Computational environments are here.

Below please find five assignments for the course.

GRED 595

Assignment 1

Monsters and spreadsheets

Part 1.

Once upon a time Hilton built a hotel in Long Beach shaped as a long parallelepiped with more than 100 suites overlooking the waterline of the ocean. The 13th story of the hotel turned out to be a dangerous place to stay: every night a monster visited a suite there. It was observed (Figure 1) that the monster started with suite #1, on the second night he emerged in suite #3, on the third night he emerged in suite # 6, then he emerged in suite # 10, and so on.

Figure 1. Hilton Long Beach (a fragment, 13th story)

The hotel's manager hired a graduate student from SUNY Potsdam to investigate the behavioral pattern of the monster. More specifically, the manager wanted to find out:

1. What suite would the monster visit on the 7th, 8th, and 9th nights?

2. Would suite # 100 be a monster-free suite?

3. If the monster wants to end up in suite # 100, which suite should he visit on the first night? Is there more than one such a suite to start with?

Part 2.

Once upon a time Hilton built a hotel in Potsdam in the form of a 13th storied tower with 8 suites on each story. The last story turned out to be a very special one &endash; every night a monster visited a suite there starting with the North-East (top left) suite and following a strange pattern shown in Figure 2. The hotel's manager could not do anything about this monster; yet he wanted to find out several things about the 13th story.

Once again, a graduate student from SUNY Potsdam was hired, to investigate the following situations.

1. Which suite would the monster visit on the 5th night? Explain your reasoning.

2. If such pattern (describe this pattern) of visits continues, is there a suite on the 13th floor, which would never be visited by the monster? Why or why not?

3. Would the monster visit some suites more often then other suites during the 16-day sequence? Why or why not?

4. Is it possible to make a reconstruction of the 13th floor by decreasing or increasing the number of suites in order to create the monster-free suite(s)? Come up with a least one such project.

5. Explore questions 1-4 under assumption that the monster has a different pattern of visits, namely 1st suite on the 1st night, 4th suite on the 2nd night, 1st suite on the 3rd night, 8th suite on the 4th night, and so on.

Figure 2. Hilton Potsdam (13th story, five nights).

Imagine that you are the student hired by the manager. Use a spreadsheet for your investigations. From a mathematical point of view, what is special about numbers involved in the above explorations? Use the Microsoft Word program to type your report for the manager.

Ideas for explorations that go beyond assignment #1.

- Two monsters may be observed on the 13th floor of the Tower, one with the pattern shown in the picture above, another with the pattern described in item 5. Assuming that they both start from the suite #1, in which suite (if any) will they meet next time?
- Invent a pattern for a third monster and explore the same idea.

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GRED 595

Assignment 2

Spreadsheet-generated music

1. Generate the following sequence on a spreadsheet:

5,5,6,5,1,7,5,5,6,5,3,1, 5,5,6,5,1,7,5,5,6,5,3,1, 5,5,6,5,1,7,5,5,6,5,3,1, 5,5,6,5,1,7,5,5,6,5,3,1, .....

2. Assign the notes to numbers as follows:

"do" to 1, "re" to 2, "mi" to 3, "fa" to 4, "sol" to 5, "la" to 6, and "ti" to 7.

3. Do you hear a piece of a familiar melody? What is this melody?

4. Continuing in the same vein, generate your own tune by using a spreadsheet (it may be very simple).

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GRED 595

Assignment 3

Steve's Video Store

Situation

Last Saturday Steve's Video Store rented two types of new movies: Titanic and Godzilla. A manager knows that the total sales for renting these movies last Saturday were $100, and that the store rented them in the price range from $3 to $6. Furthermore, it is known that Titanic was more expensive movie than Godzilla. Other than that, the manager does not have any records related to last Saturday rent and wants to regain at least part of the renting history by using a spreadsheet.

Part 1. Help the manager find answers to the following questions.

1. What is the maximum number of movies that could have been rented? What are the prices in this case?

2. What is the minimum number of movies (greater than 0) that could have been rented? What are the prices in this case?

3. How many different combinations of $5 Titanic and $3 Godzilla movies might there have been rented?

4. What rent prices were not possible within the above range? What is special about these prices regarding to the total sales?

Explore this problem by using both two-dimensional and one-dimensional spreadsheet environments. Make sure that your environments would allow for the variation of data (total sales and price range).

Part 2. Using different data, formulate your own question about the situation and find an answer to your question.

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GRED 595

Assignment 4: Help Jimmy to unlock a briefcase, please

A combination lock of Jimmy's new briefcase has three digital disks, each containing all digits from 0 through 9. Jimmy forgot his secrete code; yet he remembers that the code is a 3-digit prime number palindrome. Jimmy knows that the lock is designed in such a way that it allows one to guess a code only a limited number of times &endash; it locks up (breaks) forever after the number of trials becomes greater than the total number of 3-digit prime number palindromes.

Part 1. Construct a spreadsheet environment which would enable you to explore all possible secrete codes that Jimmy may dial. More specifically, answer the following questions:

- After how many trials would the combination lock break?

- What is the code for this lock, if in addition to the above information, Jimmy recalls that the sum of digits of his code is a square number?
- Do you need to explore 3-digit palindromes in the range 500-599 using a spreadsheet? Why or why not?
- What is the smallest number of primes that may be used to investigate this situation using a spreadsheet?

Part 2. Invent your own question about this situation (or its extension/modification) and find an answer to your question.

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GRED 595

Assignment 5

Monster is back

You are a teacher in the elementary school. You want your students to develop the concept of clock arithmetic intuitively, by recognizing patterns through a hands-on activity. With this in mind, you put this concept into the context by exposing your students to the following "realistic" situation.

Once upon a time Hilton built an 8-story hotel in Potsdam. The hotel turned out to be a very special one: every night a monster visited one story there. A monster started with the 1st (ground) story, on the next night he skipped 2 stories and visited the 4th story, then he skipped 4 stories, reached the top story and started with the ground again; that is, he emerged at the 1st story on the third night. Then he went up again, skipped 6 stories, and visited the 8th floor. Then, he started counting from the 1st story (as he has reached the top story) and, going up and down as described, he then skipped 8 stories, then 10 stories, then 12 stories, and so on.

You want your students to draw a history of the monster's visits during a 2-week period. You ask them to do this drawing on a spreadsheet by using the Smile Face button. A 1-week fragment of a "map" that your students are expected to develop is pictured below.

You are aware that your students can make mistakes in developing such a "map." In order to help them correct possible mistakes (and thus learn from mistakes) you decided to create a manipulative-computational environment that would control this coloring activity. More specifically, if a student marks (colors) a wrong story, the spreadsheet would display an "OOPS" message interactively below an incorrect icon.

So, this is your assignment: to create such an environment.