Problems
Happy Halving
Stage: 1 Challenge Level: 
Can you split each of the shapes below in half so that the two parts are exactly the same?
A Bowl of Fruit
Stage: 1 Challenge Level:
Can you work out how many apples there are in this fruit bowl if you know what fraction there are?
Pizza Portions
Stage: 2 Challenge Level:
My friends and I love pizza. Can you help us share these pizzas equally?
Dividing a Cake
Stage: 2 Challenge Level:
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
In the Money
Stage: 2 Challenge Level:
There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?
Fun Time
Stage: 2 Challenge Level:
On Saturday, Asha and Kishan's grandad took them to a Theme Park. Use the information to work out how long were they in the theme park.
Fractions in a Box
Stage: 2 Challenge Level:
The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.
World of Tan - Sharing
Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of Little Fung at the table?
Counting Triangles
Stage: 3 Challenge Level:
Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
Farey Sequences
Stage: 3 Challenge Level:
The sum of 1/2 and 1/3 is 5/6 (bigger than both fractions) but the mediant of 1/2 and 1/3 is 2/5 which lies between them. Mediants play a role in Farey sequences.
Great Granddad
Stage: 3 Challenge Level:
Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?
Basically
Stage: 3 Challenge Level:
The number 3723(in base 10) is written as 123 in another base. What is that base?
Squaresearch
Stage: 4 Challenge Level:
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
Mediant
Stage: 4 Challenge Level:
If you take two tests and get a marks out of a maximum b in the first and c marks out of d in the second, does the mediant (a+c)/(b+d)lie between the results for the two tests separately.
Lens Angle
Stage: 4 Challenge Level:
Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.
Square World
Stage: 5 Challenge Level:
P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?
Reciprocals
Stage: 5 Challenge Level:
Prove that for any positive numbers x1,x2,...,xn (x1 + x2 + ... + xn)([1/(x1)] + [1/(x2)] + ... + [1/(xn)]) is greater than or equal to n^2.
