CCGPS Mathematics Unit-by-Unit Grade Level Webinar Fourth Grade Unit 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 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 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 Mathematics Unit-by-Unit Grade Level Webinar Grade Four Unit 1: Whole Numbers, Place Value, and Rounding, in Computation May 9, 2012 Turtle Gunn Toms– 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 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 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– 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 signs between the nine figures so that they equal = 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 Unit  Overview  Standards  Enduring Understandings  Essential Questions  Concepts and Skills to Maintain  Selected Terms and Symbols  Strategies for Teaching and Learning  Common Misconceptions  Evidence of Learning  Tasks

New to the Frameworks? Enduring Understandings Essential Questions Common Misconceptions Overview

Brand Spanking New!

Navigating a Unit What’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 cooperative-learning-video cooperative-learning-video eos eos first-weeks-school first-weeks-school

Navigating a Unit Journaling/Math Workshop Downloaded article from Marilyn Burns Sense making for students and teachers Downloaded article from NCTM

Navigating a Unit Mathematical Community of Learners- 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 subsets Number 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 division Number 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 Areas In 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… Student-developed strategy using partial products No youtube in your district? Try this-

Developing Number Sense How do you know what they know? First, do no harm: (Procedural vs conceptual understanding- question and never assume) Determine strategies: Thanks, Gatorgyrl82!

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 1 View across grade bands K-6 th  Operations with whole numbers and fractions.  Numbers and their opposites. 8 th -12 th  Everything!

Coherence and Focus – Unit 1 What foundation is being built? Where does this understanding lead students?

Examples & Explanations Downloads: Rekenrek packet ispaces.net/Rekenreks ispaces.net/Rekenreks game-that-is-worth-1000-worksheets/ game-that-is-worth-1000-worksheets/

Examples and Explanations Strategy Development

Examples & Explanations

178+ m = m= 178

Examples & Explanations Journaling Revisited:

Examples & Explanations Standards: Videos for teachers explaining standards- so far: 4.NBT.6, with more to come. Tools: mmon-core-tools/unpacking/math/4th.pdf Unpacked standards from NC

Assessment How might it look? Examples of how balanced assessments can be assembled.  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 (while you are at it, have a look at their Professional Learning!)

Assessment How could it look?

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?

Resources Common Core Resources  SEDL videos - Core/Pages/Math.aspx or Core/Pages/Math.aspxhttp://secc.sedl.org/common_core_videos/  Illustrative Mathematics -  Dana Center's CCSS Toolbox -  Arizona DOE - standards/ standards/  Ohio DOE – rimary.aspx?page=2&TopicRelationID=1704http:// rimary.aspx?page=2&TopicRelationID=1704  Inside Mathematics-  Common Core Standards -  Tools for the Common Core Standards -  Phil Daro talks about the Common Core Mathematics Standards -

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-  Edutopia –  Teaching Channel -  Annenberg Learner - Assessment Resources  MARS -  MAP -  PARCC - Start of School- Parents  (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 boxes NOTHING IS REALLY GOING TO CHANGE We designed these as a platform for new kinds of instructional systems We 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

Thank You! Please visit to provide us with your feedback! Join our listserve: Turtle Gunn Toms Program Specialist (K-5) These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Join the listserve! Follow on Twitter! (yep, I’m tweeting math resources in a very informal manner)