REFORMS SUMMER INSTITUTE
AUGUST 10-21, 2009
Part 1:Pace and Compass Mapping
Part 2:Scientific Measurement and Reporting
Scientific Data
Silt & Clay Particle Size
30.00
%
20.00
10.00
0.00
Warren County Forest: Site 1C
0-5cm
5-10cm
10-20cm
20-25cm
Dr. Marty Becker and Dr. Jennifer Callanan
Science Hall 450 and 448
beckerm2@wpunj.edu
callananj@wpunj.edu
Exercise 1: Drawing a Pace and Compass Map
Perhaps the most simplistic of all maps is the Pace and Compass Map. These types of
maps have been used for centuries by explorers, navigators, surveyors and property
owners. Pace and Compass Maps represent distance and direction and like all maps, have
some type of scale. The scale converts true earth distance to distance on the map.
How to Draw a Pace and Compass Map:
Using the sheet provided, create a pace and compass map of the following set of data
below. To create an accurate map of the property, use a protractor and ruler. No lines
should be drawn freehand. Make north the top of with the paper oriented in portrait
view. Begin your map by placing a starting dot 7 centimeters from the bottom and 4
centimeters from the left edge. The scale for the map is 1cm = 10 feet plotting all legs in
sequence. You should almost end up back where you started if you plot the points
carefully. (Any minor errors in measuring distance and direction on your map of the data
become cumulative in this exercise).
Details:
A surveyor purchased a piece of property and wanted to create a Pace and Compass Map
of the property for tax purposes. The surveyor had a pace of 5 feet and a Brunton
compass. Pace is the average distance between successive strides while walking. A
Brunton compass is a precision compass utilized for surveying and measuring the
orientation of geologic features.
Using the surveyor’s pace and a Brunton compass, the following data was collected:
Leg
Number of Paces
Direction
1.
18.4
N 90 E
2.
15
N 40 E
3.
12.8
Due N
4.
15.4
N 50 W
5.
25.4
S 40 W
6.
15.4
Due S
Actual Distance
(in Feet)
Scale Distance
(in Centimeters)
A. Convert the number of paces into Actual Distance using a pace of 5 feet per pace.
B. Convert the Actual Distance into Centimeters using a scale of Scale 1 cm=10 ft.
C. Carefully plot the Pace and Compass Map on the next page.
N
Exercise 1: Pace and Compass Map. Please draw map below.
↑
Scale 1 cm=10 ft.
Extension Questions:
1) What is the perimeter of the property? (Add up all the leg lengths in centimeters
and convert to actual distance in feet).
2) Divide the property up into squares and triangles by drawing straight lines on the
Pace and Compass map you created. There are a number of different ways
this can be done. No lines should be drawn freehand.
3) The area of a square= length X width.
The area of a triangle=1/2 base X height
**Determine the area for all the squares and triangles you have drawn.
Please show work here:
4) To determine the area of the surveyor’s property add up the areas of the triangles
and squares you have drawn. Please show work here:
5) Extra Credit: 1 acre= 43,560 square feet. How many acres did the surveyor
purchase? Please show work here:
Exercise 2: Creating Your Own Pace and Compass Map
We will now gather data similar to Exercise 1 at a selected on campus location and create
our own Pace and Compass Map.
Materials:
1. Graph paper and clip board
2. Calculator, pen, ruler and protractor
3. Yellow caution tape
4. Tape measure
5. Compass
In order to do collect the necessary data: we need to 1) establish your average pace; and
2) learn how to take a bearing with a compass.
To establish your average pace:
1. Roll out 100 feet of a tape measure on a flat surface.
2. Utilizing your average walking stride, count the number of strides it takes to walk
the 100 feet length.
3. Divide the 100 foot length by the number of strides to determine the number of
feet per stride. For example, if you take 20 strides to walk the 100 foot length
your pace would be 5 feet per stride. This would be a good approximate pace for
someone who was 6 feet tall.
4. Repeat this process two additional times and take the average of the three
determined pace measurements. This will be your pace for the exercise.
How to take a bearing with a compass:
1. Make sure you are not wearing any metal. For example, your belt buckle will
alter a compass reading.
2. Adjust the Bruton compass for the magnetic declination of your area. I will
explain this in class and help you with this adjustment.
3. Holding the compass near your waist and from a starting point, align your
compass mirror and sighting arm with the object you wish to take a bearing on.
4. Use the leveling bubble to make sure the compass is level and make sure you can
see the object you are taking a bearing on as a straight line across the sighting arm
and in the mirror across the center line.
5. Read the white needle for the bearing. Many people prefer to take these types of
bearing in terms of quadrants by dividing the compass up into 4 areas of 90
degrees each.
6. These bearing will be specified as North X degrees East or West or South X
degrees East or West.
7. Like anything else, taking accurate and precise bearing takes practice.
Part A: Collect the data to create a Pace and Compass map of the designated
area.
1. Yellow caution tape has been tied around a selected group of trees and
rocks that delineates the area to be mapped.
2. Select a starting point and take a bearing to the first tree or rock. Allow
your group partner(s) to also take this bearing to confirm your reading.
Record this bearing in the table provided.
3. Carefully pace off the distance between your starting point and the tree or
rock you took a bearing on. Have your group partner (s) also pace this off.
Utilizing your pace, calculate the distance between the starting point and
the tree or rock you took a bearing on. (Be aware that your group
partner(s) pace may be different than yours in the calculation of actual
distance). Record this distance in the table provided.
4. Repeat this process in sequence for all the individual “legs” that delineate
the property boundary. Record the data in the table provided.
5. Convert your actual distance between the trees or rocks to map scale
distance. We will use a scale of 1cm = 10 feet. This is the same scale
utilized for exercise one. This will allow the map to be plotted on a
standard piece of paper.
Leg
Number of
Paces
Bearing
Actual
Distance
(number of
paces X
distance per
pace)
Map Scale
Distance
1
2
3
4
5
6
7
Part B: Utilizing the same techniques and procedures explained in Exercise 1, plot a map
of the area for which the data was collected.
N
Exercise 2: Pace and Compass Map. Please draw map below.
↑
Scale 1 cm=10 ft
Exercise 3: The Pirate’s Treasure Map
A Pirate’s Treasure Map can be created utilizing the same techniques and skills from
Exercises 1 and 2. These exercise are simply worked in reverse where you start with a
Pace and Compass Map and utilize the bearings and distances between selected objects to
discover a buried treasure.
In addition to the materials listed in exercise 1, a small treasure chest with some
chocolate coins will serve as the “prize” for being able to read and recreate a Pace and
Compass map.
Part A: Procedure
1) Carefully create a Pace and Compass Map to serve as the Pirate’s Treasure map.
(For the purposes of this exercise, I will provide you with the treasure map).
2) Select stationary objects that are not likely to move such as large trees or rocks.
3) The Pirate’s Treasure map does not have to end at a starting point.
4) At the end of the last leg, bury the small treasure chest with chocolate coins.
5) Discovery of the treasure chest allows all the “pirates” to eat the chocolate coins.
Bearing
Actual
Leg
Number of
Feet
number of
paces
1
42
S16°W
2
26
S58°W
3
46
N78°W
4
69
S56°W
5
37
S41°E
Extension Questions:
1) What problems may occur to the accuracy and precision of a Pirate’s Treasure
map over time?
2) How could you design a method to check the accuracy and precision of the
Pirate’s Treasure map? Please explain by drawing a diagram. (Hint: could objects
near the buried treasure also serve as bearing points of distance and direction?)
3) If the Pirate’s Treasure map were ever stolen or fell into the wrong hands, how
could a smart pirate always protect the secret location of the buried treasure? Be
specific.
Applying Exercises 1–3 to your classroom
***Any of these exercises can be tailored for a 3-8th grade audience.
Skill Sets:
Multiple skill sets are utilized for these exercises and represent an excellent
integration of math and science. Skills in these three exercises are
“progressive” and rely on mastery of earlier techniques.
Some include:
a) Measurement basics with ruler, protractor and compass
b) Conversion between units of measurement
c) Accuracy and Precision
d) Map Scale
e) Graphical representation of actual Earth Surface
f) Compass utilization basics
g) Basic surveyor skills
Applicability to the NJCCSS:
These exercises can be readily correlated to the following NJCCSS. Examples of some
NJCCSS that apply to Pace and Compass Mapping include:
K–8: 5.1A, B (Scientific Process-Habits of the Mind, Inquiry and Problem Solving)
K–8: 5.2 B (Science and Society-Historical Perspectives)
K–8: 5.3A, B, D (Mathematical Applications-Numerical Operations, Geometry and
Measurement, Data Analysis and Probability)
K–8: 5.4 B, C (Nature and Process of Technology-Nature of Technology and
Technological Design)
3–8: 5.8 D (Earth Science: How we study the Earth)
Assessment:
1. Grading these exercises is an easy process. An example:
a) For Exercise 1: Carefully draw the pace and compass map from the
data on an overhead transparency. This can serve as your grading
instrument.
b) Compare the individual bearings to your overlay. Each degree off for
the individual bearings is assigned a deduction. Add up the total
number of degrees off for all of the bearings. (Example: each 5
degrees off equals the loss of 1 point).
c) Compare the distance of individual bearings to your overlay. Each
centimeter between the end point of a leg on the overhead and drawn
map is assigned a deduction. (Example: each 5 degrees off equals the
loss of 1 point).
d) Closure Error: Because of the nature of the instruments utilized to
make a pace and compass map, it is very easy to be a few degrees off
on a bearing or a few feet off on a distance. Errors also occur when
these measurements are converted to map distance and plotted with a
ruler and protractor. It would be near impossible based on cumulative
errors to end up where you have started when the map is drawn. The
distance between where you start the map and where the last leg of the
map ends is called “closure error.” Establish a deduction for the
closure error. (Example: each 1 centimeter distance between the
starting and fishing points equals the loss of one point).
e) For Exercise 2: Carefully draw the pace and compass map on an
overhead transparency. Errors in the bearing part of the exercise can
be reduced by having a number of faculty or students that are skilled
with the compass take the individual bearings. Take the average
bearing as the accepted bearing for the purposes of grading. Errors in
the distance part of the exercise can be greatly reduced by simply
using the tape measure to determine the distance between the
individual trees and rocks.
f) Grading the exercise is the same as Exercise 1 where deductions are
taken for deviations of bearings and distances when compared to the
transparency.
g) For Exercise 3: The reward of finding the buried Treasure is an
indicator of mastery of pace and compass mapping skills.
Additional Notes:
Exercise 4: Density by Direct Measurement of Volume
Materials:
Funsize Snickers
Funsize 3-Musketeers
Ruler (metric)
Scale or Digital Balance (metric)
Calculator (optional)
Large plastic cup
Water
The density of an object is defined as its mass per unit volume. This can be represented
ρ = m/ V
by the equation:
“It would break
my heart if you
forgot this
formula.”
where:
ρ is the density,
m is the mass,
V is the volume.
Mass is defined as the property of a body that causes it to have weight in a
gravitational field.
Volume is defined as the amount of 3-dimensional space occupied by an object.
Consider This! Objects that are the same size, or occupy the same volume, may
not have the same density. We can illustrate this with the following experiment
whereby we determine density by direct measurement of volume.
Experiment:
For each candy bar, measure, in centimeters (cm), the length (l),
width(w), and height (h) and record the measurements in the chart
below.
Calculate the volume of each candy bar using the equation:
V=lxwxh
Record the measurements in the chart.
M
V
Candy bar
Length
Width
Height
VOLUME
(cm)
(cm)
(cm)
(cm3)
Snickers
3 Musketeers
How does the volume of each candy bar compare?
Determine the mass, in grams, of each of the candy bars by
using the digital balance and record the measurements in
the chart.
Candy bar
Mass (g)
Snickers
3 Musketeers
How does the mass of each candy bar compare?
Now that you have determined the volume and the mass for
each candy bar, you can calculate their density. Use the
following equation to calculate the density, in g/cm3, of
each candy bar and record your measurements in the chart.
ρ = m/ V
Candy bar
Density (g/cm3)
Snickers
3 Musketeers
How does the density of each candy bar compare?
Remember! Density is the ratio of weight compared to volume…it’s not just the weight
nor is it just the size (volume). Materials of the same volume, with differing densities,
will react differently when placed in water.
Fill the 2 cups each 2/3 full with water.
Drop the Snickers in one cup and the 3 Musketeers
in the other cup. Describe what happens.
Additional Math:
Have students convert the Volume, Mass, and Density measurements
to other units.
Conversion Factors:
Multiply
by
To change
To
acres
hectares
acres
square feet
acres
square miles
atmospheres
cms. of mercury
Btu
kilowatt-hour
Btu/hour
watts
bushels
cubic inches
bushels (U.S.)
hectoliters
.3524
centimeters
inches
.3937
centimeters
feet
cubic feet
cubic meters
cubic meters
cubic feet
cubic meters
cubic yards
cubic yards
cubic meters
degrees
radians
.01745
dynes
grams
.00102
fathoms
feet
feet
meters
feet
miles (nautical)
.4047
43,560
.001562
76
.0002931
.2931
2150.4
.03281
.0283
35.3145
1.3079
.7646
6.0
.3048
.0001645
feet
miles (statute)
.0001894
feet/second
miles/hour
gallons (U.S.)
liters
grains
grams
.0648
grams
grains
15.4324
grams
ounces (avdp)
grams
pounds
hectares
acres
2.4710
hectoliters
bushels (U.S.)
2.8378
horsepower
watts
745.7
horsepower
Btu/hour
2,547
hours
days
inches
millimeters
25.4000
inches
centimeters
2.5400
kilograms
pounds (avdp or troy)
2.2046
kilometers
miles
.6214
kilowatt-hour
Btu
3412
knots
nautical miles/hour
knots
statute miles/hour
1.151
liters
gallons (U.S.)
.2642
liters
pecks
.1135
liters
pints (dry)
.6818
3.7853
.0353
.002205
.04167
1.0
1.8162
liters
pints (liquid)
2.1134
liters
quarts (dry)
.9081
liters
quarts (liquid)
1.0567
meters
feet
3.2808
meters
miles
.0006214
meters
yards
1.0936
metric tons
tons (long)
.9842
metric tons
tons (short)
1.1023
miles
kilometers
1.6093
miles
feet
miles (nautical)
miles (statute)
1.1516
miles (statute)
miles (nautical)
.8684
miles/hour
feet/minute
millimeters
inches
.0394
ounces (avdp)
grams
28.3495
ounces
pounds
ounces (troy)
ounces (avdp)
pints (dry)
liters
.5506
pints (liquid)
liters
.4732
5280
88
.0625
1.09714
pounds (ap or troy)
kilograms
.3732
pounds (avdp)
kilograms
.4536
pounds
ounces
quarts (dry)
liters
1.1012
quarts (liquid)
liters
.9463
radians
degrees
57.30
square feet
square meters
.0929
square kilometers
square miles
.3861
square meters
square feet
square meters
square yards
1.1960
square miles
square kilometers
2.5900
square yards
square meters
.8361
tons (long)
metric tons
1.016
tons (short)
metric tons
.9072
tons (long)
pounds
2240
tons (short)
pounds
2000
yards
meters
.9144
yards
miles
16
10.7639
.0005682
Exercise 5: Density by Archimedes’ Principle
Materials:
Aluminum Cube
Beam Balance
Graduated Cyliner
Water
Calculator (optional)
Eureka!
The density of an object can be measured in 2 ways:
1. Direct measurement of volume
2. Archimedes’ Principle
Archimedes’ Principle states that any object, wholly or partly immersed in a fluid, is
buoyed up by a force equal to the weight of the fluid displaced by the object.
Buoyancy is the upward force that keeps things afloat.
Experiment:
Determine the mass, in grams, of the aluminum (Al) cube by using
the digital balance and record the measurement in the chart.
Record the volume of water, in cm3, in the graduated cylinder (V0)
and record your measurement in the chart.
Place the Al cube in the graduated cylinder and record the volume
of water (V1) in the chart.
Calculate the volume of the Al cube with the equation:
(VAl = V1– V0) and record the measurement in the chart.
Mass
Aluminum Cube
V0
V1
VAl
Calculate the density of the Al cube using the formula
ρ = m1/ m2 - m3
ρ = _________
Calculate the density of the Al cube using the method in Exercise 1 with the formula
ρ = m1/ V
ρ = ________
Consider This! Suppose you had an oddly shaped object. Which method would
be better suited for measuring the density?
Exercise 6: Experimental Error
Materials:
Calculator (optional)
Experimental Error is defined as the difference between a measurement and the true
value or between two measured values. It is measured by accuracy and precision. Two
common ways to describe experimental error are by percent error and percent difference.
Accuracy measures how
close a measured value is to
the true/accepted value.
Precision (Repeatability/
Reproducibility) measures
how closely two or more
measurements agree with
one another.
Percent Error measures the
accuracy of a measurement
by the difference between a
measured value and a true
value.
Percent Difference measures
precision of two
measurements by the
difference between the
measured values as a fraction
of the average of two values.
Consider This!
The true density of aluminum
is 2.7 g/cm3.
Experiment:
Determine the percent error of both your measured densities of the
aluminum cube in Exercise 2 using the equation and record your
measurements in the chart.
% Error = | E – A| x 100
A
Where:
E = measured/experimental value
A = true/accepted value
Density
(from Ex. 2)
% Error
Archimedes Principle
Direct Measurement of Volume
Determine the percent difference of both your measured densities
of the aluminum cube in Exercise 2 and those measured by the
group next to you using the equation and record your
measurements in the chart.
% Difference = | E1 – E2|
E1 + E2
2
Where:
Archimedes Principle
Direct Measurement of Volume
x 100
E1 = measured/experimental value 1
E2 = measured/experimental value 2
Density
Density
Group 1
Group 2
%
Difference
Exercise 7: Significant Figures & Instrument Sophistication
Materials:
Oak Cube
Beam Balance
Digital Balance
4-digit Balance
Calculator (optional)
A Significant Figure refers to the number of figures that are known with some degree of
reliability.
For example: 13
have 2 significant figures
13.2 has
3 significant figures
13.20 has
4 significant figures
The least significant digit in a measurement depends on the smallest unit which can be
measured using the measuring instrument. The least significant digit measured by an
instrument is a direct indication of the instrument’s sophistication, or in other words, how
technologically advanced the instrument is.
Remember! When performing mathematical calculations (average, sum, etc.) on
measurements, the result should be rounded off as to have the same number of significant
figures as in the component with the least number of significant figures.
Experiment:
Determine the mass in grams of the oak cube using the 3 different
types of balances and record your measurements in the chart.
Calculate the average mass of the oak cube from the 3
measurements and record your measurement in the chart.
Remember! Use the correct number of significant digits.
Mass (g)
Beam Balance
Oak
Cube
Mass (g)
Digital Balance
Mass (g)
4-digit Balance
Average
Mass (g)
Exercise 8: FUN Application
Density of Gold = 19.32g/cm3
Density of Pyrite = 5.01g/cm3
REAL
Golden Ring
$19.99
Order yours today!
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Discovered in Paterson, NJ
DON’T MISS YOUR CHANCE TO
STRIKE IT RICH!
Get your MAP to the location of the
GOLD NOW!
Only 10 maps will be sold.
Send a check or money order for $10,000.00 made payable to:
Ima Swindler
100 Gold Rush Road
Paterson, NJ 07501
Maps will be shipped by postal service within 8-10 business days.
Not responsible for lost or stolen maps, inability to read map or find gold, purity of gold or legitimacy of this transaction.
Additional Applications:
Is a penny made from copper?
Density of Copper = 8.96 g/cm3
Is a
made from
?
Is a nickel really made from nickel?
Density of Nickel = 8.91 g/cm3
Does
=
?
Exercise 9: Meaningful Data
Materials:
Calculator (optional)
Microsoft Excel
The chart below contains particle size data for
a forest soil in Warren County, NJ. The data
was obtained by a process called sieve
analysis where sieves of different size mesh
(holes in the screen) are nested on top of each
other—largest mesh on top, smallest on
bottom. The soil is poured into the top of the
sieve stack then shaken. The weight of soil
particles remaining in each sieve is then measured to produce the
chart below.
Procedure: Determine the total weight of soil measured at each
depth in the sieve analysis by calculating the total
(sum) of all the size fractions and record it in the
chart.
Warren County Forest: Soil Particle Size Data (Site 1C)
Phi Size
-1
0
1
Depth
>2mm
gravel
1-2mm
very
coarse
sand
12.01g
39.77g
42.50g
24.99g
4.06g
7.92g
12.16g
11.75g
0-5cm
5-10cm
10-20cm
20-25cm
0.5-1mm
2
0.250.5mm
3
0.1250.25mm
4.5
Tray
0.0625- <0.0625m
0.125mm
m
coarse
sand
medium
sand
fine sand
very fine
sand
silt & clay
10.35g
8.77g
9.64g
10.61g
4.50g
11.7g
5.56g
4.45g
15.20g
8.29g
8.37g
14.56g
9.04g
7.73g
9.56g
15.03g
17.34g
17.88g
18.97g
26.47g
The data that has been produced directly from the sieve analysis is not meaningful data.
This data can not be easily compared because the total weight of soil being analyzed is
different. It’s like comparing apples to oranges. Therefore, the data must be normalized
by converting it into percentages. This way, we will compare apples to apples.
Determine the percentage of each size fraction at each depth using the
following equation and record your results in the chart below:
% Particle Size = weightsize fraction
weighttotal
x 100
Total (g)
Warren County Forest: Soil Particle Size Data (Site 1C)
Phi Size
-1
0
1
Depth
>2mm
1-2mm
very
coarse
sand
gravel
0.5-1mm
2
0.250.5mm
3
4.5
Tray
0.1250.06250.25mm 0.125mm <0.0625mm
coarse
sand
medium
sand
fine sand
very fine
sand
silt & clay
0-5cm
5-10cm
10-20cm
20-25cm
As a check that the percentage calculations are correct, calculate the total
% (sum) of all the size fractions and record it in the chart. The total
should equal 100%.
Total (%)
Consider This! What could you do if you had to process multiple samples
such as are shown in the following chart?
Warren County Forest: Soil Particle Size Data (All Sites)
Phi Size
Site 1 - A
Site 1 - A
Site 1 - A
Site 1 - A
Site 1 - B
Site 1 - B
Site 1 - B
Site 1 - B
Site 1 - C
Site 1 - C
Site 1 - C
Site 1 - C
Site 2 - A
Site 2 - A
Site 2 - A
Site 2 - B
Site 2 - B
Site 2 - B
Site 2 - C
Site 2 - C
Site 2 - C
Site 2 - D
Site 2 - D
Site 2 - D
Site 2 - E
Site 2 - E
Site 2 - F
Site 2 - F
Site 2 - G
Site 2 - G
Site 2 - G
Site 2 - H
Site 2 - H
Site 2 - H
Site 2 - I
Site 3 - A
Site 3 - A
Site 3 - A
Depth
0-10cm
0-5cm
10-20cm
20-25
0-10cm
0-5cm
10-20cm
20-25cm
0-10cm
0-5cm
10-20cm
20-25cm
0-10cm
0-5cm
10-15cm
0-10cm
0-5cm
10-15cm
0-10cm
0-5cm
10-18cm
0-10cm
0-5cm
10-18cm
0-10cm
0-5cm
0-5cm
0-10cm
0-10cm
0-5cm
10-20cm
0-10cm
0-5cm
10-20cm
0-5cm
0-10cm
0-5cm
10-15cm
-1
>2mm
34.5
1.63
26.84
34.71
33.63
22.67
17.02
20.04
39.77
12.01
42.5
24.99
29.27
42.18
33.46
39.48
51.07
28.66
29.99
28.37
21.67
46.97
46.56
34
37.21
35.32
52.45
31.09
26.86
33.29
32.28
28.78
37.7
29.34
34.94
46.75
71.45
40.91
0
1
1-2mm 0.5-1mm
7.28
9.35
3.57
8.41
13.29
14.54
12.03
4.59
7.07
17.58
5.22
8.25
9.1
18.37
10.39
13.04
7.92
8.77
4.06
10.35
12.16
9.64
11.75
10.61
10.41
9.04
9.85
8.43
9.36
10.58
9.78
7.59
4.14
4.81
12.97
10.21
12.19
12.91
9.95
11.12
10.88
11.47
9.39
8.8
12.37
10.37
15.47
12.27
12.85
9.92
9.62
8.61
10.42
8.47
14.04
12.12
9.06
10.54
6.51
8.27
10.33
19.75
4.34
9.83
9.93
8.39
10.87
10.43
10.08
8.81
12.76
11.35
10.19
6.07
18.41
15.91
2
3
4.5
Tray
Total (g)
0.250.1250.06250.5mm
0.25mm 0.125mm <0.0625mm
5.53
6.06
9.93
27.77
20.96
12.67
10.24
23.06
5.58
13.6
10.2
23.03
5.64
11.14
10.28
20.12
2.9
12.32
9.37
19.67
6.26
12.5
11.39
26.87
19.03
12.15
12.26
21.66
5.99
15.87
15.9
28.03
11.7
8.29
7.73
17.88
4.5
15.2
9.04
17.34
5.56
8.37
9.56
18.97
4.45
14.56
15.03
26.47
3.12
10.86
11.69
28.56
3.37
9.69
8.32
18.85
4.01
11.63
11.68
25.78
7.56
9.13
8.45
21.18
1.97
8.63
10.83
21.15
4.15
13.29
16.09
23.47
3.38
11.68
13.51
26.16
3.68
9.32
9.53
25.56
6.64
14.51
14.88
26.81
3.11
8.65
9.19
23.66
6.25
5.91
5.79
20.26
10.22
7.32
9.45
19.71
3.51
10.35
10.91
26.67
3.26
8.74
8.74
20.61
6.65
6.34
6.53
14.79
3.43
7.4
11.99
24.18
3.82
10.52
10.28
26.54
8.29
99.11
7.45
14.35
6.26
9.4
12.2
16.16
3.79
12.24
10.31
22.26
2.69
10.71
10.15
25.19
3.31
17.09
15.42
30.36
3.29
9.55
8.81
16.34
3
8.08
7.84
15.31
2.27
5.75
4.22
9.69
3.7
7.8
9.77
13.65
Additional Exercises:
Have students convert particle size data in mm to other SI units or to
United States Customary Units.
International System of Units (SI) Information from:
http://physics.nist.gov/cuu/Units/units.html
The SI is the modern form of the metric system, devised around the number 10, and is the
most widely used system of measurement in the world. The United States is one of only
3 countries who have not adopted the SI system as the primary system for recording
measurement. However, all scientific data should be reported in SI units. SI was
founded on seven base units for seven base quantities, as given in Table 1.
Table 1. SI base units
SI base unit
Base quantity
length
mass
time
electric current
thermodynamic
temperature
amount of substance
luminous intensity
Name
meter
kilogram
second
ampere
Symbol
m
kg
s
A
kelvin
K
mole
candela
mol
cd
Prefixes are often added to an SI unit to produce a multiple of the original unit, which are
all integer powers of ten. Prefixes are given in the table below.
Name
Multiples
Symbol
deca- hecto- kilo- mega- giga- tera- peta- exa- zetta- yottada
Factor 100 101
Name
Subdivisions Symbol
h
k
M
G
T
P
102
103
106
109
1012 1015
E
Z
1018 1021
Y
1024
deci- centi- milli- micro- nano- pico- femto- atto- zepto- yoctod
Factor 100 10−1
c
m
µ
n
p
f
10−2
10−3
10−6
10−9
10−12 10−15
a
z
10−18 10−21
y
10−24
Exercise 10: Graphical Presentation of Data
Materials:
Graph Paper
Ruler
Microsoft Excel
The percentage of particle size information presented in the chart below is meaningful
and relates apples to apples. However, it is difficult to compare data between depths
from a chart full of numerical values. Graphically displaying the data is a better option
for observing variations in data among samples.
Warren County Forest: Soil Particle Size Data (Site 1C)
Phi Size
-1
Depth
>2mm
0-5cm
5-10cm
10-20cm
20-25cm
gravel
16.57
38.97
39.81
23.17
0
1
2
0.250.5mm
3
0.1250.25mm
4.5
Tray
Total (%)
0.0625- <0.0625m
0.125mm
m
1-2mm 0.5-1mm
very
coarse
coarse
medium
very fine
sand
sand
sand
fine sand
sand
silt & clay
5.60
14.28
6.21
20.97
12.47
23.92
7.76
8.59
11.46
8.12
7.57
17.52
11.39
9.03
5.21
7.84
8.95
17.77
10.89
9.84
4.13
13.50
13.93
24.54
100.00
100.00
100.00
100.00
Procedure: Create a bar graph to illustrate the differences in percent silt and clay at
each of the four depths on the graph paper provided.
Consider This! What could you do if you had to graphically illustrate
multiple samples such as were shown in the chart in exercise 1?
There are a variety of graph types that can be used to represent data. However, picking
the appropriate type of graph for the field of science or the type of data is important. For
example:
Particle Size Cumulative %: Site 1C
Cumulative %
Soil Scientists use a
particular type of graph
called a cumulative percent
graph to illustrate particle
size distribution. The shape
of the curve can tell a soil
scientist, very quickly,
about the distribution of
particle sizes as well as
other soil properties such as
sorting of particles.
120
100
80
60
40
20
0
0-5cm
5-10cm
10-20cm
20-25cm
-1
0
1
2
Phi Size
3
4.5 Tray
Additional Exercises:
Graphing: Have students explore various types of graphs to represent
the data.
Silt & Clay Particle Size
30.00
%
20.00
10.00
0.00
Warren County Forest: Site 1C
0-5cm
5-10cm
10-20cm
20-25cm
Silt & Clay Particle Size: Site 1C
0-5cm
5-10cm
10-20cm
20-25cm
Silt & Clay Particle Size: Site 1C
%
30.00
20.00
10.00
0.00
0-5cm
5-10cm
10-20cm
Depth
20-25cm
Exercise 11: Technology & Data
As technology improves and becomes more sophisticated, the data we can obtain
becomes more accurate and precise. Often times, large quantities of data are produced,
which without the aid of software such as Microsoft Excel, normalization and graphical
representation can be quite tedious.
For example, the instrument shown in the picture below is called a Malvern Mastersizer
2000. This sophisticated piece of laboratory equipment can measure the particle size
distribution of a soil in a matter of minutes and, unlike sieve analysis, can differentiate
silt and clay particles up to < 0.02µ! Without this piece of equipment it would take over
8 hours to determine the percentage of clay sized particles in just one sample by older
settling techniques. The Mastersizer utilizes a laser diffraction technique where particles
pass through a beam of light, scattering the light, where it is detected on a lens. The
amount of light scatter relates to the size of the particle.
The following chart is an example of a portion of the data that is obtained using the
Mastersizer. The data was reported for 67 size fractions ranging from 0.2089ų to
1905.4607ų and is already normalized to percentage. Compare this data to that given in
Exercise 1 using the sieve analysis. Note the difference in:
Number of Size Fractions
Range of Size Fractions
Significant Digits
Warren County Forest: Soil Particle Size Data: Site 1A
Particle
Size (ų)
0.2089
0.2399
0.2754
0.3162
0.3631
0.4169
0.4786
0.5495
Depth
0-5cm
5-10cm
10-20cm
20-25cm
0
0
0.0189
0
0.023
0.0337
0.0881
0.0365
0.1244
0.1812
0.2074
0.1956
0.2122
0.3014
0.3037
0.3191
0.2879
0.4079
0.4067
0.4279
0.3665
0.5199
0.5075
0.541
0.4424
0.6296
0.606
0.6508
0.5199
0.7432
0.7076
0.7639
Particle
Size (ų)
0.631
0.7244
0.8318
0.955
1.0965
1.2589
1.4454
1.6596
Depth
0-5cm
5-10cm
10-20cm
20-25cm
0.6003
0.8615
0.8128
0.8823
0.6898
0.9932
0.9296
1.0154
0.7903
1.1397
1.0591
1.166
0.9074
1.3081
1.2079
1.3421
1.0401
1.4961
1.3735
1.5415
1.1899
1.7044
1.5564
1.7649
1.3514
1.9242
1.7485
2.0017
1.5216
2.1494
1.944
2.244
Particle
Size (ų)
1.9055
2.1878
2.5119
2.884
3.3113
3.8019
4.3652
5.0119
Depth
0-5cm
5-10cm
10-20cm
20-25cm
1.694
2.369
2.133
2.4782
1.8649
2.5758
2.3092
2.6944
2.0302
2.7625
2.4663
2.8832
2.1859
2.9226
2.5989
3.0368
2.3283
3.0509
2.7024
3.149
2.4515
3.1408
2.7715
3.2141
2.5525
3.1887
2.8033
3.2297
2.6276
3.1928
2.7963
3.1962
Particle
Size (ų)
5.7544
6.6069
7.5858
8.7096
10
11.4815
13.1826
15.1356
Depth
0-5cm
5-10cm
10-20cm
20-25cm
2.6798
3.1557
2.7529
3.1181
2.7138
3.0859
2.6809
3.0069
2.7403
2.9924
2.5882
2.8728
2.7705
2.8898
2.4885
2.733
2.8173
2.7861
2.3889
2.5952
2.8889
2.6929
2.3007
2.4726
2.9922
2.612
2.2262
2.3663
3.1225
2.5459
2.1685
2.2799
Particle
Size (ų)
17.378
19.9526
22.9087
26.3027
30.1995
34.6737
39.8107
45.7088
Depth
0-5cm
5-10cm
10-20cm
20-25cm
3.2724
2.4892
2.1238
2.2088
3.4206
2.4364
2.0879
2.1492
3.5446
2.3775
2.0525
2.0928
3.6151
2.3039
2.01
2.0329
3.608
2.2072
1.9528
1.9618
3.5066
2.0836
1.8766
1.8753
3.3062
1.9325
1.7795
1.771
3.0167
1.7579
1.6635
1.6501
Particle
Size (ų)
52.4807
60.256
69.1831
79.4328
Depth
0-5cm
5-10cm
10-20cm
20-25cm
2.6614
1.5684
1.5345
1.5175
2.2706
1.3744
1.4004
1.3802
1.8834
1.1906
1.2725
1.2486
1.5284
1.0273
1.1592
1.1306
Particle
Size (ų)
91.2011 104.7129 120.2264 138.0384
1.2365
0.897
1.069
1.0358
1.018
0.8037
1.0034
0.9687
0.8822
0.7514
0.9625
0.9343
0.821
0.7368
0.941
0.9327
158.4893 181.9701 208.9296 239.8833 275.4229 316.2278 363.0781 416.8694
Consider This! How would you go about graphically representing this
data? Would you consider graphing it by hand?
YOU’RE IN LUCK!
Not only might advanced technology provide you with a larger quantity of more accurate
and precise data, often times it is equipped with software which will normalize and
graphically report it for you! Now isn’t science EASY?
Volume (%)
Particle Size Distribution
4
3.5
3
2.5
2
1.5
1
0.5
0
0.01
0.1
1
10
100
1000
3000
100
1000
3000
100
1000
3000
100
1000
3000
Particle Size (µm)
Pre 1A 0-5cm - Average, Monday, June 22, 2009 1:00:56 PM
Particle Size Distribution
3.5
Volume (%)
3
2.5
2
1.5
1
0.5
0
0.01
0.1
1
10
Particle Size (µm)
Pre 1A 0-10cm - Average, Monday, June 22, 2009 1:12:57 PM
Particle Size Distribution
Volume (%)
3
2.5
2
1.5
1
0.5
0
0.01
0.1
1
10
Particle Size (µm)
Pre 1A 10-20cm - Average, Monday, June 22, 2009 1:22:38 PM
Particle Size Distribution
3.5
Volume (%)
3
2.5
2
1.5
1
0.5
0
0.01
0.1
1
10
Particle Size (µm)
Pre 1A 20-25cm - Average, Monday, June 22, 2009 1:33:40 PM
Additional Exercises:
Ternary Diagrams
From the given table of particle size distribution for a sample obtained using
data produced by the Mastersizer, have students determine the type of soil
represented at each depth using the ternary diagram of soil classification.
Depth
% clay
% silt
% sand
0-5cm
8
20
73
5-10cm
10
23
67
10-20cm
9
22
69
20-25cm
10
24
66
Skill Sets Utilized in the Course:
Measurements using ruler, beam balance & digital scales
Mathematical operations (addition, multiplication, division, percentages, etc.)
Use of formulas to calculate measurements
Conversions between units of measurement
Accuracy, precision, and experimental error
Simple graphing
Advanced calculations and graphing using Microsoft Excel
Comparison of scientific techniques
Instrument sophistication
Ternary Diagrams
Applicability to the NJCCSS:
5.1
Scientific Processes
A.3, B.1 (K-4)
A.1-3, B.3 (5-8)
5.3
Mathematical Applications
A.1, A.3, D.1 (K-4)
A.1, D.1, D.4 (5-8)
5.4
Nature and Process of Technology
C.1 (3-4)
5.6
Physical Science-Chemistry
A.4 (3-4)
A.2 (5-6)
Assessment:
Assessment of the large majority of the Scientific Measurement course can be done by
the final answers to the problems as well as evaluation of the mathematical processes the
students’ used to obtain their measurements. Assessment of the Fun Application should
be based on the student’s ability to evaluate the legitimacy of the advertisement utilizing
the basic skills learned in the previous exercises. Assessment of the Reporting Scientific
Data course is again based largely on the students’ mathematical calculations and ability
to design a simple graph or to utilize the software to create an appropriate graph of data.
The activities of both courses are best assessed assigning partial credit for work as
students’ may arrive at incorrect measurements due to a mistake in mathematical
calculation. Award points for process as well as final answer.
Digital Balance, Universal Specific Gravity Kit, and Density Blocks can be purchased at
www.wardsci.com