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
Cool as ice

Age

11 to 16

Challenge level

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
problem
Curvy areas

Age

14 to 16

Challenge level

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
problem
Triangle midpoints

Age

14 to 16

Challenge level

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
problem
Folding squares

Age

14 to 16

Challenge level

The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?
problem
Folding fractions

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.
problem
Close to triangular

Age

14 to 16

Challenge level

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