We had several good solutions to this problem. They came from Cong who goes to St Peter's RC Primary, Aberdeen; Terence from Brumby Engineering College and Ben at Kingsbarns Primary.

Cong coloured the first image:

He said:

The green and dark blue shape is $\frac{1}{4}$ of the square's
area (each).

The blue shape is $\frac{1}{8}$ of the square's area.

From these three shapes you can work out the red shape's area
which is $\frac{3}{8}$.

Cong then sent in a new version of the large design:

He goes on to say:

This shape is made from combining 4 small squares together to
get this big shape.

The shape in the middle of the large square is a
rhombus.

The big blue shape is $\frac{1}{4}$ of the large square's area
because it is $\frac{1}{4}$ of the small square and because the
large square is four times as big as the small square, which means
that it will be the same fraction.