1. Biomaths Bites:
Pump Up the Volume

2. in Australia and New Zealand
Fairy penguins
in Australia and New Zealand
Emperor penguins
in Antarctica
120 cm
30 cm
by Tony Chiovitti
by Samuel Blanc
In what ways is Antarctica different from Australia and New Zealand?
How might the differences affect penguin survival?
Why might Emperor penguins in Antarctica be so much larger than Fairy penguins in Australia and New Zealand?
1.1

3. Animals lose heat from their surfaces
1.2

4. Single block Start with a single block.
Note the length, width and height.
Each is 1 unit.
This block represents a single
unit of volume: 1 unit3.
Count the number of faces on the block.
This is its surface area: 6 units2.
1 unit
height
1 unit
1 unit
width
length
2.1

5. Create a Bigger Cube 2 blocks Add blocks to create a cube:
length = 2 blocks long
width = 2 blocks wide
Height = 2 blocks high
Work out the volume (units3) of this cube.
Work out the surface area (units2) of this cube.
2 blocks
2 blocks
2.2

6. Create Bigger and Bigger Cubes
Keep adding blocks to create larger cubes (up to 5 blocks long, 5 blocks wide, 5 blocks high)
For each cube:
Work out the number of blocks
that make up its volume (units3).
Work out the number of block faces
that make up its surface area (units2).
Record your results in the data table.
2.3

7. Develop general rules for cubes
Use your data to come up with a general rule for the volume of a cube.
Use your data to come up with a general rule for the surface area of a cube.
Be sure to show how units, units2, and units3 are related in your general rules.
Use your general rule to predict the volume (units3) and the surface area (units2)
of a cube that is 6 blocks long, 6 blocks wide, and 6 blocks high.
Test your prediction by building the cube and working out:
* how many blocks make up its volume, and
* how many block faces make up its surface area.
2.4

8. Cross-check Use blocks of assorted sizes to build
cubes that match one that is 6 blocks
long, 6 blocks wide, and 6 blocks high.
Break down the cube and add up
the total volumes of all the individual
blocks.
Compare the total with the volume
of the original cube.
2.5

9. Investigating rectangular prisms
Add blocks to create rectangular prisms of
varying length, width, and height.
For each rectangular prism:
Work out the number of blocks that make up
its volume (units3).
Work out the number of block faces that
make up its surface area (units2).
3.1

10. Develop general rules for rectangular prisms
Use your data to come up with a general rule
for the volume of a rectangular prism.
for the surface area of a rectangular prism.
Be sure to show how units, units2, and units3
are related in your general rules.
Use your general rules to predict the volume
And surface area of a rectangular prism you have not yet built.
Build the rectangular prism and use it to test your predictions.
3.2

11. General rules for general rules …
Describe how the general rules for a cube and
a rectangular prism are the same and different.
Describe what you notice happens to the volume and surface area of a cube or a
rectangular prism as its size increases.
4.1

12. Volume and Surface Area of an Animal
Count out blocks that add up
to a fixed volume of 120 units3.
Use the blocks to build an
animal of your choosing.
For the animal you have constructed:
* Work out the number of block faces
that make up its surface area (cm2).
Don’t forget to count the underside
of the blocks.
5.1

13. Volume and Surface Area of an Animal
Compare the different animals
built in the classroom:
* What features increase an
animal’s surface area?
* What features decrease an
* Describe how an animal’s volume can be
modelled as cubes and rectangular prisms.
* Describe how an animal’s surface area can
be modelled as squares and rectangles.
5.2

14. Volume and Surface Area of a “Real” Animal
Select a small and large version of one of
the animal figurines.
Use the resources at your disposal –
Blocks, rulers, graph paper, pencils, scissors
* Work out the animal’s volume
(in mm3 or cm3 or mL).
* Work out the animal’s surface area
(in mm2 or cm2).
6.1

15. Measuring the Volume of Animal Figurines
(2)
(1)
(1) Place a jug or beaker inside a tray
and fill it to the brim.
(2) Use forceps to dunk the animal into the jug
or beaker and collect the overflow in the tray.
(3) Pour the overflow from the tray to a
measuring cylinder and measure the volume
in cm3 or mL.
(3)
6.2

16. in Australia and New Zealand
Fairy penguins
in Australia and New Zealand
Emperor penguins
in Antarctica
120 cm
30 cm
by Tony Chiovitti
by Samuel Blanc
Why might Emperor penguins in Antarctica be so much larger than Fairy penguins in Australia and New Zealand?
What other adaptations could penguins have to survive cold climates?
Why do penguins huddle in the cold?
Can you model your suggestions?
7.1