1. Single-Digit Addition Fluency Grades K-2
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.
Single-Digit Addition Fluency Grades K-2
Common Core Leadership for Mathematics
June 26, 2012
CCLM
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

2. K-8 Content Domains, CCSSM1 2 3 4 5 6 7 8
Counting & Cardinality
Ratios & Proportional Relationships
Operations & Algebraic Thinking
Expressions & Equations
Number & Operations in Base Ten
The Number System
Number & Operations - Fractions
Functions
Measurement & Data
Statistics & Probability
Geometry

3. Domain Progressions - Number

4. Learning Intentions & Success Criteria
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.
CCLM
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

5. Strategy vs. Algorithm

6. No pencil or paper please!
Getting started…
Mentally compute the answer to the following…
1005 – 998
No pencil or paper please!
CCLM
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

7. Turn and share your reasoning.
CCLM
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

8. Discuss
Reread your reflection about algorithm versus strategy completed for homework.
Reflecting on your summary, did you use a strategy or an algorithm?
What do you understand about number relationships that allow you to mentally compute answers?
CCLM
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

9. CCSS Glossary
Computation strategy Purposeful manipulations that may be chosen for specific problems, may not have a fixed order, and may be aimed at converting one problem into another. Computation algorithm A set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly.
CCLM
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

10. In Grades K-8, how many standards reference using “strategies”?
Grade K: CC
Grade 1: OA, NBT
Grade 2: OA, NBT
Grade 3: OA, NBT
Grade 4: NBT, NF
Grade 5: NBT
Grade 7: NS, EE
26 standards
11% of K-8 standards

11. K-2 Content Standards Progression

12. 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 ?
Clusters phrases highlight the “big ideas” that groups together a set of standards within and across grade levels.
CCLM
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 12

13. 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?
We end with this and the question at the end is rhetorical and hopefully they see the connection.
CCLM
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

14. A Content Standards Progression Grade K
Read pages 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?
CCLM
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

15. Using Models

16. Ten Frames
Ten frames show relationships of small numbers to five and ten, in particular, drawing attention to the role of 10.
CCLM
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

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

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

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

20. Laying a foundation for understanding
Morgan, Dot Plates, & Ten Frames Enjoy!
Command-F to get to full screen. Select chapter; click on “menu” when ready to switch, don’t click stop.
CCLM
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

21. 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...
CCLM
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

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

23. Learning Intentions & Success Criteria
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.