Math 497 Day 1 (September 24, 2008)

General Practice

Please note the instructions on the Information page about keeping a notebook.

Problems to do in class:

You will be given initially four pages comprising Session 1.

Please read carefully the instructions about what problems to do, how to work in groups, etc.
You should think about the meaning of the simplex lock problem and how to represent it, but at this point you are NOT supposed to try to solve it.
Then move on and work on the “train problems” 1-5 (and also possibly 6-7). Use the Cuisenaire rods for your own understanding and also as a way of communicating your ideas.

There will be a debriefing and a ten-minute break about 4:45. Then you will get a copy of Session 2.

Even if you have not finished all the Session 1 problems, at this time go on to problems 8-18. You will probably not have time to finish them.

Some discussion and debriefing again and then we adjourn.

HOMEWORK #1 (due next class)

Work out some additional answers to 8-19 if you did not get them all yet. But it is OK if you have not nailed them all yet (especially the Tough Stuff), but you can keep working on them.

Answer these questions; show your reasoning and problem-solving ideas as clearly as you can. (By the way, is OK if you have not nailed all the problems 1- 19 yet.)

1. How many trains of length 6 are there?

2. How many trains of length 6 are there that use exactly one rod? Two rods? Three rods?

3. Suppose that you can make 156 different two-scoop cones at a certain ice cream shop. How many different flavors does this shop offer?

4. Suppose that you can make 2730 different three-scoop cones at a certain ice cream shop. How many different flavors does this shop offer?

5. Write up what you consider your best answer from Problems 1-5. (“Best” might mean the most interesting reasoning or explanation or it might mean that the problem was particularly challenging.)

6. Write up what you consider your best answer from Problems 8-19.

7. Describe your favorite “Aha!” that you experienced doing these problems.

8. Describe a problem that you have tried but have not yet solved, and give some insights into your approach and what questions that you still have. (Not counting the Simplex Lock!)