Problems
Two Squared
Stage: 2 Challenge Level: 
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
Tri-five
Stage: 2 Challenge Level:
Find all the different shapes that can be made by joining five equilateral triangles edge to edge.
World of Tan - All in a Fluff
Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of these rabbits?
Millennium Man
Stage: 2 Challenge Level:
Liitle Millennium Man was born on Saturday 1st January 2000 and he will retire on the first Saturday 1st January that occurs after his 60th birthday. How old will he be when he retires?
1 Step 2 Step
Stage: 3 Challenge Level:
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. For example: He could go down 1 step, then one step, then 2 steps, then 2, 2, 1, 1, 1, 1. In. . . .
Triominoes
Stage: 3 Challenge Level:
A triomino is a flat L shape made from 3 square tiles. A chess board is marked into squares the same size as the tiles and just one square, anywhere on the board, is coloured red. Can you cover the. . . .
Factoring Factorials
Stage: 3 Challenge Level:
Find the highest power of 11 that will divide into 1000! exactly.
LOGO Challenge - Triangles-squares-stars
Stage: 3 and 4 Challenge Level:
Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
Natural Sum
Stage: 4 Challenge Level:
The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .
Gift of Gems
Stage: 4 Challenge Level:
Four jewellers possessing respectively eight rubies, ten saphires, a hundred pearls and five diamonds, presented, each from his own stock, one apiece to the rest in token of regard; and they. . . .
Beelines
Stage: 4 Challenge Level:
Investigate the relationship between the coordinates of the endpoint of a line through the origin and the number of grid squares it crosses.
Polynomial Relations
Stage: 5 Challenge Level:
Given any two polynomials in a single variable it is always possible to eliminate the variable and obtain a formula showing the relationship between the two polynomials. Try this one.
Stone Henge
Stage: 5 Challenge Level:
Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.
Comparing Continued Fractions
Stage: 5 Challenge Level:
Which of these continued fractions is bigger and why?
