###### Worksheets and lesson ideas to challenge students aged 11 to 16 to think hard about surface area to volume ratio (GCSE and Key Stage 3)

**Overview: **surface area to volume ratio is an important biological concept for students to master – relevant to gas exchange, heat loss and cell structure. To calculate this ratio involves some simple maths, but it’s worth practising this with students and clarifying units for area and volume. Some data to use for adults and infants can be found here

**Key concept:** when the surface area to volume ratio is small, organisms require specialised structures to exchange materials quickly.

**From big idea: **organisms are organised on a cellular basis and have a finite life span.

**Linked knowledge: **cell structure, diffusion

**Misconception [scientific idea]:** a baby has a small surface area compared to an adult [this is true, but a baby has a larger surface area to volume ratio]

## Teaching resources

#### Where to start?

Surface area can be a quite a challenging concept for students to understand. A simple way to introduce this concept is to ask students whether they would use more wrapping paper to wrap a DVD boxset, or to wrap each DVD individually. You can also think about the volume of icing required to ice one cake, or each slice individually.

#### Calculating surface area to volume ratio

GCSE worksheet to calculate surface area to volume ratio for different sized cubes..Use this thinking task to introduce the concept of surface area to volume ratio. Make sure students are comfortable with expressing quantities as ratios first e.g. ¼ = 1:3 . Then move on to calculate the surface area to volume ratios for various cubes of different sizes. Finally students consider which ice cube shape is best! (PDF)

#### Going deeper

- Why don’t large animals have large cells?
- Why do babies get cold quickly?
- Why do babies dehydrate faster than adults in warm weather?
- Why are mitochondrial membranes folded?

These are great questions to use to explore the concept of surface area to volume ratio in your classroom. Multicellular organisms require a gas exchange system as diffusion would occur too slowly. Babies get cold quickly because they have a large surface area to volume ratio and so transfer heat quickly to their surroundings. The inner membrane of mitochondria is folded to increase the surface area available for respiration to take place.