Unit 1 Webinar Slides
- 1. CCGPS Mathematics Unit-by-Unit Grade Level Webinar Fifth Grade Unit 1: Order of Operations and Whole Numbers May 10, 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. Clearing up confusion • This webinar focuses on CCGPS content specific to one grade level and one unit within that grade. • For information about CCGPS across a single grade span, please access the list of recorded GPB sessions on Georgiastandards.org. • For information about 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 this list has also been included in your document downloads.
- 3. CCGPS Mathematics Unit-by-Unit Grade Level Webinar Grade Five Unit 1: Order of Operations and Whole Numbers May 10, 2012 Turtle Gunn Toms– tgunn@doe.k12.ga.us Elementary Mathematics Specialist These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.
- 4. Welcome! • Thank you for taking the time to join us in this discussion of Unit 1. • At the end of today’s session you should have at least 3 takeaways: The big idea of Unit 1 Something to think about… food for thought How might I prepare for the start of school next year? What is my conceptual understanding of the material in this unit? a list of resources and support available for CCGPS mathematics
- 5. • 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. This is our “baby”wiki! • After reviewing the remaining units, please contact us with content area focus/format suggestions for future webinars. Wiki, anyone? Turtle Gunn Toms– tgunn@doe.k12.ga.us Elementary Mathematics Specialist
- 6. Welcome! • For today’s session: Did you read the Fifth Grade mathematics CCGPS? Did you read Fifth Grade Unit One? Make sure you download and save the documents from this session. Ask questions and share resources/ideas for the common good. Join the K-5 wiki. If you are wondering what a wiki is, we’ll discuss this near the end of the session.
- 7. Remember, Turtle, give someone a fish and they eat for a day. Teach them to fish and they’ll have no further use for you.
- 8. Activate your Brain Place any of the four operation signs between the nine figures so that they equal 100. 1 2 3 4 5 6 7 8 9 = 100 Write to help explain your best thinking using words, numbers, or pictures.
- 9. What’s the big idea? Deepen understanding of number, and its usefulness in whole number operations.
- 10. Navigating a Unit Overview Standards Enduring Understandings Essential Questions Concepts and Skills to Maintain Selected Terms and Symbols Strategies for Teaching and Learning Common Misconceptions Evidence of Learning Tasks
- 11. New to the Frameworks? • Enduring Understandings • Essential Questions • Common Misconceptions • Overview
- 13. Navigating a Unit What’s Different/What’s the Same? •SMP’s (analyzing, estimating, reasoning, describing patterns, defending, discussing, peer feedback, contentious discourse, •modeling, etc.) •Grade Level Overview •Collaborative skills (How collaborative are •your collaborative activities?) •Productive Struggle •Journaling/Notebook •Development of own understanding •(yours and students’) •The regular use of routines is important to the development of students’ number sense, flexibility, fluency, collaborative skills and communication.
- 15. Navigating a Unit Classroom Routines and Rituals •http://www.edutopia.org/math-social-activity- cooperative-learning-video •http://www.edutopia.org/math-social-activity-sel •http://www.youtube.com/user/responsiveclassroom/vid eos •http://www.responsiveclassroom.org/category/category/ first-weeks-school
- 16. Navigating a Unit Journaling/Math Workshop •Downloaded article from Marilyn Burns http://letsplaymath.net/2007/08/21/writing-to-learn-math/ Sense making for students and teachers •Downloaded article from NCTM http://www.youtube.com/user/mitcccnyorg?feature=watch
- 17. Navigating a Unit Mathematical Community of Learners- http://www.insidemathematics.org/index.php/video-tours-of- inside-mathematics/classroom-teachers/157-teachers-reflect- mathematics-teaching-practices
- 18. “Remember that we all climb the hills differently. We take different paths, different steps, and different journeys. We each reach landmarks in different ways and at different times. If we push or pull children up the hill and make them practice our steps, our ways, or, worse yet, drop them by helicopter at points of the journey without the climb of getting there, we may get them up the mountain - but they won’t own it. They may reach the vista, but they won’t feel empowered by the climb. They won’t take on the next hill in the journey. And most important, they won’t have learned how to climb, how to mathematize their own lived worlds. If, however, we support their steps, work with them as young mathematicians, the climbs and the vistas and the joys of the journey will be theirs forever” C. Fosnot
- 19. What’s the big idea? Deepen understanding of number, and its usefulness in whole number operations.
- 20. What do Fifth Grade students bring? What are they connecting to later? From 4- Later- • Deep understanding of addition and • Deep understanding of operations and subtraction, multiplication and algebraic thinking. division. • Understanding of scale, orders of • Useful place value understanding. magnitude. • Understanding of defining attributes • Understanding of defining attributes about shape, comparison of shape. of shapes. • Foundational fractional relationships. • Fluent operations with all numbers. • Continuation of fluency/algebraic • Continuation of fluency, algebraic thinking. thinking. • Measurement/addition/subtraction • Data analysis, relationships. relationships • Data analysis
- 21. Transition Standards?! • Tasks from Unit 1, Grade 4 work beautifully to meet MCC.OA.4. You may wish to use them at the beginning of the year, or before beginning Unit 4. I’ve also downloaded a task. (thanks, Graham and Mike!) • Tasks from Units 2-4 work well to meet MCC4.NF.1, 2, 3, and 4. You may wish to use them before beginning Unit 4. • Some districts have chosen to teach these now, to 4th graders, in anticipation of the shift.
- 23. What’s Different in Fifth Grade? Operations and Algebraic Thinking • Identify relationships between corresponding terms Number and Operations in Base Ten • Rounding decimals to any place • Use of whole number exponents to denote powers of ten Number and Operations- Fractions • Unit fractions (see Third and Fourth grade) • Fractions as numbers on number line (see Third and Fourth grade) • Relating operations with fractions to operations with whole numbers.
- 24. Map Changes? • Units 4 and 5 have switched places. Where can you find the maps? Look in Learning Village, K-12 Mathematics, CCGPS K-5 folder, FIFTH GRADE
- 25. Critical Areas In Fifth Grade, instructional time should focus on three critical areas: • Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions) • Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations • Developing understanding of volume.
- 26. Tools for Teaching Number Sense • Subitization • Comparison • Counting • One- to- one correspondence • Cardinality This is from Kindergarten Unit 1 • Hierarchical Inclusion (shocking!) • Number Conservation Dot Cards/TenFrames Number Cubes • Spatial Relationship Dominoes • One and Two More or Less Cups • Understanding Anchors Collections • Part/Part Whole Relationships Rekenrek
- 27. Problem Types- + and -
- 28. Problem Types- x and ÷
- 29. Tools for Teaching Strategy
- 30. More strategy tools… • http://youtu.be/Y8Bj5KVLmaY Student-developed strategy using partial products • http://powersof10.com/film Powers of ten visualized! (oldie but goodie) No youtube in your district? Try this- http://www.cleanvideosearch.com
- 31. Developing Number Sense How do you know what they know? • First, do no harm: http://youtu.be/YyMshld9RLM (Procedural vs conceptual understanding- question and never assume) • Determine strategies: http://youtu.be/Q7E6nu4Zy0I Thanks, Gatorgyrl82! http://www.youtube.com/user/Gatorgyrl82?feature=watch
- 32. Coherence and Focus – Unit 1 What are students coming with?
- 33. Coherence and Focus – Unit 1 What foundation will have been built? Where does this understanding lead incoming students?
- 34. Coherence and Focus – Unit 1 What foundation is being built? Where does this understanding lead students?
- 35. Coherence and Focus – Unit 1 View across grade bands • K-6th Operations with whole numbers and fractions. Numbers and their opposites. • 8th-12th Everything!
- 36. Coherence and Focus – Unit 1 What foundation is being built? Where does this understanding lead students?
- 37. Examples & Explanations Downloads: •Rekenrek packet •http://gradekcommoncoremath.hcpss.wik ispaces.net/Rekenreks •http://letsplaymath.net/2006/12/29/the- game-that-is-worth-1000-worksheets/
- 38. Examples and Explanations Strategy Development
- 40. Examples & Explanations 178+ m = 245 245- m= 178
- 41. Examples & Explanations Journaling Revisited:
- 42. Examples & Explanations Standards: http://secc.sedl.org/common_core_videos/ Videos for teachers explaining standards- so far: 5.NF.5b, and 5.NF.7a,b,c with more to come. Tools: http://www.dpi.state.nc.us/docs/acre/standards/co mmon-core-tools/unpacking/math/5th.pdf Unpacked standards from NC
- 43. Assessment How might it look? Examples of how balanced assessments can be assembled. http://map.mathshell.org/materials/tests.php The target audience for these sample assessments : 1. teachers who have already begun work with mathematical practice standards 2. designers of future CCSSM-aligned assessments http://map.mathshell.org/materials/pd.php (while you are at it, have a look at their Professional Learning!)
- 44. Assessment How could it look? http://nzmaths.co.nz/mathematics-assessment
- 45. How is a GA county using this? Thank you, Dr. Snell, and Henry County!
- 46. Helping to identify concerns… Thank you, Dr. Snell, and Henry County!
- 47. What should we do first? • Read the Grade Level Overview • Read the unit, and discuss with your colleagues. • Complete the culminating task with your team. Now you know where you are going, what you need, where your students will end up. What do you notice? What do you wonder? Share your thoughts on the wiki.
- 48. 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.
- 49. What in the world is a wiki? http://ccgpsmathematicsk-5.wikispaces.com/5th+Grade
- 50. Resources • Common Core Resources SEDL videos - https://www.georgiastandards.org/Common- Core/Pages/Math.aspx or http://secc.sedl.org/common_core_videos/ Illustrative Mathematics - http://www.illustrativemathematics.org/ Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/ Arizona DOE - http://www.azed.gov/standards-practices/mathematics- standards/ Ohio DOE –http://www.ode.state.oh.us/GD/Templates/Pages/ODE/ODEP rimary.aspx?page=2&TopicRelationID=1704 Inside Mathematics- http://www.insidemathematics.org/ Common Core Standards - http://www.corestandards.org/ Tools for the Common Core Standards - http://commoncoretools.me/ Phil Daro talks about the Common Core Mathematics Standards - http://serpmedia.org/daro-talks/index.html
- 51. Resources • Books Van De Walle and Lovin, Teaching Student-Centered Mathematics, 3-5 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 (preview!) Wedekind, Math Exchanges (preview!)
- 52. Resources • Professional Learning Resources Inside Mathematics- http://www.insidemathematics.org/ Edutopia – http://www.edutopia.org Teaching Channel - http://www.teachingchannel.org Annenberg Learner - http://www.learner.org/resources/series32.html • Assessment Resources MARS - http://www.nottingham.ac.uk/~ttzedweb/MARS/ MAP - http://www.map.mathshell.org.uk/materials/index.php PARCC - http://www.parcconline.org/parcc-states •Start of School- Parents http://www.youtube.com/watch?v=Vvk4-evBS-8&feature=plcp (how to support your school and teacher)
- 53. Phil Daro says: it’s just the easy part to design and write something down. The hard part comes… with putting them to work. And the users have ultimate control over how they’re used. So no matter how well designed the tool is – the user has control. And there you see my granddaughter Sadie using a well-designed crayon. So , … if all people do, is take out their old state standards, toss them out, and replace these common core state standards into those old boxes NOTHING IS REALLY GOING TO CHANGE We designed these as a platform for new kinds of instructional systems We didn’t design these to be thrown into the old boxes. The old boxes in fact, are the infrastructure for making things a mile wide, inch deep.
- 54. As you start your day tomorrow… Who dares to teach must never cease to learn ~ John Cotton Dana http://www.youtube.com/watch?v=JEa0xpWi7C4
- 55. Thank You! Please visit http://ccgpsmathematicsK-5.wikispaces.com/ to provide us with your feedback! 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)