Exploring and noticing

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?

A napkin is folded so that a corner coincides with the midpoint of an opposite edge. Investigate the three triangles formed.

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

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.

If a sum invested gains 10% each year how long before it has doubled its value?

What is the same and what is different about these circle questions? What connections can you make?

Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?

Starting with two basic vector steps, which destinations can you reach on a vector walk?

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?