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

K-8 Content Domains, CCSSM 1 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

Domain Progressions - Number

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

Strategy vs. Algorithm

No pencil or paper please! Getting started… Mentally compute the answer to the following… 1005 – 998 54 + 48 No pencil or paper please! CCLM Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

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

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

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

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

K-2 Content Standards Progression

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

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

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

Using Models

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

How many dots? How did you see it?

How many dots? How did you see it?

How many dots? How did you see it?

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

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

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

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.