The DOE CCGPS tab is static, viewable for anyone. Teacher pages and any updates or additional resources, including hot links, are only available through Learning Village.

30. Unit 3 Challenges Adapted from Illustrative Mathematics 6.EE Rectangle Perimeter 2

31. Unit 3 Challenges Adapted from Illustrative Mathematics 6.EE Rectangle Perimeter 2

32. Unit 3 Challenges Adapted from Illustrative Mathematics 6.EE Rectangle Perimeter 2

33. Unit 3 Challenges Adapted from Illustrative Mathematics 6.EE Rectangle Perimeter 2

34. Unit 3 Challenges Adapted from Illustrative Mathematics 6.EE Rectangle Perimeter 2

35. Unit 3 Challenges MCC.6.EE.4

36. Unit 3 Challenges MCC.6.EE.4

37. Unit 3 Challenges MCC.6.EE.4

38. Unit 3 Challenges MCC.6.EE.4

39. Unit 3 Challenges MCC.6.EE.4

40. Unit 3 Challenges MCC.6.EE.4

41. Unit 3 Challenges MCC.6.EE.4

42. GaDOE Resources  Fall 2011 CCGPS Standards for Mathematical Practices Webinars - https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx  Spring 2012 CCGPS Mathematics Professional Learning Sessions on GPB - https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx  2012 – 2013 CCGPS Mathematics Unit-by-Unit Webinar Series - https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx  Georgia Mathematics Teacher Forums - http://ccgpsmathematics6-8.wikispaces.com/http://ccgpsmathematics6-8.wikispaces.com/  CCGPS Mathematics Frameworks and Comprehensive Course Overviews - https://www.georgiastandards.org/Common-Core/Pages/Math-6-8.aspx https://www.georgiastandards.org/Common-Core/Pages/Math-6-8.aspx  Mathematics Formative Assessment Lesson Videos - https://www.georgiastandards.org/Common-Core/Pages/Mathematics-Formative- Assessment-Lessons-Videos.aspx https://www.georgiastandards.org/Common-Core/Pages/Mathematics-Formative- Assessment-Lessons-Videos.aspx Resources

43. 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.

44. CCGPS 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  Online Assessment System - http://bit.ly/OoyaK5http://bit.ly/OoyaK5  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/  Smarter Balanced - http://www.smarterbalanced.org/smarter-balanced-assessments/http://www.smarterbalanced.org/smarter-balanced-assessments/  PARCC - http://www.parcconline.org/http://www.parcconline.org/ 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/  Robert Kaplinsky - http://robertkaplinsky.com/http://robertkaplinsky.com/ Books  Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8

47. Resources http://robertkaplinsky.com/

48. Mathematical Understanding? http://robertkaplinsky.com/what-does-it-mean-to- understand-mathematics/

49. http://robertkaplinsky.com/what-does-it-mean-to- understand-mathematics/ Procedural skill and fluency Conceptual understanding The ability to apply mathematics Mathematical Understanding?

50. Feedback http://www.surveymonkey.com/s/WZKG5G2 James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.usjpratt@doe.k12.ga.usbkline@doe.k12.ga.us

51. 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.