NSW Syllabuses

# Mathematics K–10 - Stage 2 - Measurement and Geometry Volume and Capacity

## Volume and Capacity 1

### Outcomes

#### A student:

• MA2-1WM

uses appropriate terminology to describe, and symbols to represent, mathematical ideas

• MA2-3WM

checks the accuracy of a statement and explains the reasoning used

• MA2-11MG

measures, records, compares and estimates volumes and capacities using litres, millilitres and cubic centimetres

### Content

• Students:
• Measure, order and compare objects using familiar metric units of capacity (ACMMG061)
• recognise the need for formal units to measure volume and capacity
• explain the need for formal units to measure volume and capacity (Communicating, Reasoning)
• use the litre as a unit to measure volumes and capacities to the nearest litre
• relate the litre to familiar everyday containers, eg milk cartons (Reasoning)
• recognise that one-litre containers can be a variety of shapes (Reasoning)
• record volumes and capacities using the abbreviation for litres (L)
• compare and order two or more containers by capacity measured in litres
• estimate the capacity of a container in litres and check by measuring
• estimate the number of cups needed to fill a container with a capacity of one litre (Reasoning)
• Compare objects using familiar metric units of volume (ACMMG290)
• recognise the advantages of using a cube as a unit when packing and stacking
• use the cubic centimetre as a unit to measure volumes
• pack small containers with cubic-centimetre blocks and describe packing in terms of layers, eg 2 layers of 10 cubic-centimetre blocks (Problem Solving)
• construct three-dimensional objects using cubic-centimetre blocks and count the blocks to determine the volumes of the objects
• devise and explain strategies for counting blocks (Communicating, Problem Solving)
• record volumes using the abbreviation for cubic centimetres (cm3)
• compare the volumes of two or more objects made from cubic-centimetre blocks by counting blocks
• distinguish between mass and volume, eg 'This stone is heavier than the ball but it takes up less space'

### Background Information

Volume and capacity relate to the measurement of three-dimensional space, in the same way that area relates to the measurement of two-dimensional space and length relates to the measurement of one dimension.

The attribute of volume is the amount of space occupied by an object or substance and is usually measured in cubic units, eg cubic centimetres (cm3) and cubic metres (m3).

Capacity refers to the amount a container can hold and is measured in units such as millilitres (mL), litres (L) and kilolitres (kL). Capacity is only used in relation to containers and generally refers to liquid measurement. The capacity of a closed container will be slightly less than its volume – capacity is based on the inside dimensions, while volume is determined by the outside dimensions of the container. It is not necessary to refer to these definitions with students (capacity is not taught as a concept separate from volume until Stage 4).

In Stage 2, students should appreciate that formal units allow for easier and more accurate communication of measures. Students should be introduced to the litre, millilitre and cubic centimetre.

Measurement experiences should enable students to develop an understanding of the size of a unit, to estimate and measure using the unit, and to select the appropriate unit and measuring device.

Liquids are commonly measured in litres and millilitres. The capacities of containers used to hold liquids are therefore usually measured in litres and millilitres, eg a litre of milk will fill a container that has a capacity of one litre.

The cubic centimetre can be related to the centimetre as a unit to measure length and the square centimetre as a unit to measure area.

### Language

Students should be able to communicate using the following language: capacity, container, litre, volume, layers, cubic centimetre, measure, estimate.

The abbreviation cm3 is read as 'cubic centimetre(s)' and not 'centimetres cubed'.

### National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MA2‑11MG the sub-elements (and levels) of Understanding units of measurement (UuM4-UuM7) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.

## Volume and Capacity 2

### Outcomes

#### A student:

• MA2-1WM

uses appropriate terminology to describe, and symbols to represent, mathematical ideas

• MA2-11MG

measures, records, compares and estimates volumes and capacities using litres, millilitres and cubic centimetres

### Content

• Students:
• Use scaled instruments to measure and compare capacities (ACMMG084)
• recognise the need for a formal unit smaller than the litre to measure volume and capacity
• recognise that there are 1000 millilitres in one litre, ie 1000 millilitres = 1 litre
• relate the millilitre to familiar everyday containers and familiar informal units, eg 250 mL fruit juice containers, 1 teaspoon is approximately 5 mL (Reasoning)
• make a measuring device calibrated in multiples of 100 mL to measure volume and capacity to the nearest 100 mL
• use the millilitre as a unit to measure volume and capacity, using a device calibrated in millilitres, eg place a measuring cylinder under a dripping tap to measure the volume of water lost over a particular period of time
• record volumes and capacities using the abbreviation for millilitres (mL)
• convert between millilitres and litres, eg 1250 mL = 1 litre 250 millilitres
• compare and order the capacities of two or more containers measured in millilitres
• interpret information about volume and capacity on commercial packaging (Communicating)
• estimate the capacity of a container in millilitres and check by measuring
• compare the volumes of two or more objects by marking the change in water level when each is submerged in a container
• estimate the change in water level when an object is submerged (Reasoning)
• measure the overflow in millilitres when different objects are submerged in a container filled to the brim with water
• estimate the volume of a substance in a partially filled container from the information on the label detailing the contents of the container

### Background Information

The displacement strategy for finding the volume of an object relies on the fact that an object displaces its own volume when it is totally submerged in a liquid. The strategy may be applied in two ways: using a partially filled, calibrated, clear container and noting the change in the level of the liquid when an object is submerged; or submerging an object in a container filled to the brim with liquid and measuring the overflow.

Refer also to background information in Volume and Capacity 1.

### Language

Students should be able to communicate using the following language: capacity, container, litre, millilitre, volume, measure, estimate.

Capacity refers to the amount a container can hold, whereas volume refers to the amount of space an object or substance (including liquids) occupies. For example, we refer to the capacity of a dam (the amount of water it can hold) and the volume of water in the dam, which is usually less than the capacity of the dam.

### National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MA2‑11MG the sub-elements (and levels) of Multiplicative strategies (MuS3) and Understanding units of measurement (UuM6-UuM8) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.