CURR 383: Elementary Mathematics
Class 8: Measurement
Tuesday January 26, 2010
Agenda
 Openers: Measurement Referents, One Minute Challenge, Useful Units and Fun
Facts
 How much is a million? (video based on book by David Schwartz)
 The Megapenny Project
 How big is a foot? (a book by Rolf Meyer) and some shoe size
history
 Making a Simple Protractor
 The Aboriginal method for measuring the height of a tree
 How big is a cubic metre?
Referents
Other Everyday Referents
Useful Units
 How long would it take to count, out loud, by ones to 1
million? 1 billion?
 How many grains on sand in 1 cup? 1 bathtub? 1
classroom?
 Do you know anyone 1 billion seconds old? Who? Why
don’t we measure age in seconds?
 What kind of vehicles would you need to transport 1
billion pennies?
 The Megapenny Project
 How much is a million? by David Schwartz
The MegaPenny Project
Understanding the size of
numbers using pennies
One Penny
Most people in North America have seen them
and you probably have one in your pocket right now.
Using this small metal disk, with a size and weight familiar
to almost everyone.
value
1¢, (one cent)
width
0.75 inches, (3/4 of an inch)
height
0.75 inches, (3/4 of an inch)
thickness
0.0625 inches, (1/16 of an inch)
weight
0.1 ounces, (1/10 of an ounce)
area
0.5625 square inches
Ten Pennies
Place one penny on
each of your ten
fingers.
When we multiply our one penny by a factor of ten, we
get ten pennies.
value
10¢, (ten cents)
width (side-by-side)
7.5 inches
height (stacked)
5/8 of an inch
thickness
0.0625 inches, (1/16 of an inch)
weight
1.0 ounce
area (laid flat)
5.625 square inches
Sixteen Pennies
Lay sixteen pennies in a line and you have one foot.
Stack them and you have an inch.
value
16¢, (sixteen cents)
width (side-by-side)
12 inches, (one foot)
height (stacked)
1 inch
thickness
0.0625 inches, (1/16 of an inch)
weight
1.6 ounces
area (laid flat)
9 square inches
One Thousand Pennies
One thousand pennies in your pocket
would be the same as having 20 rolls of
pennies in your pocket from a bank.
5 pennies wide x
5 pennies high x
40 pennies tall
value
$10.00,
(Ten dollars and no cents)
width
3.75 inches
height
3.75 inches
thickness
2.5 inches
weight
100 ounces, (6.25 pounds)
height
stacked
62.4 inches, (5.2 feet)
area
(laid flat)
562.5 square inches
(3.9 square feet)
One Hundred Thousand Pennies
Doubling our 50,000 pennies to 100,000, we now
have two one-foot cubes.
Given, this wasn't a big jump, but now we're going
to start climbing the numerical ladder by powers of
ten.
Ninety-eight
thousand three
hundred and four
Pennies
[ Two cubic feet ]
$98,304
value
$983.04
(Nine hundred eightythree dollars and four
cents)
width
24 inches, (two feet)
height
12 inches, (one foot)
thickness
12 inches, (one foot)
weight
614.4 pounds
height stacked
512 feet
area (laid flat)
384 square feet
Fifty Thousand Pennies
Remember the stack of 16 pennies? It was one inch tall.
Well, take 12 of those and stack them and you'll have onefoot-tall stack. The cube above is made up of 256 of those
one-foot stacks, making one cubic foot of pennies.
Remember this cube, since it will be the building block for all
upcoming penny-structures you see.
[16w x 16h x 192 tall]
one cubic foot
Forty-nine thousand one
hundred and fifty-two
Pennies
$49,152
value
$491.52
(Four hundred ninety-one
dollars and fifty-two cents)
width
12 inches, (one foot)
height
12 inches, (one foot)
thickness
12 inches, (one foot)
weight
4,915.2 ounces, (307.2
pounds)
height
stacked
3,072 inches, (256 feet)
area
(laid flat)
192 square feet
SCALE REFERENCE
5 Feet , 10 inches
G-Money
One Million Pennies
Say hello to our friend G-Money. Now that the
pennies have really begun to pile up, he'll be
standing in for scale. G-Money is about 5 feet,
10 inches tall, and he weighs about 180 pounds,
or about 35 times less than the 1 million pennies
stacked beside him.
value
width
One million, three
thousand, seven hundred
and seventy-six Pennies
[ A wall five feet by four
feet by one feet thick with a
9-inch cube stepstool
$1,003,77
$10,037.76
(Ten thousand, thirty-seven
dollars and seventy-six
cents)
]
Four feet
height
Five feet
thickness
12 inches, (one foot)
weight
6273.6 pounds (3.14 tons)
height stacked
5,228 feet ( 0.99 Miles )
area (laid flat)
3,921 square feet
Ten Million Pennies
Ten Million cents. If you laid these all out
flat, side-by-side, like a huge carpet of
pennies, it would nearly cover one acre.
value
$100,170.24
(One hundred thousand, one
hundred seventy dollars and
twenty-four cents)
width
Six feet
height
Six feet
thickness Six feet
Ten million, seventeen
thousand and twentyfour Pennies
[ A cube 6 x 6 x 6 feet ]
$10,017,024
weight
31.3 tons
height
stacked
9.88 Miles
area
(laid flat)
39,129 square feet (0.9 acres)
SCALE REFERENCE
Blue Whale
largest living animal, the Blue Whale, weighs less than 150 tons as an adult
— longest ever recorded was a 108 ft female —
modern blue whales in the Southern Hemisphere reach lengths of 90-100
feet
Northern Hemisphere counterparts are smaller, on average 75 to 80 feet
(23 to 24.5 m)
One Hundred Million Pennies
Since these cubes are mostly dense
metal, their weight is impressive. One
hundred million pennies weighs over
300 tons. For comparison, the largest
living animal, the Blue Whale, weighs
less than 150 tons as an adult.
One hundred million,
sixteen thousand, six
hundred and forty Pennies
[ Two cubes, one 12x12x12
feet, the other 7x7x7 feet ]
$ 100,016,640
value
$1,000,166.40 (One million,
one hundred sixty-six
dollars and forty cents)
width
12 feet (7 feet)
height
12 feet (7 feet)
thickness
12 feet (7 feet)
total weight
312.5 tons
height
stacked
99 Miles
area (laid flat)
390,690 square feet
(9 acres)
SCALE REFERENCE
9 Feet Wide X 11 Feet High X 41 Feet Long
One Billion Pennies
value
One billion, eighteen
thousand, one hundred
and seventy-six Pennies
[ Five school buses. ]
$1,000,018,176
If you were to stack all these
pennies in a single pile, one atop
the other, the stack would reach
nearly one thousand miles high.
For comparison, note that the
Space Shuttle typically orbits
only 225 miles above the Earth's
surface.
$10,000,181.76
(Ten million, one hundred
eighty-one dollars and
seventy-six cents)
width
45 feet
height
11 feet
thickness
41 feet
total weight
3,125 tons
height
stacked
987 Miles
area (laid flat)
3,906,321 square feet
(89.7 acres)
SCALE REFERENCE
Ten Billion Pennies
value
Value
width
width
Ten billion, twenty-three
thousand, five hundred
and fifty-two Pennies
[ Fifty school buses. ]
$10,000,023,552
Current estimates place the world's
population at six billion people. The
pile of pennies above would then be
nearly enough for two pennies for
every person on Earth. The U.S.Mint
currently manufactures about this
many pennies every year. Also, note
G-Money standing in the front.
$100,000,235.52
(One hundred million, two
hundred thirty-five dollars
and fifty-two cents)
90 feet
height 11 feet
thickness
205 feet
total weight
31,250 tons
height
stacked
9,864 Miles
area
(laid flat)
897 acres
One Hundred Billion Pennies
If you took these hundred billion pennies and
laid them out like a carpet, you could cover
14 square miles. The cube you see is made
up of over 4.1 million stacks of 24,330
pennies.
value
One hundred billion,
seventeen million, six
hundred fifty-nine thousand
three hundred and thirty-six
Pennies
[ One cube measuring 127 x
127 x 127 feet ]
$100,017,659,336
$1,000,176,593.36
(One billion, one hundred
seventy-six thousand five
hundred and ninety-three
dollars and thirty-six cents)
width
126.72 feet
height
126.72 feet
thickness
126.72 feet
total weight
312,555.2 tons
height
stacked
98,660 Miles
area
(laid flat)
8,969 acres
Two Hundred Billion Pennies
Since the first penny was minted in
1787, until present-day, over 300
billion pennies have been minted in
the United States.
value
Two hundred billion,
thirty-five million, three
hundred eighteen
thousand
six hundred and
seventy-two Pennies
[ Two cubes, each
measuring 127 x 127 x
127 feet ]
$200,035,318,672
$2,000,353,186.72 (Two
billion, three hundred fiftythree thousand one hundred
and eighty-six dollars and
seventy-two cents)
width
height
253.44 feet
thickness
126.72 feet
total
weight
625,110.4 tons
height
stacked
197,320 Miles
area
(laid flat)
17,938 acres
126.72 feet
One Trillion Pennies
value
$10,000,000,166.
40 (Ten billion,
one hundred and
sixty-six dollars
and forty cents)
width
273 feet
height
273 feet
thickness 273 feet
One trillion, sixteen
thousand six hundred and
forty Pennies
[ One cube measuring 273
x 273 x 273 feet ]
$1,000,000,016,640
The same football
field as the last two
pages, set beside our
new cube for scale.
Notice our friend GMoney, still barely
visible as a speck at
lower left.
total
weight
3,125,000 tons
height
stacked
986,426 Miles
area
(laid flat)
89,675.2 acres
SCALE REFERENCE
One Trillion Pennies (part II)
From right to left (to scale), we have the same old football field, then
the Lincoln Memorial (yes, the one pictured on the back of the penny),
then the Washington Monument (555 feet tall), then our cube of one
trillion pennies, then the Empire State Building (1,250 feet tall), then
the Sears Tower (1,450 feet tall).
value
$10,000,000,166.40
(Ten billion, one hundred and
sixty-six dollars and forty cents)
width
273 feet
height
273 feet
thickness 273 feet
One trillion, sixteen
thousand six hundred
and forty Pennies
[ One cube measuring
273 x 273 x 273 feet ]
$1,000,000,016,640
total
weight
3,125,000 tons
height
stacked
986,426 Miles
area
(laid flat)
89,675.2 acres
The Empire State Building
1.8 Trillion Pennies
New York's Empire State Building contains 37 million cubic
feet of space (minus the antenna structure). Using our cubic
foot of pennies (49,152 total), it's just a simple multiplication
problem - 37,000,000 x 49,152 = 1,818,624,000,000 pennies.
One trillion, eight hundred
eighteen billion, six
hundred
twenty-four million Pennies
$1,818,624,000,000
value
$18,186,240,000.00
(Eighteen billion, one
hundred
eighty-six million, two
hundred forty
thousand dollars and zero
cents)
total weight
5,683,200 tons
height stacked
1,793,939 Miles
area
(laid flat)
163,085 acres
The Sears Tower
2.6 Trillion Pennies
Chicago's Sears Tower occupies 53.4 million cubic feet of
space. Using our cubic foot of pennies (49,152 total), it's
once again just another multiplication problem 53,379,000 x 49,152 = 2,623,684,608,000 pennies.
value
Two trillion, six hundred twentythree billion, six hundred eightyfour million six hundred and
eight thousand Pennies
$2,623,684,608,000
$26,236,846,080.00
(Twenty-six billion, two
hundred thirty-six
million, eight hundred
forty-six thousand and
eighty dollars)
total weight
8,199,014 tons
height
stacked
2,588,073 Miles
area (laid flat)
235,279.3 acres
One Quadrillion Pennies
Here we have the buildings we used for scale back at a trillion, but they're now a bit
dwarfed by our new cube of pennies. This is a quadrillion, or a thousand times one trillion.
This cube is roughly a half-mile wide and would weigh an astonishing three billion tons.
value
$10,000,670,883,840.00
(Ten trillion, six hundred
seventy million, eight
hundred eighty-three
thousand, eight hundred and
forty dollars and zero cents)
width
2,730 feet
height
2,730 feet
thickness 2,730 feet
One quadrillion, sixty-seven
billion, eighty-eight million,
three hundred and eightyfour thousand Pennies [ One
cube measuring 2,730 x
2,730 x 2,730 feet ]
$1,000,067,088,384,000
total
weight
3,125,000,000 tons
height
stacked
986,426,768 Miles
area
(laid flat)
89,675,161 acres
One Quintillion Pennies
$10,000,670,883,840,000.00
(Ten quadrillion, six
hundred seventy billion,
value
eight hundred eighty-three
million, eight hundred and
forty thousand dollars and
zero cents)
Here we have the buildings we used for scale back at a trillion,
but they're now a bit
dwarfed by our new cube of pennies. This is
a quadrillion,27,300
or a thousand
width
feet times one trillion.
This cube is roughly a half-mile wide and would weigh an astonishing three billion tons.
One quintillion, sixty-seven
trillion, eighty-eight billion,
three hundred and eightyfour million Pennies
[ One cube measuring 27,300
x 27,300 x 27,300 feet ]
$1,000,067,088,384,000,000
height
27,300 feet
thickness
27,300 feet
total
weight
3,125,000,000,000 tons
height
stacked
986,426,767,677 Miles
area
(laid flat)
89,675,160,698 acres
One Quintillion Pennies
Now we've stepped up another factor
of 1,000. One quintillion pennies.
This many pennies, if laid out flat like
a carpet, would cover the surface of
the earth - twice. If you look hard,
you can still see the Sears Tower
and other buildings at lower right.
Another way to see it is to realize
that
Everest
ft.) isaonly
Here we have the buildings we used for scale back
at Mt.
a trillion,
but(29,000
they're now
bit
1,700 feet
than this
27,300-foot
dwarfed by our new cube of pennies. This is a quadrillion,
ortaller
a thousand
times
one trillion.
cube.
This cube is roughly a half-mile wide and would weigh an astonishing three billion tons.
Three trillion tons of pennies is quite
enough. To imagine larger cubes,
(stepping by factors of 1,000), just
imagine cubes roughly ten times
larger than the last one. For
instance, one quintillion pennies
makes the cube above - about 5
miles on each side. If you step up to
one sextillion, imagine a cube about
50 miles wide tall and thick
Table of Very Big Numbers (from 1 to 10120)
one
1
ten
10
hundred
thousand
100
1,000
million
1,000,000
billion
1,000,000,000
trillion
1,000,000,000,000
quadrillion
quintillion
1,000,000,000,000,000
1,000,000,000,000,000,000
sextillion
1,000,000,000,000,000,000,000
septillion
1,000,000,000,000,000,000,000,000
octillion
1,000,000,000,000,000,000,000,000,000
nonillion
1,000,000,000,000,000,000,000,000,000,000
decillion
1,000,000,000,000,000,000,000,000,000,000,000
undecillion
1,000,000,000,000,000,000,000,000,000,000,000,000
duodecillion
tredecillion
quattuordecillion
quindecillion
sexdecillion
septendecillion
octodecillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
novemdecillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
vigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
,000
unvigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
,000,000
duovigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
,000,000,000
trevigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
,000,000,000,000
quattuorvigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
,000,000,000,000,000
quinvigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
,000,000,000,000,000,000
sexvigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
septenvigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000
octovigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000
novemvigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
trigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00
0
untrigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00
0,000
duotrigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00
0,000,000
googol (google)
10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,0
00,000,000
tretrigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,0
00,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000
quattuortrigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,0
00,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000
quintrigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,0
00,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000
sextrigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,0
00,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000
septentrigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,0
00,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000
octotrigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,0
00,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000
novemtrigintillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,0
00,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000
One Penny
You Have to Start Somewhere
Shoe Size History
Shoe Size History
Coffee Filter Protractor
•Cut a coffee filter in half.
•Fold the filter in half. Mark the fold with a marker and the angle
measure.
•Fold in half again. Mark and indicate the angle measure.
•Your coffee filter has creases? What is the angle measure of
each crease?
•How could you use this in class?
How to Measure the Height of a
Tree Video – 5min.com
How big is a cubic metre?
•Building a cubic metre in the classroom…
•Why? Alternatives? Questions?