CCGPS Mathematics
Unit-by-Unit Grade Level Webinar
Third Grade
Unit 2: Operations and Algebraic Thinking: The
Relationship Between Multiplication and Division
August 7, 2012
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CCGPS Mathematics
Unit-by-Unit Grade Level Webinar
Grade Three
Unit 2: Operations and Algebraic Thinking: The
Relationship Between Multiplication and Division
August 7, 2012
Turtle Toms– tgunn@doe.k12.ga.us
Elementary Mathematics Specialist
These materials are for nonprofit educational
purposes only. Any other use may constitute
copyright infringement.
Expectations and clearing up confusion
• This webinar focuses on CCGPS content specific to Unit 2, Grade 3.
• For information about CCGPS across a single grade span, please
access the list of recorded GPB sessions on Georgiastandards.org.
• For information on 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 these
documents are posted on the K-5 wiki.
http://ccgpsmathematicsk-5.wikispaces.com/
Expectations and clearing up confusion
• The intent of this webinar is to bring awareness to:
the types of tasks contained in the unit.
your conceptual understanding of the mathematics in this
unit.
approaches to tasks which provide deeper learning
situations for your students.
We will not be working through each task during this
webinar.
Welcome!
• Thank you for taking the time to join us in this discussion of
Unit 2.
• At the end of today’s session you should have at least 3
takeaways:
 The big idea of Unit 2
 Something to think about… food for thought
 How can I support student problem solving?
 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.
• After reviewing the remaining units, please contact us with
content area focus/format suggestions for future webinars.
Turtle Gunn Toms– tgunn@doe.k12.ga.us
Elementary Mathematics Specialist
Welcome!
• For today’s session:
Have you read the mathematics CCGPS?
 Did you read Unit Two and work through the tasks?
 Make sure you download and save the documents from
this session. If you didn’t, they are posted for your
convenience on the K-5 wiki.
Ask questions and share resources/ideas for the common
good.
Join the K-5 wiki. If you are still wondering what a wiki is,
we’ll discuss this near the end of the session.
Activate your Brain
My brother has a candy store. He sells candy in
special boxes that hold 10 assorted candies.
He orders his candy from a factory, and it comes
in different amounts based on weight. His last
order had 72 chocolate truffles, 72 vanilla creams,
23 chocolate almonds, 33 jellies, 80 caramels,
and 16 nougats. How many boxes does he need?
What’s the big idea?
• Enduring Understandings
• Essential Questions
• Common Misconceptions
•Strategies for Teaching and Learning
• Overview
Remember this…?
What’s the big idea?
Deepen understanding of number,
the operations of multiplication and
division, and relationships between
the two.
What’s the big idea?
Standards for Mathematical Practice
• What might this look like in the classroom?
• Wiki- http://ccgpsmathematicsk5.wikispaces.com/3rd+Grade/
•
•
•
•
•
Inside math- http://bit.ly/Mg07ml
Games- http://bit.ly/vJEbdG
Edutopia- http://bit.ly/o1qaKf
Teaching channel- http://bit.ly/wm0OcJ
Math Solutions- http://bit.ly/MqPf6w
Thanks to Education Week for these slides.
Thanks to Education Week for these slides.
Coherence and Focus – Unit 2
What are students coming with?
Coherence and Focus – Unit 2
What are students coming with from Unit 1?
Coherence and Focus- Unit 2
Where does this understanding lead students?
• Look in your unit and find the Enduring
Understandings.
Coherence and Focus – Unit 1
View across grade bands
• K-6th
Operations with whole numbers and fractions.
Numbers and their opposites.
• 8th-12th
Everything!
Navigating Unit Two
•The only way to gain deep understanding is to work
through each task. No one else can understand for you.
•Make note of where, when, and what the big ideas are.
•Make note of where, when, and what the pitfalls might
be.
•Look for additional tools/ideas you want to use
•Determine any changes which might need to be made
to make this work for your students.
•Share, ask, and collaborate on the wiki.
http://ccgpsmathematicsk-5.wikispaces.com/Home
Revision-ish Unit 2
• Pg. 7 Skip counting- be careful!
• Terms- if they are useful and make the mathematics
clearer, use them. Not for memorization
• Pg. 28- MATHEMATICAL not MATNEMATICAL
• Pg. 48- alignment issue with triangle
• Pg. 59- one of my favorite tasks!
Activate your Brain
My brother has a candy store. He sells candy in
special boxes that hold 10 assorted candies.
He orders his candy from a factory, and it comes
in different amounts based on weight. His last
order had 72 chocolate truffles, 72 vanilla creams,
23 chocolate almonds, 33 jellies, 80 caramels,
and 16 nougats. How many boxes does he need?
What’s the big idea?
Deepen understanding of number,
the operations of multiplication and
division, and relationships between
the two.
Examples & Explanations
Standards addressed in Unit 2
MCC3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the
total number of objects in 5 groups of 7 objects each. For example, describe
a context in which a total number of objects can be expressed as 5× 7.
MCC3.OA.2 Interpret whole-number quotients of whole numbers, e.g.,
interpret 56 ÷ 8 as the number of objects in each share when 56 objects are
partitioned equally into 8 shares, or as a number of shares when 56 objects
are partitioned into equal shares of 8 objects each. For example, describe a
context in which a number of shares or a number of groups can be
expressed as 56 ÷ 8.
MCC3.OA.3 Use multiplication and division within 100 to solve word
problems in situations involving equal groups, arrays, and measurement
quantities, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
Examples & Explanations
Standards addressed in Unit 2
MCC3.OA.4 Determine the unknown whole number in a multiplication or division
equation relating three whole numbers. For example, determine the unknown
number that makes the equation true in each of the equations 8 × ? = 48, 5 = □
÷ 3, 6 × 6 = ?. × ? = 48, 5 = □ ÷ 3, 6 × 6 = ?.
MCC3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a
data set with several categories. Solve one- and two-step “how many more” and
“how many less” problems using information presented in scaled bar graphs. For
example, draw a bar graph in which each square in the bar graph might
represent 5 pets.
MCC3.MD.4 Generate measurement data by measuring lengths using rulers
marked with halves and fourths of an inch. Show the data by making a line plot,
where the horizontal scale is marked off in appropriate units— whole numbers,
halves, or quarters.
Examples & Explanations
Resources which work with Unit 2:
•This is the time to go back to stuff.
•Number line
•Arrays
•Thinking…
•Big Ideas
Examples and Explanations
What do students need in order to understand
multiplication and division?
• Understanding of place value
• Additive thinking
• Multiplicative thinking
Examples & Explanations
Multiplicative Thinking
• Additive strategies/replication
•Countable units
•Sharing
•Array and region
•Cartesian product (later)
•Simple proportional reasoning (later)
Examples & Explanations
Examples & Explanations
•http://www.learner.org/courses/learningmath/n
umber/session4/part_a/multiplication.html
Examples & Explanations
Thinking about Division
•Commutativity for multiplication, but not
division
• Think multiplication
• Partitive- sharing
•Quotative- measurement
Partitive (sharing)
“How many in each group?”
Quotative (Measurement)
“How many groups?”
http://www.learner.org/courses/learningmath/number/session4
/part_a/division.html
Examples and Explanations
Examples and Explanations
http://mrwendler.wordpress.com/math-in-the-class/math/division/
Examples & Explanations
How to develop all of these?
• Do number talks regularly, expand them to include
equations that support development of understanding.
http://bit.ly/OYVpKN
Not sure about the strategies yourself?
• VandeWalle,
“Teaching Student-Centered Mathematics- 3-5”
• Fosnot, “Young Mathematicians at Work” Constructing
Multiplication and Division
Examples & Explanations
Examples & Explanations
http://letsplaymath.net/2007/01/13/number-bondsbetter-understanding/
Examples & Explanations
Journaling :
http://letsplaymath.net/2007/08/21/writing-tolearn-math/
Examples & Explanations
Nice extrahttp://bedtimemathproblem.org/
Examples & Explanations
Standards:
http://secc.sedl.org/common_core_videos/grade.php?grade=3
Videos for teachers explaining standards- so far: NF.2a,b
MD.7d
Tools:
Tools for the Common Core:
http://commoncoretools.me/2012/04/02/general-questionsabout-the-standards/
On the wiki:
Discussion threads
Unpacked standards from other states. Proceed with caution.
Assessment
Assessment
Try thinking about assessment in this way:
The chef tasting the soup in the kitchen is engaged
in formative assessment. The person eating the
soup in the restaurant is engaged in summative
assessment.
You are the chef. Adjust constantly with the end in
mind.
What one county has done:
1. Marcus has 36 marbles. He is putting an equal number
of marbles into 4 bags.
For 1a–1d, Circle Yes or No to indicate whether each
number sentence could be
used to find the number of marbles Marcus puts in each
bag.
1a. 36 x 4 =
Yes
No
1b. 36 ÷ 4 =
Yes
No
1c. 4 x
= 36
Yes
No
1d. 4 ÷ = 36
Yes
No
Score: ______/4
Hall County Schools
What one county has done:
Hall County School System
2. Sarah is 12 years old.
George is g years old.
Sarah is 3 times as old as George.
For numbers 2a–2c, Circle Yes or No to indicate whether
each statement is true.
2a. George’s age, in years, can be represented by the
expression 12 ÷ 3.
Yes
No
2b. George is 15 years old.
Yes
No
2c. George’s age, in years, can be found by solving
the equation 12 = 3 × g. Yes No
What one county has done:
Hall County Schools
What one county has done:
Hall County Schools
What one county has done:
Hall County Schools
What one county has done:
• C. Based on the data, which teacher do you think
will need to buy new pencils first? Justify your
answer.
Hall County Schools
Want more?
• http://insidemathematics.org/index.php/3rd-grade
Again, thanks to Education
Week for these slides.
Navigating Unit Two
•The only way to gain deep understanding is to work
through each task. No one else can understand for you.
•Make note of where, when, and what the big ideas are.
•Make note of where, when, and what the pitfalls might
be.
•Look for additional tools/ideas you want to use
•Determine any changes which might need to be made
to make this work for your students.
•Share, ask, and collaborate on the wiki.
http://ccgpsmathematicsk-5.wikispaces.com/Home
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
What’s the big idea?
Standards for Mathematical Practice
• What might this look like in the classroom?
• Wiki- http://ccgpsmathematicsk5.wikispaces.com/3rd+Grade/
•
•
•
•
•
Inside math- http://bit.ly/Mg07ml
Games- http://bit.ly/vJEbdG
Edutopia- http://bit.ly/o1qaKf
Teaching channel- http://bit.ly/wm0OcJ
Math Solutions- http://bit.ly/MqPf6w
Resources
Common Core Resources
 SEDL videos - https://www.georgiastandards.org/CommonCore/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/standardspractices/mathematics-standards/
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
• Books
Resources
 Van De Walle and Lovin, Teaching Student-Centered
Mathematics, K-3
 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
 Wedekind, Math Exchanges
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)
As you start your day tomorrow…
Remember thisBasically, the standards are not units of instruction; you don’t
always “teach a standard” in one chunk, whatever the order.
For example, the OA and NBT standards in any given great
level are very closely related, and a curriculum might be
touching on these two domains simultaneously at times, not to
mention supporting standards in MD and other domains. The
standards describe achievements we want students to have. As
my colleague Jason Zimba likes to say, you don’t teach
standards, you teach mathematics.
Bill McCallum
As you start your day tomorrow…
Thank You!
Please visit http://ccgpsmathematicsK-5.wikispaces.com/ to provide us with
your feedback!
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)