Constructions

problem
The farmers' field boundary

Age

11 to 14

Challenge level

The farmers want to redraw their field boundary but keep the area the same. Can you advise them?
problem
The square under the hypotenuse

Age

14 to 16

Challenge level

Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?
project
Flip your mat!

What shape and size of drinks mat is best for flipping and catching?
problem
Cool as ice

Age

11 to 16

Challenge level

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
problem
Constructing triangles

Age

11 to 14

Challenge level

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
problem
A rational search

Age

16 to 18

Challenge level

Investigate constructible images which contain rational areas.
problem
Attractive rotations

Age

11 to 14

Challenge level

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
problem
Moving squares

Age

14 to 16

Challenge level

How can you represent the curvature of a cylinder on a flat piece of paper?
problem
Close to triangular

Age

14 to 16

Challenge level

Drawing a triangle is not always as easy as you might think!
problem
Folding fractions

Age

14 to 16

Challenge level

What fractions can you divide the diagonal of a square into by simple folding?