Transcript
CCGPS MathematicsUnit-by-Unit Grade Level Webinar
Fourth Grade Unit 1: Whole Numbers, Place Value, and Rounding
in ComputationMay 9, 2012
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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.
CCGPS MathematicsUnit-by-Unit Grade Level Webinar
Grade FourUnit 1: Whole Numbers, Place Value, and
Rounding, in ComputationMay 9, 2012
Turtle Gunn Toms– tgunn@doe.k12.ga.usElementary 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 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
• 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.usElementary 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 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.
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 of students’ number sense, flexibility, fluency, collaborative skills and communication.
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/videos
•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 Unit
Mathematical 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 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
What’s the big idea?
Deepen and expand understanding 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• Deep understanding of addition and
subtraction strategies (within 1000)• Developing understanding of
multiplication and division (products within 100)
• Useful place value understanding. • Understanding of defining attributes
about shape, comparison of shape.• Foundational fractional relationships.• Continuation of fluency/algebraic
thinking.• Measurement/addition/subtraction
relationships• Data analysis
Later• Deep understanding of addition and
subtraction, multiplication and division. • Useful place value understanding. • Understanding of defining attributes
about shape, comparison of shape.• Foundational fractional relationships,
fraction operations.• Continuation of fluency/algebraic
thinking.• Measurement/addition/subtraction/ fraction 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• Hierarchical Inclusion• Number Conservation• Spatial Relationship• One and Two More or Less• Understanding Anchors• Part/Part Whole Relationships
Dot Cards/TenFrames Number Cubes Dominoes Cups Collections Rekenrek
This is from Kindergarten Unit 1
Problem Types- + and -
Problem Types- x and ÷
Tools for Teaching Strategy
More strategy tools…
• http://youtu.be/Y8Bj5KVLmaYStudent-developed strategy using partial
products
No youtube in your district? Try this-http://www.cleanvideosearch.com
Developing Number SenseHow 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
Coherence and Focus – Unit 1What are students coming with?
Coherence and Focus – Unit 1What foundation will have been built?
Where does this understanding lead incoming students?
Coherence and Focus – Unit 1What 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 1What foundation is being built?
Where does this understanding lead students?
Examples & Explanations Downloads:•Rekenrek packet•http://gradekcommoncoremath.hcpss.wikispaces.net/Rekenreks•http://letsplaymath.net/2006/12/29/the-game-that-is-worth-1000-worksheets
/
Examples and ExplanationsStrategy Development
Examples & Explanations
Examples & Explanations
178+ m = 245 245- m= 178
Examples & Explanations
Journaling Revisited:
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
AssessmentHow might it look?
Examples of how balanced assessments can be assembled.
http://map.mathshell.org/materials/tests.phpThe target audience for these sample assessments :
1. teachers who have already begun work with mathematical practice standards
2. designers of future CCSSM-aligned assessmentshttp://map.mathshell.org/materials/pd.php
(while you are at it, have a look at their Professional Learning!)
AssessmentHow 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 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.
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 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=1704Inside 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 WorkWright, et al, Teaching Number in the ClassroomWright, et al, Teaching Number-Advancing children’s skills
and StrategiesWright, et al, Developing Number KnowledgeParrish, 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.orgAnnenberg 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- Parentshttp://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 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 boxesNOTHING IS REALLY GOING TO CHANGE
We 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:
join-mathematics-k-5@list.doe.k12.ga.us
Turtle Gunn TomsProgram 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)
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