Section 4 (Four Credits)
Sizing Things Up – Measurement
Measurement is the most expensive of all
mathematics.
Mistakes are made with measurement in the building industry which
require more
time and more material to repair or fix. There is a fundamental
truth in
measurement as well! “Measure twice, cut once.”
The history of measurement is a fascinating
study. As
civilisations became more agricultural, more technical and more
trade based so
the need to quantify length, weight, capacity and time became more and more
essential. The
History
of the Metric System.
Time – Unit is 1 second
It became pretty obvious from very early times
that time
cycled and involved the Sun, the Moon and the Stars. The four
seasons became a
year. Human culture and religions embraced the seasons and remain
so today. The
Harvest
Festival for example happens around the end of summer and
autumn every
year, or harvest time.
A solar year is the
time it takes
the Earth to complete its orbit around the Sun — about one year.
But the actual
time it takes for the Earth to travel around the Sun is in fact
a little longer
than that—about 365 ¼ days (365 days, 5 hours, 48 minutes, and
46 seconds, to
be precise).
Time becomes a study all on its own. How to
measure small
time intervals was a problem solved first by Galileo in the 1600’s
and is now
measured with incredible accuracy using atomic vibrations. The Global
Positioning
System in use today measures time to 14 nanoseconds or 14
billionths of a second.
Length – Unit is 1 metre
Original measures of length include an inch, a
fathom, a
cubit and a chain. unfamiliar names now but they all made sense at
the time of
use.
Mass – Unit is 1 kilogram
The term mass is correct rather than the common
term called
weight. The value of gravity on Earth is the connection between
Weight and mass
where w = mg. Mass is the amount of matter in something. Like
length there were
some strange units in early days.
Capacity – 1 litre
This is the term for liquid measure and is
distinct from
volume.
There are also units for temperature, charge,
light, sound,
radiation, magnetism.
Task 1
Find twenty unusual measures not in common
and everyday
use.
Derived Measures
These compare two measures and there are many
in common
usage.
When travelling on the road speed is measured
as a rate and
expressed in kph or kilometres per hour. In one hour this is how
far the car
travels. The speed limit on most NZ roads is 100km/hr. Notice the
different way
of writing the unit for speed.
Task 2
Name three other derived units in common
use.
Measurements needs Axiom 1 and Axiom 2.
Axiom 1 is “One can be anything I choose one to
be”.
Axiom 2 is “When combining or comparing in
mathematics we do
so using the same size units.”
The UNITS of measurement we choose are a direct
result of
Axiom 1.
Axiom 2 allows combining and comparing of these
units so
that we get sensible answers at all times.
Task 3
(a)
Add 1mm, 1cm and
1m
(b)
How much bigger or
smaller is 1 pound
compared to 1 kg?
(c)
How old are you in
seconds?
Converting between Units of Measure
These questions can be typed directly into most
search
engines such as Google.
It is useful to be able to convert common
units.
Task 4
(a)
Convert 680
seconds to minutes
(b)
Convert 12345m to
kilometres
(c)
Convert 1 day to
seconds
(d)
300 degrees
Fahrenheit is how many
degrees Celsius?
(e)
1 cup is how many
millilitres?
A more detailed explanation for conversions is
available on
the COVID
FILES #5 and #6.
Tools of Measurement
Common tools used for measuring units and
derived units.
Task 5
Complete the table
Measurement 
Tool 
Temperature 
Thermometer 
Length 


Scales 

Lux meter 

Odometer 
Speed 

Intelligence 


Tape Measure 
There is a job called a tool maker who
specialises in making
tools for measurement.
Accuracy and Precision
Quite quickly when measuring it becomes
apparent that one
person’s answer might not be what another person expects. This is
heavily
connected to number and rounding.
Task 6
Using a ruler or tape measure have someone
measure the
height of a door. Now repeat the process yourself. How close are
the measures?
Task 7
Measure the height of someone or yourself.
What
difficulties did you encounter?
Task 8
Throw three darts at the bull’s eye on a
dartboard. What
happened?
The darts are accurate if they are all near the
bull’s eye.
The darts are precise if they are close to each
other. They
do not have to be near the bull’s eye!
https://en.wikipedia.org/wiki/Accuracy_and_precision
Finally another Axiom that is almost never
talked about.
“If you require a more precise and accurate
measure then
purchase a more expensive tool”
There is no point in trying to measure the size
of an atom
with a 50m tape measure!
Electronic scales now weigh to the nearest gram
which is
usually unnecessary precision when cooking.
Error in Measurement
A general guide is the error is ±half of
the smallest
division. This could be an axiom.
Task 9
Here is a
measurement in
progress. Read the scales to find the mass of the person.
The smallest
division is 1kg
so the answer should be either 52 kg or 53kg and both are correct.
A standard 50kg
mass carefully
made to be as close to 50kg as possible could be used to calibrate
a set of
scales such as those shown in the picture.
It is doubtful
cheap bathroom
scales are very accurate at all! Spend a bit more money if
accuracy is
important!
Assessment
Section 4 (Four Credits)
Sizing Things Up – Measurement
1.
Find
the length of this line.
2.
Find
the weight of a typical grain of dried rice.
(a)
Describe your method or
strategy
(b) Complete
the
task.
3.
Use
the stopwatch feature on a cell phone.
(a)
Shut your eyes for ten
seconds. Repeat 10 times.
Did you improve?
(b) Shut
your
eyes for 1 minute. Repeat a few times. Did you improve?
4.
Locate
a water jog and a cup. Estimate how many cups of water there are
in the water
jug. Check your answer!
5.
Draw
a line 15cm long.
6.
Cut
a block of butter that weighs 150gm.
7.
Mix
hot and cold water to get a cup of water at 35C. Check with a
thermometer.
8.
What
is the density of milk?
(a)
Describe you strategy or
method.
(b) Complete
the
task.
9.
Find
the mass of 1 litre of water.
(a)
Describe you strategy or
method.
(b) Complete
the
task
10. The
cold
tap (15C) turned on full fills a bath in 30 minutes. The hot tap
(60C)
fills the empty bath in 1 hr. If both taps are turned on full…
(a)
How long does it take to
get half a bath of
water?
(b) What
temperature
is the bath water after filling?
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awarded the 3 credits a fee of $5 will be requested for this
section.
Well done, four sections over! On to Section 5!
Is the
course fun?