Geometry and Measurement: Measurement
Level 1
AO1: Order and compare objects or events by length, area, volume and capacity, weight (mass), turn (angle), temperature, and time by direct comparison and/or counting whole numbers of units. This means students will classify or sort objects by their characteristics. These characteristics include shape, size, colour, texture, weight, and temperature. Students should be able to justify why they have sorted objects in the way they have and be encouraged to develop increasingly sophisticated classifications such as colour and size.
Click to download a PDF of second-tier material relating to Level 1 Measurement (115KB)
Level 2
AO1: Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time. This means students will recognise that the attributes length, area, volume and capacity, and weight can be measured. At Level Two students are expected to recognise that measurement units are countable and therefore able to be partitioned and recombined in the same way as other units of one, e.g. If a 8 unit length is cut from a 14 unit long strip the remainder will measure 6 units. Units of measure have other characteristics including being a part of the attribute they measure and uniformity (same size). When measuring the units need to fill a length, space, time etc, with no gaps or overlaps (this is known as tiling). Students should create measurement devices, e.g. rulers, rod towers, scales, to quantify the attributes of objects in numbers of units. In doing so they should develop an understanding that the marks on a linear scale show the endpoint of units and that scales always have a baseline (zero). Less tangible attributes such as turn (angle), temperature and time should also be measured. While the focus at Level Two is on students’ understanding the role of units in measurement it is also expected that students will encounter simple standard measures such as metres, centimetres, kilometres, minutes, seconds, kilograms, litres, etc, through using everyday measurement instruments.
AO2: Partition and/or combine like measures and communicate them, using numbers and units. This means students will perform and communicate calculations involving like measures. Like measures involve the same units for the same attribute. This allows the result of joining or separating units to be anticipated using additive number strategies, e.g. A box has a volume of 36 cubes. If a 3 by 4 cube layer is put in the empty box then there will be space for 36 – 12 = 24 more cubes. At Level Two students should be able to use numbers and common symbols to communicate measurement results, e.g. my lunchbox holds 60 cubes. I took 13 minutes to walk home. My pencil is 14 cm long. I weigh 26 kg.
Click to download a PDF of second-tier material relating to Level 2 Measurement (119KB)
Level 3
AO1: Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time. This means students will recognise that length, area, volume and capacity, weight, angle, and temperature are the characteristics (attributes) of objects people most commonly measure in everyday life. Time is a special attribute since it is not tangibly attached to physical objects. Measurement involves quantifying an attribute using units. Units of measure have characteristics including being a part of the attribute they measure and uniformity (same size). When measuring the units need to fill a length, space, time etc., with no gaps or overlaps (this is known as tiling). At Level Three, students should be familiar with common units in the metric system for the attributes listed. These units include, metres, centimetres, millimetres, and kilometres for length/distance, square and cubic centimetres, and metres for area and volume, kilograms and grams for weight, quarter and half turns for angles, degrees Celsius for temperature, and seconds, minutes, hours, days, etc for time. It is not expected that students will know the size relationships between measures though they should have opportunities to explore these relationships, e.g. 15cm = 150mm. Using measurement instruments involves reading linear scales (an analogue clock face is three connected linear scales). Students should understand that the marks on a linear scale show the endpoint of units and that scales always have a baseline (zero). Part of measurement is selecting the scale, with the precision of unit, suitable for a task. Level Three students should apply their additive and multiplicative number strategies to measurement problems that involve whole numbers of units, e.g. how many cubic centimetres will fit in this packet?
AO2: Find areas of rectangles and volumes of cuboids by applying multiplication. This means students will begin by measuring the areas of rectangles and other shapes using square units. This is because square units of the same size tessellate, that is join together with no laps or overlaps. That means that the measurement is consistent whereas the use of a non-tessellating unit would give variable results due to gaps and overlaps. Similarly, volume is measured in cubes of the same size. At Level Three students should apply whole number multiplication to make the process of counting squares or cubes more efficient..
|
|
|
4 x 6 = 24 square units |
3 x 4 x 6 = 72 cubic units |
Click to download a PDF of second-tier material relating to Level 3 Measurement (354KB)
Level 4
AO1: Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time. This means students will work with the commonly used units of the metric system and measurement devices for:
- Length- kilometre, metre, centimetre, millimetre, using rulers and tape measures
- Area- square kilometre, hectare, square metre, square centimetre
- Volume/Capacity- Cubic kilometre, cubic metre, litre (cubic decimetre), cubic centimetre using jugs, measurement cylinders
- Weight- tonne, kilogram, gram, using scales
- Temperature- degrees Celcius using thermometers
AO2: Convert between metric units, using whole numbers and commonly used decimals. This means students will apply their knowledge of decimal place value to convert between units for the same attribute, e.g. between units for weight. They should know the meaning of prefixes used in the metric system that act as “scalars” on base units, e.g. “kilo” means one thousand, “centi” means one hundredth. Conversions are restricted to whole number and simple decimal (tenth, hundredth, thousandth) scalars, e.g. 5kg = 5000g or 300ml = 0.3L, that act on whole number or decimal measures involving tenths, e.g. 0.6ha = 6000m2 or 675mm = 67.5cm.
AO3: Use side or edge lengths to fi nd the perimeters and areas of rectangles, parallelograms, and triangles and the volumes of cuboids. At Level Four students should apply their multiplicative strategies to find perimeters and areas of commonly used polygons and volumes of cuboids where the lengths of sides and edges are given as whole number measures. Calculations required are:.
|
|
|
|
Rectangle: Area = base x height |
Parallelogram: Area = base x height |
Triangle: Area = 1/2 (base x height) |
|
|
Cuboid: Volume = base x height x depth |
Students should express the areas and volumes using symbols, e.g. 48cm3 (48 cubic centimetres).
AO4: Interpret and use scales, timetables, and charts. This means students will be literate in getting required information from the following:
- Scales, such as thermometers, analogue (and digital) clocks, rulers, protractors, weight scales, capacity containers.
- Timetables, such as those used in transport (12 or 24-hour time), tides, broadcast programming, telephone books (international calls), sports events.
- Charts used to convey measurement information, such as weather reports, cooking recipes, Guiness Book of Records, statistics on living organisms.
Click to download a PDF of second-tier material relating to Level 4 Measurement (150KB)
Level 5
AO1: Select and use appropriate metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time, with awareness that measurements are approximate. Further detail on this Achievement Objective will be added shortly.
AO2: Convert between metric units, using decimals. Further detail on this Achievement Objective will be added shortly.
AO3: Deduce and use formulae to find the perimeters and areas of polygons and the volumes of prisms. Further detail on this Achievement Objective will be added shortly.
AO4: Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders. Further detail on this Achievement Objective will be added shortly.
Click to download a PDF of second-tier material relating to Level 5 Measurement (207KB)
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.
