NSW Syllabuses

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

## Outcomes

#### A student:

• MAe-1WM

describes mathematical situations using everyday language, actions, materials and informal recordings

• MAe-11MG

describes and compares the capacities of containers and the volumes of objects or substances using everyday language

## Content

• Students:
• Use direct and indirect comparisons to decide which holds more, and explain their reasoning using everyday language (ACMMG006)
• identify the attribute of 'capacity' as the amount of liquid a container can hold
• fill and empty containers using materials such as water and sand
• use the terms 'full', 'empty' and 'about half-full'
• recognise when a container, such as a watering can, is nearly full, about half-full or empty (Reasoning)
• compare the capacities of two containers directly by filling one and pouring into the other
• predict which container has the greater capacity and explain the reasons for this prediction, eg plant pots of different sizes (Communicating, Reasoning)
• compare the capacities of two containers indirectly by pouring their contents into two other identical containers and observing the level reached by each
• establish that containers of different shapes may have the same capacity, eg a tall narrow container may hold the same amount as a short wide container
• identify the attribute of 'volume' as the amount of space an object or substance occupies
• stack and pack blocks into defined spaces, eg boxes
• identify which three-dimensional objects stack and pack easily (Reasoning)
• compare the volumes of two objects made from blocks or connecting cubes directly by deconstructing one object and using its parts to construct a copy of the other object
• compare the volumes of two piles of material directly by filling two identical containers, eg 'This pile of rice has a larger volume as it takes up more space in the container'
• compare the volumes of two objects by observing the amount of space each occupies, eg a garbage truck takes up more space than a car
• use comparative language to describe volume and capacity, eg has more, has less, will hold more, will hold less, takes up more space
• record volume and capacity comparisons informally using drawings, numerals and words

### 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. Capacity is only used in relation to containers and generally refers to liquid measurement. It is not necessary to refer to these definitions with students.

In Early Stage 1, comparisons are made directly, using methods such as pouring or packing the contents of one container into another. Early experiences often lead students to the conclusion that taller containers 'hold more'. To develop beyond this, students need to directly compare containers that are short and hold more, tall and hold less, short and hold less, tall and hold more, and short and hold the same as a tall container, etc.

Many opportunities to emphasise volume (stacking, packing and making models) and capacity (pouring and filling) concepts occur when students pack toys or objects into cupboards, or in play situations, eg sand pit play, water play.

### Language

Students should be able to communicate using the following language: capacity, container, liquid, full, empty, about half-full, volume, space, has more, has less, will hold more, will hold less, takes up more space.

Students need meaningful practice in using the general word 'container' to include bottles, jars, tubs and other everyday containers.

The term 'big' is often used by students to describe a variety of attributes. Depending on the context, it could mean long, tall, heavy, etc. It is important to model with students more precise language to describe volume and capacity.

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

When working towards the outcome MAe‑11MG the sub-elements (and levels) of Interpreting fractions (InF1) and Understanding units of measurement (UuM2) 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.