Transcript Lesson Plan 1: Metric System

UNDERSTANDING
AND USING THE
METRIC SYSTEM
I. ADVANTAGES OF THE METRIC SYSTEM
FOR SCIENCE
A.
INTERNATIONAL
STANDARDS
B.
EASE
OF
II. UNITS OF MEASUREMENT
RECORDING
C. B.
EASE
OF
A.
DEFINED
UNITS
DERIVED
III.CALCULATIONS
THE IMPORTANCE OF PREFIXES
NANO- TO OF
PICO-THE
THE COMMONLY
USEDAND
PREFIXES
IV.A.UNITS
IMAGES
VERY LARGE
B. CONVERTING
UNITS BY MOVING THE DECIMAL
VERY
SMALL
A. Extreme images
B. THE POWERS OF
TEN
I. ADVANTAGES OF
THE METRIC SYSTEM
FOR SCIENTIFIC
MEASUREMENT
A. INTERNATIONAL STANDARDS
B. EASE OF RECORDING
C. EASE OF CALCULATIONS
I. ADVANTAGES OF THE METRIC SYSTEM FOR
SCIENTIFIC MEASUREMENT
A. INTERNATIONAL STANDARDS…
* All metric system units are based on
very specific definitions which are
Volume =1.0 liter
internationally known standards and are
precisely
reproducable…
*
THAT IS, MEASUREMENTS ARE THE
SAME
ALL =1.0
OVER
THE
Length
meter
Mass = 1.0
WORLD…REGARDLESS OF COUNTRY,
kilogram
LANGUAGE, OR DISCIPLINE…
*
*
I. ADVANTAGES OF THE METRIC SYSTEM FOR
SCIENTIFIC MEASUREMENT
B. EASE OF RECORDING MEASUREMENTS… *
•All metric system units are based on
TENS, that is subdivisions of the main
units are based on ‘tenths’, ‘hundreths’,
thousandths’, etc.
.1 unit
One whole unit
(subdivisions can be subdivided
again for more precision…but
again by tenths…)
.1 unit
.01 unit
.001 unit
This means that very precise
measurements can be recorded as
“DECIMAL VALUES” !!
.1 unit
.01 unit
.001 unit
EXAMPLES: 2.351
5.45
.802
5.613meters
9.023
centimeters
liters
grams
meters
This is a huge advantage over the
older “fraction” based systems…
Recording measurements is too
complex, prone to errors…
1/12 unit
1/16 unit 1/2 unit
Examples:
2 miles,
gallons,
pounds,
235 yards,
18 quart,
9/32
27feet,
ounce
5¾
7inch
inches
ounces
524 yards,
2 feet,
1/16
I. ADVANTAGES OF THE METRIC SYSTEM FOR
SCIENTIFIC MEASUREMENT
C. EASE OF PERFORMING MATH FUNCTIONS…
*
•Since almost all measurements done by
scientists are intended to be used in math
formulas…
•It is important that measurements be
recorded carefully, and with as much
precision as possible….
•With numbers that are easily
manipulated, and/or entered into
calculators…
I. ADVANTAGES OF THE METRIC SYSTEM FOR
SCIENTIFIC MEASUREMENT
C. EASE OF PERFORMING MATH FUNCTIONS…
*
Examples:
1.62 kg
(5.4 cm) (8.65 cm) (362 cm)
Is far easier to do than…
(1 lb., 9 ½ oz.)
(11 ¾ in)(1 ft.4 11/16 in)(1 yd.1ft 1½ in)
II.UNITS OF MEASUREMENT
A. DEFINED UNITS
B. DERIVED UNITS
II.UNITS OF MEASUREMENT
A. DEFINED UNITS
THE “BASE” UNITS:
#1:
SOME QUANTITIES HAVE TO BE
THEunit
STARTING
POINTS…
The
of LENGTH:
the METER–
originally
defined
as
ONE
TENTHAT IS, SOME BASIC UNITS
MILLIONTH
the
distance
from
HAVE TO BE DEFINED…
NORTH POLE TO EQUATOR
II.UNITS OF MEASUREMENT
A. DEFINED UNITS
THE “BASE” UNITS:
#2
The unit of VOLUME: the LITER…
defined as the space occupied by a cube
measuring .1m x .1m x .1m (1 cubic
decimeter—1.0 dm3)
1 liter = 1dm3
1 DECIMETER
II.UNITS OF MEASUREMENT
A. DEFINED UNITS
THE “BASE” UNITS:
#2
(since
the cube
dm
x 1dm
x 1dm, its
(and since
1 dmis=110
cm,
its volume
3 )
volume
=
1
dm
( 10 cm x 10 cm x 10 cm) also
= 1000 cm3 )
3
1dm
1 liter =
3
also = 1000 cm
10 centimeters
II.UNITS OF MEASUREMENT
A. DEFINED UNITS
THE “BASE” UNITS:
#2
Using the
Since
‘prefixes’,
cube’s volume
1/1000thisof
1000
a liter
cm=3 , 1
1/1000th of
millilter;
then
its 1volume
cm3 = =
1 ml
1 cm3
1 milliliter =
1 cm3
II.UNITS OF MEASUREMENT
A. DEFINED UNITS
THE “BASE” UNITS:
#3
1.0 kilogram =
The unit of MASS: the KILOGRAM…
ofof1pure
literLwater
Since
.001
=
defined as the mass of 1.0mass
liter
3, then
1
cm
of H2O
at 4.0oC…
3
1 cm of water =
.001 kg = 1.0 gr
II.UNITS OF MEASUREMENT
b. DERIVED UNITS
UNITS THAT ARE FOUND AS THE RESULT OF
CALCULATIONS…
1. The unit of DENSITY: the MASS PER
VOLUME…that is, what is the mass of
1.0 cm3 (or 1.0 dm3)of a substance?
To calculate DENSITY: divide the MASS
by the VOLUME…
If, for example, an object has a mass of 15
grams and occupies a volume of 5.0 cm3,
Mass = 15
grams
Volume =
5.0 cm3
Divide the mass by the volume…
Density =
m = 15 g
15 grams
5.0 cm3
= 3.0
Grams/cm3
Divide numbers
Divide
to
to get ½units
of the
get the
other ½
answer
of the answer
V = 5.0 cm3
Divide the mass by the volume…
Density =
15 grams
5.0 cm3
= 3.0
Grams/cm3
The ‘division’
This new, more
slash iscomplex
read as unit is
“per”…
called a ‘derived’
unit…
= “x”
When two values are multiplied, •their
units multiply also…
symbol for
multiplcation
(5.0 kilograms) (7.0 meters)
= 35
Kgm
Numeric value
The ‘derived’ unit is read as
“kilogram meter” or “kilogram
dot meter”
If two numbers which have the same units are to be
multiplied…
For example,
(5.0 seconds) (3.0 seconds)
= 15
Sec2
‘derived’ unit is read as
NumericThe
value
“seconds squared”…
Some more complex calculations may require both mul. and
div…
For example,
(8.0 kg) (6.0 meters)
(2.0 sec) (2.0 sec)
= 12
kgm
Sec2
Numeric value
The ‘derived’ unit
is read as
“kilogram meter
per second
squared”…
Some more complex calculations may require both mul. and
div…
(8.0 kg) (6.0 meters)
(2.0 sec) (2.0 sec)
= 12
kgm
Sec2
= 12 Newtons
When
This
unittheis
‘derived’
defined unit
as a is
“NEWTON”…
a
complex,
it may
be assigned
unit
of force.a
‘nickname’…
III. THE IMPORTANCE OF
PREFIXES
•A. FROM NANO TO PICO
•B. MOVING THE DECIMAL
III. THE IMPORTANCE OF PREFIXES
•A. FROM NANO TO PICO
THE PREFIXES USED ARE COMMON
TO ALL TYPES OF MEASUREMENT:
EXAMPLES:
milligram
millimeter
milliliter
milliamp
millisecond
kilogram
kilometer
kiloliter
kilojoule
microgram
micrometer
microliter
microvolt
III. THE IMPORTANCE OF PREFIXES
•A. FROM NANO TO PICOThis prefix
This that
prefix
A prefix
makes
changes
the
The
base
of
any
This
prefix
changes
the
a
unit
10x
larger
Important prefixes
to
know:
This
prefix
base
into
aunit
unit
defined
or
This
prefix
changes
the
base
base
into
a
than
the
base
This
This
prefix
prefix
This
prefix
changes
the
1000x
larger
derived
unit
changes
the
into
a
100x larger
changes
changes
the
the
changes
the
base
into
unit
base
into
a aunit
1,000,000,000x
base
base
into
into
a
a
unit
unit
base
into
a
unit
1,000,000x
1/100
as
large
larger
1/1000
1/10
as
as
large
large
as
1/1,000,000
as
1/1,000,000,000
larger
as the
base
as
the
base
large
as largeasasthe
the
base
base
Let
this
entire
box
Understanding prefixes…
represent 1.0 liter…
1/10th (.1) of the box
could be called a
‘deciliter
How
many of these
To get those values,
would be in 1 liter?
Didyou
youjust
do ain
mental
5 liter?short-cut
did
multiply
and10?
just tackDid
on you
a zero?
That
answer
10 ?
by
is, just slide Then
the decimal
50? over
and fill in with zero?
Understanding prefixes…
If
theismeasured
That
the secretvalue
of gets
too
big (or too
small),
converting
to more
change
to aunits
morewithin the
convienent
convienent
unit by moving
metric system!!
the decimal to the left or to
the right, then fill in
zeros… that’s really all
there is to conversion!!
Understanding prefixes…
Simply move the decimal 3
If this
little
What
places
did
to
the
you
right
dorepresents
toand
get in
fillthe
how
many
ofbox
these
are
th of the liter, what
1/1000
that
in with
answer?
zero’s
1000?
(make a
1.0
liter?
milliliter??
could it be
called?
number
1000x
bigger…)
1.0 0 0 = 1000 ml
To
change to
a larger
smaller
unit,
unit
move the
decimal to
the
rightleft
to the
and fill in
the zero’s
SAMPLE PROBLEM:
AN ANSWER TO A CALCULATION GAVE
A VALUE OF “54,500 METERS”
ALTHOUGH
‘CORRECT’,
THE
VALUE
METERS
are 1000xcan
smaller
than
“54,500
METERS”
be
IS LARGE AND CUMBERSOME; IT
KILOMETERS…
therefore
the
shortened
by changing
unit
CAN
BE SHORTENED
ANDthe
REDUCED
th
converted
value
will
be
1/1000
TO
A SMALLER
BY A SIMPLE
from
‘meters’ VALUE
to ‘kilometers’
CONVERSION…
the original! That is, move the
decimal 3 places to the left!!!
54,500 METERS
= 54.5 KILOMETERS
KILOMETER
METER
REMEMBER…
To change to a
larger unit move
the decimal to the
left and fill in the
zero’s
SAMPLE PROBLEM:
A physics student has this value for the current
in a circuit:
14.3 amps
However, the formula in which she has to use the
value calls for the current in MILLIAMPS…
A quick conversion by moving the decimal point is
easy:
To change to a
smaller unit,
move the decimal to
the right and fill in the
zero’s
SAMPLE PROBLEM:
14.3 amps
Converts to:
14.3
, 0 0 . milliamps
IV. IMAGES THE VERY LARGE
AND VERY SMALL-POWERS OF 10
A. THE COSMOS—
astronomical images
B. SUB-MICROSCOPIC-- atm
imageS
C. WEB SITES-POWERS OF 10
A. THE COSMOS—
images
astronomical
B. SUB-MICROSCOPIC-atm imageS
Approx. 1 micrometer
(.000 001m)
Image formed by an ‘ATOMIC FORCE
MICROSCOPE’…
Approx. 1.5 m
Trenches etched onto a
silicon wafer by exposure to
an electron beam…
Lesson Plan 1:
Metric System
Powers of ten animation:
http://www.wordwizz.com/pwrsof10.htm
http://micro.magnet.fsu.edu/primer/java/scienc
eopticsu/powersof10/