Wheel of Fortune
(1/8 credit in math)
Do you suspect that there are some letters of the alphabet used more than others? Are there some letters that we hardly use at all? Do you think you could improve your chances of winning word games such as Wheel of Fortune, Hangman, or Scrabble if you knew some mathematical rules?
TURN IN YOUR ANSWERS TO THE ABOVE BEFORE YOU BEGIN!!
If your answer is "yes" to all of the above, you're right on target. Now let's prove it!
Choose any page in a book, magazine, newspaper, or on the Internet to begin researching our use of the alphabet. You may start tallying letters at any point on the page, but you'll have to have at least 500 or more letters. You may not "jump around" on the page, but you may begin anywhere you like. You may quit anywhere after 500 letters.
Create a tally sheet like the example below; fill in the totals and figure the percentages. To figure the percentages, you can use a calculator. For each letter, divide the number the tally marks total by the total number of letters you tallied. Then move the decimal point over two places; keep at least one number after the decimal, but round it. For example, if you found 68 A's and counted 504 letters (you forgot to quit!), divide 68 by 504. Your answer at that point will be .1349206349206359206349. Whoa! Big number! Move the decimal point two places to the right so that the whole number is now 13. You've keeping one place after the decimal, so now you've got 13.4. And you've going to round that one place. Since the next number is 9, the four should round up, so your percentage of A's in the sample would be 13.5%
WORKSHEET ONE-TALLY SHEET
LETTER TALLY TOTAL %
A
B
etc.
GRAND TOTAL:
The Grand total of the "total" column must be 500 or more letters, and the % could be either 99 or 100% depending on how the rounding figured out.
Now complete the following (on your worksheet paper). Please write the question before answering it!
1. Top ten letters and percentage of each.
2. Bottom five letters and percentage of each.
3. How many vowels are in the "top ten"?
4. What percentage of all the letters of the alphabet are vowels? (do include "y," even though it's only sometimes a vowel.
5. Which SIX consonants would be the most useful in a word game?
6. True or false: You're not likely to need the letter "Q" in a word game.
7. True or false: Every word requires a vowel.
8. True or false: The letter "K" is a very useful one in word games.
9. True or false: "I" and "O" are the two most useful vowel.
10. True or false: The top ten letters account for about 75% of the letters needed in the English language.
11. True or false: The English language could get along just fine without the letters "J, "Q," and "X."
12. Explain any of your answers to questions 6 through 11. Be sure to tell me which one you're explaining!
13. If you were producing stickers with letters of the alphabet for use in labeling personal items, such as books, pens, bags, and bedroom doors, which FIVE of the following letters would you need most? A, B, C, D, E, F, G, H, I, J
14. In the game of "Scrabble," which of the following letters would you expect to be worth the most points: H, V, S. (Hint: the harder it is to use, the more points it is worth).
15. In "Scrabble," which of the following letters would you expect to be worth only one point: Q, N, K?
16. Was this the best way to solve the question of how frequently letters are used? Why or why not?
17. Define "sampling" in math~check a math book or a dictionary. You have just done a sampling project. Can you guarantee your accuracy in the results? Why or why not?
TWO FINAL PROJECTS:
1) First, use a spreadsheet program to create THREE different attractive presentation of the results of your tally sheet. One must be a pie chart; one a single dimensional graph, and the third a three-dimensional chart. If you don't know how, ask!
2) Find a buddy! Knowing what you know now, find someone to play "Hangman" with. It doesn't matter who plays with you--older, younger, same age, whatever. You must play at least SIX games or any other larger number. Turn in your game sheets and write a few sentences explaining whether you won the most rounds or not and why!
Benchmarks: 69, 138, 157, 158, 159, 163, 180, 182, 183, 184, 185, 186, 187, 188, 189, 192, 193, 200, 201, 204, 213, 220, 225
