1. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 Laying the Foundation for Single-Digit Addition & Subtraction Fluency Grades K-2 and Beyond Common Core Leadership for Mathematics June 25, 2012 This material was developed for use by participants in the Common Core Leadership in Mathematics (CCLM^2) 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.

2. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Operations and Algebraic Thinking Domain

3. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 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

4. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 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

5. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 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.

6. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Early Counting and Subitizing

7. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Where does Operations and Algebraic Thinking begin? Kindergarten Domain: Counting and Cardinality

8. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 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.

9. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 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.

10. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 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.

11. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Turn and Talk What are some characteristics of a proficient counter?

12. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 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.

13. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Dot Patterns Play “Flash” – How many dots did you see? – How did you see it?

14. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 How many dots? How did you see it?

15. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 How many dots? How did you see it?

16. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 How many dots? How did you see it?

17. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 How many dots? How did you see it?

18. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 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.

19. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 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.

20. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 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.

21. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 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?

22. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 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.