This video (3:29) explains some of the ways in which nanotechnology is at the cutting edge of science and technology.

The main thing to note here is that the ratio of surface area to volume is not fixed as shown in the figure below.

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 area compared to its volume.

The following graph shows the surface area (A) against volume (V) of the five Platonic solids and a sphere. Note the following:

The following video (2:26) contains two examples of how nanotechnology is being used in the field of medical research to fight cancer.

The logical behind the metric system

The metric system is logical because it is uses the same base 10 system which we use with our number. In addition to this there are some important things to know about the properties of water and how these how been used to calibrate the Celsius scale for temperature. Water freezes at 0 degrees Celsius and boils at 100 degrees.

The temperature inside a refrigerator is generally set around 4 degrees Celsius.
Human bodies are generally around 37 degrees Celsius.

The metric system also uses water as the basis for quantifying volume and mass. This is not coincidental but by design.

Types of 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?

https://en.wikipedia.org/wiki/Mohs_scale_of_mineral_hardness

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).

https://commons.wikimedia.org/wiki/File:2713_pH_Scale-01.jpg

Review the information provided in the article at https://www.abc.net.au/news/2015-11-19/tropical-cyclone-categories-explained/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.

Combinations and permutations

In mathematics, when the order doesn't matter it is a combination. When the order does matter it is a permutation. A permutation is an ordered combination.This means that what are commonly called combination locks are really permutation locks.

Exponents

Exponents are not part of the curriculum in primary school but they can be discussed and informally introduced in various ways.

How many permutations are there with a six-character number plate?

(Answer is at the bottom of this page)

The inverse square law

The inverse square law describes how the intensity of a physical quantity radiating from a point source decreases with distance. The intensity is inversely proportional to the square of the distance from the source. This principle applies to various physical phenomena including light, sound, gravity and radiation. The following image shows how the intensity at double the distance is 1/4 of its original value and 1/9 when the distance is three times further.

(Image source Borb, CC BY-SA 3.0, Link)

Static electricity

This video (2:08) includes a vivid example of how water molecules are polarised.

How might the inverse square law affect the static electricity and water experiment?

The International system of units

The International System of Units (abbreviated as SI) is based on the metric system and is the world's most widely used system of measurement. It is the only system of measurement with official status in nearly every country in the world. The seven SI base units are:

Symbol	Name	Quantity
s	second	time
m	metre	length
kg	kilogram	mass
A	ampere	electric current
K	kelvin	thermodynamic temperature
mol	mole	amount of substance
cd	candela	luminous intensity

The following image is way beyond what primary school students are expected to know but it is a really good visualisation of how the SI units are related to one another.It is an arrangement of the principal measurements in physics based on the mathematical manipulation of length, time and mass.

(Image source https://en.wikipedia.org/wiki/International_System_of_Units#/media/File:Physics_measurements_SI_units.png)

Moderated self-assessment

Discussions with students around the key components of conceptual topics and how they fit together can generate insights into student achievement.

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

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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.


SILO 6.1 (DRAFT) Year 6, Term 1: Nanotechnology Focus: Ratios Scope and sequence: Calibration, Exponents, Ratios, Scales
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 near-atomic 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." (MA3-3DS-02)	"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)

SILO 6.1 (DRAFT)

Year 6, Term 1: Nanotechnology

Focus: Ratios Scope and sequence: Calibration, Exponents, Ratios, Scales

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

Introduction to nanotechnology

Exploring the ratio of surface area to volume