Problems
Halving
Stage: 1 Challenge Level: 
These pictures show squares split into halves. Can you find other ways?
Dienes' Logiblocs
Stage: 1 Challenge Level:
This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?
Transformations Tables
Stage: 2 Challenge Level:
These grids are filled according to some rules - can you complete them?
Clocks
Stage: 2 Challenge Level:
These clocks have been reflected in a mirror. What times do they say?
Transformations on a Pegboard
Stage: 2 Challenge Level:
How would you move the bands on the pegboard to alter these shapes?
Transforming the Letters
Stage: 2 Challenge Level:
What happens to these capital letters when they are rotated through one half turn, or flipped sideways and from top to bottom?
Let's Reflect
Stage: 2 Challenge Level:
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
The Number Crunching Machine
Stage: 2 Challenge Level:
Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?
Counting Cards
Stage: 2 Challenge Level:
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
Reflecting Squarely
Stage: 3 Challenge Level:
In how many ways can you fit all three pieces together to make shapes with line symmetry?
Threesomes
Stage: 3 Challenge Level:
Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
Bow Tie
Stage: 3 Challenge Level:
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.
Excel Investigation: Planks
Stage: 3 and 4 Challenge Level:
I have an unlimited supply of planks, of lengths 7 and 9 units. Putting planks end to end, what total lengths can be achieved? Use Excel to investigate.
Excel Interactive Resource: the up and Down Game
Stage: 3 and 4 Challenge Level:
Use an interactive Excel spreadsheet to explore number in this exciting game!
Rots and Refs
Stage: 5 Challenge Level:
Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.
Complex Rotations
Stage: 5 Challenge Level:
Choose some complex numbers and mark them by points on a graph. Multiply your numbers by i once, twice, three times, four times, ..., n times? What happens?
Reflect Again
Stage: 5 Challenge Level:
Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.
