Volume and Capacity Units of Work
Volume is the measure of space taken up by a threedimensional object. The space within a container is known as its capacity but as the thickness of many containers is negligible, it has become acceptable to refer to the space inside as volume too. (The terms volume and capacity are used interchangeably throughout the measurement strand of the NZ curriculum document although the glossary defines capacity as the interior volume of an object.)
Two different practical situations need to be experienced by students as they learn about volume. One relates to experiences involving "how much space does a threedimensional object occupy?" which eventually leads to measures of volume derived from measuring the length of the object’s dimensions. The other set of experiences relates to measures of fluids.
Learning Sequence  Curriculum Achievement Objectives  Specific Learning Outcomes  Units of Work  
 Level 1 Measurement AO1 
 
Comparing and ordering  Level 1 Measurement AO1 
 Three Bears  
Nonstandard units  Level 1 Measurement AO1 
 Spoonfuls, Cupfuls and Handfuls  

 Dino Cylinders  

 Counting on Measurement  
Standard units  Level 2 Measurement AO1 
 Popcorn  
Level 2 Measurement AO1 
 How Much Cereal?  

 Party Volumes  
Level 2 Measurement AO1 
 Making Benchmarks  
Level 3 Measurement AO1 
 Rainbow Jelly  

 Slosh, Dribble and Plop  
Level 3 Measurement AO1 
 Boxing on  
Level 3 Measurement AO1 
 Oranges L3  

 Marshmallows  
Level 4 Measurement AO1 
 Oranges L4  

 Spaced Out  
Level 4 Measurement AO3 
 Measurement investigations I  
Level 5 Measurement AO1 
 Measurement investigations II  

 Ratios  

 Scale Factors 
Stage One: Identifying the attribute
As with other measures, students require practical experience to begin to form the concept of an object taking up space. Students need lots of experiences of filling and emptying containers with sand and water. They need to have pouring experiences with containers of similar shape but different capacity and vice versa. They also need to fill containers with objects and build structures with blocks. The use of language such as it’s full, it’s empty, there’s no space left and it can hold more, focus attention on the attribute of volume. The awareness of the attribute of volume is extended as comparisons of volume are made at the next stage.
Stage Two: Comparing and ordering
It is important that students experience activities in which they compare and order attributes as these extend their understanding of the attribute and introduce them to informal measuring processes. Containers can sometimes be measured directly by placing one container inside another. Most comparisons however, need to be made indirectly by pouring from one container to another container to see which holds more.
If students realise that two matched amounts of liquid remain the same when one amount is poured into a container of a different shape, they are said to conserve volume.
Now A > B, B > C implied A > C is a transitive relation. These are extremely important in life and even more so in maths. In life we actually put too much store by them and wonder why, when the All Black beat the Springboks and the Springboks beat the Wallabies, that the All Blacks can’t beat the Wallabies.
Stage 3: NonStandard units
When a comparison between two containers requires the student to find out how much more one container holds, then a unit of volume is required. Measuring the area of objects using nonstandard or informal units is the third stage in the learning sequence. Beginning with nonstandard, but familiar units such as eggcupfuls and cupfuls allows the students to focus on the process of repeatedly using a unit as a measuring device.
In addition to lots of filling activities using liquids, the students can pack containers with marbles and blocks. They can also build different objects with blocks.
From the earliest of these experiences, students should be encouraged to estimate. Initially these estimates may be no more than guesses, but estimating involves the students in developing a sense of the size of the unit. As everyday life involves estimating at least as frequently as finding exact measures, the skill of estimating is important.
At this stage students can also be introduced to the appropriateness of units of measure. For example, a cup is more appropriate than a spoon for measuring the volume of a bucket.
Although nonstandard units reinforce most of the basic measuring principles, students need to realise that they are limited as a means of communication. This can be highlighted through activities that involve the students measuring the volume of an object using different sized cups.
Stage 4: Standard units
When students can measure areas effectively using nonstandard units, they are ready to move to the use of standard units. The motivation for moving to this stage, often follows from experiences where the students have used different nonstandard units for the same volume. This allows them to appreciate that consistency in the units used allows for easier and more accurate communication.
The usual sequence used in primary school is to introduce the litre as a measurement of volume before using cubic centimetres and cubic metres.
Student’s measurement experiences must enable them to:
 develop an understanding of the size of a litre and 10 millilitres. (1 millilitre is too small to be appreciated);
 estimate and measure using litres and millilitres;
 develop an understanding of the size of a cubic metre and a cubic centimetre;
 estimate and measure using cubic metres and cubic centimetres.
The standard units can be made meaningful by looking at the volumes of everyday objects. For example, the litre milk carton, the 2litre icecream container and the 100millilitre yoghurt pottle. Students should be able to use measuring jugs and to say what the measuring intervals on the scale represent.
Cubic centimetres are usually in abundant supply in classrooms and can be used to construct larger cubes and other shapes. A cubic metre can be built using metre rulers and compared with spaces such as that under the teacher’s desk.
Stage 5: Applying and Interpreting
When the students are able to measure efficiently and effectively using standard units, their learning experiences can be directed to situations that encourage them to "discover" measurement formulae and investigate the relationship between litres and cubic centimetres.
Students could find out that a container that holds 1000 centimetre cubes can also hold one litre of water. They can then deduce that one cubic centimetre and 1 millilitre represent the same amount of space, although when you pour a millilitre of water onto a surface it is difficult to believe it has the same volume as a centimetre cube.
The students can also use sets of centimetre cubes to construct rectangular prisms and then calculate the volume and "discover" the volume formula. Given the links between area and volume it is important that students first understand how to calculate the area of a surface so that they can see how to use this is used in calculating the volume of an object.
Volume of a cube = l x l x l.
Volume of a rectangular prism = l x w x h