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.
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CCGPS MathematicsUnit-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 pmWhile 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 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 FiveUnit 1: Order of Operations and Whole Numbers
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?
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.
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 understanding of number, and its usefulness in whole number operations.
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
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 understanding of number, and its usefulness in
whole number operations.
What do Fifth Grade students bring? What are they connecting to later?
From 4-• 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.• Continuation of fluency/algebraic
thinking.• Measurement/addition/subtraction
relationships• Data analysis
Later-• Deep understanding of operations and
algebraic thinking. • Understanding of scale, orders of
magnitude. • Understanding of defining attributes of
shapes.• Fluent operations with all numbers.• Continuation of fluency, algebraic
thinking.• Data analysis, relationships.
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.
What’s Different in Fifth Grade?
Operations and Algebraic Thinking• Identify relationships between corresponding termsNumber and Operations in Base Ten• Rounding decimals to any place• Use of whole number exponents to denote powers of tenNumber 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.
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
Critical AreasIn 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.
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(shocking!)
Problem Types- + and -
Problem Types- x and ÷
Tools for Teaching Strategy
More strategy tools…
• http://youtu.be/Y8Bj5KVLmaYStudent-developed strategy using partial
products• http://powersof10.com/filmPowers of ten visualized! (oldie but goodie)No youtube in your district? Try this-http://www.cleanvideosearch.com
Examples & ExplanationsStandards: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/common-core-tools/unpacking/math/5th.pdfUnpacked standards from NC
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.
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
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!)
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