Scale Lab / Student-led STEM
What changes
when size changes?
Scale Lab starts with a deceptively simple idea: changing the size of something can change the way it behaves.
Explore the scaling lawsWhat students will learn
- Length changes by the scale factor k.
- Surface area changes by k2.
- Volume changes by k3.
- Surface area relative to volume falls as an object gets larger.
The big idea
Doubling an object’s length does not double everything about it. Its surface area becomes four times larger, while its volume becomes eight times larger.
That difference connects physics, biology, chemistry, engineering, mathematics and computing through data analysis.
Interactive explorer
One change. Four consequences.
Start with a cube. Change every edge by the same scale factor, then see what happens to its outside surface and inside volume.
Geometrically similar cube
Move the slider for intermediate values, or choose a useful scale below.
- Length
- ×1 Changes with k
- Surface area
- ×1 Changes with k2
- Volume
- ×1 Changes with k3
- Surface area : volume
- ×1 Changes with 1 / k
At ×1: this is the original cube. Every result is compared with this starting point.
Try this
Make a prediction. Then test it.
- What happens to volume when you double the length?
- Can you find a size where volume is about 27 times the original?
- What happens to surface-area-to-volume ratio as the cube grows?
- Why might this matter for an animal, a building or a hot object?
From model to world
More inside, less outside.
As objects become larger, they have less surface area relative to their volume. This can affect how quickly they lose heat, how materials diffuse, and how engineers design structures.
Real objects also differ in shape, material, insulation and airflow. The cube is a useful model for asking better questions, not a complete prediction of every real situation.
Investigate it yourself
Why do small things cool faster?
Use the explorer to develop a hypothesis, then take a student-led research question from observation and pilot work to data, uncertainty and a next investigation.
Where Scale Lab can grow
More questions, not more worksheets.
Future investigations could explore the same question through:
- Structures & strength
- Flight & drag
- Sound & resonance
- Energy & area
- Measurement & uncertainty
Scale Lab begins here
Use the model before investigating.
Try the explorer, explain a surprising result, then plan how you could test a scale-related question fairly.
Licence: This educational resource is licensed under CC BY-NC-SA 4.0. Created by Just How Big? / Katipo Technologies Ltd.