1. CCGPS Mathematics Unit-by-Unit Grade Level Webinar 8 th Grade Unit 3: Geometric Applications of Exponents September 4, 2012 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 3: Geometric Applications of Exponents September 4, 2012 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 This webinar focuses on CCGPS content specific to Unit 3, 8 th Grade. For information about CCGPS across a single grade span, please access the list of recorded GPB sessions on Georgiastandards.org. For information on the Standards for Mathematical Practice, please access the list of recorded Blackboard sessions from Fall 2011 on GeorgiaStandards.org. CCGPS is taught and assessed from 2012-2013 and beyond. A list of resources will be provided at the end of this webinar and these documents are posted in the 6-8 wiki. http://ccgpsmathematics6-8.wikispaces.com/

4. Expectations and clearing up confusion The intent of this webinar is to bring awareness to:  the types of tasks that are contained within the unit.  your conceptual understanding of the mathematics in this unit.  approaches to the tasks which provide deeper learning situations for your students. We will not be working through each task during this webinar.

5. Welcome! Thank you for taking the time to join us in this discussion of Unit 3. At the end of today’s session you should have at least 3 takeaways:  the big idea of Unit 3  something to think about…some food for thought  how might I support student problem solving?  what is my conceptual understanding of the material in this unit?  a list of resources and support available for CCGPS mathematics

6. Welcome! Please provide feedback at the end of today’s session.  Feedback helps us become better teachers and learners.  Feedback helps as we develop the remaining unit-by-unit webinars.  Please visit http://ccgpsmathematics6-8.wikispaces.com/ to share your feedback..http://ccgpsmathematics6-8.wikispaces.com/ After reviewing the remaining units, please contact us with content area focus/format suggestions for future webinars. 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

7. Misconception? Richard Benson: The Very Best Totally Wrong Answers

8. Misconception? Richard Benson: The Very Best Totally Wrong Answers

9. Welcome! For today’s session have you:  read the mathematics CCGPS?  read the unit and worked through the tasks in the unit?  downloaded and saved the documents from this session? Ask questions and share resources/ideas for the common good. Bookmark and become active in the 6-8 wiki. If you are still wondering what a wiki is, we will discuss this near the end of the session.

10. Activate your Brain Use the Pythagorean Theorem to find the length of orange line segment inside the cube. 5 in

11. Activate your Brain Use the Pythagorean Theorem to find the length of orange line segment inside the cube. 5 in Do you like this question? Does this question require students to reveal their understanding of when to apply the Pythagorean Theorem to determine lengths in 3-D figures? Could you improve this question in order to assist in revealing student misconceptions with the Pythagorean Theorem and 3-D figures?

12. Misconceptions It is important to realize that inevitably students will develop misconceptions… Askew and Wiliam 1995; Leinwand, 2010; NCTM, 1995; Shulman, 1996

13. Misconception – Invented Rule? Richard Benson: The Very Best Totally Wrong Answers

14. Misconception – Invented Rule? Richard Benson: The Very Best Totally Wrong Answers

15. Misconceptions Therefore it is important to have strategies for identifying, remedying, as well as for avoiding misconceptions. Leinwand, 2010; Swan 2001; NBPTS, 1998; NCTM, 1995; Shulman, 1986;

16. Activate your Brain Use the Pythagorean Theorem to find the length of orange line segment inside the cube. 5 in

17. Activate your Brain How do you find the length of the orange line segment inside of the cube? Adapted from Learnzillion.com 8.G.7 & 8.EE.2 5 in

18. Activate your Brain How do you find the length of the orange line segment inside of the cube? Adapted from Learnzillion.com 8.G.7 & 8.EE.2 5 in

19. Activate your Brain How do you find the length of the orange line segment inside of the cube? Adapted from Learnzillion.com 8.G.7 & 8.EE.2 5 in

20. Activate your Brain How do you find the length of the orange line segment inside of the cube? Adapted from Learnzillion.com 8.G.7 & 8.EE.2 5 in leg 2 + leg 2 = hypotenuse 2 5 2 + 5 2 = x 2 25 + 25 = x 2 50 = x 2

21. Activate your Brain How do you find the length of the orange line segment inside of the cube? Adapted from Learnzillion.com 8.G.7 & 8.EE.2 5 in 7.1 in 5 in leg 2 + leg 2 = hypotenuse 2 5 2 + 5 2 = x 2 25 + 25 = x 2 50 = x 2 7.1 = x

22. Activate your Brain How do you find the length of the orange line segment inside of the cube? Adapted from Learnzillion.com 8.G.7 & 8.EE.2 leg 2 + leg 2 = hypotenuse 2 5 in 7.1 in x

23. Activate your Brain How do you find the length of the orange line segment inside of the cube? Adapted from Learnzillion.com 8.G.7 & 8.EE.2 leg 2 + leg 2 = hypotenuse 2 5 in 7.1 in x 5 2 + 7.1 2 = x 2 25 + 50.4 = x 2 75.4 = x 2

24. Activate your Brain How do you find the length of the orange line segment inside of the cube? Adapted from Learnzillion.com 8.G.7 & 8.EE.2 leg 2 + leg 2 = hypotenuse 2 5 in 7.1 in x 5 2 + 7.1 2 = x 2 25 + 50.4 = x 2 75.4 = x 2 8.68… = x 8.7 = x

25. Activate your Brain Learnzillion.com Review Common Mistakes Core Lesson Guided Practice Extension Activities Quick Quiz

26. What’s the big idea? Overview Key Standards Enduring Understandings Essential Questions Strategies for Teaching & Learning

27. What’s the big idea? Deepen understanding with evaluating square roots and cube roots. Develop deep understanding with using square root and cube root symbols to represent solutions of simple quadratic and cubic equations. Develop deep understanding with applications of the Pythagorean Theorem. Deepen understanding with volume. Develop deep understanding with using and applying the volume formulas for a cone, cylinder and sphere.

28. What’s the big idea? Standards for Mathematical Practice Education Week Webinar – Bristol CT School District

29. What’s the big idea? Standards for Mathematical Practice Education Week Webinar – Math Practices and the Common Core

30. Questions that arose Converse of the Pythagorean Theorem “Small” perfect squares and cubes Operations with radicals

31. Questions that arose Essential Questions

32. Questions that arose Enduring Understandings estimate

33. Questions that arose Acting Out Task – Essential Questions

34. Questions that arose Angry Bird Task – Essential Questions

35. Questions that arose Angry Bird Task Extension – Distance Formula

36. Coherence and Focus – Unit 3 Education Week Webinar – Jason Zimba, lead writer of the CCSM

37. Coherence and Focus – Unit 3 What are students coming with?

38. Coherence and Focus – Unit 3 What foundation is being built? Where does this understanding lead students? Enduring Understandings Evidence of Learning

39. Coherence and Focus – Unit 3 View across grade bands K-7 th  3-D shapes & volume  Rational/Irrational numbers, square roots & cube roots  Solving Equations 9 th -12 th  Distance Formula  Solving quadratic and cubic equations  Trigonometry

40. Misconception? Richard Benson: The Very Best Totally Wrong Answers

41. Examples & Explanations Use the right triangle with side lengths of 3 cm, 4cm, and 5 cm to explain a proof of the Pythagorean Theorem? 4 cm 3 cm 5 cm

42. Examples & Explanations How can you explain a proof of the Pythagorean Theorem using the diagram below? Adapted from Learnzillion.com 8.G.6

43. Examples & Explanations Adapted from Learnzillion.com 8.G.6 4 cm 3 cm

44. Examples & Explanations Adapted from Learnzillion.com 8.G.6 9 cm 2 16 cm 2

45. Examples & Explanations Adapted from Learnzillion.com 8.G.6 9 cm 2 16 cm 2

46. Examples & Explanations Adapted from Learnzillion.com 8.G.6 9 cm 2 16 cm 2

47. Examples & Explanations Adapted from Learnzillion.com 8.G.6 9 cm 2 16 cm 2 6 6 6 6 1

48. Examples & Explanations Adapted from Learnzillion.com 8.G.6 9 cm 2 16 cm 2 6 6 6 6 1 25 cm 2

49. Examples & Explanations Adapted from Learnzillion.com 8.G.6 9 cm 2 16 cm 2 6 6 6 6 1 25 cm 2 3 2 + 4 2 = 5 2 9 cm 2 +16 cm 2 =25 cm 2

50. Examples & Explanations Adapted from Learnzillion.com 8.G.6 a c leg hypotenuse bleg 3 2 + 4 2 = 5 2 9 cm 2 +16 cm 2 =25 cm 2 a 2 + b 2 = c 2 Pythagorean Theorem leg 2 + leg 2 = hypotenuse 2

51. Examples & Explanations Use the Pythagorean Theorem to determine if the triangle is a right triangle.

52. Examples & Explanations Is it possible to determine if the triangle is a right triangle? If so, explain how you could prove whether it is or is not a right triangle. If not possible, explain why you can not make this determination. 8.G.6, 8.G.8, & 8.EE.2

53. Examples & Explanations 8.G.6, 8.G.8, & 8.EE.2

54. Examples & Explanations 8.G.6, 8.G.8, & 8.EE.2 8 6

55. Examples & Explanations 8.G.6, 8.G.8, & 8.EE.2 8 6 x

56. Examples & Explanations 8.G.6, 8.G.8, & 8.EE.2 8 6 x 4 4 4 10 y z

57. Examples & Explanations 8.G.6, 8.G.8, & 8.EE.2 8 6 x 4 4 4 10 y z

58. Examples & Explanations 8.G.6, 8.G.8, & 8.EE.2 8 6 x 4 4 4 10 y z If the triangle is a right triangle, then the squares of the two shorter sides must equal the square of the longest side, or x² + y² = z².

59. Examples & Explanations 8.G.6, 8.G.8, & 8.EE.2 8 6 x 4 4 4 10 y z If the triangle is a right triangle, then the squares of the two shorter sides must equal the square of the longest side, or x² + y² = z². x² = 100, y² = 32, z² = 116 100 + 32 ? 116 132 ≠ 116 Therefore, the triangle is not a right triangle.

60. Assessment How might it look? Mathematics Assessment Project - http://map.mathshell.org/materials/tests.php Illustrative Mathematics - http://illustrativemathematics.org/ http://illustrativemathematics.org/ Dana Center’s CCSS Toolbox: PARCC Prototype Project - http://www.ccsstoolbox.org/ http://www.ccsstoolbox.org/ Online Assessment System - http://www.gadoe.org/Curriculum- Instruction-and-Assessment/Assessment/Pages/OAS.aspx http://www.gadoe.org/Curriculum- Instruction-and-Assessment/Assessment/Pages/OAS.aspx

61. Race to the Top Assessment Toolbox Update Fall 2012

62. RT3 Assessment Initiatives Purpose – To support teachers in preparing the students for the Common Core Assessment that is to occur in spring 2015 – To provide assessment resources that reflect the rigor of the CCGPS – To balance the use of formative and summative assessments in the classroom 62

63. RT3 Assessment Initiatives Development of a three-prong toolkit to support teachers and districts and to promote student learning – A professional development opportunity that focuses on assessment literacy – A set of benchmarks in ELA, Math, and selected grades for Science and Social Studies – An expansive bank of formative assessment items/tasks based on CCGPS in ELA and Math as a teacher resource 63

64. Formative Assessment Conducted during instruction (lesson, unit, etc.) Identifies student strengths and weaknesses Helps teacher determine next steps – Review – Differentiation – Continuation Supplies information to provide students with detailed feedback Assessment for the purpose of improving achievement LOW stakes 64

65. Purpose of the Formative Item Bank The purpose of the Formative Item Bank is to provide items and tasks used to assess students’ knowledge while they are learning the curriculum. The items will provide an opportunity for students to show what they know and show teachers what students do not understand. 65

66. Formative Item Bank Assessments Aligned to CCGPS Format aligned with Common Core Assessments Open-ended and constructed response items as well as multiple choice items Holistic Rubrics Anchor Papers Student Exemplars 750+ Items Available in OAS by late September 66

67. Formative Item Bank Availability All items that pass data review will be uploaded to the Georgia OAS at Level 2. Formative Item Bank will be ready for use by all Georgia educators mid-September, 2012. 67

68. 68 Item Types – Multiple Choice (MC) – Extended Response (ER) – Scaffolded Item (SC)

69. Extended Response Items Performance-based tasks May address multiple standards, multiple domains, and/or multiple areas of the curriculum May allow for multiple correct responses and/or varying methods of arriving at a correct answer Scored through use of a rubric and associated student exemplars 69

70. Mathematics Sample Item – Grade HS an extended response item 70

71. Example Rubric 71

72. Scaffolded Items Include a sequence of items or tasks Designed to demonstrate deeper understanding May be multi-standard and multi-domain May guide a student to mapping out a response to a more extended task Scored through use of a rubric and associated student exemplars 72

73. Mathematics Sample Item – Grade 3 a scaffolded item 73

74. Mathematics Items Assess students’ conceptual and computational understanding Tasks require students to – Apply the mathematics they know to real world problems – Express mathematical reasoning by showing their work or explaining their answer 74

75. Where do you Find the Items? 75 rt1234567890 student

76. Georgia Department of Education Assessment and Accountability Melissa Fincher Associate Superintendent Assessment and Accountability mfincher@doe.k12.ga.us Dr. Melodee Davis Director Assessment Research and Development medavis@doe.k12.ga.us Robert Anthony Assessment Specialist Formative Item Bank Race to the Top ranthony@doe.k12.ga.us Jan Reyes Assessment Specialist Interim Benchmark Assessments Race to the Top jreyes@doe.k12.ga.us Dr. Dawn Souter Project Manager Race to the Top dsouter@doe.k12.ga.us

77. Suggestions for getting started: Read the unit and work through the tasks with your colleagues. The only way to gain deep understanding is to work through each task. Make note of where, when, and what the big ideas are. Discuss the focus and coherence of the unit. Make note of where, when, and what the pitfalls might be. Look for additional tools/ideas you want to use. Determine any changes which might need to be made to make this work for your students. Share, ask, and collaborate on the wiki. http://ccgpsmathematics6-8.wikispaces.com/

78. 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.

79. What is a Wiki?

80. Resources Common Core Resources  SEDL videos - https://www.georgiastandards.org/Common-Core/Pages/Math.aspx or http://secc.sedl.org/common_core_videos/https://www.georgiastandards.org/Common-Core/Pages/Math.aspx http://secc.sedl.org/common_core_videos/  Illustrative Mathematics - http://www.illustrativemathematics.org/http://www.illustrativemathematics.org/  Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/http://www.ccsstoolbox.com/  Arizona DOE - http://www.azed.gov/standards-practices/mathematics-standards/http://www.azed.gov/standards-practices/mathematics-standards/  Ohio DOE - http://www.ode.state.oh.us/GD/Templates/Pages/ODE/ODEPrimary.aspx?page=2&TopicRel ationID=1704 http://www.ode.state.oh.us/GD/Templates/Pages/ODE/ODEPrimary.aspx?page=2&TopicRel ationID=1704  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://serpmedia.org/daro-talks/index.html http://serpmedia.org/daro-talks/index.html Books  Van DeWalle and Lovin, Teaching Student-Centered Mathematics, 6-8

81. Resources 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 Assessment Resources  MAP - http://www.map.mathshell.org.uk/materials/index.phphttp://www.map.mathshell.org.uk/materials/index.php  CCSS Toolbox: PARCC Prototyping Project - http://www.ccsstoolbox.org/http://www.ccsstoolbox.org/  PARCC - http://www.parcconline.org/parcc-stateshttp://www.parcconline.org/parcc-states 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/

82. Resources Dana Center’s CCSS Toolbox - PARCC Prototyping Project  http://www.ccsstoolbox.com/ http://www.ccsstoolbox.com/

83. Resources Dan Meyer’s Three-Act Math Tasks  https://docs.google.com/spreadsheet/lv?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWn M2YWxWYVM1UWowTEE https://docs.google.com/spreadsheet/lv?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWn M2YWxWYVM1UWowTEE

84. As you start your day tomorrow… …the standards are not units of instruction; you don’t always “teach a standard” in one chunk, whatever the order…The standards describe achievements we want students to have. As my colleague Jason Zimba likes to say, you don’t teach standards, you teach mathematics. Bill McCallum – lead writer of the CCSM

85. 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.http://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.