CCGPS MathematicsUnit-by-Unit Grade Level Webinar

Second Grade Unit 1: Extending Base Ten Understanding

May 3, 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 TwoUnit 1: Extending Base Ten Understanding

May 3, 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 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.

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 When 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?

Activate your Brain What 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.

What’s the big idea?

Developing deep understanding of quantity, relationships among numbers, and representation of number, specifically as they relate to place value, addition and subtraction, and the emergent understanding of multiplication.

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

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 OverviewCollaborative skills (How collaborative are your collaborative activities?)Productive StruggleJournaling/NotebookDevelopment 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.

Brand Spanking New!

Navigating a Unit

Classroom Routines and Ritualshttp://www.edutopia.org/math-social-activity-cooperati

ve-learning-videohttp://www.edutopia.org/math-social-activity-selhttp://www.youtube.com/user/responsiveclassroom/vi

deoshttp://www.responsiveclassroom.org/category/categor

y/first-weeks-school

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

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?

Developing deep understanding of quantity, relationships among numbers, and representation of number, specifically as they relate to place value, addition and subtraction, and the emergent understanding of multiplication.

What do Second Grade students bring? What are they connecting to later?

From 1-• Fluent addition and subtraction to 10.This means students have developed strategies

and have solved different problem types.• Foundational place value understanding.This means students have a conceptual

understanding.• Foundational ideas about shape and

position in space.• Ability to compare and catagorize.• Understanding of quantities to 120.• Measurement as unit iteration• Transitive propertyLater-

• Deep understanding of addition and subtraction.

• 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

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)

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

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)

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

Developing Number SenseHow 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=relmfu• Determine strategies:http://www.youtube.com/watch?v=yYdjCjEsdSw&feature=channel&list=UL

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?

http://www.k-5mathteachingresources.com/2nd-grade-math-journals.html

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

Examples and ExplanationsGroupable Materials

Examples & Explanations

Examples & Explanations

Examples & Explanations

Journaling Revisited:

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

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

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/2nd+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, K-3

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.

follow@turtletoms (yep, I’m tweeting math resources in a very informal manner)