1. CCGPS Mathematics 6 th Grade Update Webinar Unit 2: Rate, Ratio and Proportional Reasoning Using Equivalent Fractions September 13, 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 2 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 2 Task Chart- Ashley Powell SMP’s, Strategies and Misconceptions – Janet Kennedy Unit 2 changes – Beverly Harvey FALs for Unit 2 (Guide for FALs along with specific information on the two FALs in this unit. – Anne Gay

6. 6 th grade Math Comprehensive Course Guide 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. 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

8. Begin at www.georgiastandards.org Direct Link to Page

9. Select the CCGPS ELA/Math Tab Direct Link to Page

10. Select the Mathematics option under Browse CCGPS Direct Link to Page

11. Select the 6-8 option in the Mathematics section Direct Link to Page

12. Select the Grade 6 option Direct Link to Page

13. Select the Comprehensive Course Guide

14. This is your Comprehensive Course Guide

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

16. Content Domain Flipbook Resources Active links to standard resources

17. Standard Specific Information  Each Standard is Linked to Flipbook information  Select the Standard to gain quick access to clarification without having to scroll through multiple pages

18. Standards for Mathematical Practice Active Links Provided to Videos and Information on the Standards for Mathematical Practice Active Links Provided for EACH Standard for Mathematical Practice

19. Task Descriptions Scaffolding Task -Tasks that build up to the learning task. Learning Task- Constructing understanding through deep/rich contextualized problem solving tasks. Practice Task -Tasks that provide students opportunities to practice skills and concepts. Performance Task -Tasks which may be a formative or summative assessment that checks for student understanding/misunderstanding and or progress toward the standard/learning goals at different points during a unit of instruction. Culminating Task -Designed to require students to use several concepts learned during the unit to answer a new or unique situation. Allows students to give evidence of their own understanding toward the mastery of the standard and requires them to extend their chain of mathematical reasoning.

20. Formative Assessment Lessons (FALs)

21. Formative Assessment Lessons (“Classroom Challenges”) Developed by the Shell Center Embedded in the FY14 Units, also available at http://map.mathshell.org.uk/materials/lessons.php http://map.mathshell.org.uk/materials/lessons.php Usually 2/3 into a unit Intended to guide instructional decisions for the rest of the unit Not intended to be graded, but for feedback Plan is to have at least one per unit Details coming in Unit 2, when the first available 6 th grade FAL occurs

22. Short Cycle Tasks Also from the Shell Center (Mathematics Assessment Project web site) “Tasks” tab: Short assessments with rubrics Included in each unit as available “Mathematical skills and practices might be assessed partly in isolation, partly under scaffolded conditions, and partly when students face substantial problems without scaffolded support. We call tasks that assess these three different types of performance novice, apprentice, and expert tasks respectively”

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

24. Examples of Resources Assessment Resources and Instructional Support Resources The resource sites listed below are designed to support the instructional and assessment needs of teachers. All BLUE links will direct teachers to the site mentioned. CCGPS Frameworks are "models of instruction" designed to support teachers in the implementation of the Common Core Georgia Performance Standards (CCGPS). The Georgia Department of Education, Office of Standards, Instruction, and Assessment has provided an example of the Curriculum Map for each grade level and examples of Frameworks aligned with the CCGPS to illustrate what can be implemented within the grade level. School systems and teachers are free to use these models as is; modify them to better serve classroom needs; or create their own curriculum maps, units and tasks. The Teacher Resource Link (TRL) is an application that delivers vetted and aligned digital resources to Georgia’s teachers. TRL is accessible via the GaDOE “tunnel” in conjunction with LDS using the single sign-on process. The content is aligned to Common Core Georgia Performance Standards, Georgia Performance Standards, and National Education Technology Standards and pushed to teachers based on course schedule. Georgia Online Assessment (OAS) System Teachers can use the OAS as a tool for Assessment for Learning. Student results on assessments help teachers identify learner needs and strengths and inform instructional practices. Robust reports also allow teachers to communicate with students and parents about learner goals, intentions, and outcomes. The OAS helps with a cycle of assessments, instruction, feedback, and communication that allows teachers, students, and parents to be confident with instructional success. Teachers will be particularly interested in the Formative Item Bank.

25. Examples of Resources Webinar support and links will direct teachers to archived webinars as well as links to join or view upcoming webinars. Course/Grade Level WIKI spaces are available to post questions about a unit, a standard, the course, or any other CCGPS math related concern. Shared resources and information are also available at the site. CRCT Resources are available to provide more information for the CRCT as provided by the GaDoe. Georgiastandards.org provides a gateway to a wealth of instructional links and information. Open the Common Core GPS tab at the top to access specific math resources for CCGPS. Formula Sheet is the formula sheet found on the GaDoe website and the formula sheet used on the CRCT.

26. Tasks Unit 2

27. Standards for Mathematical Practice, Strategies Misconceptions Unit 2 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. For example in the TASK: UNDERSTANDING THE LONG DIVISION ALGORITHM the following standards were listed: Before- 1. Make sense of problems and persevere in solving them. Now-1. Make sense of problems and persevere in solving them. Students make sense of multi-digit division problems using the standard algorithm. Students represent this visually through a base-ten chart.

28. Standards for Mathematical Practice, Strategies and Misconceptions Unit 2 Before-4. Model with mathematics. Now-4. Model with mathematics. Students will model multi-digit division with base-ten charts. Before- 5. Use appropriate tools strategically. Now-5. Use appropriate tools strategically. Students will use visual tools (base-ten charts) for of multi-digit division. Before- 7. Look for and make use of structure. Now-7. Look for and make use of structure. Students examine the relationship between the dividend, quotient, and divisor in a multi-digit division problem using the base-ten chart. This addition of specific standards is an important bonus for the classroom teacher.

29. Standards for Mathematical Practice, Strategies and Misconceptions Unit 2 Strategies The Strategies in this unit were greatly enhanced with some helpful explanations and samples.

30. Standards for Mathematical Practice, Strategies and Misconceptions Unit 2 Misconceptions The team added misconceptions to each unit as documented by research. This addition was in- line with other states, as we previewed other states’ documents. It was the teams hope that math teachers in our state will find this information useful when writing lesson plans and being effective teachers in the their classroom

31. Types of Tasks Unit 2 Types of Tasks (Chart in each unit) Each task is listed in a chart with the task type, content addressed and standard the task will address. Learning Task/Scaffolding Task Performance Task Formative Task/Formative Assessment lesson Summative Performance

32. Tasks -  No changes to the tasks in the unit  Only unit not to have additions/deletions and big changes  Changes made to make the student pages more user friendly  Misconceptions added to most individual task as well as unit  Look for changes in Units 3-7. We will discuss those changes in detail during those webinars.

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

34. 2 Types of FALs  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

35. Concept Development and Problem Solving FALs  Given 2/3 of the way through a unit  Pre and Post assessments  Teachers give feedback to pre- assessment and use it to group students  Accessible to all students  Not graded  Make effective use of Standards for Mathematical Practice

36. 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

37. Problem Solving FALs  Intended to assess and develop capacity to select and deploy mathematical knowledge in non-routine contexts  Feedback is given as part of the task  Students may be grouped based on different approaches to pre-assessment task

38. First 6 th Grade FAL is in Unit 2 (There are Two!) Addresses: SMP 1. Make sense of problems and persevere in solving them. SMP 2. Reason abstractly and quantitatively. SMP 4. Model with mathematics. 6.RP Understand ratio concepts and use ratio reasoning to solve problems.

39. Also… Addresses: SMP 1. Make sense of problems and persevere in solving them. SMP 2. Reason abstractly and quantitatively. SMP 3. Construct viable arguments and critique the reasoning of others. SMP 4. Model with mathematics. 6.RP Understand ratio concepts and use ratio reasoning to solve problems. 6.G Solve real-world and mathematical problems involving area, surface area and volume. Note the quick links to sections of the task on the side bar.

40. What do I need to do to get started on this first FAL – Traveling to School? 1. Print the FAL; print copies of pages S-1 through S-5 for students. 2. Before the lesson, students work individually on the pre-assessment task- Sharing Gasoline Costs. 3. Review their work and write questions to help students improve their work. Note the Common Issues, pg.T-3 4. During the lesson, students work in 2’s or 3’s on the task. 1. They plan a strategy, share ideas on chart paper 2. They examine samples of other student work (provided) 3. Teacher notes strategies used 5. In whole class discussion, share and compare strategies

41. Preparation: 6 th grade Example  Each small group needs a piece of poster paper, markers, a copy of each of the Sample Solutions to Discuss  There are slides provided to support the task  Proposed Time:  20 minutes before the lesson (pre-assessment)  80 minute lesson  20 minutes for follow-up lesson

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

43. Short Cycle Tasks  Located under the Tasks tab  Short tasks  To be graded  Rubrics provided  Often student work samples provided  None at this time for unit 2 – first 6 th grade SCT is in Unit 5

44.  Instructions and detailed information is available under the “Instructions” tab

45. 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.

46. 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.

47. Julianna participated in a walk-a-thon to raise money for cancer research. She recorded the total distance she walked at several different points in time, but a few of the entries got smudged and can no longer be read. The times and distances that can still be read are listed in the table below. Assume Julianna walked at a constant speed. Complete the table and plot Julianna’s progress in the coordinate plane. Unit 2 Challenges Adapted from Illustrative Mathematics 6.RP Walk-a-thon 1

48. Assume Julianna walked at a constant speed. Complete the table and plot Julianna’s progress in the coordinate plane. Unit 2 Challenges Adapted from Illustrative Mathematics 6.RP Walk-a-thon 1

49. Julianna participated in a walk-a-thon to raise money for cancer research. She recorded the total distance she walked at several different points in time, but a few of the entries got smudged and can no longer be read. The times and distances that can still be read are listed in the table below. How fast was Julianna walking in miles per hour? How long did it take Julianna to walk one mile? Unit 2 Challenges Adapted from Illustrative Mathematics 6.RP Walk-a-thon 1

50. How fast was Julianna walking in miles per hour? How long did it take Julianna to walk one mile? Unit 2 Challenges Adapted from Illustrative Mathematics 6.RP Walk-a-thon 1

51. How fast was Julianna walking in miles per hour? How long did it take Julianna to walk one mile? Unit 2 Challenges Adapted from Illustrative Mathematics 6.RP Walk-a-thon 1

52. Julianna participated in a walk-a-thon to raise money for cancer research. She recorded the total distance she walked at several different points in time, but a few of the entries got smudged and can no longer be read. The times and distances that can still be read are listed in the table below. Next year Julianna is planning to walk for seven hours. If she walks at the same speed next year, how many miles will she walk? Unit 2 Challenges Adapted from Illustrative Mathematics 6.RP Walk-a-thon 1

53. Next year Julianna is planning to walk for seven hours. If she walks at the same speed next year, how many miles will she walk? Unit 2 Challenges Adapted from Illustrative Mathematics 6.RP Walk-a-thon 1

54. Emily wants to make lemonade, the container says that she needs one scoop of lemonade powder for one quart of water. How many cups of water does she need to mix with two scoops of powder? Unit 2 Challenges

55. Emily wants to make lemonade, the container says that she needs one scoop of lemonade powder for one quart of water. How many cups of water does she need to mix with two scoops of powder? Unit 2 Challenges

56. Emily wants to make lemonade, the container says that she needs one scoop of lemonade powder for one quart of water. How many cups of water does she need to mix with two scoops of powder? Unit 2 Challenges

57. Emily wants to make lemonade, the container says that she needs one scoop of lemonade powder for one quart of water. How many cups of water does she need to mix with two scoops of powder? Unit 2 Challenges

58. Emily wants to make lemonade, the container says that she needs one scoop of lemonade powder for one quart of water. How many cups of water does she need to mix with two scoops of powder? Unit 2 Challenges

59. Emily wants to make lemonade, the container says that she needs one scoop of lemonade powder for one quart of water. How many cups of water does she need to mix with two scoops of powder? Emily needs 8 cups of water. Unit 2 Challenges

60. Assessment July 22, 2013 – State School Superintendent Dr. John Barge and Gov. Nathan Deal announced today that Georgia is withdrawing from the Partnership for Assessment of Readiness for College and Careers (PARCC) test development consortium. Instead, the Georgia Department of Education (GaDOE) will work with educators across the state to create standardized tests aligned to Georgia’s current academic standards in mathematics and English language arts for elementary, middle and high school students. Additionally, Georgia will seek opportunities to collaborate with other states. The press release in its entirety can be found at: http://www.gadoe.org/External-Affairs-and- Policy/communications/Pages/PressReleaseDetails.aspx?PressView=default&pid=123http://www.gadoe.org/External-Affairs-and- Policy/communications/Pages/PressReleaseDetails.aspx?PressView=default&pid=123

61. 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

62. 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.

63. 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

64. 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

65. Resources http://robertkaplinsky.com/

66. Resources http://robertkaplinsky.com/

67. 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

68. 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.