Your assignment for the next week is toÂ try to prove the conjecture that your group created in class on Tuesday, 10/14/15. Â **You must spend at least 90 minutesÂ working on this.** Â Trying to prove somethingÂ can consist of many different activities,Â such as the following (you do NOT have to do all of these things – you can choose how to spend your time – they are provided for inspiration only).

- coming up with ideas, and testing them out (for example, by creating puzzles and trying to solve them)
- trying to understand what the conjecture says
- trying to solve puzzles that other people created
- trying to create puzzles (and solve them yourself)
- communicatingÂ with other members of your group (talking, emailing, etc.)
- trying to write down a proof
- other stuff…

As you work, keep track of what you are doing, thinking, and feeling (this is **metacognition** – an idea that discussed way back in OpenLab #2). Â What did you do during the time you spent? Â Did you create any puzzles? Â Did you solve puzzles? Â Did you change your mind about whether the conjecture is true or false? Â Did you have any new ideas about how to prove the conjecture? Â Did you have any ideas that you gave up on? Â How did you feel as you worked – were you frustrated/confused/happy/depressed? Why? Did your mood change along the way?

**Assignment (Due Thursday, 11/3/15)**: Â Submit a journal of your efforts in the comments below. Â Your response should be **at least 300 words**. Â DescribeÂ what you did during the 90 minutesÂ you worked, andÂ express in some way what you were thinking and feeling during the process. Â Your response can include puzzles (use sketchtoy.com) or other work you did along the way.

**Extra Credit**. Â Respond to a fellow student’s comment. Â Did you do similar things? Different things? Do you have any suggestions for them? Be kind.

GROUP CONJECTURES:

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