This material was developed for use by participants in the Common Core Leadership in Mathematics (CCLM^2) project through the University of Wisconsin-Milwau
Use by school district personnel to support learning of its teachers and staff is permitted provided appropriate acknowledgement of its source.
Use by others is prohibited except by prior written permission.
Laying the Foundation for
Single-Digit Addition & Subtraction Fluency
Grades K-2 and Beyond
Common Core Leadership for Mathematics
June 25, 2012
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Operations and Algebraic
Thinking Domain
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
Counting and Cardinality and
Operations and Algebraic Thinking
Read and highlight pages 2-3 of the Progressions
document on the Counting and Cardinality and
Operations and Algebraic Thinking domains.
!
?
Important Idea
Idea I don’t understand
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
Counting and Cardinality;
Operations and Algebraic Thinking
What is it?
K-2 OA
Quickly list out any words, ideas, or phrases
the come to mind as you think of
“Counting and Cardinality” and
Operations and Algebraic Thinking.”
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
Why an “Operations and Algebraic
Thinking” Domain?
http://youtu.be/HMMe8_4s9KE
Reflect on your Word Splash in the context
of the video.
What ideas surfaced in the video that affirmed
your word splash?
Using a different color marker, add any new
ideas to your word splash.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
Early Counting
and Subitizing
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
Where does Operations and
Algebraic Thinking begin?
Kindergarten Domain: Counting and Cardinality
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
Learning Intention and Success Criteria
We are learning to …
– Understand the relationship between
numbers and quantities.
– Connect counting to cardinality.
We will be successful when we can ….
– Clearly explain the mathematical content in
K.CC.4a and K.CC.4b and be able to
provide examples of the mathematics.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
Cluster: Count to tell the number of objects.
Standard K.CC.4
K.CC.4. Understand the relationship between numbers
and quantities; connect counting to cardinality.
a.
When counting objects, say the number names in
the standard order, pairing each object with one and only
one number name and each number name with one and
only one object.
b.
Understand that the last number name said tells the
number of objects counted. The number of objects is the
same regardless of their arrangement or the order in
which they were counted.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
Standard K.CC.4a & K.CC.4b
Use the letter you were assigned to
read K.CC.4a or K.CC.4b.
•Divide your whiteboard in half.
•On one side, rephrase this standard and on
the other side, provide an example.
•Share with your partner.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
Turn and Talk
What are some characteristics of
a proficient counter?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
Milestones to Counting
• Rote Counting
– Number word list is accurately recited.
• Symbol-word pairing
– Match written number symbols with number name stated
out loud (e.g., recognize the symbol “2” when the word
“two” is said out loud).
• One-to-one Correspondence
– Each object counted is paired with exactly one number word.
• Cardinality
– The last number word stated tells how many there are in the
counted set.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
Dot Patterns
Play “Flash”
–How many dots did you see?
–How did you see it?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
How many dots?
How did you see it?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
How many dots?
How did you see it?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
How many dots?
How did you see it?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
How many dots?
How did you see it?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
What is at Work? Subitizing
Perceptual Subitizing
• Quickly recognize the cardinality of small groups
without having to count the objects.
• Identifying the number of items in a small set (2-5)
without counting.
Conceptual Subitizing (develops from perceptual subitizing)
• Recognize that a collection of objects is composed of
two subcollections and quickly combining their
cardinalities to find the cardinality of the collection.
• Quickly seeing the quantity in larger sets by
decomposing into smaller sets.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
Beyond Counting By Ones
Read pages 8-9 of “Beyond Counting By Ones: ‘Thinking
in Groups’ as a Foundation for Number and Operation
Sense” (Huinker, 2011).
Start on page 8 at “Common Core Standards Learning
Expectations.” Stop at the end of page 9.
Share how this reading clarified your understanding of
subitizing and its importance for connecting counting
with cardinality.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
Find the Same Amount
•
•
•
•
•
Lay the cards out face up.
Pick one card in the collection.
Find another card with the same amount.
Tell how you know they are the same.
Take turns and continue finding pairs.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012
Revisit K.CC.4a & K.CC.4b
In what ways do the Find the Same Amount and
Dot Pattern Flash activities help young children
as they connect counting to cardinality?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012
Learning Intention and Success
Criteria
We are learning to …
– Understand the relationship between
numbers and quantities.
– Connect counting to cardinality.
We will be successful when we can ….
– Clearly explain the mathematical content in
K.CC.4a and K.CC.4b and be able to
provide examples of the mathematics.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
2012