Volume and capacity
Measurement
Definition
Volume refers to the space occupied by a three-dimensional object or solid. It is expressed in cubic units that are derived from units of length. Capacity refers to the same three-dimensional attribute, but specifically refers to measures of how much will fit in a volume of space (Siemon, et al., 2015). More commonly it refers to the amount of liquid a solid can hold.
Students become increasingly able to recognise attributes that can be measured and how units of measure are used and calculated. In making the transition from informal to formal units, a student attends to the structure of units used to measure, how they are assembled in end-to-end, side-by-side or in layers without gaps or overlapping. The structure of the units gives rise to ways of calculating volume.
In dealing with capacity, experience helps develop estimates associated with commonly available reference objects (for example a cupful in cooking). Developing standard and agreed units of measurement is critically vital in areas as diverse as medicine ad trade. (National Numeracy Learning Progression)
Teaching and learning activities
The resources below provide targeted teaching strategies to support student improvement in this skill.
Each downloadable lesson activity includes:
learning intentions
a list of required resources
a step-by-step lesson sequence
printable classroom materials
Select the download all icon to download all available activities or select each activity separately.
PLAN2 Areas of focus
An Areas of focus template has been created in PLAN2 to support targeted teaching of Text structure in your learning area.
Search for the DoE template titled ‘DoE HSCMinStd Writing: Text structure’ in the Areas of focus template library tab within the Plan menu, and customise it for your students’ needs.
For more information about using PLAN2 Areas of focus templates with this resource, visit the Using this resource with PLAN2 page.
Relevance to the numeracy test marking
The relevant Level 3 ACSF descriptors for numeracy are shown here to demonstrate how estimating, measuring and calculating volume and capacity is assessed in the HSC minimum standard online test. The performance features identified show what a student is able to do in order to achieve at this level and are provided to support teachers to understand what is required to achieve a Level 3 in this skill.
Connections with ACSF Level 3 descriptors
The relevant Level 3 ACSF descriptors for numeracy are shown here to demonstrate how estimating, measuring and calculating volume and capacity is assessed in the HSC minimum standard online test. The performance features identified show what a student is able to do in order to achieve at this level and are provided to support teachers to understand what is required to achieve a Level 3 in this skill.
Numeracy Indicator 3.09: Selects and interprets mathematical information that may be partly embedded in a range of familiar, and some less familiar, tasks and texts
Focus area: Explicitness and Complexity of mathematical information
Level 3 performance features:
interprets and comprehends familiar and routine volume and capacity
Numeracy Indicator 3.10: Selects from and uses a variety of developing mathematical and problem solving strategies in a range of familiar and some less familiar contexts.
Focus area: Mathematical knowledge and skills: measurement and geometry
Level 3 performance features:
measures, estimates and calculates volume and capacity
converts between routine metric units
Connections with Numeracy Learning Progression:
The progressions describe a typical developmental sequence of literacy and numeracy learning. The numeracy progression sub-elements, levels and indicators relevant to measuring time are provided here to assist teachers to identify students’ capabilities and needs to support targeted teaching.
Element: Measurement and Geometry
Sub-element: Understanding units of measurement (UuM)
UuM2 — Comparing and ordering objects
uses direct comparison to compare two objects and indicates whether they are the same or different based on attributes such as length, height, mass or capacity (e.g. compares the length of two objects by aligning the ends; pours sand or water from one container to another to decide which holds more)
UuM3 — Using informal units of measurement
measures an attribute by choosing and using multiple identical, informal units
chooses and uses appropriate uniform informal units to measure length and area without gaps or overlaps (e.g. uses the same sized paper clips to measure the length of a line; uses tiles, rather than counters to measure the area of a sheet of paper because the tiles fit together without gaps)
uses multiple uniform informal units to measure and make direct comparisons between the mass or capacity of objects (e.g. uses a balance scale and a number of same-sized marbles to compare mass; uses a number of cups of water or buckets of sand to measure capacity)
UuM3 — Estimating measurements
estimates the total number of uniform informal units needed to measure or compare attributes (e.g. uses a handspan or a finger width; stands an arm length apart)
checks an estimate using informal units to compare to predicted measurement
UuM4 — Repeating a single informal unit to measure
measures an attribute by counting the number of units used
UuM4 — Estimating measurements
uses familiar household items as benchmarks when estimating mass and capacity (e.g. compares capacities based on knowing the capacity of a bottle of water)
UuM5 — Using abstract units
uses rows, columns and layers to calculate the volume in cubes of a rectangular prism (e.g. My prism has four rows of two cubes in the first layer and I’ve made it three layers high so that’s 4 × 2 = 8 and 3 × 8 = 24, so the volume is 24 cubes)
estimates the measurement of an attribute by visualising between known informal units (e.g. uses a cup to measure a half cup of rice; determines that about three sheets of paper would fit across a desk, and close to six might fit along it, so the area of the desk is about eighteen sheets of paper)
explains the difference between different attributes of the same shape or object (e.g. area and perimeter, mass and capacity)
UuM6 — Using formal units
uses scaled instruments to measure length, mass, capacity and temperature
estimates measurements of an attribute using formal units (e.g. estimates the width of their thumb is close to a centimetre; compares capacities based on the capacity of a 600 ml bottle of water)
UuM8 — Converting units
converts between metric units of measurement
describes the relationship between metric units of measurement and the base-ten place value system
UuM9 — Using formal units and formulas
establishes and uses formulas for calculating the volume of a range of prisms
UuM10 — Using formal units and formulas
uses the conversion between units of volume and capacity to calculate the capacity of objects based on the internal volume and vice versa