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PROBLEM:

PROBLEM:. A fourth-grade class needs 5 leaves each day to feed its 2 caterpillars. How many leaves would the students need each day for 12 caterpillars? Use drawings, words, or numbers to show how you got your answer.

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PROBLEM:

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  1. PROBLEM: • A fourth-grade class needs 5 leaves each day to feed its 2 caterpillars. How many leaves would the students need each day for 12 caterpillars? • Use drawings, words, or numbers to show how you got your answer. • Please try to do this problem in as many ways as you can, both correct and incorrect. What might a 4th grader do?

  2. 5 Practices for Orchestrating Productive Mathematics Discussions Margaret S. Smith Mary Kay Stein

  3. WHAT’S LACKING IN OUR MATH CLASSROOMS? • NOT ENOUGH PROBLEM SOLVING • Textbook problems are not really “problems” • NOT ENOUGH SOCIAL INTERACTION • “Research tells us that complex knowledge and skills are learned through social interactions.”

  4. WHAT TEACHERS CAN DO • Find problems that are conducive to problem solving (cognitively demanding tasks) • Orchestrate the discussions by guiding and supporting the students • Launch the problem • Explore the problem • Discuss and summarize the problem

  5. THE CASE OF DAVID CRANE • Read pages 3-4 of Introduction • After reading, at your table group, please discuss and record two things: • What did Mr. Crane do well? • What could he have done differently? • Whole group sharing

  6. CHAPTER 1 Introducing the Five Practices

  7. The Five Practices • Anticipating • Monitoring • Selecting • Sequencing • Connecting Chris Maria Fawn

  8. Anticipating • How students might interpret the problem • The different strategies they might use • How these strategies relate to the math they are to learn • How is the “doing math” support one or more of the 8 CCSS math practices

  9. Monitoring • Circulating while students work • Recording interpretations, strategies, other ideas • (Resisting urge to help!)

  10. Selecting • Choosing particular students because of strategies used and/or the mathematics in their responses • Gaining some control over the discussion content

  11. Sequencing • Ordering presentations to facilitate the building of mathematical content • Scaffolding

  12. Connecting • Encouraging students to make connections between presenters • Making the key mathematical ideas of the task prominent

  13. GOING BEYOND SHOW AND TELL

  14. If you don't make mistakes, you're not working on hard enough problems. And that's a big mistake. — Frank Wilczek, MIT Physics professor, Nobel laureate

  15. Dyads • Six Discussion Questions • Quiet time to read through all 6, then choose 2 to answer. (5 minutes) • Then, we’ll do a dyadand share like this…(4 minutes total)

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