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THE E-JOURNAL OF STUDENT RESEARCH has been made possible through grants provided by the United States Department of Education, South Central Bell Telephone, American Petroleum Institute, Intertel Foundation, Springhouse Publishing Corporation, Graham Resources, Inc., Chevron Oil Company, Central Louisiana Electric Company, Louisiana State Department of Education, and National Science Foundation. Mandeville Middle School and the National Student Research Center thank these organizations for their generous support of education.
TABLE OF CONTENTS
1. Is The Algorithm For Adding And Subtracting Integers
Correct?
2. Probability Theory And Flipping A Coin
3. The Probability Of Odd Or Even Totals When Rolling Dice
4. Skittle Frequency
5. Probability Of Getting Any Number When Rolling A Die
6. The Probability of Rolling a Six
7. Is The Pythagorean Theorem Valid?
8. Color Frequency of M&M's
9. Probability Theory
10. Perception of Circumference and Height
TITLE: Is The Algorithm For Adding And Subtracting Integers
Correct?
STUDENT RESEARCHER: Ricky Hill
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
I want to find out if an algorithm for adding and subtracting
integers is correct. An algorithm is, in mathematics, any
special method of solving a certain kind of problem. My
hypothesis states that the algorithm for adding and subtracting
integers will be correct.
II. METHODOLOGY:
First, I wrote my statement of purpose and hypothesis. Then I
conducted a review of literature on integers and algorithms.
After that I developed a methodology which enabled me to test
my hypothesis. Next, I gathered my materials. Then I made my
data collection sheet and began my experiment.
My variable held constant is the algorithm. My manipulated
variables are the integers I used, and my responding variables
are the answers I get using the integer.
I made a number line chart of the integer scale ranging from -
10 to +10. Zero being in the center. I then created 15 random
integer problems and solved them by using the algorithm that we
learned in class. I checked my answers by using the integer
scale that I made. I compared both answers derived from the
algorithm and the integer scale. After doing that I recorded
my data on my data collection sheet.
After completing my experiment, I conducted an analysis of data
and wrote a summary and conclusion where I accepted or rejected
my hypothesis. Finally, I applied my findings to everyday life
and published my research project in a journal.
III. ANALYSIS OF DATA:
My data indicated that the ten addition problems that I worked
out by using the integer algorithm we used in class were
correct. I checked them with the integer scale and the answers
were always the same. The five subtraction integer problems
were correct, also.
IV. SUMMARY AND CONCLUSION:
I found out that the algorithm for adding and subtracting
integers was correct. Therefore I accept my hypothesis which
stated that the algorithm for adding and subtracting integers
is correct.
V. APPLICATION:
I can apply my findings to everyday life by telling kids who
are studying integers in their classroom to use the algorithm
for adding and subtracting integers that we used in our
classroom.
TITLE: Probability Theory And Flipping A Coin
STUDENT RESEARCHER: Austin Feldbaum
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
I wanted to test probability theory to see if it is true.
Probability deals with the likelihood of something happening.
My hypothesis states that probability theory is correct.
II. METHODOLOGY:
First, I wrote my statement of purpose and conducted my review
of literature on probability. Then I developed my hypothesis
and wrote my methodology. After that I listed my materials
used in the research. Next, I flipped a nickel 300 times and
recorded my data on whether it was heads or tails on my data
collection sheet. After that I analyzed my data and wrote my
summary and conclusion. Finally, I turned in my completed
research and published my project in the N.S.R.C.'s electronic
journal.
III. ANALYSIS OF DATA:
I tested probability theory by flipping a nickel 300 times.
Heads came up 150 times. Tails also came up 150 times.
Probability theory states that the probability of getting a
head or a tail when flipping a coin is 50 /50.
IV. SUMMARY AND CONCLUSION:
Probability theory predicted that both the head and the tail of
the coin should come up 50% of the time. Both heads and tails
came up 150 times out of 300. Therefore, I accept my
hypothesis which stated that probability theory is correct.
V. APPLICATION:
I can apply my findings to the world outside the classroom next
time I have to call a coin toss. Now I know that I have a 50
/50 chance of calling the correct side.
TITLE: The Probability Of Odd Or Even Totals When Rolling Dice
STUDENT RESEARCHER: Casey Blanchette
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: Ellen Marino, M.Ed.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
I want to do a scientific research project on probability. I
want to see if the total of two dice rolled together will add
up to be an odd number or an even number more often. My
hypothesis states that the total of the two dice rolled will
add up to be an even number at least 60% of the time.
II. METHODOLOGY:
First, I stated my purpose, did a review of literature, and
developed a hypothesis. Then I rolled two dice thirty times.
I then recorded if the total of the two dice was even or odd on
my data collection form. I repeated the entire procedure two
more times and determined the average. Finally, I analyzed the
data, wrote a summary and conclusion, and applied my project to
the real world.
III. ANALYSIS OF DATA:
On trial one, the sum of the two dice rolled was even 14 times
and odd 16 times. On trial two, the sum of the two dice rolled
was even 19 times and odd 11 times. On trial three, the sum of
the two dice rolled was even 16 and odd 14 times. The average
number of throws with even sums was 16.3. The average number
of throws with even sums was 13.7.
IV. SUMMARY AND CONCLUSION:
Out of ninety rolls, 49 rolls or 54% had an even sum, while 41
rolls or 46% had an odd sum. Therefore, I rejected my
hypothesis which stated that the total of two dice rolled will
add up to be an even number at least 60% of the time.
V. APPLICATION:
Now that I know more about probability, I would use this
information next time I take a chance, or play a game involving
dice.
TITLE: Skittle Frequency
STUDENT RESEARCHER: Drew McLaughlin
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
I want to find out which color of Skittles candies occurs the
most frequently in a 61.5 gm bag. The Scott Foresman
Intermediate Dictionary defines frequency as "rate of
occurrence." My hypothesis states that purple is the most
frequent color in a bag of Skittles candies.
II. METHODOLOGY:
First, I wrote my statement of purpose. Then I conducted my
review of the literature on frequency and probability. After
that I developed a methodology which enabled me to test my
hypothesis. Next, I gathered my materials. Then I made my
data collection form and began my research.
I poured each bag out on the table separately. I then counted
and recorded the number of each color in each separate bag. I
then analyzed my data.
After completing my experiment I conducted my analysis of data
and then wrote my summary and conclusion where I accepted or
rejected my hypothesis. And last, I applied my findings to the
world outside of the classroom and published my project in the
NSRC.
III. ANALYSIS OF DATA:
In bag one, Red had a count of 12, purple 9, orange 16, yellow
13, and green 12. In bag two, red had 9, purple 8, orange 16,
yellow 13, and green 12. In bag three, red had 10, purple 16,
orange 12, yellow 15, and green 6. In bag four, red had 15,
purple 12, orange 16, yellow 9, and green was 10. In bag five,
red had 15, purple 12, orange 10, yellow 9, and green had 12.
In bag six, red had 14, purple had 12, orange 7, yellow 11, and
green 14.
Red had an average of 12.5 and a count of 75. Purple had an
average of 11.5 and a count of 69. Orange had an average of
12.83 and a count of 77. Yellow had an average of 12.0 and a
count of 72. Green had an average of 11.0 and a count of 66.
IV. SUMMARY AND CONCLUSION:
Since every color except green had a higher average than
purple, I reject my hypothesis which states that purple would
be the most frequent color in a bag of Skittles. Orange was the
most frequent color in a bag of Skittles.
V. APPLICATION:
When you buy Skittles you are most likely going to get orange
more than any other color. In other research projects I
reviewed, yellow, purple, orange, and red were more frequent.
TITLE: Probability Of Getting Any Number When Rolling A Die
STUDENT RESEARCHER: Greg Horn
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
I would like to conduct a scientific research project using a
die to see if probability theory is true. Probability is the
ratio of the number of times a certain outcome can occur to the
number of total possible outcomes. My hypothesis states that
probability theory will be correct.
II. METHODOLOGY:
First, I wrote a statement of purpose. Next, I reviewed the
literature on probability. Then I developed a hypothesis and a
methodology to test it. I developed a data collection form
upon which to record my data. I then rolled a die 100 times.
I did this three times for a total of 300 rolls. I then
recorded on my data collection form the number of times each
number on the die came up. According to probability theory
each number, one through six, should come up 50 times in 300
rolls of the die. Then I analyzed my data. Next, I wrote my
summary and conclusion. Then I applied what I found out to the
real world outside the classroom. Finally, I turned in my
abstract. Then I published it in the national journal of
student research.
III. ANALYSIS OF DATA:
I rolled the die 300 times. The number one came up 44 times,
the number two came up 60 times, the number three came up 46
times, the number four came up 52 times, the number five came
up 52 times, and the number six came up 46 times.
IV. SUMMARY AND CONCLUSION:
My results did not exactly match what probability theory
predicted would happen. The number of times each number on the
die came up was close to fifty. Therefore, I reject my
hypothesis which stated that probability theory would be
correct because it did not exactly predict what my results
would be. According to my review of the literature though, I'm
sure that if I did more trials and rolled the die many, many
more times, my results would be closer to that which
probability theory predicts.
V. APPLICATION:
When playing a game of chance involving the use of a die I now
know that I have a one in six chance of rolling any of the
numbers on the die.
TITLE: The Probability of Rolling a Six
STUDENT RESEARCHER: Jeff Carollo
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
I want to do a scientific research project on the probability
of rolling a six on a six sided die. Probability theory is a
branch of mathematics that deals with the likelihood of
something happening. My hypothesis states that there is a
about a 17% chance of rolling a six.
II. METHODOLOGY:
First, I stated my purpose, reviewed the literature on the
probability theory, and developed my hypothesis. Next, I
obtained a six sided die and created a data collection sheet.
Then I took the die and rolled it 300 times. Each time I
recorded the result of the trial. When I finished rolling the
die I totaled the number of times each digit on the die
appeared. I divided 300 into the number of sixes to find the
percent of times it was thrown. I finally analyzed my data,
drew my conclusions, and applied my findings to the world
outside of the classroom.
III. ANALYSIS OF DATA:
I found in my experiment that the number one came up 40 times
in 300 rolls. The number two came up 63 times in 300 rolls.
The number three came up 40 times in 300 rolls. The number
four came up 51 times in 300 rolls. The number five came up 45
times in 300 rolls. The number six came up 61 times in 300
rolls.
The number 1 came up 13% of the time. The number 2 came up 21%
of the time. The number 3 came up 13% of the time. The number
4 came up a perfect 17% of the time. The number 5 came up 15%
of the time. And the number 6 came up 20% of the time.
IV. SUMMARY AND CONCLUSION:
Six came up 20% of the time. According to probability theory,
it should have come up 17% of the time. Therefore, I reject my
hypothesis which stated that there is a 17% chance of rolling a
six.
V. APPLICATION:
The findings of my experiment were not what probability theory
predicted. I now know to roll a die more times in order to
approximate the number of times the number six should come up
according to probability theory.
TITLE: Is The Pythagorean Theorem Valid?
STUDENT RESEARCHER: Justin Moree
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
I wanted to know if the Pythagorean Theorem is true for all
triangles or just right triangles. The Pythagorean Theorem
states that, for a right triangle, side A squared plus side B
squared equals the hypotenuse C squared. My hypothesis states
that the Pythagorean Theorem works only for right triangles.
II. METHODOLOGY:
First, I wrote my statement of purpose. Then I conducted a
review of the literature on triangles, angles, Pythagoreans,
and the Pythagorean Theorem. I then wrote a hypothesis and a
methodology to test my hypothesis.
My manipulated variable was the type and size of triangle. The
responding variable is the answer to the theorem. The variable
held constant was the Pythagorean Theorem.
First, I chose two right triangles, two obtuse triangles, and
two acute triangles. Then I labeled each leg of the triangles.
For the non-right triangles, I labeled the two shortest legs A
and B. The longest leg was labeled C. For the right
triangles, the hypotenuse was the side of the triangle opposite
the right angle. The other two sides were labeled A and B. I
then measured each leg, squared the length of each, and added
the two values of leg A and B together. This value should
equal the value of C (the hypotenuse) squared as predicted by
the theorem. Then I measured the side C (the hypotenuse) and
squared the length. I then compared my two values for side C
(the hypotenuse), that obtained from the theorem and that
obtained by actually measuring it.
III. ANALYSIS OF DATA:
In the first right triangle, leg A squared was 6.25 squared
cm., Leg B squared was 4 squared cm., and the hypotenuse
squared was 10.25 squared cm. The Pythagorean Theroum
predicted that the hypotenuse squared should have been 10.24
squared cm. (This .01 squared cm. difference was due to the
fact that my measurements were not exact enough.)
In the second right triangle, leg A squared was 26.01 squared
cm., leg B squared was 26.01 squared cm., and the hypotenuse
squared was 51.84 squared cm. The Pythagorean Theroum
predicted that the hypotenuse squared should have been 52.02
squared cm. (This .18 squared cm. difference was due to the
fact that my measurements were not exact enough.)
In the first obtuse triangle, leg A squared was 6.25 squared
cm., Leg B squared was 9 squared cm., and leg C squared was
30.25 squared cm. The Pythagorean Theorem predicted that leg C
should have been 15.25 squared cm.
In the second obtuse triangle, leg A squared was 9 squared cm.,
leg B squared was 20.25 squared cm., and leg C squared was 49
squared cm. The Pythagorean Theorem predicted that the
hypotenuse should have been 29.25 square cm.
In the first acute triangle, leg A squared was 42.25 squared
cm., leg B squared was 81 squared cm., and leg C squared was
144 squared cm. The Pythagorean Theorem predicted that the
hypotenuse should have been 123.25 squared cm.
In the second acute triangle, leg A squared was 4 squared cm.,
leg B squared was 1.44 squared cm., and leg C square was 9
squared cm. The Pythagorean Theorem predicted that the
hypotenuse should have been 5.44 squared cm.
IV. SUMMARY AND CONCLUSION:
The Pythagorean Theorem only worked for right triangles.
Therefore I accept my hypothesis, which stated that the
Pythagorean Theorem would only work for right triangles.
V. APPLICATION:
This information could be used in architecture. If an
architect knew the length of two sides of a triangular room,
with one corner a right angle, then he could find the length of
the third wall without measuring it.
TITLE: Circumference
STUDENT RESEARCHER: Jonathan Landry
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: Ellen Marino, M.Ed.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
I would like to do a scientific research project to see if
students estimate the distance around a coke can as being
longer, shorter, or the same as its height. My hypothesis
states that most students and adults will say that a coke can
is greater in height than the distance around the center.
II. METHODOLOGY:
First, I stated my purpose and did a review of literature.
Next, I developed my hypothesis. Following that I listed my
materials. Next, I asked 29 sixth grade students at M.M.S. if
the distance around a coke can is longer, shorter, or the same
as its height and recorded the results on my Data Collection
Form. Then I asked 29 adults the same question and recorded the
results. I then did my analysis of data and wrote my summary
and conclusion. I applied my findings and published my report.
III. ANALYSIS OF DATA:
I asked 29 adults and 29 students if the distance around a coke
can (the circumference) is shorter, longer, or the same as it's
height. Out of 29 adults, 1 said that it was shorter, 12 said
it was longer, and 11 said it was the same. Out of 29
students, 4 said it was longer, 1 said it was shorter, and 10
said it was the same.
IV. SUMMARY AND CONCLUSION:
The circumference or distance around a coke can is greater than
its height. I found that more students correctly estimated
that the circumference was greater than the height and more
adults said it was shorter. Therefore, I partially reject my
hypothesis which stated that most students and adults will say
that a coke can is greater in height than the distance around
its center.
V. APPLICATION:
Now that I have all my data, I can apply my findings to the
real world outside the classroom. Students study circumference
and may be more aware of this. I will share this information
with the sixth grade math teachers.
TITLE: Probability
STUDENT RESEARCHER: Dana Beuhler
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: Ellen Marino, M.Ed.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
The main point of my research was to learn how to determine
probability of what is likely to happen. I used probability to
determine what color I would likely draw out of a bag of four
red tiles and one blue. My hypothesis stated that if I have
one blue tile and four red tiles in a bag, and I draw one tile
out of the bag, I will get a blue chip four times out of
twenty.
II. METHODOLOGY:
I stated my purpose, reviewed the literature, and developed my
hypothesis. I placed one blue tile and four red tiles in a
non-transparent bag. Then I drew one tile out of the bag. I
then recorded the color and placed the tile back in the bag
twenty times. I repeated this procedure three times for a
total of sixty pulls. I analyzed my data, and wrote my summary
and conclusion. Then I applied findings to the real world.
III. ANALYSIS OF DATA:
On trial one, I drew three blue tiles and seventeen red tiles.
On the second trial, I drew two blue tiles and eighteen red
tiles. On the third trial, I was right on the dot and drew
four blue tiles and sixteen red tiles. On average, I drew
three blue tiles and seventeen red tiles for each trial.
IV. SUMMARY AND CONCLUSION:
I pulled an average of three blue tiles and seventeen red
tiles. Therefore, I reject my hypothesis which stated that if
I had one blue tile and four red tiles in a bag, and I draw a
tile twenty times, I will draw four blue tiles and sixteen red
tiles.
V. APPLICATION:
Now that I have completed my experiment, I have learned that if
there is more of one thing than another, you are more likely to
get the thing there is more of. Therefore, I will share my
results with my family, classmates, friends, and teachers.
TITLE: The Color Frequency of M&M's
STUDENT RESEARCHERS: John Cummings and Matt Laptewicz
SCHOOL: Dawson Elementary School
Holden, MA
GRADE: 5
TEACHER: Wayne Boisselle M. Ed.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
We wanted to find out the color frequency of plain M&M's in a
47.9 g package. Our hypothesis stated that brown will show up
the most in a 47.9 g plain M&M's package.
II. METHODOLOGY:
First, we wrote a statement of purpose, a literature review,
and developed a hypothesis. Secondly, we bought 10 bags of
plain M&M's. Then we opened the bags one at a time and
separated the colors into groups. Next, we put the number of
each color into a chart and then made our graphs. Then we
conducted our analysis of data and our summary and conclusion.
We then accepted or rejected our hypothesis and applied our
findings to the real world.
III. ANALYSIS OF DATA:
When we finished counting all the M&M's the results were 53
oranges, 57 tans, 58 greens, 105 reds, 114 yellows, and 191
browns in all the 10 bags.
IV. SUMMARY AND CONCLUSION:
Our data indicated that brown shows up the most in 10 bags of
plain M&M's. Therefore, we accepted our hypothesis which
stated that brown will show up the most in 10 bags of 47.9g.
plain M&M's.
V. APPLICATION:
Our information could help other people if they were making
cookies for Halloween with orange + brown M&M's. They would
know how many plain 47.9g. bags to buy.
© 1995 John I. Swang, Ph.D.