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Contemplative Mathematics: Leading Math Discussion Groups

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  1. Introduction

    Introduction to Socratic Mathematics (Preview Content)
    2 Topics
    |
    1 Quiz
  2. Sessions
    Session 1: Figurate Numbers
    2 Topics
    |
    1 Quiz
  3. Session 2: Square Numbers
    2 Topics
    |
    1 Quiz
  4. Session 3: Co-primality
    3 Topics
    |
    1 Quiz
  5. Session 4: Co-primality and Fractions
    2 Topics
    |
    1 Quiz
  6. Session 5: A Numerical Puzzle
    2 Topics
    |
    1 Quiz
  7. Session 6: Another Numerical Puzzle
    2 Topics
    |
    1 Quiz
  8. Session 7: The Bridges of Köningsberg
    2 Topics
    |
    1 Quiz
  9. Session 8: Patterns in Graphs
    2 Topics
    |
    1 Quiz
  10. Session 9: Chromatic Graphs
    2 Topics
    |
    1 Quiz
  11. Conclusion
    Concluding Remarks
    1 Topic
  12. End of Course Test
    End of Course Test: Contemplative Mathematics
    1 Quiz
Lesson Progress
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  • Discussion Questions: Remember that the goal here is to seek out truth together, and convince yourselves that you’ve found it. As the facilitator, part of your responsibility is to make sure that everyone in the group is heard and on board!
    • If I tell you that I’m thinking of two numbers, and that they add up to 100 and that the difference between them is 40, could you tell me the numbers?
    • If I tell you that I’m thinking of two numbers, and that they add up to 18 and that the difference between them is 4, could you tell me the numbers?
    • If I tell you that I’m thinking of two numbers, and that they add up to 17 and that the difference between them is 4, could you tell me the numbers?
    • If I tell you that I’m thinking of two numbers, and that they add up to 12 and that the difference between them is 3, could you tell me the numbers?
    • Can you craft some conjectures about the difference between the first two questions and the second two questions? Feel free to play around with more examples of your own looking for patterns! (I don’t want to be too specific here, as there are a couple of interesting conjectures!)
    • Can you describe a general rule that you could use to solve a puzzle like this whatever the numbers add up to and whatever their difference is?

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