NSW Syllabuses

# Mathematics K–10 - Stage 1 - Measurement and Geometry Volume and Capacity

## Volume and Capacity 1

### Outcomes

#### A student:

• MA1-1WM

describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols

• MA1-3WM

supports conclusions by explaining or demonstrating how answers were obtained

• MA1-11MG

measures, records, compares and estimates volumes and capacities using uniform informal units

### Content

• use uniform informal units to measure the capacities of containers by counting the number of times a smaller container can be filled and emptied into the container being measured
• select appropriate uniform informal units to measure the capacities of containers, eg using cups rather than teaspoons to fill a bucket (Problem Solving)
• explain the relationship between the size of a unit and the number of units needed, eg more cups than ice cream containers will be needed to fill a bucket (Communicating, Reasoning)
• record capacities by referring to the number and type of uniform informal unit used
• compare the capacities of two or more containers using appropriate uniform informal units
• recognise that containers of different shapes may have the same capacity (Reasoning)
• estimate capacities by referring to the number and type of uniform informal unit used and check by measuring
• pack cubic units (eg blocks) into rectangular containers so that there are no gaps
• recognise that cubes pack better than other objects in rectangular containers (Reasoning)
• measure the volume of a container by filling the container with uniform informal units and counting the number of units used, eg the number of blocks a box can hold
• devise and explain strategies for packing and counting units to fill a box, eg packing in layers and ensuring that there are no gaps between units (Communicating, Problem Solving)
• explain that if there are gaps when packing and stacking, this will affect the accuracy of measuring the volume (Communicating, Reasoning)
• record volumes by referring to the number and type of uniform informal unit used
• estimate volumes of containers by referring to the number and type of uniform informal unit used and check by measuring
• explain a strategy used for estimating a volume (Communicating, Problem Solving)
• predict the larger volume of two or more containers and check by measuring using uniform informal units (Reasoning)
• estimate the volume of a pile of material and check by measuring, eg estimate how many buckets would be used to form a pile of sand

### Background Information

The order in which volume and capacity appear in the content is not necessarily indicative of the order in which they should be taught.

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.

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

Capacity refers to the amount a container can hold, and can be measured in millilitres (mL) and/or litres (L). 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).

Students need experience in filling containers both with continuous material (eg water) and with discrete objects (eg marbles). The use of continuous material leads to measurement using the units litre and millilitre in later stages. The use of blocks leads to measurement using the units cubic metre and cubic centimetre.

### Language

Students should be able to communicate using the following language: capacity, container, liquid, full, empty, volume, gap, measure, estimate.

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

When working towards the outcome MA1‑11MG the sub-elements (and levels) of Understanding units of measurement (UuM3-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:

• MA1-1WM

describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols

• MA1-2WM

uses objects, diagrams and technology to explore mathematical problems

• MA1-3WM

supports conclusions by explaining or demonstrating how answers were obtained

• MA1-11MG

measures, records, compares and estimates volumes and capacities using uniform informal units

### Content

• make and use a measuring device for capacity calibrated in uniform informal units, eg calibrate a bottle by adding cups of water and marking the new level as each cup is added
• compare and order the capacities of two or more containers by measuring each container in uniform informal units
• compare and order the volumes of two or more models by counting the number of blocks used in each model
• recognise that models with different appearances may have the same volume (Reasoning)
• compare and order the volumes of two or more objects by marking the change in water level when each is submerged
• recognise that changing the shape of an object does not change the amount of water it displaces (Reasoning)
• record volume and capacity comparisons informally using drawings, numerals and words, and by referring to the uniform informal unit used

### Background Information

The order in which volume and capacity appear in the content is not necessarily indicative of the order in which they should be taught.

Calibrating a container using uniform informal units is a precursor to students using measuring cylinders calibrated in formal units (litres and millilitres) at a later stage.

An object displaces its own volume when totally submerged.

Refer also to background information in Volume and Capacity 1.

### Language

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

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

When working towards the outcome MA1‑11MG the sub-elements (and levels) of Understanding units of measurement (UuM3-UuM5) 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.