1. CCGPS Mathematics Unit-by-Unit Grade Level Webinar Third Grade Unit 2: Operations and Algebraic Thinking: The Relationship Between Multiplication and Division August 7, 2012 Session will be begin at 3:15 pm 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 Grade Three Unit 2: Operations and Algebraic Thinking: The Relationship Between Multiplication and Division August 7, 2012 Turtle Toms– tgunn@doe.k12.ga.ustgunn@doe.k12.ga.us Elementary Mathematics Specialist 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 2, Grade 3. 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 on the K-5 wiki. http://ccgpsmathematicsk-5.wikispaces.com/

4. Expectations and clearing up confusion The intent of this webinar is to bring awareness to:  the types of tasks contained in the unit.  your conceptual understanding of the mathematics in this unit.  approaches to 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 2. At the end of today’s session you should have at least 3 takeaways:  The big idea of Unit 2  Something to think about… food for thought  How can 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. Please provide feedback at the end of today’s session.  Feedback helps us all to become better teachers and learners.  Feedback helps as we develop the remaining unit-by-unit webinars.  Please visit http://ccgpsmathematicsK-5.wikispaces.com/ to share your feedback.http://ccgpsmathematicsK-5.wikispaces.com/ After reviewing the remaining units, please contact us with content area focus/format suggestions for future webinars. Turtle Gunn Toms– tgunn@doe.k12.ga.ustgunn@doe.k12.ga.us Elementary Mathematics Specialist

8. Welcome! For today’s session:  Have you read the mathematics CCGPS?  Did you read Unit Two and work through the tasks?  Make sure you download and save the documents from this session. If you didn’t, they are posted for your convenience on the K-5 wiki.  Ask questions and share resources/ideas for the common good.  Join the K-5 wiki. If you are still wondering what a wiki is, we’ll discuss this near the end of the session.

9. Activate your Brain My brother has a candy store. He sells candy in special boxes that hold 10 assorted candies. He orders his candy from a factory, and it comes in different amounts based on weight. His last order had 72 chocolate truffles, 72 vanilla creams, 23 chocolate almonds, 33 jellies, 80 caramels, and 16 nougats. How many boxes does he need?

10. What’s the big idea? Enduring Understandings Essential Questions Common Misconceptions Strategies for Teaching and Learning Overview

11. Remember this…?

12. What’s the big idea? Deepen understanding of number, the operations of multiplication and division, and relationships between the two.

14. What’s the big idea? Standards for Mathematical Practice What might this look like in the classroom? Wiki- http://ccgpsmathematicsk- 5.wikispaces.com/3rd+Grade/ http://ccgpsmathematicsk- 5.wikispaces.com/3rd+Grade/ Inside math- http://bit.ly/Mg07mlhttp://bit.ly/Mg07ml Games- http://bit.ly/vJEbdGhttp://bit.ly/vJEbdG Edutopia- http://bit.ly/o1qaKfhttp://bit.ly/o1qaKf Teaching channel- http://bit.ly/wm0OcJhttp://bit.ly/wm0OcJ Math Solutions- http://bit.ly/MqPf6whttp://bit.ly/MqPf6w

15. Thanks to Education Week for these slides.

20. Coherence and Focus – Unit 2 What are students coming with?

21. Coherence and Focus – Unit 2 What are students coming with from Unit 1?

22. Coherence and Focus- Unit 2 Where does this understanding lead students? Look in your unit and find the Enduring Understandings.

23. Coherence and Focus – Unit 1 View across grade bands K-6 th  Operations with whole numbers and fractions.  Numbers and their opposites. 8 th -12 th  Everything!

24. Navigating Unit Two The only way to gain deep understanding is to work through each task. No one else can understand for you. Make note of where, when, and what the big ideas are. 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://ccgpsmathematicsk-5.wikispaces.com/Home

25. Revision-ish Unit 2 Pg. 7 Skip counting- be careful! Terms- if they are useful and make the mathematics clearer, use them. Not for memorization Pg. 28- MATHEMATICAL not MATNEMATICAL Pg. 48- alignment issue with triangle Pg. 59- one of my favorite tasks!

26. Activate your Brain My brother has a candy store. He sells candy in special boxes that hold 10 assorted candies. He orders his candy from a factory, and it comes in different amounts based on weight. His last order had 72 chocolate truffles, 72 vanilla creams, 23 chocolate almonds, 33 jellies, 80 caramels, and 16 nougats. How many boxes does he need?

27. What’s the big idea? Deepen understanding of number, the operations of multiplication and division, and relationships between the two.

28. Examples & Explanations Standards addressed in Unit 2 MCC3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5× 7. MCC3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. MCC3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

29. Examples & Explanations Standards addressed in Unit 2 MCC3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = □ ÷ 3, 6 × 6 = ?. × ? = 48, 5 = □ ÷ 3, 6 × 6 = ?. MCC3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. MCC3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

30. Examples & Explanations Resources which work with Unit 2: This is the time to go back to stuff. Number line Arrays Thinking… Big Ideas

31. Examples and Explanations What do students need in order to understand multiplication and division? Understanding of place value Additive thinking Multiplicative thinking

32. Examples & Explanations Multiplicative Thinking Additive strategies/replication Countable units Sharing Array and region Cartesian product (later) Simple proportional reasoning (later)

33. Examples & Explanations

34. http://www.learner.org/courses/learningmath/n umber/session4/part_a/multiplication.html http://www.learner.org/courses/learningmath/n umber/session4/part_a/multiplication.html

35. Examples & Explanations Thinking about Division Commutativity for multiplication, but not division Think multiplication Partitive- sharing Quotative- measurement

36. Partitive (sharing) “How many in each group?”

37. Quotative (Measurement) “How many groups?” http://www.learner.org/courses/learningmath/number/session4 /part_a/division.html

38. Examples and Explanations

39. http://mrwendler.wordpress.com/math-in-the-class/math/division /

40. Examples & Explanations

41. How to develop all of these? Do number talks regularly, expand them to include equations that support development of understanding. http://bit.ly/OYVpKN http://bit.ly/OYVpKN Not sure about the strategies yourself? VandeWalle, “Teaching Student-Centered Mathematics- 3-5” Fosnot, “Young Mathematicians at Work” Constructing Multiplication and Division

42. Examples & Explanations

43. http://letsplaymath.net/2007/01/13/number-bonds- better-understanding/

44. Examples & Explanations Journaling : http://letsplaymath.net/2007/08/21/writing-to- learn-math/

45. Examples & Explanations Nice extra- http://bedtimemathproblem.org/

46. Examples & Explanations Standards: http://secc.sedl.org/common_core_videos/grade.php?grade=3 Videos for teachers explaining standards- so far: NF.2a,b MD.7d Tools: Tools for the Common Core: http://commoncoretools.me/2012/04/02/general-questions- about-the-standards/ On the wiki: Discussion threads Unpacked standards from other states. Proceed with caution.

47. Assessment

48. Try thinking about assessment in this way: The chef tasting the soup in the kitchen is engaged in formative assessment. The person eating the soup in the restaurant is engaged in summative assessment. You are the chef. Adjust constantly with the end in mind.

49. What one county has done: 1. Marcus has 36 marbles. He is putting an equal number of marbles into 4 bags. For 1a–1d, Circle Yes or No to indicate whether each number sentence could be used to find the number of marbles Marcus puts in each bag. 1a. 36 x 4 =  Yes No 1b. 36 ÷ 4 =  Yes No 1c. 4 x  = 36 Yes No 1d. 4 ÷  = 36 Yes No Score: ______/4 Hall County Schools

50. What one county has done: Hall County School System 2. Sarah is 12 years old. George is g years old. Sarah is 3 times as old as George. For numbers 2a–2c, Circle Yes or No to indicate whether each statement is true. 2a. George’s age, in years, can be represented by the expression 12 ÷ 3. Yes No 2b. George is 15 years old. Yes No 2c. George’s age, in years, can be found by solving the equation 12 = 3 × g. Yes No

51. What one county has done: Hall County Schools

52. What one county has done: Hall County Schools

53. What one county has done: Hall County Schools

54. What one county has done: C. Based on the data, which teacher do you think will need to buy new pencils first? Justify your answer. Hall County Schools

55. Want more? http://insidemathematics.org/index.php/3rd-grade

56. Again, thanks to Education Week for these slides.

57. Navigating Unit Two The only way to gain deep understanding is to work through each task. No one else can understand for you. Make note of where, when, and what the big ideas are. 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://ccgpsmathematicsk-5.wikispaces.com/Home

58. 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.

59. What in the world is a wiki? http://ccgpsmathematicsk-5.wikispaces.com

60. What’s the big idea? Standards for Mathematical Practice What might this look like in the classroom? Wiki- http://ccgpsmathematicsk- 5.wikispaces.com/3rd+Grade/ http://ccgpsmathematicsk- 5.wikispaces.com/3rd+Grade/ Inside math- http://bit.ly/Mg07mlhttp://bit.ly/Mg07ml Games- http://bit.ly/vJEbdGhttp://bit.ly/vJEbdG Edutopia- http://bit.ly/o1qaKfhttp://bit.ly/o1qaKf Teaching channel- http://bit.ly/wm0OcJhttp://bit.ly/wm0OcJ Math Solutions- http://bit.ly/MqPf6whttp://bit.ly/MqPf6w

61. 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.aspxhttp://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/  Inside Mathematics- http://www.insidemathematics.org/http://www.insidemathematics.org/  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

62. Resources Books  Van De Walle and Lovin, Teaching Student-Centered Mathematics, K-3  Fosnot and Dolk, Young Mathematicians at Work  Wright, et al, Teaching Number in the Classroom  Wright, et al, Teaching Number-Advancing children’s skills and Strategies  Wright, et al, Developing Number Knowledge  Parrish, Number Talks  Shumway, Number Sense Routines  Wedekind, Math Exchanges

63. Resources 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  Annenberg Learner - http://www.learner.org/resources/series32.htmlhttp://www.learner.org/resources/series32.html Assessment Resources  MARS - http://www.nottingham.ac.uk/~ttzedweb/MARS/http://www.nottingham.ac.uk/~ttzedweb/MARS/  MAP - http://www.map.mathshell.org.uk/materials/index.phphttp://www.map.mathshell.org.uk/materials/index.php  PARCC - http://www.parcconline.org/parcc-stateshttp://www.parcconline.org/parcc-states Start of School- Parents  http://www.youtube.com/watch?v=Vvk4-evBS-8&feature=plcp http://www.youtube.com/watch?v=Vvk4-evBS-8&feature=plcp ( how to support your school and teacher )

64. As you start your day tomorrow… Remember this- Basically, the standards are not units of instruction; you don’t always “teach a standard” in one chunk, whatever the order. For example, the OA and NBT standards in any given great level are very closely related, and a curriculum might be touching on these two domains simultaneously at times, not to mention supporting standards in MD and other domains. 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

65. As you start your day tomorrow…

66. Thank You! Please visit http://ccgpsmathematicsK-5.wikispaces.com/ to provide us with your feedback!http://ccgpsmathematicsK-5.wikispaces.com/ Turtle Gunn Toms Program Specialist (K-5) tgunn@doe.k12.ga.us These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Join the listserve! join-mathematics-k-5@list.doe.k12.ga.us Follow on Twitter! follow@turtletoms (yep, I’m tweeting math resources in a very informal manner)