Single-Digit Addition Fluency: Part 2 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: Part 2 Grades K-2 Common Core Leadership for Mathematics June 27, 2012 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. CCLM Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

Progression Toward Fluency

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

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

Level Jigsaw CCLM 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 summarize & teach Level 1 #2s summarize & teach Level 2 #3s summarize & teach Level 3 CCLM Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

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 Optional slide….. Point being, not all standards are created equal and this one standard might require attention all school year in first grade and be a major component of your instruction and assessment. CCLM Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

Strategies for Single Digit Addition Counting on. Make a ten. Use an easier “equivalent” problem. Use fives Use a helping fact Use doubles Transform the problem in some way CCLM Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

8 + 6 Strategies: Make a ten. Use a double. Use fives. Put 8 counters on your first frame & 6 counters on your second frame. Strategies: Make a ten. Use a double. Use fives. Use some other equivalent problem.

Make a ten: 8 + 6 How could you make a ten?

Make a ten: 8 + 6 How could you make a ten? Move 2 counters to the top frame. Then you have 10 and 4 more counters. Write an equation. 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14

Use a double: 8 + 6 What doubles might you use?

Use a double: 8 + 6 What doubles might you use? Reason 6 + 6 = 12; then add 2 more. Write an equation. 8 + 6 = 6 + 6 + 2 = 12 + 2 = 14

Use fives: 8 + 6 Can you see some fives? Where?

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

1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. Divide your whiteboard in half. Rephrase in your own words – provide an example and a non-example.

Reflect: Which strategies seem to work best for each problem? 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. Strategy Cards: Counting on, Make a ten, Use a double, Use fives Reflect: Which strategies seem to work best for each problem?

Learning Intentions CCLM 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