CCGPS Mathematics Unit-by-Unit Grade Level Webinar Fourth GradeUnit 1: Whole Numbers, Place Value, and Rounding in Computation May 9, 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.
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 Mathematical Practice,please access the list of recorded Blackboard sessions from Fall2011 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.
CCGPS MathematicsUnit-by-Unit Grade Level Webinar Grade Four Unit 1: Whole Numbers, Place Value, and Rounding, in Computation May 9, 2012 Turtle Gunn Toms– firstname.lastname@example.org Elementary Mathematics Specialist These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.
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
• 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– email@example.com Elementary Mathematics Specialist
Welcome!• For today’s session: Did you read the Fourth Grade mathematics CCGPS? Did you read Fourth 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.
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.
Activate your Brain Place any of the four operation signsbetween 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.
What’s the big idea? Deepen and expand understanding of place value,and its usefulness in estimation and computation.
Navigating a UnitOverviewStandardsEnduring UnderstandingsEssential QuestionsConcepts and Skills to MaintainSelected Terms and SymbolsStrategies for Teaching and LearningCommon MisconceptionsEvidence of LearningTasks
New to the Frameworks?• Enduring Understandings• Essential Questions• Common Misconceptions• Overview
Brand Spanking New!
Navigating a UnitWhat’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 ofstudents’ number sense, flexibility, fluency, collaborative skills andcommunication.
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/vid eos •http://www.responsiveclassroom.org/category/category/ first-weeks-school
Navigating a Unit Journaling/Math Workshop•Downloaded article from Marilyn Burnshttp://letsplaymath.net/2007/08/21/writing-to-learn-math/ Sense making for students and teachers•Downloaded article from NCTMhttp://www.youtube.com/user/mitcccnyorg?feature=watch
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
“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
What’s the big idea? Deepen and expandunderstanding of place value, and its usefulness in estimation and computation.
What do Fourth Grade students bring? What are they connecting to later?From 3 to 4 Later• Deep understanding of addition and • Deep understanding of addition and subtraction strategies (within 1000) subtraction, multiplication and division.• Developing understanding of • Useful place value understanding. multiplication and division (products • Understanding of defining attributes within 100) about shape, comparison of shape.• Useful place value understanding. • Foundational fractional relationships,• Understanding of defining attributes fraction operations. about shape, comparison of shape. • Continuation of fluency/algebraic• Foundational fractional relationships. thinking.• Continuation of fluency/algebraic • Measurement/addition/subtraction/ thinking. fraction relationships• Measurement/addition/subtraction • Data analysis relationships• Data analysis
What’s Different in Fourth Grade?Operations and Algebraic Thinking• Classification of counting numbers into subsetsNumber and Operations in Base Ten• Relative magnitude• Rounding to 1,000,000• Fluency in addition and subtraction with standard algorithm- dependent upon all reasoning strategies• Strategy-based divisionNumber and Operations- Fractions• A fraction a/b is equivalent to a fraction (nxa)/(nxb) (with models!)• Compare fractions using benchmark fractions• Multiply a fraction by a whole number
Critical AreasIn Fourth Grade, instructional time should focus on three critical areas:• Developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends• Developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers• Understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry
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
Problem Types- + and -
Problem Types- x and ÷
Tools for Teaching Strategy
More strategy tools…• http://youtu.be/Y8Bj5KVLmaYStudent-developed strategy using partial productsNo youtube in your district? Try this-http://www.cleanvideosearch.com
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/Q7E6nu4Zy0IThanks, Gatorgyrl82!http://www.youtube.com/user/Gatorgyrl82?feature=watch
Coherence and Focus – Unit 1 What are students coming with?
Coherence and Focus – Unit 1 What foundation will have been built?Where does this understanding lead incoming students?
Coherence and Focus – Unit 1 What foundation is being built?Where does this understanding lead students?
Coherence and Focus – Unit 1View across grade bands • K-6th Operations with whole numbers and fractions. Numbers and their opposites. • 8th-12th Everything!
Coherence and Focus – Unit 1 What foundation is being built? Where does this understanding lead students?
Examples & ExplanationsStandards:http://secc.sedl.org/common_core_videos/Videos for teachers explaining standards- so far:4.NBT.6, with more to come.Tools:http://www.dpi.state.nc.us/docs/acre/standards/common-core-tools/unpacking/math/4th.pdfUnpacked standards from NC
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!)
Assessment How could it look?http://nzmaths.co.nz/mathematics-assessment
How is a GA county using this? Thank you, Dr. Snell, and Henry County!
Helping to identify concerns… Thank you, Dr. Snell, and Henry County!
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.
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.
What in the world is a wiki? http://ccgpsmathematicsk-5.wikispaces.com/4th+Grade
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
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!)
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)
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.
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
Thank You! Please visit http://ccgpsmathematicsK-5.wikispaces.com/ to provide us with your feedback! Join our listserve: firstname.lastname@example.org Turtle Gunn Toms Program Specialist (K-5) email@example.com These materials are for nonprofit educational purposesonly. Any other use may constitute copyright infringement. Join the listserve! firstname.lastname@example.org Follow on Twitter! follow@turtletoms (yep, I’m tweeting math resources in a very informal manner)