Laying the Foundation for Single-Digit Addition

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Laying the Foundation for Single-Digit Addition
Subtraction Fluency Grades K-2 and Beyond
This material was developed for use by
participants in the Common Core Leadership in
Mathematics (CCLM2) project through the
University of Wisconsin-Milwaukee. 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.

• Common Core Leadership for Mathematics
• June 25, 2012

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Operations and Algebraic Thinking Domain
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Counting and Cardinality andOperations 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 dont understand

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Counting and Cardinality Operations and
Algebraic Thinking What is it?

• Quickly list out any words, ideas, or phrases
• the come to mind as you think of
• Counting and Cardinality and
• Operations and Algebraic Thinking.

Word Splash!
K-2 OA
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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.

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Early Counting and Subitizing
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Where does Operations and Algebraic Thinking
begin?Kindergarten Domain Counting and
Cardinality

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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.

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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.

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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.

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Turn and Talk

• What are some characteristics of a proficient
  counter?

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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.

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Dot Patterns

• Play Flash
• How many dots did you see?
• How did you see it?

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How many dots? How did you see it?
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How many dots? How did you see it?
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How many dots? How did you see it?
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How many dots? How did you see it?
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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.

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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.

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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.

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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?

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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.