1. CCGPS Mathematics 6 th Grade Update Webinar Unit 7: Rational Explorations: Numbers and their Opposites March 14, 2014 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. Update on the work of the 2013 Resource Revision Team  Overall revisions  Unit 7 revisions Addressing areas which teachers have found to be more challenging Resources What are update webinars?

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. Unit 7: Rational Explorations: Numbers and Their Opposites Standards for Mathematical Practice Strategies for Teaching and Learning Changes to Tasks

6. UNIT 7 Standards for Mathematical Practice Specific Standards for Mathematical Practice Below are the relevant Standards for Mathematical Practice for the task: WHAT’S YOUR SIGN?

7. UNIT 7 Strategies for Teaching and Learning The Strategies for Teaching and Learning section has some very important notes regarding concepts and the intent of this unit, as the foundation for Integers is set here in sixth grade.

8. UNIT 7 Strategies for Teaching and Learning

9. Unit 7 Changes TASKS Kept the Same:  Representing Rational Numbers on the Number Line  Symbols of Inequalities and the Coordinate System  Graphing on the Coordinate Plane  Sounds of the Band Minor typo corrections to some of these, nothing significant!

10. Unit 7 Changes TASKS Changed and Added:  What’s Your Sign?  Note the STOP sign: Discussion of opposite numbers should occur at this time.  Absolute Value and Ordering

11. Unit 7 Changes TASK ADDED:  Absolute Value and Ordering  Two versions of this task Version 1: Scaffolded Version 2: Open-ended  Includes an emphasis on 6.NS.7d. Distinguish between comparisons of absolute value and statements about order  For negative numbers, as the absolute value of a number increases, the value of the number decreases! Great opportunity for mathematical discourse!

12. NEW FALS for 6 th Grade! Proportional Reasoning  Possibly with Unit 2 Fractions, Decimals and Percents  Assessing comparing & ordering positive rationals before introducing negatives

13. KEEP CHECKING BACK TO THE COMPREHENSIVE COURSE GUIDE THE FLIP CHART ILLUSTRATIVE MATH LEARNZILLION ROBERT KAPLINSKY INSIDE MATHEMATICS AND OTHER RESOURCES SUGGESTED BY THE DOE Remember…

14. The table shows the lowest elevation above sea level for three cities. Adapted from Illustrative Mathematics 6.NS Above and below sea level Unit 7 Challenges City, StateElevation above sea level (ft) Elevation below sea level (ft) Denver, Colorado 5130 New Orleans, Louisiana -8 Seattle, Washington 0

15. The table shows the lowest elevation above sea level for three cities. New Orleans is |-8| ft below sea level. T or F Adapted from Illustrative Mathematics 6.NS Above and below sea level Unit 7 Challenges City, StateElevation above sea level (ft) Elevation below sea level (ft) Denver, Colorado 5130 New Orleans, Louisiana -8 Seattle, Washington 0

16. The table shows the lowest elevation above sea level for three cities. Seattle is 0 ft below sea level. T or F Adapted from Illustrative Mathematics 6.NS Above and below sea level Unit 7 Challenges City, StateElevation above sea level (ft) Elevation below sea level (ft) Denver, Colorado 5130 New Orleans, Louisiana -8 Seattle, Washington 0

17. The table shows the lowest elevation above sea level for three cities. Denver is |5130| ft below sea level. T or F Adapted from Illustrative Mathematics 6.NS Above and below sea level Unit 7 Challenges City, StateElevation above sea level (ft) Elevation below sea level (ft) Denver, Colorado 5130 New Orleans, Louisiana -8 Seattle, Washington 0

18. The table shows the lowest elevation above sea level for three cities. Adapted from Illustrative Mathematics 6.NS Above and below sea level Unit 7 Challenges City, StateElevation above sea level (ft) Elevation below sea level (ft) Denver, Colorado 5130-5130 New Orleans, Louisiana -88 Seattle, Washington 00

19. Adapted from Illustrative Mathematics 6.NS Distance between points Unit 7 Challenges

20. What is the distance between points B and C? Adapted from Illustrative Mathematics 6.NS Distance between points Unit 7 Challenges

21. What is the distance between points B and C? Adapted from Illustrative Mathematics 6.NS Distance between points Unit 7 Challenges

22. What is the distance between points B and C? 5 units Adapted from Illustrative Mathematics 6.NS Distance between points Unit 7 Challenges

23. What is the distance between points B and C? B is |2| units above the x - axis. C is |3| units below the x - axis. Adapted from Illustrative Mathematics 6.NS Distance between points Unit 7 Challenges

24. What is the distance between points B and C? B is |2| units above the x - axis. C is |3| units below the x - axis. Total distance: |2| + |3| = 5 units Adapted from Illustrative Mathematics 6.NS Distance between points Unit 7 Challenges

25. 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://ccgpsmathematics9-10.wikispaces.com/http://ccgpsmathematics9-10.wikispaces.com/  CCGPS Mathematics Frameworks and Comprehensive Course Overviews - https://www.georgiastandards.org/Common-Core/Pages/Math-9-12.aspx https://www.georgiastandards.org/Common-Core/Pages/Math-9-12.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

26. 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. Resources

27. CCGPS Resources  Georgia Virtual Learning - http://www.gavirtuallearning.org/Resources.aspxhttp://www.gavirtuallearning.org/Resources.aspx  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/  Mathematics Vision Project - http://www.mathematicsvisionproject.org/index.htmlhttp://www.mathematicsvisionproject.org/index.html  LearnZillion - http://learnzillion.com/http://learnzillion.com/  ShareMyLesson - http://www.sharemylesson.com/http://www.sharemylesson.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/  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/  Online Assessment System - http://bit.ly/OoyaK5http://bit.ly/OoyaK5 Resources

28. sharemylesson.com http://www.sharemylesson.com/teaching-resources/

29. sharemylesson.com http://www.sharemylesson.com/teaching-resources/

30. sharemylesson.com http://www.sharemylesson.com/teaching-resources/

31. sharemylesson.com http://www.sharemylesson.com/teaching-resources/

32. Professional Learning Resources  Inside Mathematics- http://www.insidemathematics.org/http://www.insidemathematics.org/  Edutopia – http://www.edutopia.orghttp://www.edutopia.org  Teaching Channel - http://www.teachingchannel.orghttp://www.teachingchannel.org  Achieve - http://www.achieve.org/http://www.achieve.org/  Expeditionary Learning: Center for Student Work - http://elschools.org/student-workhttp://elschools.org/student-work Blogs  Dan Meyer – http://blog.mrmeyer.com/http://blog.mrmeyer.com/  Robert Kaplinsky - http://robertkaplinsky.com/http://robertkaplinsky.com/  Estimation 180 - http://www.estimation180.com/http://www.estimation180.com/  Graphing Stories - http://graphingstories.com/http://graphingstories.com/ Books  Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8 Resources

33. 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 Feedback

34. 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. Thank You!