Due Monday:

Proof for Feedback:

Cups proof

Tasks:

1. Be aware that weekly wednesday in-class assessments begin next week.  You will write a proof in class.  Schedule is on the Grading tab above.
2. Note:  I encourage collaboration on your daily posts!  Talking about math is great practice.  But make sure you are using a strict strategy to make sure you are writing your own solutions and not relying too much on other people (which I would consider copying).  For example, if you discuss a proof and work out a solution together, then finish that conversation before you start writing up your solution, and write up your own solution in silence, without using written notes, just from your own brain.  This is an important strategy to make sure you are internalizing what you learn.  If you get stuck, that’s good!  You’ve got an opportunity to struggle and learn.  It’s ok to go back to discussion, but give yourself some space between the collaborative phase and private writing phase.  Even better, take a 15 minute break between.  Be honest with yourself and only give yourself full credit on your self-evaluation sheet if you are using an effective strategy of this sort.
3. Solutions to last proof problem are here (we discussed in class).
4. Do your proof for feedback, which is about the cups problem we discussed in class on Friday.  If you forget what we talked about in class Friday, here’s a reminder/hint:  it turns out you can’t get from an even number of cups turned up to an odd number of cups turned up.  Why is that?  Try to write the most beautiful proof you can, whether using what I said in class or another method.
5. Counting!  Here’s the counting sheet we started in class Friday.  First off, please write out all 12 possible burritos in the first problem (you can use abbreviations).  Make sure you really truly understand why the answer is .  Not sure?  Let’s chat!
6. For general counting problems, my method is to imagine the process of creating each burrito (or triathlon team or bagged cat situation, etc.), and break it down into phases.  The formula for the answer is often a reflection of this process (just as the burrito problem can be thought of as progressing along the burrito bar making choices one-by-one).  Keep this in mind and do problems 1-6 on the worksheet (or as many as time permits).  Write out your reasoning, not just the answer.  You may wish to avoid doing problems 7 and above since I will leave time in class on Monday to work on these problems further (although I should never tell you not to think about mathematics!).
7. Don’t forget to keep filling in your self-evaluation sheet.