Geometry and Measurement: Measurement, Level 6
AO1: Measure at a level of precision appropriate to the task.
This means students will be able to identify and use a unit of measurement the meets the requirements of a given task, for example, the length of a fence paling in millimetres. This involves understanding of the accuracy required in a given context including appreciation of the practical consequences of both less accuracy and greater precision. This includes the effect of using different measures of length on the accuracy of the resulting area and volume measures. Students need to understand the necessary compromise at times between accuracy and adequacy, that is, something could be measured more precisely but there is greater effort required and no gain to meeting the demands of the task. This objective also includes making sensible estimates where appropriate, for example, estimating the number of rolls of wallpaper or litres of paint needed for a given space.
AO2: Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures.
This means students will know the commonly used units including the role of prefixes as conversion factors of base units, e.g. kilo meaning one thousand, micro meaning one millionth. Below is a list of units for key attributes that should be expected.
Attribute | Units |
Length | metre (m), micrometre ( m), millimetre (mm), centimetre (cm), kilometre (km) |
Area | square metre (m2), square millimetre (mm2),square centimetre (cm2), hectare (ha), square kilometre (km2) |
Volume | cubic metre (m3), cubic centimetre (cm3), cubic decimetre (litre),cubic kilometre (km3) |
Capacity | litre (L), millilitre (mL), decilitre (dL) |
Mass | gram (g), microgram (μ g), milligram (mg), kilogram (kg), tonne (t) |
Time | second (s), microsecond (μs), millisecond (ms), minute, hour, day, etc | Temperature | degree Celsius (° C). |
Angle | degree (° ). |
Students are also expected to know derived measures that describe rates involving the units above and other common units. Attributes and the derived units used to measure them include speed (kilometres per hour km/h, metres per second m/s), fuel and energy consumption (litres per 100 kilometres L/100km, joules or calories per minute ), unit price (cents or dollars per gram), and density (kilograms per cubic metre kg/m3 , grams per cubic centimetre g/cm3). More complicated derived measures such as those for pressure, force, and power are not expected at Level Six.
Students should be able to connect the units for volume (capacity) and mass, e.g. Find the mass of 345mL of water, and convert between the simple derived units above, e.g. 140 km/h = 
m/s.
AO3: Calculate volumes, including prisms, pyramids, cones, and spheres, using formulae.
This means students will connect the formulae for the volume of prisms, including cylinders, as area of the cross-section or base multiplied by the third dimension, e.g. for a rectangular based prism v = l x w x h (l x w is the area of the cross section). This involves recognising how to apply the formula for prisms given any orientation of the solid that is presented. Similarly students should connect the formulae for the volume of pyramids, including cones, as the area of the base multiplied by one third of the height, e.g. for a cone v = πr2h (πr2 is the area of the base). Students should know and apply the formula for volume of a sphere as v = 4/3 πr3. At Level Six students are expected to work with decimal measures as well as whole number measures.
