MAe-11MG: describes and compares the capacities of containers and the volumes of objects or substances using everyday language
|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.|
Measure and compare the capacities of pairs of objects using uniform informal units
|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|