Volume and Capacity - Overview

**Key terms from Teaching Measurement (NSW Department of Education and Training, 2004)**

*Capacity*: A term used for a measure of internal volume (often used for liquid measure and given in litres or millilitres)

*Tessellation*: A covering of a surface with identical shapes (a paving). The shapes fit together without gaps or overlap and can be extended infinitely in any direction

*Volume*: The amount of space occupied by an object or substance. One aspect of volume is capacity (the term usually used for liquids measured in kilolitres, litres and millilitres) and means the amount a container can hold. The capacity of a jug might be measured in cups, millilitres or litres

A second aspect of volume is the volume of a model made with blocks. This aspect enables comparisons to be made easily —which model has more or fewer blocks—by counting the blocks. However, students may focus on counting and not associate this activity with volume

A third aspect of volume is the capacity (interior volume) of containers, when measured in cubic centimetres. The cubic units make this aspect of volume measurement more difficult than liquid measure

A fourth aspect of volume is exterior volume, or the amount of space a container takes up.

The fifth aspect of volume is that of displacement. This concept is difficult because it is not obvious that the amount of water displaced by an object is the volume of the object

Key principles

Metalanguage: taller, smaller, compare, estimate, capacity etc

Once students are able to identify what is being measured, and can directly compare and order quantities, the next step is to learn to use measurement units

Once a number is associated with a quantity, that quantity can be compared with other quantities and ordered more easily than by using direct comparison.

A fundamental principle of measurement is that quantities can only be compared if the units used to measure each quantity are identical. Students can be assisted to develop this principle through discussion of results when different-sized units are used.

Another important idea about units is that use of smaller units gives increased precision. As students begin to measure with units they gradually learn an important principle of measurement, that the quantity is unchanged if it is rearranged (conservation)

Tessellation of measurement units

Estimation

Recording

Questioning

# Level of understanding

Using *Teaching measurement *as a guide* *the students in 3W will be at levels 2 (Informal measurement), 3 (Structure of repeated units) and 4 (Measure using conventional units)

# Outcomes and indicators

**MS1.3 **Estimates, measures, compares and records volumes and capacities using informal units

The student, for example:

• Counts and compares the number of cups of sand or water needed to fill two different containers

• Recognizes that two containers of different shape may hold the same amount of material

e.g. ‘This short fat cup holds about the same amount of drink as this tall thin glass.’

• Estimates and measures the capacity of a container using informal units

• Orders three containers according to their capacity

• Calibrates a clear bottle using a cup as the informal unit

• Selects an appropriate informal unit to measure and compare the capacities of two containers

• Compares the capacities of two containers by filling each and counting the number of informal units used

• Builds models using blocks and compares their volume by counting the number of identical blocks used

• Orders three models according to their volume

• Compares the volumes of two objects by marking the change in water level when each is submerged

**MS2.3: **Estimates, measures, compares and records volumes and capacities using litres, millilitres and cubic centimetres

The student, for example:

• Selects from a range of containers those that have a capacity of more than, less than and about one litre

• Uses the abbreviation for litre (L) and millilitre (mL)

• Estimates and measures the capacity of containers to the nearest litre

• Gives examples of situations where a unit smaller than the litre is needed for measurement

• Estimates, measures and compares volume and capacity using millilitres

• Describes the litre as being the same as 1000 millilitres

• Compares packaging quantities measured in millilitres

• Compares the volumes of three objects by marking the change in water level when each is submerged in a container

• Measures volume using cubic centimetres