Unit 1 Webinar Slides

CCGPS MathematicsUnit-by-Unit Grade Level Webinar

Fifth Grade Unit 1: Order of Operations and Whole Numbers

May 10, 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 FiveUnit 1: Order of Operations and Whole Numbers

May 10, 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 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

•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 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

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: 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

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/5th+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!

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)