Day 03: Heart of Mathematics

Last Time

Next Time

Announcements:
- Any more agreements to submit?
- Assignment (for next time):
  1. We begin our unit on estimation. Read 2.1, and discover how one might estimate how many hairs are on a human body.
    On Wednesday of next week (remember Monday is a holiday), I'll assign some exercises on estimation for your enjoyment;). For example,
    - How much gasoline do you use in a year?
    - How many times will you breathe today?
    That sort of thing....
- Remember to take the attitude survey about mathematics. You need to do this on blackboard. Take the survey by Sunday night (it's under assignments on Blackboard).
Wrapping up the "Fun and Games":
- One question you may have is, what will exam questions look like? On an exam, you may see a problem like one of these. Ideally, you might solve it; on the other hand, if you can't, if you can propose and justify some of the strategies that our authors suggest, or some that we've discussed in class, that will get you some credit even if you don't arrive at the right answer. So pay careful attention to the strategies for solving problems!
  Number one of course is "Just do it!": if you merely write "I have no idea how to approach this," imagine how many points you'll get....
- Let's summarize some of what we learned last time:
  - Switch or Stick? Which strategy is better, and by how much?
  - One strategy for solving the "Let's make a deal" problem is by simulating the game: find some way to actually play the game; collect data, and see if it suggests a solution.
  - How does generalizing the game help us see which strategy was more effective?
  - Can we apply the lessons of "Let's make a deal" to "real life"? Can we become more effective thinkers, and "livers"? Can you think of a practical application?
- Let's divide up for a look at the remaining problems: In your group, you'll want to
  - Arrive at a solution, and
  - Describe what strategie(s) proved useful.
  - In the following games, can you generalize?
  - Can you solve any simpler, related problems?
  - These will be shared with the class. You'll have fifteen minutes to come to your solutions.
  - Here are the games:
    - Meanie Genie
      - What other numbers of stones could we weigh, subject to these conditions?
    - Fountain
      - What other quantities of liquid can we dispense with these cups? Are there quantities that we can't dispense, subject to these same conditions?
    - Dodge Ball
      - Can you always win?
    - Dot of Fortune
      - What part do your opponents play in your play?

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