A Statistical Study on the Letters of the Alphabet

A STATISTICAL STUDY ON THE LETTERS OF THE ALPHABET

Enduring Understanding: Develop a better understanding of how to analyze mathematical information and to organize, clarify, and/or refine an argument.

Essential Questions:

· How is data gathered in a systematic way?

· How is data biased by the sources used?

· How is a position defended or refuted by using mathematical data?

· How can trends be identified in order to make inferences/predictions from a set of data?

· How is data used to support a conclusion?

· How accurate is data that are collected?

· What sources of bias will influence data?

· What is meant by dependent and independent events?

· What factors influence a trend that may not be reflected in the collected data?

· How is a prediction or inference justified?

Lesson Overview:

· Before allowing the students the opportunity to start the activity: access their prior knowledge with regards to collecting and using data. Discuss with students the games of Scrabble and Wheel of Fortune? How many have played or seen the games on television?

· Discuss whether or not this situation involves dependent or independent events.

· What is meant by a vowel or consonant?

· Discuss sources of data and bias that can be created by using certain sources.

· What is the relationship between sets of data?

· What is being asked by the questions in the problem? How do you decode what the problem is asking you to do?

· A good warm-up could be Automobile Maintenance or Baseball.

· How can the students make their thinking visible?

· How can you support a conclusion that you make?

· Use resources from your building.

· An alternative method of conducting this activity:

Divide the class into groups of three students. Each person in the group chooses a book. Roll three dice to determine the line on the page on which to start. Count the next 100 letters. Tally the letters in the sample, one at a time, filling out the table provided.
Each member of the three person group combines their individual totals to create a group total.
Calculate (2 decimal places) the probability (percentage) of finding each letter, based on the group’s total of 300 letters. Check the accuracy of the calculations as the percents should add up to 100%.
On the overhead, combine the numbers for all groups, then calculate the overall percent for each letter for the “CLASS%”. That percentage will be used by the students to answer the questions on the following pages.

EALRs/GLEs:

1.4.3

1.4.6

3.2.2

4.1.2

Item Specifications: PS02; PS03; SR04; CU01

Assessment:

· Use WASL format items that link to what is being covered by the classroom activity

· Include multiple choice questions

A Statistical Study on the Letters of the Alphabet

Or how to win on “The Wheel of Fortune”

1. Choose a page from a book in your book bag and tally the letters, one at a time, filling out the table below (Table 1). Do not “jump around” the page!!!!!!! Stop when you have counted 300 letters.

2. Calculate (2 decimal places) the probability (percentage) of finding each letter. Check for accuracy.

3. After completing the table for the letters that you counted, ten students need to write their totals for each letter (out of 300) on the board. Determine the overall percent for each letter using the information from the 10 students and put that percent in the column “CLASS %”. That percentage will be what you will use to answer the questions on the next pages.

TABLE 1

LETTER

TALLY

TOTAL

/ GROUP
% / CLASS %
A

B

C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z

4. Were your percentages close to the percentages tabulated by the ten people who wrote

on the board? ______Why or why not?

______

5. Ranking of the letters

TOP TEN LETTERS: BOTTOM FIVE LETTERS:

1. ______% 22. ______%

2. ______% 23. ______%

3. ______% 24. ______%

4. ______% 25. ______%

5. ______% 26. ______%

6. ______%

7. ______%

8. ______%

9. ______%

10. ______%

6. How many vowels are in the top ten? ______; Which ones? ______

7. Which consonants would be the most useful in the “Wheel of Fortune”? ______, ______, ______, ______, ______, ______, ______

8. Which vowel might be the least useful? ______; What was its percent? ______

9. See if you can make 10 words using only the top five letters: ______,

______, ______, ______, ______,

______, ______, ______,

______, ______.

10. You should never expect to find the letter Q on “The Wheel of Fortune”. T or F

11. Almost every word requires a vowel. T or F

12. The letter K is useful when playing the game “The Wheel of Fortune”. T or F

13. Is I or O the most useful vowel? ______Why? ______

______

14. The English language could get along fine without, if any, what three letters? ______

Justify your answer using data from your table.

______

15. 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 5 of these letters would be most beneficial to have?

A B C D E F G H I J K L M

Justify your choices with information from the table. ______

______

16. To do a more accurate study for the above “alphabet stickers”, I would need to make a survey of letters found in … (circle the best answer)

a. a popular magazine

b. a list of students’ names

c. a dictionary

d. a novel

Why did you make the selection that you did? ______

______

17. In the game of “Scrabble”, which of these letters would you expect to be worth the most points? Hint: the harder it is to use to make a word, the more points it is worth. Circle the best answer

H V S

Why did you make the selection that you did? ______

______

18. In “Scrabble”, which of these letters would you expect to be worth the least amount of points (the easier it is to use to make a word)? Circle the best answer

Q N K

Why did you make the selection that you did? ______

______

19. To win the big prize in a lottery, you have to decide which six numbers between 1 and 52 will be randomly selected.

Which has the greatest chance of winning the prize?

O A. ALL THREE PEOPLE have exactly the same chance of winning.

O B. Kenneth, who picks 1, 2, 3, 4, 5 and 6

O C. Kathleen, who picks 22, 24, 26, 28, 30 and 32

O D. Kyle, who picks 11, 19, 26, 34, 41 and 47

20. Each event described below is performed randomly.

Which is a dependent event?

O A. From a bag of 10 marbles (4 red, 6 blue), Sam pulls a blue marble, puts it back, and then pulls a red marble.

O B. On a spinner with 6 congruent sectors numbered 1 through 6, Greg first spins a 4 and then a 2 on the second spin.

O C. From a pack of 20 cards, Jose picks 1 card, sets it aside, and then picks a matching card on his second try.

O D. Monica tosses a fair coin two consecutive times, and it lands on heads both times.

21. In a jar full of red and blue jelly beans there are 300 jelly beans altogether. There are times as many red jelly beans as blue.

Which represents the number of red jelly beans in the jar?

O A. 60

O B. 100

O C. 180

O D. 200