Exploring Volume

Today in Year 5 we have been learning how to calculate the volume of cubes and cuboids. We discovered that volume is the amount of space inside a 3D shape and that we can find it by multiplying the: length × width × height
We practised finding the volume of different shapes and used cubes to help us understand how the space inside the shapes could be measured.

After this, we were given a challenge: How many different cuboids can you make with a volume of 12 cm³? We worked systematically to find different combinations. Some of the cuboids we found were:

• 1 cm × 1 cm × 12 cm
• 1 cm × 2 cm × 6 cm
• 1 cm × 3 cm × 4 cm
• 2 cm × 2 cm × 3 cm

Although the cuboids looked very different, they all had the same volume of 12 cm³.
We then explored our reasoning by answering the statement: “The taller the cuboid, the greater the volume.” We had to decide whether this was sometimes, always or never true. To test our thinking, we built and compared cuboids using different numbers of cubes and discovered that the answer is sometimes.
Our reasoning was because a cuboid can be taller but still have the same volume if the other dimensions are smaller. For example, a cuboid measuring 1 cm × 3 cm × 4 cm has the same volume as one measuring 2 cm × 2 cm × 3 cm, even though one is taller than the other.
Today’s lesson helped us to understand that volume depends on all three dimensions, not just height. We enjoyed building shapes, investigating patterns and proving our ideas using mathematical reasoning.