Biomaths Bites: Pump Up the Volume

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

Animals lose heat from their surfaces 1.2

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

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

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

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

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

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

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

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

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

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

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

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

in Australia and New Zealand Fairy penguins in Australia and New Zealand Emperor penguins in Antarctica 120 cm https://commons.wikimedia.org/wiki/File:Emperor_Penguin_Manchot_empereur.jpg 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