CCGPS Mathematics
Unit-by-Unit Grade Level Webinar
Fourth Grade
Unit 2: Fraction Equivalents
August 8, 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.
CCGPS Mathematics
Unit-by-Unit Grade Level Webinar
Grade Four
Unit 2: Fraction Equivalents
August 8, 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
Maria went to the music store to buy
some CDs. She had twenty four
dollars with her. She spent eighteen
dollars.
What fractional part of her money
did she spend?
In its lowest form?
What’s the big idea?
• Enduring Understandings
• Essential Questions
• Common Misconceptions
•Strategies for Teaching and Learning
• Overview
Remember this…?
What’s the big idea?
Deep understanding of equivalent
fractions, using a visual model.
Deep understanding of factors and
multiples, primes and composites.
What’s the big idea?
Standards for Mathematical Practice
• What might this look like in the classroom?
• Wiki- http://ccgpsmathematicsk5.wikispaces.com/4th+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 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 2
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. 17- alignment issues
• Pg. 25-26- denominators that are outside the
suggested range.
• Pg. 31- Last paragraph- not yet
• Pg. 37- Great game! Play often…
• Pg. 49- Factor Trail gameboard
Activate your Brain
Maria went to the music store to buy
some CDs. She had twenty four
dollars with her. She spent eighteen
dollars.
What fractional part of her money
did she spend?
In its lowest form?
Activate your Brain
A fourth- grade class traveled on a field trip in four separate vehicles. The
school provided a lunch of submarine sandwiches for each group. When
they stopped for lunch, the subs were cut and shared as follows:
The first group had 3 people and shared 2 subs equally.
The second group had 4 people and shared 3 subs equally.
The third group had 9 people and shared 6 subs equally.
The last group had 6 people and shared 4 subs equally.
When they returned from the field trip, the children began to argue that the
portion of the sandwiches they received was not fair, that some children
got more to eat than others. Were they right? Or did everyone get the
same amount?
What’s the big idea?
Deep understanding of equivalent
fractions, using a visual model.
Deep understanding of factors and
multiples.
Examples & Explanations
Standards addressed in Unit 2
MCC4.NF.1 Explain why a fraction a/b is equivalent to
a fraction (n × a)/(n × b) by using visual fraction
models, with attention to how the number and size of
the parts differ even though the two fractions
themselves are the same size. Use this principle to
recognize and generate equivalent fractions.
Examples & Explanations
Standards addressed in Unit 2
MCC4.NF.2 Compare two fractions with different numerators
and different denominators, e.g., by creating common
denominators or numerators, or by comparing to a
benchmark fraction such as 1/2. Recognize that
comparisons are valid only when the two fractions refer to
the same whole. Record the results of comparisons with
symbols >, =, or <, and justify the conclusions, e.g., by using
a visual fraction model.
* Grade 4 expectations in this domain are limited to fractions
with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Examples & Explanations
Standards addressed in Unit 2
MCC4.OA.4 Find all factor pairs for a whole number in the
range 1–100. Recognize that a whole number is a multiple
of each of its factors. Determine whether a given whole
number in the range 1–100 is a multiple of a given one-digit
number. Determine whether a given whole number in the
range 1–100 is prime or composite.
Examples & Explanations
Resources which work with Unit 2:
This is the time to use stuff.
•Number line
•Fraction Strips
•Pattern Blocks
•Arrays
•Thinking…
•Big Ideas
Examples and Explanations
What understandings do students need in order
to understand fraction equivalence?
• Meaning of numerator
• Meaning of denominator
• Valid comparisons involve same-sized whole
• Multiplicative thinking
• Experience dividing multiple shapes into equal
shares/parts
Examples & Explanations
Multiplicative Thinking
• Additive strategies/replication
•Countable units
•Sharing
•Array and region
•Cartesian product (later)
•Simple proportional reasoning (later)
Examples & Explanations
Thinking about Division
•Commutativity for multiplication, but not
division
• Think multiplication
• Partitive- sharing
•Quotative- measurement
Examples & Explanations
Examples & Explanations
Examples & Explanations
Examples & Explanations
Examples & Explanations
•http://www.learner.org/courses/learningmat
h/number/session8/index.html
Examples & Explanations
What do students need in order to
understand factors, primes, and
composites?
•The vocabulary
•Experiences from Unit 1- pages 73-114
•visuals
Examples & Explanations
http://realteachingmeansreallearning.blogspot.c
om/2011/02/prime-and-composite-numbers.html
“The Transformation of a math teacher from
one who “drilled and killed” to one who
engages”
Examples & Explanations
You are planning a wedding and you and your
spouse are very particular about seating
arrangements. You can arrange the tables in
any way as long as there is the same amount of
people at each table. You have a total of 100
people coming to your wedding, how can you
arrange the tables?
http://realteachingmeansreallearning.blogspot.c
om/2011/02/prime-and-composite-numbers.html
Explanations and Examples
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
Fractions, Decimals, and Percents
Examples & Explanations
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=4
Videos for teachers explaining standards- so far: NBT.6, NF.1,
NF.3 a,b,c,d
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:
Hall County Schools
1. Jesus says that 50 is a factor of 100. Emily
says that 50 is a multiple of 5. Who is correct?
Explain your answer with numbers and words.
What one county has done:
Hall County School System
2. Peter made the statement shown below.
“The number 32 is a multiple
of 8. That means all of the
factors of 8 are also factors
of 32.”
Part A
Is Peter’s statement correct? In the space below,
use numbers and words to explain why or why not.
Part B
Does Peter’s rule apply to other numbers? Give an
example where it does or does not apply and explain
your thinking using numbers and words.
What one county has done:
Hall County Schools
What one county has done:
Hall County Schools
What one county has done:
Part C
We know that Benito’s bag has a total of 10 pencils inside,
and James’ bag has a total of 5 pencils inside but they
both have the same fraction of sharpened pencils to total
pencils. Another student, Tommy, also has the same
fraction of sharpened pencils to total pencils as Benito and
James.
Draw a picture of what Tommy’s bag of pencils might look
like and write a fraction to match your picture to show the
number of sharpened pencils to all pencils.
Hall County Schools
What one county has done:
How can the fraction of Tommy’s bag be the same as
Benito’s and James’ even though they have a
different number of pencils? Explain your answer
using both numbers and words.
Hall County Schools
What one county has done:
4. Each of three people started at the same point and ran in
the same direction.
• Quintrel ran three fourths of a mile and then stopped.
• Gregory ran one eighth of a mile and then stopped.
• Henry ran ½ of a mile and then stopped.
Hall County Schools
What one county has done:
Hall County Schools
Want more?
• http://insidemathematics.org/index.php/4th-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/4th+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, 3-5
 Fosnot and Dolk, Young Mathematicians at Work
 Parrish, Number Talks
 NCTM, Developing Essential Understanding of Rational Numbers
 Shumway, Number Sense Routines
 Wedekind, Math Exchanges
 New- Burns and Silbey, So You Have to Teach Math?
 New- Teaching with Intention- Debbie Miller
 New- Moynihan, Math Sense
 New- Confer and Ramirez, Math Tools in Action
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)