1. CCGPS Mathematics Unit-by-Unit Grade Level Webinar Fourth Grade Unit 2: Fraction Equivalents August 8, 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 Four Unit 2: Fraction Equivalents August 8, 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 Maria went to the music store to buy some CDs. She had twenty four dollars with her. She spent eighteen dollars. What fractional part of her money did she spend? In its lowest form?

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? Deep understanding of equivalent fractions, using a visual model. Deep understanding of factors and multiples, primes and composites.

14. What’s the big idea? Standards for Mathematical Practice What might this look like in the classroom? Wiki- http://ccgpsmathematicsk- 5.wikispaces.com/4th+Grade/ http://ccgpsmathematicsk- 5.wikispaces.com/4th+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 from Unit 1?

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

22. Coherence and Focus – Unit 2 View across grade bands K-6 th  Operations with whole numbers and fractions.  Numbers and their opposites. 8 th -12 th  Everything!

23. 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

24. Revision-ish Unit 2 Pg. 17- alignment issues Pg. 25-26- denominators that are outside the suggested range. Pg. 31- Last paragraph- not yet Pg. 37- Great game! Play often… Pg. 49- Factor Trail gameboard

25. Activate your Brain Maria went to the music store to buy some CDs. She had twenty four dollars with her. She spent eighteen dollars. What fractional part of her money did she spend? In its lowest form?

26. Activate your Brain A fourth- grade class traveled on a field trip in four separate vehicles. The school provided a lunch of submarine sandwiches for each group. When they stopped for lunch, the subs were cut and shared as follows: The first group had 3 people and shared 2 subs equally. The second group had 4 people and shared 3 subs equally. The third group had 9 people and shared 6 subs equally. The last group had 6 people and shared 4 subs equally. When they returned from the field trip, the children began to argue that the portion of the sandwiches they received was not fair, that some children got more to eat than others. Were they right? Or did everyone get the same amount?

27. What’s the big idea? Deep understanding of equivalent fractions, using a visual model. Deep understanding of factors and multiples.

28. Examples & Explanations Standards addressed in Unit 2 MCC4.NF.1 Explain why a fraction a / b is equivalent to a fraction ( n × a )/( n × b ) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

29. Examples & Explanations Standards addressed in Unit 2 MCC4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. * Grade 4 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.

30. Examples & Explanations Standards addressed in Unit 2 MCC4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

31. Examples & Explanations Resources which work with Unit 2: This is the time to use stuff. Number line Fraction Strips Pattern Blocks Arrays Thinking… Big Ideas

32. Examples and Explanations What understandings do students need in order to understand fraction equivalence? Meaning of numerator Meaning of denominator Valid comparisons involve same-sized whole Multiplicative thinking Experience dividing multiple shapes into equal shares/parts

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

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

35. Examples & Explanations

39. http://www.learner.org/courses/learningmat h/number/session8/index.html http://www.learner.org/courses/learningmat h/number/session8/index.html

40. Examples & Explanations What do students need in order to understand factors, primes, and composites? The vocabulary Experiences from Unit 1- pages 73-114 visuals

41. Examples & Explanations http://realteachingmeansreallearning.blogspot.c om/2011/02/prime-and-composite-numbers.html “The Transformation of a math teacher from one who “drilled and killed” to one who engages”

42. Examples & Explanations You are planning a wedding and you and your spouse are very particular about seating arrangements. You can arrange the tables in any way as long as there is the same amount of people at each table. You have a total of 100 people coming to your wedding, how can you arrange the tables? http://realteachingmeansreallearning.blogspot.c om/2011/02/prime-and-composite-numbers.html

43. Explanations and Examples

44. 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 Fractions, Decimals, and Percents

45. Examples & Explanations

46. Journaling : http://letsplaymath.net/2007/08/21/writing-to- learn-math/

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

48. Examples & Explanations Standards: http://secc.sedl.org/common_core_videos/grade.php?grade=4 Videos for teachers explaining standards- so far: NBT.6, NF.1, NF.3 a,b,c,d 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.

49. Assessment

50. 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.

51. What one county has done: Hall County Schools 1. Jesus says that 50 is a factor of 100. Emily says that 50 is a multiple of 5. Who is correct? Explain your answer with numbers and words.

52. 2. Peter made the statement shown below. Part A Is Peter ’ s statement correct? In the space below, use numbers and words to explain why or why not. Part B Does Peter ’ s rule apply to other numbers? Give an example where it does or does not apply and explain your thinking using numbers and words. What one county has done: Hall County School System “The number 32 is a multiple of 8. That means all of the factors of 8 are also factors of 32.”

53. What one county has done: Hall County Schools

54. What one county has done: Hall County Schools

55. What one county has done: Hall County Schools Part C We know that Benito’s bag has a total of 10 pencils inside, and James’ bag has a total of 5 pencils inside but they both have the same fraction of sharpened pencils to total pencils. Another student, Tommy, also has the same fraction of sharpened pencils to total pencils as Benito and James. Draw a picture of what Tommy’s bag of pencils might look like and write a fraction to match your picture to show the number of sharpened pencils to all pencils.

56. What one county has done: How can the fraction of Tommy’s bag be the same as Benito’s and James’ even though they have a different number of pencils? Explain your answer using both numbers and words. Hall County Schools

57. What one county has done: 4. Each of three people started at the same point and ran in the same direction. Quintrel ran three fourths of a mile and then stopped. Gregory ran one eighth of a mile and then stopped. Henry ran ½ of a mile and then stopped. Hall County Schools

58. What one county has done: Hall County Schools

59. Want more? http://insidemathematics.org/index.php/4th-grade

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

61. 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

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

64. What’s the big idea? Standards for Mathematical Practice What might this look like in the classroom? Wiki- http://ccgpsmathematicsk- 5.wikispaces.com/4th+Grade/ http://ccgpsmathematicsk- 5.wikispaces.com/4th+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

65. 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

66. Resources Books  Van De Walle and Lovin, Teaching Student-Centered Mathematics, 3-5  Fosnot and Dolk, Young Mathematicians at Work  Parrish, Number Talks  NCTM, Developing Essential Understanding of Rational Numbers  Shumway, Number Sense Routines  Wedekind, Math Exchanges  New- Burns and Silbey, So You Have to Teach Math?  New- Teaching with Intention- Debbie Miller  New- Moynihan, Math Sense  New- Confer and Ramirez, Math Tools in Action

67. 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 )

68. 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

69. As you start your day tomorrow…

70. 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)