Recently I was looking with pupils at the link between enlargement and area. This was only in Year 8 so we weren't looking at ratio at this stage, rather sentences like "If the lengths are enlarged by scale factor 3, then the area is enlarged by scale factor ...". We did an investigation with a 3cm x 5cm rectangle, with pupils exploring different scale factors and the effect this had on the area.
Pupils were very quick to notice that the numbers at the end were the square numbers, allowing us to make the link and answer questions. It seems basic I know but I think this reinforced for me the idea that sometimes pupils discovering results and relationships for themselves is much more powerful than being shown a relationship and told what it is.