1. Laying the Foundation for Single-Digit Addition & Subtraction Fluency Grades K-2 and Beyond Common Core Leadership for Mathematics June 21, 2011 DeAnn Huinker & Melissa Hedges University of Wisconsin-Milwaukee Common Core Leadership in Mathematics Project

2. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 K-8 Domains K12345678 Counting & Cardinality Ratios & Proportional Relationships Operations & Algebraic ThinkingExpressions & Equations Number & Operations in Base TenThe Number System Number & Operations - Fractions Functions Measurement & Data Statistics & Probability Geometry K-8 Content Domains, CCSSM

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

4. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Learning Intentions We are learning to… Understand how fluency with single-digit addition & subtraction develops and progresses in CCSSM. Read & interpret the cluster of CCSSM standards related to adding and subtracting within 20. We will know we are successful when we can… Understand the strategies students use for solving single-digit addition and subtraction problems.

5. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Getting started… Mentally compute the answer to the following… 1005 – 998 54 + 48 No pencil or paper please!

6. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Turn and share your reasoning.

7. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Reflecting on your homework reading, compare the definitions of a computational strategy versus algorithm. Did you use a strategy or an algorithm? What do you understand about number relationships that allow you to mentally compute answers? Discuss

8. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 A Content Standards Progression Grade 1 Page 15 of the CCSSM. Read the OA domain for Grade 1: “Operations and Algebraic Thinking” 1.OA.1-8 As you read, mark the following: familiar ideas: ✓ surprising ideas: ! confusing ideas: ? Then turn and share a ✓ or ! and a ?

9. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 A Content Standards Progression Grade 2 Page 19 of the CCSSM. Read the 2.OA.1 and 2.OA.2 In what ways do the grade 2 standards build from the grade 1 standards?

10. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 A Content Standards Progression Grade K Read pages 11-12 of CCSSM: K.CC.4a-c, K.OA.3, K.OA.4, and K.NBT. In what ways do these standards in kindergarten lay the foundation for learning single-digit addition and subtraction problems?

11. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Dot Patterns & Ten Frames Play “Flash” How many dots did you see? How did you see it? What’s the math?

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

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

14. Common 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 2011 Ten Frames Ten frames show relationships of small numbers to five and ten, in particular, drawing attention to the role of 10.

16. Common 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 2011 How many dots? How did you see it?

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

19. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Laying a foundation for understanding Morgan, Dot Plates, & Ten Frames Enjoy!

20. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Through the lens of the Math Content What does Morgan understand about number? K.OA.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings… K.OA.4: For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings...

21. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Through the lens of the Math Content What is the difference between K.OA.3 and K.OA.4 in the classroom? What value does this foundation have for our middle and high school students? K.OA.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., use objects or drawings… K.OA.4: For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., using objects or drawings...

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

24. Building Understanding Through Context How might a student solve this problem? There were 6 cookies on the plate. Mom put 5 more cookies on the plate. How many cookies are on the plate now?

25. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Progression toward fluency Methods for solving single-digit problems pp. 36-38 of the OA progressions document Level 1: Direct Modeling Level 2: Counting on Level 3: Convert to an Easier Problem

26. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Level Jigsaw Form Groups of Three. Number off 1-3. Read and highlight your assigned level. Using examples, teach your colleagues how student thinking and reasoning would sound at your level. #1s read & teach Level 1 #2s read & teach Level 2 #3s read & teach Level 3

27. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Grade 1: Content Standard 1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on making ten decomposing a number leading to a ten using the relationship between addition & subtraction creating equivalent but easier or known sums

28. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Strategies for Single Digit Addition Counting on. Make a ten. Use an easier “equivalent” problem. Transform the problem in some way Use fives Use a helping fact Use doubles

29. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 8 + 6 Strategies: Make a ten. Use a double. Use fives. Use some other equivalent problem. Put 8 counters on your first frame & 6 counters on your second frame.

30. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Make a ten: 8 + 6 How could you make a ten?

31. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Make a ten: 8 + 6 How could you make a ten? Move 2 counters to the top frame. Write an equation. 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14 Then you have 10 and 4 more counters.

32. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Use a double: 8 + 6 What doubles might you use?

33. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Use a double: 8 + 6 What doubles might you use? Write an equation. 8 + 6 = 6 + 6 + 2 = 12 + 2 = 14 Reason 6 + 6 = 12; then add 2 more.

34. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Use fives: 8 + 6 Can you see some fives? Where?

35. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Use fives: 8 + 6 Can you see some fives? Where? Reason: 5 + 5 is 10; need to add 3 more and 1 more. Write an equation. 8 + 6 = 5 + 5 + 3 + 1 = 10 + 4 = 14

36. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 7 + 9 9 + 8 6 + 7 Select a problem. Tell an addition story. Draw a strategy card for the group. Everyone uses ten frames and counters to reason through the strategy and writes an equation(s) that shows the reasoning. Share, compare, and discuss as a group. Repeat with another strategy card for the the same problem or a new problem. Reflect: Which strategies seem to work best for each problem?

37. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Learning Intentions We are learning to… Understand how fluency with single-digit addition & subtraction develops and progresses in CCSSM. Read & interpret the cluster of CCSSM standards related to adding and subtracting within 20. We will know we are successful when we can… Understand the strategies students use for solving single-digit addition and subtraction problems.