The National Student Research Center
E-Journal of Student Research: Math
Volume 5, Number 2, July, 1998
The National Student Research Center
is dedicated to promoting student research and the use of the
scientific method in all subject areas across the curriculum,
especially science and math.
For more information contact:
- 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
- Is The Formula For Finding The Volume
Of A Rectangular Prism Always Correct?
- Is The Formula C = D x Pi Always
Correct?
- Does The Area Of A Rectangle Always
Equal Base x Height?
- Does The Area Of A Triangle Always
Equal 1/2 Base x Height?
- Is The Formula For Finding The Surface
Area Of A Rectangular Prism Accurate?
- Does The Pythagorean Theorem Work?
- Probability Theory
TITLE: Is The Formula For Finding The Volume Of A Rectangular
Prism Always Correct?
STUDENT RESEARCHERS: Joshua Foster and Lalita Mondkar
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
We would like to do a mathematical proof to see if the formula
for finding the volume of a rectangular prism is correct. Our
hypothesis states that the formula for finding the volume of a
rectangular prism, v=lxwxh, is correct.
II. METHODOLOGY:
First, we chose our topic. Then we wrote our statement of
purpose and we did a review of literature. Next, we developed
our hypothesis. Then we wrote a methodology to test our
hypothesis. Next, we gathered our materials needed to conduct
the research. Then we filled six hollow rectangular prisms with
water. We poured out the water and measured the amount of
water. This amount of water was the volume of the prism. One
millimeter is equal to one cubic centimeter. Next, we measured
the length, width, and height of the prisms and multiplied them.
Then we compared and recorded the two volumes representing the
volume of the rectangular prisms.
Then we analyzed our data using charts and graphs. Next, we
wrote our summary and conclusion where we accepted/rejected our
hypothesis. Last, we applied our findings to the world outside
the classroom.
III. ANALYSIS OF DATA:
Due to measurement errors, there was a percent of difference
between the two values for volume. On prisms A, B, and C, there
was plastic wrap inside to waterproof them, and that lowered the
capacity of those prisms.
Our data show that prism A was 11.2 cm long, 3.2 cm wide, and
4.8 cm tall. It had a volume of 145.4 cm3. It held 122.9 ml of
water, so the percent of difference was 15.5%
Our data show that prism B was 6.5 cm long, 5.5 cm wide, and 2.8
cm tall, so it had a volume of 100.1 cm3. It held 86.6 ml of
water, so the percent of difference was 13.5%
Our data show that prism C was 3.2 cm long, 2.4 cm wide, and 1.9
cm tall, so it had a volume of 14.592 cm3. It held 11.6 ml of
water, so the percent of difference was 20.5%
Our data show that prism D was 6.5 cm long, 5.3 cm wide, and 4.8
cm tall, so it had a volume of 165.52 cm3. It held 165 ml of
water, so the percent of difference was 0.3%
Our data show that prism E was 6.6 cm long, 5.4 cm wide, and
10.5 cm tall, so it had a volume of 374.22 cm3. It held 370 ml
of water, so the percent of difference was 1.1%
Our data show that prism F was 12.1 cm long, 8.4 cm wide, and
11.4 cm tall, so it had a volume of 1,158.696 cm3. It held
1,015.5 ml of water, so the percent of difference was 12%
| in cm | in cm3 | in mL |
|Prism| L x W x H = V |Differ.|Diff. %|Water Volume|
| A |11.2 | 3.2 | 4.8 | 145.4 |26.632 | 15.5% | 122.9 |
| B | 6.5 | 5.5 | 2.8 | 100.1 | 13.5 | 13.5% | 86.6 |
| C | 3.2 | 2.4 | 1.9 | 14.592 | 2.992 | 20.5% | 11.6 |
| D | 6.5 | 5.3 | 4.8 | 165.52 | 0.52 | 0.3% | 165 |
| E | 6.6 | 5.4 |10.5 | 374.22 | 4.22 | 1.1% | 370 |
| F |12.1 | 8.4 |11.4 |1,158.696|143.196| 12% | 1,015.5 |
IV. SUMMARY AND CONCLUSION:
Our data shows that the percent of differences between the two
values for volume was more than 0. We had some measuring error.
On the prisms with large differences, there was plastic wrap in
the boxes to waterproof them, so there was less capacity than
normal in the prisms.
Therefore, we mostly accept our hypothesis, which states that
the formula for finding the volume of a rectangular prism,
v=lxwxh, is correct.
This research should be repeated making sure to accurately
measure the inside dimensions of the rectangular prisms. The
walls of the prisms take up space and could have contributed to
the differences we found in the two values for volume.
V. APPLICATION:
We can apply our findings to the world outside the classroom by
showing people how they can use the formula for volume to
calculate how much a container will hold.
TITLE: Is The Formula C = D x Pi Always Correct?
STUDENT RESEARCHERS: Chris Chugden and Amber French
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
We would like to see if the formula for finding the
circumference of a circle, C = Pi x D, is always correct no
matter how big or small a circle is. Our hypothesis states that
the formula C = Pi x D will always be accurate no matter how big
or small the circle is.
II. METHODOLOGY:
First, we chose a topic. Then we wrote our statement of
purpose. Next we wrote our review of literature about
mathematics, Pi, geometry, circumference, diameter, and circles.
Then we wrote a hypothesis.
Next, we developed a methodology to test our hypothesis. Then
we gathered our materials for our experiment which included
cardboard, paper, pencil, scissors, tape measure, and the
formula C = Pi x D. Next, we made 10 circles out of cardboard
with different diameters. We calculated the circumference of
the circles three times each using the formula C = Pi x D. To
test the formula we got a tape measure and measured around the
circle. We repeated these steps three times with the other
circles, also. We recorded our results on our data collection
sheet.
After we gathered our data, we marked down the results on a data
collection form. We used the form to conduct our analysis of
data (charts, graphs). Then we wrote a summary and conclusion
where we accepted/rejected our hypothesis. After concluding the
project, we applied our findings to the world outside the
classroom.
III. ANALYSIS OF DATA:
Our first circle had a diameter of 17 cm. The difference
between the circle's circumference calculated by the formula and
measured a tape measure was 3.98 cm. The second circle had a
diameter of 19.5 cm. The difference between the circle's
circumference calculated by the formula and a tape measure was
2.9 cm. The third circle had a diameter of 11.2 cm. The
difference between the circle's circumference calculated by the
formula and a tape measure was 1.83 cm. The fourth circle used
had a diameter of 7.4 cm. The difference between the circle's
circumference calculated by the formula and a tape measure was
0.24 cm. Circle five had a diameter of 8.3 cm. The difference
between the circle's circumference calculated by the formula and
a tape measure was 0.86 cm. Circle six had a diameter of 5 cm.
The difference between the circle's circumference calculated by
the formula and a tape measure was 0.30 cm. Circle seven had a
diameter of 10 cm. The difference between the circle's
circumference calculated by the formula and a tape measure was
0.10 cm. Circle eight had a diameter of 13.5 cm. The
difference between the circle's circumference calculated by the
formula and a tape measure was 0.61 cm. Circle nine had a
diameter of 16 cm. The difference between the circle's
circumference calculated by the formula and a tape measure was
3.24 cm. Circle ten had a diameter of 10.4 cm. The difference
between the circle's circumference calculated by the formula and
a tape measure was 0.26 cm.
Measured
Circle | Pi x Diameter = Circum. | Circum. | Difference |
| 1 | 3.14 | 17.0cm | 53.38cm | 49.40cm | 3.98cm |
| 2 | 3.14 | 19.5cm | 61.30cm | 58.40cm | 2.90cm |
| 3 | 3.14 | 11.2cm | 35.17cm | 37.00cm | 1.83cm |
| 4 | 3.14 | 7.4cm | 23.24cm | 23.00cm | 0.24cm |
| 5 | 3.14 | 8.3cm | 26.06cm | 25.20cm | 0.86cm |
| 6 | 3.14 | 5.0cm | 15.70cm | 16.00cm | 0.30cm |
| 7 | 3.14 | 10.0cm | 31.40cm | 31.50cm | 0.10cm |
| 8 | 3.14 | 13.5cm | 42.39cm | 43.00cm | 0.61cm |
| 9 | 3.14 | 16.0cm | 50.24cm | 47.00cm | 3.24cm |
| 10 | 3.14 | 10.4cm | 32.66cm | 32.40cm | 0.26cm |
|AVERAGE DIFFERENCE 1.43cm |
IV. SUMMARY AND CONCLUSION:
The average difference between the measured circumference and
the calculated circumference for all the circles was 1.43 cm.
Six of the ten circles had a difference of less than one
centimeter. Therefore, we accept our hypothesis which stated
that the formula C = Pi x D will always give the correct length
of a circle's circumference no matter how big or small the
circle is. Our experimental data wasn't always exactly the same
as the data obtained from the formula because the precision of
our measuring instruments and procedure was lacking. This
project needs to be repeated with more precise measuring
utensils.
V. APPLICATION:
We can apply our findings by using the formula in calculating
the circumference of circles for math projects in schools and
for other everyday uses such as constructing a fence. If the
area is circular, than you would need the circumference of the
area to find out how much fencing you need. Another use of our
findings could be in projects in the future that have to do with
Pi.
TITLE: Does The Area Of A Rectangle Always Equal Base x
Height?
STUDENT RESEARCHERS: James Rees and Jane Bordelon
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
We would like to do a mathematical proof to find out if the
formula for finding the area of a rectangle, A=bh, is correct.
Our hypothesis states that the area of a rectangle always equals
the base of the rectangle times the height of the rectangle.
II. METHODOLOGY:
First, we chose our topic. Next, we wrote our statement of
purpose. Then we conducted a review of literature about
mathematics, geometry, base, height, rectangles, and area.
Next, we wrote our hypothesis. We then developed a methodology
to test our hypothesis. Next, we made a data collection sheet.
The materials we used to perform the experiment were: six
different sized rectangles, ruler, and permanent marker. Then
we chose one base and one height for each of the six rectangles
(three for each student researcher), and used the formula, A=bh,
to figure out the area of the rectangle. We then drew out each
rectangle on square centimeter graph paper. Next, we counted
the number of square centimeters in each rectangle and compared
the amount of square centimeters that we counted on graph paper
to the amount of square centimeters we found when we used the
formula. We repeated this process with the five remaining
rectangles. Then we recorded our data on our data collection
form. Next, we analyzed our data using statistics, charts, and
graphs. Then we wrote our summary and conclusion where we
accepted or rejected our hypothesis. Finally, we applied our
findings to the world outside the classroom.
III. ANALYSIS OF DATA:
Area of a Rectangle
|Rectangle | Base X Height = Area | Count
| #1 | 5 | 8 | 40 | 40
| #2 | 6 | 9 | 54 | 54
| #3 | 3 | 7 | 21 | 21
| #4 | 2 | 5 | 10 | 10
| #5 | 8 | 3 | 24 | 24
| #6 | 9 | 4 | 36 | 36
IX. ANALYSIS OF DATA:
In rectangle number one, the area derived from the formula was
40 square centimeters and the actual count was also 40 square
centimeters. In rectangle number two, the area derived from the
formula was 54 square centimeters and the actual count was also
54 square centimeters. In rectangle number three, the area
derived from the formula was 21 square centimeters and the
actual count was also 21 square centimeters. In rectangle
number four, the area derived from the formula was 10 square
centimeters and the actual count was also 10 square centimeters.
In rectangle number five, the area derived from the formula was
24 square centimeters and the actual count was 24 square
centimeters. In rectangle number six, the area derived from the
formula was 36 square centimeters and the actual count was 36
square centimeters.
IV. SUMMARY AND CONCLUSION:
Our data showed that the formula, A=bh, will always equal the
area of a rectangle. Therefore, we accept out hypothesis which
states that the area of a rectangle will always equal the base
of the rectangle times the height of the rectangle.
V. APPLICATION:
Our findings can be applied to the world outside the classroom
during math tests or other math-related projects. We now know
that the area of a rectangle equals its base times its height.
TITLE: Does The Area Of A Triangle Always Equal 1/2 Base x
Height?
STUDENT RESEARCHER: Jane Bordelon and Barrett Ainsworth
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
We would like to do a mathematical proof to see if the area of a
triangle is always equal to 1/2 the size of a rectangle with the
same base and height. Our hypothesis states that the area of a
triangle is equal to 1/2 the area of a rectangle with the same
base and height.
II. METHODOLOGY:
First, we chose our topic. Next, we wrote our statement of
purpose. Then we conducted a review of literature about
triangles. Next, we wrote our hypothesis. We then developed a
methodology to test our hypothesis. The materials we used to
perform the experiment were: six different sized wooden
rectangles, ruler, saw, and permanent marker. Next, we made a
data collection sheet. Then we drew a triangle. Next, we drew
a rectangle with the same base and height as the triangle. Then
we drew cubic centimeters on the rectangle and triangle. Next,
we multiplied the base and height of the rectangle to find it's
area. Then we multiplied the base and height of the triangle
and divided it's product in half to find it's area. We then
counted the cubic centimeters in both the rectangle and the
triangle to see if they were the same as what the formula said
they would be. We repeated this process with the five remaining
rectangles. Then we recorded our data on our data collection
sheet. Then we analyzed our data using statistics, charts, and
graphs. Next, we wrote our summary and conclusion where we
accepted or rejected our hypothesis. Finally, we applied our
findings to the world outside the classroom.
III. ANALYSIS OF DATA:
Does The Area Of A Triangle Always Equal 1/2 Base x Height?
Triangle
| | Count | Area | 1/2 | Base | Height |
| #1 | 12.8 | 12 | 1/2 | 6 | 4 |
| #2 | 6.7 | 6 | 1/2 | 6 | 2 |
| #3 | 4.3 | 4 | 1/2 | 4 | 2 |
| #4 | 24.9 | 24 | 1/2 | 8 | 6 |
| #5 | 16.13 | 16 | 1/2 | 4 | 8 |
| #6 | 41.2 | 40 | 1/2 | 8 | 10 |
For triangle number one, the area from the formula was 12 cm2
and the actual count of square centimeters on the graph paper
was 12.8 cm2. In triangle number two, the area from the formula
was 6 cm2 and the actual count was 6.7 cm2. In triangle number
three, the area from the formula was 4 cm2 and the count was 4.3
cm2. In triangle number four, the area from the formula was 24
cm2 and the count was 24.9 cm2. In triangle number five, the
area from the formula was 16 cm2 and the count was 16.13 cm2.
In triangle number six, the area from the formula was 40 cm2 and
the count was 41.2 cm2. In rectangle number one, the area from
the formula was 24 cm2 and the count was 24 cm2. In rectangle
number two, the area from the formula was 12 cm2 and the count
was 12 cm2. In rectangle number three, the area from the
formula was 8 cm2 and the count was 8 cm2. In rectangle number
four, the area from the formula was 48 cm2 and the count was 48
cm2. In rectangle number five, the area from the formula was 32
cm2 and the count was 32 cm2. In rectangle number six, the area
from the formula was 80 cm2 and the count was 80 cm2.
For triangle one's area, the difference between the count for
the triangle and the count for 1/2 the rectangle (with the same
base and height) is .8 cm2. For triangle two's area, the
difference between the count for the triangle and the count for
1/2 the rectangle (with the same base and height) is .7 cm2.
For triangle three's area, the difference between the count for
the triangle and the count for 1/2 the rectangle (with the same
base and height) is .3 cm2. For triangle four's area, the
difference between the count for the triangle and the count for
1/2 the rectangle (with the same base and height) is .9 cm2.
For triangle five's area, the difference between the count for
the triangle and the count for 1/2 the rectangle (with the same
base and height) is .13 cm2. For triangle six's area, the
difference between the count for the triangle and the count
for 1/2 the rectangle (with the same base and height) is
1.2 cm2.
The average difference of the area counted for the triangle and
for 1/2 the rectangle was .7 cm2.
IV. SUMMARY AND CONCLUSION:
Or findings indicate that the formula, A = 1/2 x base x height,
will always equal the area of a triangle. Therefore, we accept
our hypothesis which states that the area of a triangle is equal
to 1/2 the area of a rectangle with the same base and height.
V. APPLICATION:
Our findings can be applied during math tests or other related
math projects. We now know that the area of a triangle equals
1/2 the area of a rectangle with the same base and height.
TITLE: Is The Formula For Finding The Surface Area Of A
Rectangular Prism Accurate?
STUDENT RESEARCHER: Christine O'Rourke And John Casey
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
We would like to do a mathematical proof to find out if the
formula for finding the surface area of a rectangular prism,
2(lw + lh + wh), is accurate. Our hypothesis states that the
formula for finding the surface area of a rectangular prism,
2(lw + lh + wh), is accurate.
II. METHODOLOGY:
First, we choose our topic. Then we wrote our statement of
purpose. Next, we researched our topics and wrote a review of
literature about mathematics, geometry, prisms, and rectangles.
Then we wrote our hypothesis.
Next, we developed a methodology. Then we conducted our
research. First, we found ten different size rectangular
prisms. Then we glued graph paper to all of the faces of the
ten rectangular prisms. Then we counted all the squares on the
graph paper to find the surface area of each rectangular prism.
Then we measured the length, width, and height of the prism and
used these values in the formula, 2(lw + lh + wh), to find the
surface area of each prism. Next, we recorded our information
in our data collection sheet. Then we compared the two surface
area values for each prism to see if the formula really worked.
After that, we wrote our summary and conclusion where we
accepted or rejected our hypothesis. Finally, we applied our
findings to the world outside our classroom.
III. ANALYSIS OF DATA:
The Surface Area Of Ten Rectangular Prisms
|Height |Width|Length|Formula|Squares|Difference|
R.P. 1 | 17.4 |10.4 | 2.2 | 484.24| 484.24| 0.0 |
R.P. 2 | 12.5 | 1.5 | 14.0 | 409.00| 411.3 | 2.3 |
R.P. 3 | 17.5 | 2.5 | 10.5 | 497.00| 500.2 | 3.2 |
R.P. 4 | 19.0 |11.6 | 4.0 | 685.6 | 685.6 | 0.0 |
R.P. 5 | 20.4 |13.4 | 3.6 | 776.48| 785.28| 8.8 |
R.P. 6 | 20.2 | 7.4 | 16.8 |1203.88|1205.36| 1.48 |
R.P. 7 | 19.6 |16.8 | 9.4 | 940.56| 944.4 | 3.88 |
Average Difference | | | | 2.9 |
R.P.- Rectangular Prism
When the squares on the graph paper were counted for rectangular
prism 1, it had a surface area of 484.24 sq. centimeters. When
using the formula, it had a surface area of 484.24 sq.
centimeters. The difference was 0. When the squares on the
graph paper were counted for rectangular prism 2, it had a
surface area of 411.3. When using the formula, it had a surface
area of 409. The difference was 2.3. When the squares on the
graph paper were counted for rectangular prism 3, it had a
surface area of 497. When using the formula, it had a surface
area of 500.2. The difference was 3.2. When the squares on the
graph paper were counted for rectangular prism 4, it had a
surface area of 685.6. When using the formula, it had a surface
area of 685.6. The difference was 0. When the squares on the
graph paper were counted for rectangular prism 5, it had a
surface area of 785.28. When using the formula, it had a
surface area of 776.48. The difference was 8.8. When the
squares on the graph paper were counted for rectangular prism 6,
it had a surface area of 1205.36. When using the formula, it
had a surface area of 1203.38. The difference was 1.98. When
the squares on the graph paper were counted for rectangular
prism 7, it had a surface area of 944.4. When using the
formula, it had a surface area of 940.56. The difference was
3.84. The average difference between the values for the surface
area found with the graph paper and the formula was 2.9 sq.
centimeters.
IV. SUMMARY AND CONCLUSION:
We have found in this experiment that the formula for finding
the surface area of a rectangular prism, 2(lw + lh + wh), is
accurate. Therefore we except our hypothesis which stated that
the formula, 2(lw + lh + wh), is accurate for rectangular prisms
of all sizes.
This research needs to be repeated using more precise instrument
measurements to reduce measurement error. The differences we
found between the values for the surface area when counting
square on the graph paper and using the formula were due to
inaccurate measurements.
V. APPLICATION:
We can apply this to the world by telling math text book
companies that they don't have to change their books because the
formula, 2(lw + lh + wh), is accurate.
TITLE: Does The Pythagorean Theorem Work?
STUDENT RESEARCHERS: John Casey and Whitney Stoppel
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE:
We would like to do a mathematical proof regarding the
Pythagorean Theorem which states that for any right triangle the
square of the hypotenuse is equal to the sum of the squares of
the other two sides (a2 + b2 = c2). We want to see if the
theorem works with right triangles of all sizes. Our hypothesis
states that the Pythagorean Theorem will always work for any
size of right triangle.
II. METHODOLOGY:
First we chose a topic. Then we developed a statement of
purpose. Then we wrote a review of literature about Pythagoras,
triangles, angles, the Pythagorean Theorem, and mathematics.
Then we developed a hypothesis.
Then we wrote a methodology to test our hypothesis. Then we
gathered our materials which included a ruler, graph paper,
pencils, grid, and a data collection sheet. Then we drew ten
different sized right triangles on the graph paper. Then we
measured the sides of all ten triangles. We took the
measurements for each triangle and calculated the size of the
hypotenuse using the Pythagorean Theorem. Then we used the
graph paper to find the size of the hypotenuse. We squared each
side of the right triangle and counted the number of square
centimeters inside each side's square. Then we compared the
size of the hypotenuse found using the formula and the graph
paper. We did this to each of the triangles recording our data
on a data collection sheet.
Then we analyzed our data on charts and graphs. Next, we wrote
our summary and conclusion where we accepted/rejected our
hypothesis. Finally, we applied our findings to the world
outside the classroom.
III. ANALYSIS OF DATA:
For triangle one, the hypotenuse was 40.8 centimeters squared
when counted and 41 centimeters squared when calculated with the
formula a2 + b2 = c2. The difference between the counted and
calculated values was .20 centimeters squared. For triangle
two, the hypotenuse was 10.24 centimeters squared when counted
and 10 centimeters squared when calculated using the formula.
The difference between the counted and calculated values was .24
centimeters squared. For triangle three, the hypotenuse was
34.2 centimeters squared when counted and 34 centimeters squared
when calculated. The difference between the counted and
calculated values was .20 centimeters squared. For triangle
four, the hypotenuse was 17.6 centimeters squared when counted
and 17 centimeters squared when calculated. The difference
between the counted and calculated values was .40 centimeters
squared. For triangle five, the hypotenuse was 25.0 centimeters
squared when counted and 25 centimeters squared when calculated.
The difference between the counted and calculated values was .0
centimeters squared. For triangle six, the hypotenuse was 13.68
centimeters squared when counted and 13 centimeters squared when
calculated. The difference between the counted and calculated
values was .68 centimeters squared. For triangle seven, the
hypotenuse was 84.64 centimeters squared when counted and 85
centimeters squared when calculated. The difference between the
counted and calculated values was .36 centimeters squared. For
triangle eight, the hypotenuse was 9.0 centimeters squared when
counted and 8 centimeters squared when calculated. The
difference between the counted and calculated values was 1.0
centimeters squared. For triangle nine, the hypotenuse was
27.04 centimeters squared when counted and 26 centimeters
squared when calculated. The difference between the counted and
calculated values was 1.04 centimeters squared. For triangle
ten, the hypotenuse was 73.96 centimeters squared when counted
and 74 centimeters squared when calculated. The difference
between the counted and calculated values was .04 centimeters
squared.
The average difference between the counted and calculated values
for all hypotenuse was .42 centimeters squared.
Does The Pythagorean Theorem Always Work For Right Triangles?
|cm squared|cm squared|cm squared|
|Difference| Counted |Calculated|
| Between |Hypotenuse|Hypotenuse = A | B
| C and M | Squared | Squared | Squared| Squared|
(M) (C)
1 | 0.20cm2 | 40.8 | 41 | 16 | 25 |
2 | 0.24cm2 | 10.24 | 10 | 1 | 9 |
3 | 0.20cm2 | 34.2 | 34 | 9 | 25 |
4 | 0.40cm2 | 17.6 | 17 | 1 | 16 |
5 | 0.00cm2 | 25.0 | 25 | 16 | 9 |
6 | 0.68cm2 | 13.68 | 13 | 04 | 9 |
7 | 0.36cm2 | 84.64 | 85 | 36 | 49 |
8 | 1.00cm2 | 9.0 | 8 | 4 | 4 |
9 | 1.04cm2 | 27.04 | 26 | 1 | 25 |
10| 0.04cm2 | 73.96 | 74 | 49 | 25 |
| 0.42cm2 | Average Difference
IV. SUMMARY AND CONCLUSION:
We found that this formula does work, therefore we accept our
hypothesis which stated that the Pythagorean Theorem will always
work for any size of right triangle. The small difference
between the counted and calculated values for the hypotenuse was
due to the inaccuracy of our ruler and graph paper. The
research should be done again using more accurate instruments of
measurement.
V. APPLICATION:
We are able to apply our findings to the world outside the
classroom by showing construction workers how to build roofs for
houses or other triangular objects. We can also use this
information when we are in school. Another thing we can use our
finding for is making ramps with a specific height or length.
TITLE: Probability Theory
STUDENT RESEARCHER: Rick Dupont and James Rees
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
We want to see if the probability theory works. Is the
probability of picking a red poker chip that is in a bag with a
blue or white poker chip one out of three. Our hypothesis
states that the probability of pulling a red chip out of a paper
bag, with one blue, one red, and one white chip in it, is 1/3.
II. METHODOLOGY:
First, we selected a topic. Then we wrote a statement of
purpose. Then we did a review of literature on chance, luck,
probability, and mathematics.
Then we wrote a methodology to test our hypothesis. We put 3
poker chips in a brown paper bag. There was 1 blue chips, 1 red
chips, and 1 white chips. We pulled out one chip and placed it
back in the bag. We repeated this 600 times.
After each pull we recorded the chip color on our data
collection sheet. Then we analyzed our data using simple
statistics, charts, and graphs. Next, we wrote our summary and
conclusion. Then we rejected or accepted our hypothesis.
Finally, we applied our findings to life.
III. ANALYSIS OF DATA:
The total number of times the blue poker chip was pulled was
202. The total number of times the red poker chip was pulled
was 200. The total number of times the white poker chip was
drawn was 198. The expected outcomes was 200 for all three
chips.
Probability With Chip
|Chip | |Times Pulled|
|Color | | Observed | Expected|
| | Rick | James | Total | Total | Probability |
|Blue | 103 | 99 | 202 | 200 | 1/3 |
|White | 99 | 99 | 198 | 200 | 1/3 |
|Red | 98 | 102 | 200 | 200 | 1/3 |
|Total | 300 | 300 | 600 | 600 | 1/3 |
IV. SUMMARY AND CONCLUSION:
According to our data, the probability of pulling a red chip 200
times out of a paper bag with 1 blue, red, and white chip in,
was close too 1/3. Two of the chips were two off and one was
exactly the expected outcome. Therefore we accept our
hypothesis which stated that the probability of pulling a red
chip out of a paper bag, with one blue, one red, and one white
chip in it, is 1/3.
We feel that if we repeated this experiment with more trials
that the outcome would be closer to, if not right on, the
expected outcome predicted by probability theory.
V. APPLICATION:
Probability Theory can help us determine the outcomes of winning
games of chance like the lottery or poker.
© 1998 John I. Swang, Ph.D.