Year 6, Term 4: NanotechnologyFocus: RatiosScope and sequence: Calibration, Ordinal scales, Linear scales, Logarithmic scales, Nanotechnology 

Learning
intention: Students
convert between metric units of length, mass and capacity
and make relevant connections to the properties of water.


Overview: Nanotechnology
involves the manipulation of matter on a nearatomic scale which
might suggest that this is beyond what Year 6 students can
investigate, but certain principles such as the ratio between
surface area and volume are manageable and relevant for this age
group. These concepts are scaffolded by looking at the
metric system, calibration and various scales used in science,
namely; ordinal, linear and logarithmic.


NSW Syllabus

Australian Curriculum
(version 9.0)

"A student selects and uses the
appropriate unit to estimate, measure and calculate volumes and
capacities." (MA33DS02)

"Students learn to convert between
common metric units of length, mass and capacity; choose and use
decimal representations of metric measurements relevant to the
context of a problem." (AC9M6M01)

Introduction to the topic
A nanometre is one billionth of a metre (i.e., one millionth of a millimetre).
This video (3:29) explains some of the ways in which
nanotechnology is at the cutting edge of science and technology.
The logic behind the metric system
The properties of water
Water freezes at 0 degrees Celsius and boils at 100 degrees.
The metric system also uses water as the basis for quantifying volume and mass.
Introduction to exponents
How many combinations are there with sixcharacter numbers plates? 
(Answer is at the bottom of this page)
Exploring the ratio of surface area to volume
The main thing to note here is that the ratio of surface
area to volume is not fixed as shown in the figure below.
https://commons.wikimedia.org/wiki/File:Unit_cell_for_SA_to_V_ratio_with_tables.png
There are many examples of this principle in nature. For example:
The ratio of surface area to volume can also be seen in
everyday phenomena. For example, when building a fire it is common
to use small pieces of wood first which is know as kindling.
Because the kindling is small, it has a larger surface ares compared to
its volume.
The following video (2:26) from the Siteman Cancer Center
contains two examples of how nanotechnology is being used in the field
of medical research to fight cancer.
Introduction to scales
Ordinal scales
An ordinal scale has a non specified degree of variation. In other words, the scale is somewhat arbitrary. An example is the Mohs scale of mineral hardness introduced in 1822 by the German geologist and mineralogist Friedrich Mohs.
What do you
notice when you compare the 'Mohs hardness' numbers with the
'Absolute hardness' numbers? 
Is there a direct correlation? 
Linear scales
A linear scale has a specified degree of variation. In
other words, there is a direct mathematical correlation along the scale
due to the way that it has been calibrated. An example is the Celsius
scale.
Logarithmic scales
In a logarithmic scale, each interval is increased by a factor of the base of the logarithm, which is often a multiple of 10. Examples of common logarithmic scales are pH (to measure acidity), decibels (sound intensity), and the Richter scale (earthquakes).
Revision of scales
Review the information provided in this article (https://www.abc.net.au/news/20151119/tropicalcyclonecategoriesexplained/6956092).
Are cyclone
categories ordinal, linear or logarithmic? 
Calibration
Calibration is the process of configuring an instrument to improve the accuracy of measurements and readings.
The following video (1:39) uses calibration to improve the
accuracy of a digital compass.
The International system of units
(https://en.wikipedia.org/wiki/International_System_of_Units).

Answer to the exponents question about combinations with six character number plates: