Multiplication

1. Multiplication Common Core Leadership in Mathematics (CCLM) Friday June 29, 2012 This material was developed for use by the project staff and 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. CCLM Homework Debrief Share with your shoulder partner a few ideas that strike you as critical to developing a sound understanding of multiplication and division. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

3. CCLM Learning Intentions We are learning to… • Understand how the CCSSM views the development of multiplicative thinking. • Apply strategies that promoting fluency with single-digit multiplication. We will be successful when we can … • Help students apply properties of operations as strategies to multiply. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

4. CCLM From Counting by Ones to Thinking In Groups • Place a large amount of counters in the middle of the table. • On the word “go” grab as many groups of two that you can before we say stop. Don’t count the total number of sets, just concentrate on making groups of two. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

5. CCLM Return the counters to the middle of the table. On the word “go” grab as many sets of ________ that you can before we say stop. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

6. CCLM Making groups: What did you notice? What kind of thinking were you doing as you were making groups? What would this activity tell you about students’ thinking? You were just unitizing! Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

7. CCLM Pre-requisites to Thinking Multiplicatively Cardinality- Understand that the last counting word indicates the amount of quantity of the set of objects Subitize: Perceive an amount (1-7) without counting Unitizing: Using numbers to count groups of objects, rather than single objects Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

8. CCLM Dot Images How many dots so you see? How do you see It? Draw what you see in your notebook. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

9. Image 1

10. CCLM Grounding Thinking in CCSSM With your shoulder partner, use an example, remind each other how these “rules of numbers work.” 3.OA.5: Apply properties of operations as strategies to multiply and divide. • Commutative • Associative • Distributive Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

11. Image 2

12. CCLM Reflect back on 3.OA.5. Think about how the images were described. Where do the properties show up in the reasoning? Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012

13. Learning Intentions We are learning to… • Understand how the CCSSM views the development of multiplicative thinking. • Apply strategies that promoting fluency with single-digit multiplication. We will be successful when we can … • Help students apply properties of operations as strategies to multiply.