An attribute is a characteristic of an object or event.

Similarities and differences of objects can be determined based on particular measurable attributes.

Attributes can be compared based on one or more of the following methods:

• perceptual comparison – attributes of the objects look the same or look different

• direct comparison – objects are placed beside each other to compare the attribute

• indirect comparison – the attribute of objects is compared using a third object

• direct comparison – objects are placed beside each other to compare the attribute

• indirect comparison – the attribute of objects is compared using a third object

• transitivity – three or more objects are ordered using transitive thinking.

An appropriate unit is used to measure the attribute of an object; a unit is a uniform ‘piece’ of that attribute.

Conservation is when an attribute of an object changes while the other attributes remain the same.  

The attribute which has not changed is said to be ‘conserved’. Conservation is not applicable to 'time'.

The same measure can be expressed using different related units.

The size of a quantity can be measured using counts of a unit.

Attributes and common metric units of measurement: length, area, volume, perimeter, capacity, mass, time, temperature, angle. 

More complex attributes come from relationships between the basic attributes listed; for example, speed is the relationship of distance to time and is measured using a rate (kilometres per hour).  

Other common measurement attributes measured by rates are density, flow and pressure.

The metric system forms part of the Standard International (SI) set of standardised measures.  

Developed by mathematicians and scientists in France during Napoleon Bonaparte's reign, the metric system is based on 10, like the place value system.  

The metre was the founding unit in the system and was created to be one ten-millionth of the distance from the equator to the North Pole.  It is also the length of a pendulum that completes one swing in one second. 

Units for other attributes were derived from the metre.  

One litre is the volume of a cube that has edges of 10 cm.  

One kilogram is the mass of one litre of water.  

In the metric system, prefixes are used to convert the base unit into smaller units or collections of units.  

The most commonly used prefixes are: deci-, centi-, milli-, micro-, kilo-, hecto-, mega-.

Different attributes present variable difficulty for students due to how easily the attributes are sensed and perceived; for example, the attributes of physical space proceed in complexity from length to area, from area to volume, and from volume to capacity.  

Measurement of mass tends to be easier than measurement of time, since mass is more easily ‘felt’ than time.

The same measure can be expressed using different related units.

Informal units tend to be personal, such as foot lengths, blobs of playdough or handfuls. Formal measures, however, are commonly accepted so that the sizing of units is known and shared by a community; for example, metres, cups and hours.  Students need to be aware that units have the following properties:

1. Units are a piece of the attribute they measure.

2. Units are uniform (i.e. are all of equal size).

3. Units iterate (i.e. a single unit is used repeatedly to find a measurement without gaps or overlaps).

4. Units can be added and subtracted just like other countable objects.

5. Units for the same attribute are related by size in an inversely proportional way. The larger the unit, the smaller the measure. The same pencil might measure 10 white rods or 5 grey rods in length if white rods are half the length of grey rods.

Measurement scales are created to remove the need to use individual units and to make measurement more efficient. Most devices have scales.  Students need to be aware that scales have the following properties:

1. Marks show the endpoints of units not the centre of the units.

2. Zero marks the start of the scale, although any point on the scale can act as the baseline or arbitrary zero.

3. Intervals on scales can be equally partitioned into smaller units if more precision is required.

4. Scales are read using a combination of two processes:

i) iteration: the repeated copying of a trusted measure or interval

ii) equi-partitioning: the division of an interval into equal more precise intervals.

Measures can be calculated, calculated with and converted if more appropriate units are required or if attributes are related. The most common types of calculations are:

• finding differences between measures

• calculating areas and volumes by multiplication

• converting between units of measures for the same attribute

• converting between measures for different attributes.

Lehrer (2003) has outlined eight key concepts of spatial measurement:

1. Unit attribute relationship – units match the attribute being measured

2. Iteration – a single unit can be moved to measure a spatial attribute

3. Tiling – units fill lines, planes, volumes and angles without spaces

4. Identical units – if the units are identical, a count represents the measure, and mixtures of units have to be specified

5. Standardisation – formal units are used to facilitate communication

6. Proportionality – the size of the unit is inversely proportional to the count of the units, and the larger the unit the smaller the measure

7. Additivity – the whole is the sum of the parts

8. Origin of zero point – any point can be used as the zero point (for example, the difference between 0 and 10 is the same as between 30 and 40).