Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
We have four rods of equal lengths hinged at their endpoints to form a rhombus ABCD. Keeping AB fixed we allow CD to take all possible positions in the plane. What is the locus (or path) of the point. . . .
If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
What is the total number of squares that can be made on a 5 by 5 geoboard?
Can you find a way to turn a rectangle into a square?
Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.
Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?