After you do this, write a report that summarizes what you said, what your friend said, and what your friend had difficulty with. How did you get past the difficult parts? Are there any particular parts of the proof that you understand better (or worse) than before you explained it to your friend?
Format: Use correct grammar, which includes writing in complete sentences, and breaking material into paragraphs. Please type your paper, double-spaced (or 1 1/2 spacing) to allow room for my comments. Please do not use binders, folders, plastic sleeves, etc.; simply staple the pages together. You do not need a cover sheet, though you can use one if you like. Make sure your name is on the first sheet. I anticipate most papers being 2-4 pages, but you should feel free to go above or below that range.
Format: Use correct grammar, which includes writing in complete sentences, and breaking material into paragraphs. Please type your paper, double-spaced (or 1 1/2 spacing) to allow room for my comments. Please do not use binders, folders, plastic sleeves, etc.; simply staple the pages together. You do not need a cover sheet, though you can use one if you like. Make sure your name is on the first sheet. I anticipate most papers being 1-3 pages, but you should feel free to go above or below that range.
Try these problems first by yourself, gathering enough data to make a hypothesis about what happens in each case. (Be sure to try problem 13 on a variety of rectangles.) Then check with one or two other students to see how your hypotheses compare, and try to combine them. Finally test your hypothesis on several more examples. Note that problem 12 is really just a warmup for problem 13, which should be your main focus.
Part 2, the writeup. Write a report of your experiments and conclusions in two parts as follows:
Part A. Describe the experiments you did, including pictures. Write about the process by which you arrived at, and then tested, your hypotheses. This written description of your process should be clear and detailed enough for someone else to recreate your thinking.
Part B. Clearly state your conclusions of what you think happens in each of problems 12 and 13. Show a wide enough variety of examples (especially for problem 13) to convince a skeptic that your conclusions are correct.
Format: Use correct grammar, which includes writing in complete sentences, and breaking material into paragraphs. Please type your paper, double-spaced (or 1 1/2 spacing) to allow room for my comments. Please do not use binders, folders, plastic sleeves, etc.; simply staple the pages together. You do not need a cover sheet, though you can use one if you like. Make sure your name is on the first sheet. I anticipate most papers being 1-3 pages, not including diagrams, but you should feel free to go above or below that range.
Rubric:
5 Clearly-written narrative showing your motivation for each step you did. Correct, thorough conclusions, stated clearly, for both problems, with a good variety of examples.
4 Clearly-written narrative showing some of your thought process. Correct conclusions for both problems, with many examples, including some variety.
3 Readable narrative showing the steps you took. Some correct conclusions for one or both problems, with many examples.
2 Narrative is readable enough, not very detailed. At least one correct conclusion about one problem, with some examples.
1 Some confusion as to the procedure of the problems, or writing that is confusing or hard to read.
0 Minimal work, or extreme confusion about the problem.
Rubric:
5 Engaging recounting of the activity, including a careful interview before and after. An analysis of your friend's feelings, including how they changed (or did not change) as a result of the activity. Writing is inspiring or clever, very clear, and well-organized.
4 Detailed recounting of the activity, including a good interview before and after. A good idea of your friend's feelings, before, during and after. Writing is clear and organized.
3 Detailed recounting of the activity, including some sort of interview before and after, and some hint of your friend's feelings. Writing is readable and somewhat organized.
2 Complete recounting of the activity, including some of your friend's response during the experiment. Writing is readable enough, not very detailed.
1 Incomplete recounting of the activity, or conducting the experiment incorrectly, or writing that is confusing or hard to read.
0 Minimal work, or extreme confusion about the experiment.