Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

Sometimes area and perimeter of rectangles are taught separately, and are often confused. In this problem students consider the relationship between them.

Working on this problem will give students a deeper understanding of area and perimeter, and how they change as a shape is altered.

This problem combines both area and perimeter by inviting students to consider the different possibilities for the perimeter when the area of a rectangle is fixed.

What are the possible areas of triangles drawn in a square?

This problem challenges students to work systematically while applying their knowledge of areas of rectangles.

Can you deduce the perimeters of the shapes from the information given?

This problem encourages students to use coordinates, area and isosceles triangles to solve a non-standard problem. To find all possible solutions they will need to work systematically.

This problem allows students to consolidate their understanding of how to calculate the area of irregular shapes, while offering an opportunity to explore and discover an interesting result.

This problem offers the opportunity to practise calculating areas of circles and fractions of a circle in the context of an optimisation task.

If you move the tiles around, can you make squares with different coloured edges?

This problem offers students a chance to develop strategies for organising and understanding mixed up information within the context of calculating areas and perimeters of rectangles.