Finding the volumes of cuboids by measuring edge lengths
The purpose of this activity is to support students in finding volumes of cuboids by measuring the edges in centimetres or interpreting diagrams in which the dimensions are given in whole numbers of centimetres. Students also use cubic centimetres (cm3) to represent volume.
About this resource
New Zealand Curriculum: Level 3 to 4
Learning Progression Frameworks: Measurement sense, Signpost 5 to Signpost 7
These activities are intended for students who understand how to use units of measure to find length and areas of rectangles. They should understand the following:
- Units relate to the attribute being measured (for example, area is measured with iterations of area).
- Identical units need to be used when measuring.
- Units should be tiled (or iterated) with no gaps or overlaps to create a measure.
- Units can be equally partitioned into smaller units when greater accuracy is needed.
Students should also know how to use a measurement scale, such as a ruler or tape measure. They should be familiar with the common metric units of length, metres, centimetres, and possibly millimetres, though they may not be able to convert measures (e.g., 45 cm = 450 mm). Students should have a partial or full grasp of their basic multiplication facts and the division equivalents.
Finding the volumes of cuboids by measuring edge lengths
Achievement objectives
GM3-2: Find areas of rectangles and volumes of cuboids by applying multiplication.
Required materials
- carboard boxes with dimensions that are whole numbers of centimetres
- rulers
- unit place value blocks – 1cm3
- calculators
1.
Show students a cardboard box with whole number dimensions, such as 9cm x 9cm x 7cm. Hold up a 1cm3 cube (place value block).
I want to work out the volume of this box. I am using cubic centimetres like this.
- How can I work out the number of cubic centimetres that will fit into this box?
Let students discuss a strategy to try. This might include the following:
- Considering that the side lengths must be measured in centimetres.
- Recognising that volume is the amount of space enclosed by the box.
- Using arrays to simplify the counting of cubic units.
- Using multiplication, such as 9 x 9 x 7 = 567cm3.
2.
Discuss the strategies students suggest. As much as possible, act out the placement of cubic centimetres along the interior edges of the box. Encourage the students to visualise the structure of the 3-dimensional array created within these cube borders.
3.
Ask students to measure the dimensions of the box in centimetres. Draw a cuboid diagram and record the measurements.
Record the calculation as 9cm x 9cm x 7cm = 567cm3, pointing to the dimensions as you record the relevant measurement.
Discuss the use of the exponent 3 which means that the units are 1cm long in each of three dimensions: length, height, and depth.
Introduce relevant te reo Māori kupu, such as the rōrahi (volume) and poro-tapawhā hāngai (cuboid).
4.
Pose similar problems using boxes with dimensions given in whole numbers of centimetres. Record the volumes of the boxes using the equations above. You might have students explore and record these volumes in pairs. Consider pairing students to encourage tuakana-teina. Alternatively, it may be appropriate for students to continue to work with the teacher or to work independently.
Together, use the volume calculations to put the boxes in order by volume, from smallest to greatest.
Note that 3-dimensional objects can be deceiving: some boxes look bigger than they are, and some look smaller than they are.
5.
Present another box and ask students where in the sequence of volumes they think it should be. Tell them to direct you on how to calculate the volume of the box. Decide collectively where in the order the box should be.
1.
Pose problems where the students create cuboids of a given volume. Do not stipulate that the dimensions must be whole numbers of centimetres, as that will happen naturally. Some students may challenge themselves by experimenting with decimal dimensions.
Two ways students can create the cuboids are:
- Making models with connecting cubes. These cubes are usually 2cm x 2cm x 2 cm, so the target volumes should be multiples of eight.
- Creating nets and building the boxes from flat patterns. This makes the task more complex but includes elements of geometry, particularly spatial visualisation. Students need to visualise which edges on the net meet to form edges on the box.
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