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Multiplicative Thinking

Academic coaches discuss multiplication and division situations, explore types of problems, use tape diagrams, and delve into unknown factor problems as per learning intentions and success criteria. Collaboration and reflection enhance learning.

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Multiplicative Thinking

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  1. Multiplicative Thinking Academic Coaches – Math Meeting March 15, 2013 Beth Schefelker Bridget Schock Connie Laughlin Hank Kepner Kevin McLeod

  2. Learning Intentions & Success Criteria Learning Intentions We are learning to understand common multiplication and division situations. Success Criteria We will be successful when we can recognize multiplication and division situations and represent them appropriately (visually and abstractly).

  3. Multiplication Situations Work with a partner • Read the problems. • Draw a representation for each problem. How do your representations differ?

  4. Problem Types • Classify the problems as • equal groups • array/area • or compare • What is a useful model? • Which problem type was the most difficult to find a model for?

  5. OA K-5 Progressions Read page 22 of OA K-5 Progression document. Table Discussion: • What are 2 important ideas that resonated with you?

  6. Tape Diagram Representation Beth has 8 pairs of dress shoes. Sharonda has 6 times as many pairs of dress shoes as Beth. How many pairs of dress shoes does Sharonda have? Beth Sharonda

  7. Comparison Problem #1 Use tape diagram to represent the problem. Connie ran 50 meters and Bridget ran 6 times as far as Connie. How many meters did Bridget run?

  8. Comparison Problem #2 Use tape diagram to represent the problem. Eratosthenes thought that the diameter of the earth was 8,000 miles and the distance from the earth to the moon is 9 times the earth’s diameter. How far did Eratosthenes think the earth was from the moon?

  9. Comparison Problem #3 Use tape diagram to represent the problem. Bernard traveled 10 miles to a soccer game. The next day he traveled 4 times as far to another game. How many miles did Bernard travel for both trips?

  10. Comparison Problem #4 Use tape diagram to represent the problem. Dylan has a collection of 150 matchbox cars and trucks. He has 4 times as many cars as trucks. How many cars does he have?

  11. Unknown Factor Problems Rewrite each of the problems on your cards as unknown factor problems in two different ways. 3.OA. Understand properties of multiplication and the relationship between multiplication and division. 6. Understand division as an unknown-factor problem. For example, find by finding the number that makes 32 when multiplied by 8.

  12. Summarizing Our Work Operations and Algebraic Thinking Progressions • Read p. 24 – 25 Stop at Levels in problem representation and solution • Read p. 29 (first 2 paragraphs only) How did our work today on multiplication and division help clarify the ideas in the progression?

  13. Learning Intentions & Success Criteria Learning Intentions We are learning to understand common multiplication and division situations. Success Criteria We will be successful when we can recognize multiplication and division situations and represent them appropriately (visually and abstractly).

  14. Reflection Describe at least one way that you’ve deepened your understanding around the Common Core student expectations for multiplication and division.

  15. Professional Practice Engage in a coaching conversation with your teachers around these ideas. Be prepared to share these experiences with your peers on April 12th ACM meeting.

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