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- 1. CCGPS MathematicsUnit-by-Unit Grade Level Webinar Second Grade Unit 1: Extending Base Ten Understanding May 3, 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 leveland one unit within that grade.• For information about CCGPS across a single grade span, pleaseaccess the list of recorded GPB sessions on Georgiastandards.org.• For information about the Standards for MathematicalPractice, please access the list of recorded Blackboard sessions fromFall 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 andthis list has also been included in your document downloads.
- 3. CCGPS MathematicsUnit-by-Unit Grade Level Webinar Grade Two Unit 1: Extending Base Ten Understanding May 3, 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 thisdiscussion of Unit 1.• At the end of today’s session you should have at least 3takeaways: 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 uswith content area focus/format suggestions for futurewebinars. Wiki, anyone? Turtle Gunn Toms– tgunn@doe.k12.ga.us Elementary Mathematics Specialist
- 6. Welcome!• For today’s session: Did you read the Second Grade mathematics CCGPS? Did you read Second 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 BrainWhen you think of 7, what do you see?When you think of 27, what do you see? How about 127? How about 1,027? How about 1,000,027? 1,000,000,027?
- 9. Activate your BrainWhat numbers less than 100 make eight when the digits are added together?(example 17 is a solution because 1+7=8) Write to help explain your best thinking using words, numbers, or pictures.
- 10. What’s the big idea?Developing deep understanding of quantity,relationships among numbers, and representationof number, specifically as they relate to placevalue, addition and subtraction, and theemergent understanding of multiplication.
- 11. Navigating a UnitOverviewStandardsEnduring UnderstandingsEssential QuestionsConcepts and Skills to MaintainSelected Terms and SymbolsStrategies for Teaching and LearningCommon MisconceptionsEvidence of LearningTasks
- 12. New to the Frameworks?• Enduring Understandings• Essential Questions• Common Misconceptions• Overview
- 13. Navigating a UnitWhat’s Different/What’s the Same?SMP’s (analyzing, estimating, reasoning, describingpatterns, defending, discussing, peer feedback, contentiousdiscourse,modeling, etc.)Grade Level OverviewCollaborative skills (How collaborative areyour collaborative activities?)Productive StruggleJournaling/NotebookDevelopment of own understanding(yours and students’)The regular use of routines is important to the development ofstudents’ number sense, flexibility, fluency, collaborative skills andcommunication.
- 14. Brand Spanking New!
- 15. Navigating a UnitClassroom 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/vi deos http://www.responsiveclassroom.org/category/categor y/first-weeks-school
- 16. Navigating a Unit Journaling/Math Workshop•Downloaded article from Marilyn Burns•http://mrsshannonsclass.weebly.com/guided-math.html Sense making•Downloaded article from NCTM•http://www.youtube.com/user/mitcccnyorg?feature=watch
- 17. Navigating a UnitMathematical 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 takedifferent paths, different steps, and different journeys. Weeach reach landmarks in different ways and at different times.If we push or pull children up the hill and make them practiceour steps, our ways, or, worse yet, drop them by helicopter atpoints of the journey without the climb of getting there, wemay get them up the mountain - but they won’t own it. Theymay reach the vista, but they won’t feel empowered by theclimb. They won’t take on the next hill in the journey. Andmost important, they won’t have learned how to climb, howto mathematize their own lived worlds. If, however, wesupport their steps, work with them as youngmathematicians, the climbs and the vistas and the joys of thejourney will be theirs forever” C. Fosnot
- 19. What’s the big idea?Developing deep understanding ofquantity, relationships among numbers, andrepresentation of number, specifically as theyrelate to place value, addition andsubtraction, and the emergent understanding ofmultiplication.
- 20. What do Second Grade students bring? What are they connecting to later?From 1- Later-• Fluent addition and subtraction to 10. • Deep understanding of addition andThis means students have developed strategies subtraction. and have solved different problem types. • Useful place value understanding.• Foundational place value understanding. • Understanding of defining attributes aboutThis means students have a conceptual shape, comparison of shape. understanding. • Foundational fractional relationships.• Foundational ideas about shape and • Continuation of fluency/algebraic thinking. position in space. • Measurement/addition/subtraction• Ability to compare and catagorize. relationships• Understanding of quantities to 120. • Data analysis• Measurement as unit iteration• Transitive property
- 21. What’s Different in Second Grade?Operations and Algebraic Thinking• One- and two-step word problems within 100• Fluently + and – within 20 w/mental strategies• Know from memory sums of two one digit numbers to 18• Odd and even (to 20)Number and Operations in Base Ten• Fluently add and subtract within 100 using strategies, explaining strategies, and relating to written method.• Skip count forward and backward by 5, 10, 100 to 1000 instead of to 100• Add up to four 2-digit numbers using strategies• Add and subtract within 1000 using concrete models or drawings, and strategies• Add and subtract multiples of 10 and 100 to 900.• Write an equation to express total as sum of addends (foundation of multiplication)
- 22. Critical AreasIn Second Grade, instructional time should focus on four critical areas:• Extending understanding of base-ten notation• Building fluency with addition and subtraction• Using standard units of measure• Describing and analyzing shapes
- 23. What is no longer in Second Grade ?• Regrouping without understanding• Multiplication table• ≠• Seconds in minute, minutes in hour, hours in day• Representations of numbers over 1000• Making change, mixing coins and currency• Temperature (this is science)• Rectangle and square• Cutting 3-D shapes• Calendar (this is social studies)
- 24. Tools for Teaching Number Sense• Subitization• Comparison• Counting• One- to- one correspondence• Cardinality This is from Kindergarten Unit 1• Hierarchical Inclusion• 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
- 25. Developing Number Sense How do you know what they know?• First, do no harm:http://www.youtube.com/watch?v=I9jaJREEAI&feature=channel &list=ULhttp://www.youtube.com/watch?v=nK63kRN5xPo&feature=rel mfu• Determine strategies:http://www.youtube.com/watch?v=yYdjCjEsdSw&feature=chan nel&list=ULThanks, Gatorgyrl82!http://www.youtube.com/user/Gatorgyrl82?feature=watch
- 26. Coherence and Focus – Unit 1 What are students coming with?
- 27. Coherence and Focus – Unit 1 What foundation will have been built?Where does this understanding lead incoming students?
- 28. Coherence and Focus – Unit 1 What foundation is being built?Where does this understanding lead students?
- 29. Coherence and Focus – Unit 1View across grade bands • K-6th Operations with whole numbers and fractions. Numbers and their opposites. • 8th-12th Everything!
- 30. Coherence and Focus – Unit 1 What foundation is being built? Where does this understanding lead students?http://www.k-5mathteachingresources.com/2nd-grade-math-journals.html
- 31. Examples & Explanations Downloads:•Dot cards and ten frames packet•Rekenrek packet•http://gradekcommoncoremath.hcpss.wikispaces.net/Rekenreks•http://www.youtube.com/watch?v=jcmELkgrJ_g&list=UUcBRC4oQCDKnO9phCKcSSZQ&index=1&feature=plcp
- 32. Examples and Explanations Groupable Materials
- 33. Examples & Explanations
- 34. Examples & Explanations
- 35. Examples & ExplanationsJournaling Revisited:
- 36. Examples & ExplanationsStandards:http://secc.sedl.org/common_core_videos/Videos for teachers explaining standards- so far:2.NBT.7, with more to come.Tools:http://www.dpi.state.nc.us/docs/acre/standards/common-core-tools/unpacking/math/2nd.pdfUnpacked standards from NC
- 37. Assessment How might it look?Examples of how balanced assessments can beassembled. 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!)
- 38. Assessment How could it look?http://nzmaths.co.nz/mathematics-assessment
- 39. 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.
- 40. Resource ListThe following list is provided as a sample ofavailable resources and is for informationalpurposes only. It is your responsibility toinvestigate them to determine their value andappropriateness for your district. GaDOE doesnot endorse or recommend the purchase of oruse of any particular resource.
- 41. What in the world is a wiki? http://ccgpsmathematicsk-5.wikispaces.com/2nd+Grade
- 42. 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 Centers 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
- 43. 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 (preview!) Wedekind, Math Exchanges (preview!)
- 44. 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)
- 45. 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 Sadieusing a well-designed crayon.So , … if all people do, is take out theirold state standards, toss them out, and replace thesecommon core state standards into those old boxesNOTHING IS REALLY GOING TO CHANGEWe designed these as a platform for new kinds of instructional systemsWe 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.
- 46. 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
- 47. Thank You! Please visit http://ccgpsmathematicsK-5.wikispaces.com/ to provide us with your feedback! Join our listserve: join-mathematics-k-5@list.doe.k12.ga.us Turtle Gunn Toms Program Specialist (K-5) tgunn@doe.k12.ga.us These materials are for nonprofit educational purposesonly. Any other use may constitute copyright infringement. follow@turtletoms (yep, I’m tweeting math resources in a very informal manner)

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