This webinar provided an overview of the 4th grade CCGPS mathematics unit on whole numbers, place value, and rounding in computation. The big idea of the unit is to deepen understanding of place value and its usefulness in estimation and computation. Resources were shared for exploring strategies for teaching key concepts like multi-digit multiplication and comparing fractions. Feedback was requested to help improve future unit-by-unit webinars. Participants were also encouraged to join a wiki for ongoing discussion of CCGPS mathematics.

1. 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.

2. 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.

3. 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– tgunn@doe.k12.ga.us
Elementary Mathematics Specialist
These materials are for nonprofit educational
purposes only. Any other use may constitute
copyright infringement.

4. 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

5. • 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.us
Elementary Mathematics Specialist

6. 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.

7. 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.

8. 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.

9. What’s the big idea?
Deepen and expand
understanding of place value,
and its usefulness in estimation
and computation.

10. 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

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

12. Brand Spanking New!

13. 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.

15. 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/vid
eos
•http://www.responsiveclassroom.org/category/category/
first-weeks-school

16. Navigating a Unit
Journaling/Math Workshop
•Downloaded article from Marilyn Burns
http://letsplaymath.net/2007/08/21/writing-to-learn-math/
Sense making for students and teachers
•Downloaded article from NCTM
http://www.youtube.com/user/mitcccnyorg?feature=watch

17. 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

18. “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

19. What’s the big idea?
Deepen and expand
understanding of place value, and
its usefulness in estimation and
computation.

20. What do Fourth Grade students bring?
What are they connecting to later?
From 3 to 4 Later
• Deep understanding of addition and • Deep understanding of addition and
subtraction strategies (within 1000) subtraction, multiplication and division.
• Developing understanding of • Useful place value understanding.
multiplication and division (products • Understanding of defining attributes
within 100) about shape, comparison of shape.
• Useful place value understanding. • Foundational fractional relationships,
• Understanding of defining attributes fraction operations.
about shape, comparison of shape. • Continuation of fluency/algebraic
• Foundational fractional relationships. thinking.
• Continuation of fluency/algebraic • Measurement/addition/subtraction/
thinking. fraction relationships
• Measurement/addition/subtraction • Data analysis
relationships
• Data analysis

21. 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

22. 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

23. Tools for Teaching Number Sense
• Subitization
• Comparison
• Counting
• One- to- one correspondence
• Cardinality
This is from Kindergarten Unit 1
• Hierarchical Inclusion
• Number Conservation  Dot Cards/TenFrames
 Number Cubes
• Spatial Relationship
 Dominoes
• One and Two More or Less  Cups
• Understanding Anchors  Collections
• Part/Part Whole Relationships  Rekenrek

24. Problem Types- + and -

25. Problem Types- x and ÷

26. Tools for Teaching Strategy

27. More strategy tools…
• http://youtu.be/Y8Bj5KVLmaY
Student-developed strategy using partial
products
No youtube in your district? Try this-
http://www.cleanvideosearch.com

28. Developing Number Sense
How 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

29. Coherence and Focus – Unit 1
What are students coming with?

30. Coherence and Focus – Unit 1
What foundation will have been built?
Where does this understanding lead incoming students?

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

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

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

34. Examples & Explanations
Downloads:
•Rekenrek packet
•http://gradekcommoncoremath.hcpss.wik
ispaces.net/Rekenreks
•http://letsplaymath.net/2006/12/29/the-
game-that-is-worth-1000-worksheets/

35. Examples and Explanations
Strategy Development

36. Examples & Explanations

37. Examples & Explanations
178+ m = 245 245- m= 178

38. Examples & Explanations
Journaling Revisited:

39. Examples & Explanations
Standards:
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/co
mmon-core-tools/unpacking/math/4th.pdf
Unpacked standards from NC

40. Assessment
How might it look?
Examples of how balanced assessments can be
assembled.
http://map.mathshell.org/materials/tests.php
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
http://map.mathshell.org/materials/pd.php
(while you are at it, have a look at their Professional Learning!)

41. Assessment
How could it look?
http://nzmaths.co.nz/mathematics-assessment

42. How is a GA county using this?
Thank you, Dr. Snell, and Henry County!

43. Helping to identify concerns…
Thank you, Dr. Snell, and Henry County!

44. 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.

45. 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.

46. What in the world is a wiki?
http://ccgpsmathematicsk-5.wikispaces.com/4th+Grade

47. 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=1704
Inside 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

48. 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!)

49. Resources
• Professional Learning Resources
 Inside Mathematics- http://www.insidemathematics.org/
 Edutopia – http://www.edutopia.org
 Teaching Channel - http://www.teachingchannel.org
Annenberg 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- Parents
http://www.youtube.com/watch?v=Vvk4-evBS-8&feature=plcp
(how to support your school and teacher)

50. 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.

51. 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

52. 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 Toms
Program 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)