The National Student Research Center

E-Journal of Student Research: Math

Volume 3, Number 1, November, 1996

John I. Swang, Ph.D.

Founder/Director

National Student Research Center

2024 Livingston Street

Mandeville, Louisiana 70448

U.S.A.

E-Mail: nsrcmms@communique.net

http://youth.net/nsrc/nsrc.html

TABLE OF CONTENTS

1. Probability: Fact or Fiction?
2. Surface Area of Rectangular Prisms
3. Probability Theory and Dice

TITLE:   Probability: Fact or Fiction?   

STUDENT RESEARCHER:   Karla Hardberger and Erin Phillips  
SCHOOL:  Mandeville Middle School
         Mandeville, Louisiana
GRADE:  6
TEACHER:  John I. Swang, Ph.D.

I.  STATEMENT OF PURPOSE AND HYPOTHESIS:

We want to find out if probability theory really works.  We 
want to see if we can draw each of three chips out of a bag an 
equal number of times (N=200) after drawing and replacing the 
chips 600 times.  Our hypothesis states that the probability of 
pulling a blue chip out of a bag that contains a red, white, 
and blue chip is one out of three. 

II.  METHODOLOGY:

First, we wrote our statement of purpose and review of the 
literature on probability, permutations, and combinations.  
Then we wrote our hypothesis.  Next, we took one red chip, one 
blue chip, and one white chip and put them in a bag together.  
Then we pulled out one chip and replaced it.  We repeated this 
procedure 600 times and recorded, on our data collection sheet, 
how many times each chip was drawn.  When we finished we wrote 
our summary and conclusion where we accepted or rejected our 
hypothesis and applied our findings to the world out side the 
classroom.  

III.  ANALYSIS OF DATA:

In the first trial of our experiment, the red chip was drawn 50 
times, the white chip 54 times, and the blue chip 46 times.  In 
the second trial, the red chip was drawn 55 times, the white 
chip was drawn 54 times and the blue chip was drawn 41 times.  
In the third trial, the red chip was drawn 50 times, the white 
chip was drawn 50 times, and the blue chip was drawn 50 times.  
In the fourth trial, the red chip was drawn 43 times, the white 
chip was drawn 52 times, and the blue chip was drawn 55 times.  
The total draws for each color chip were 198 for red, 210 for 
white, and 192 for blue.  Probability predicted that all of our 
totals would be 200.

IV.  SUMMARY AND CONCLUSION:

In our experiment, probability theory predicted that the total 
draw for each chip would be 200 after 600 draws.  In the actual 
experiment, the total draws for each color chip were: 198 for 
red (less than one out of three), 210 for white (more than one 
out of three), and 192 for blue (less than one out of three).  
Therefore, we must reject our hypothesis which states that the 
probability of pulling a blue chip out of a bag containing a 
blue, a red, and a white chip, is one out of three.  If we had 
done this experiment many more times, we know we would have had 
results that would have been even closer to what probability 
theory predicts.  

V.  APPLICATION:

From our experiment, we now know that probability will work in 
the long run.  So now, whenever we are playing games that 
involve chance, we will know the probability of something 
happening.  For example, whenever we roll a die, we know that 
the chance of rolling a 3 is one out of six.  Whenever we flip 
a coin, we know that the probability of getting heads is one 
out of two.



TITLE:  Surface Area of Rectangular Prisms

STUDENT RESEARCHER:  Corey Sanders and Amanda Guillory
SCHOOL:  Mandeville Middle School
         Mandeville, Louisiana
GRADE:  6
TEACHER:  John I. Swang, Ph.D.


I.  STATEMENT OF PURPOSE AND HYPOTHESIS:

We want to know if the formula for finding the surface area of 
geometric figures will give you an accurate answer.  Our 
hypothesis states that the formula for finding the surface area 
of a rectangular prism will give you an accurate answer.

II.  METHODOLOGY:

First, we wrote our statement of purpose and reviewed the 
literature on rectangular prisms, the metric system, and 
geometry.  Then we developed our hypothesis.  Next, we gathered 
our materials to test our hypothesis.  Then we created square 
centimeter grids on the 6 surfaces of each of four prisms by 
drawing them with a ruler or covering the surface with graph 
paper.  Next, we counted each square centimeter and recorded 
the data on the data collection form.  Then we found the 
surface area for each rectangular prisms by using the formula 
2(lw+lh+wh) and recorded the answer on the data collection 
forms.  Then we compared the answer we computed from using the 
formula to the answer we got from drawing and counting the 
square centimeters.  Next, we wrote our analysis of data, 
summary and conclusion, and applied our findings to the outside 
world. 

III.  ANALYSIS OF DATA:

In our experiment, we found that the surface area of the 
Kleenex box was 522 sq. cm. using the formula and 522 sq. cm. 
using the grid.  We found that the surface area of the CD disc 
box was 486 sq. cm. using the formula and 486 sq. cm. using the 
grid.  We found that the surface area of the trinket box was 
304 sq. cm. using the formula and 304 sq. cm. using the grid.  
We found that the surface area of the paperclip box was 136 sq. 
cm. using the formula and 136 sq. cm. using the grid.  We found 
that there was no difference in the surface area for all prisms 
when computed by the formula or counted on the sq. cm. grid.

IV.  SUMMARY AND CONCLUSION:

We have concluded that the formula for finding the surface area 
of a rectangular prism will give you an accurate answer.  
Therefore, we accept our hypothesis which stated that the 
formula for finding the surface area of a rectangular prism 
will give you an accurate answer.

V.  APPLICATION:

Now that we know that the formula for finding the surface area 
of a rectangular prism will give you an accurate answer, we can 
use it for calculating the surface area of a rectangular prism 
that we are going to cover with a type of material.  For 
example, if you wanted to cover a file cabinet with craft 
paper, you could use the formula 2(lw+lh+wh) to find out how 
much craft paper to buy.



TITLE:  Probability Theory and Dice
  
STUDENT RESEARCHER:  Josh DeHaan  
SCHOOL:  Mandeville Middle School
         Mandeville, Louisiana
GRADE:  6
TEACHER:  John I. Swang, Ph.D.


I.  STATEMENT OF PURPOSE AND HYPOTHESIS: 

I want to know if the probability of any number coming up on a 
six - sided die really is one out of six.  My hypothesis states 
that the die will have a 1 in 6 chance of falling on the number 
5.

II.  METHODOLOGY:

First, I wrote a statement of purpose.  Next, I did a review of 
literature on probability, luck, chance, odds, and gambling.  
Then I gathered my materials: a die and a data collection 
sheet.  After that I roll the die 300 times and recorded my 
data on the data collection sheet.  Then I analyzed my data, 
wrote my summary and conclusion, and applied my findings to the 
world outside the classroom.

III.  ANALYSIS OF DATA:

a)  For the number one, trial one got eight marks.  Trial two 
got four marks.  Trial three got seven marks.  Trial four got 
seven marks.  Trial five got two marks.  Trial six got eight 
marks, for a total of thirty-six marks.  

b)  For the number two, trial one got twelve marks.  Trial two 
got five marks.  Trial three got ten marks.  Trial four got 
eight marks.  Trial five got fifteen marks. Trial six got six 
marks.   For a total of fifty-six marks.

c)  For the number three, trial one got five marks.  Trial two 
got thirteen marks.  Trial three got five marks.  Trial four 
got ten marks.  Trial five got six marks.  Trial six got 
seventeen marks.  For a total of fifty-six marks.

d)  For the number four, Trial one got four marks.  Trial two 
got seven marks.  Trial three got six marks.  Trial four seven 
marks.  Trial five got ten marks.  Trial six got nine marks. 
For a total of forty-three marks.

e)  For the number five, trial one got twelve marks.  Trial two 
got eight marks. Trial three got eight marks.  Trial four got 
eight marks.  Trial five got eleven marks.  Trial six got three 
marks.  For a total of fifty marks.  

f)  For the number six, trial one got nine marks.  Trial two 
got thirteen marks.  Trial three got fourteen marks.  Trial 
four got ten marks.  Trial five got six marks.  Trial six got 
seven marks.  For a total of fifty-nine marks. 

IV.  SUMMARY AND CONCLUSION:

The conclusions that can be made from the data are as follows:

If the die is an even die, which means that it is evenly 
balanced, than the number that will be face up, should be the 
same for each value that is on each of the six faces. The 
number five (5) should be face up as often as the number six 
(6).  I threw the die in a series of six trials. There were 
fifty throws in each trial for a total of three hundred throws.  
The numbers that were face up most of the time were 6, which 
came up 58 times, and 2 & 3 which came up 56 times.  The number 
1 came up only 36 times, therefore the die may not have been 
even.  My hypothesis which stated that "the die will have a 1 
in 6 chance of falling on the number 5" was confirmed, although 
the rest of the data is not evenly divided.  

V.  APPLICATION:

Probability theory is good to know if you want to take your 
chances on winning a bet or laying the Lotto.  Kids may want to 
know about probability when playing dice games or flipping a 
coin.

© 1996 John I. Swang, Ph.D.