Problems
Let's Investigate Triangles
Stage: 1 Challenge Level: 
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
Claire's Counting Cards
Stage: 1 Challenge Level:
Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .
Back to School
Stage: 2 Challenge Level:
Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?
Dodecamagic
Stage: 2 Challenge Level:
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
Mystery Matrix
Stage: 2 Challenge Level:
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
A-magical Number Maze
Stage: 2 Challenge Level:
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
World of Tan - an Appealing Stroll
Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of the child walking home from school?
Adding All Nine
Stage: 3 Challenge Level:
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .
Chocolate Maths
Stage: 3 Challenge Level:
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
Tetra Square
Stage: 3 Challenge Level:
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
More Mathematical Mysteries
Stage: 3 Challenge Level:
Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .
Hex
Stage: 3 Challenge Level:
Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.
Overlaid
Stage: 2, 3 and 4 Challenge Level:
Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?
One or Both
Stage: 3 Challenge Level:
Problem one was solved by 70% of the pupils. Problem 2 was solved by 60% of them. Every pupil solved at least one of the problems. Nine pupils solved both problems. How many pupils took the exam?
American Billions
Stage: 3 Challenge Level:
Find the ten-digit number in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3, the first four digits make a number divisible by 4...
Reciprocal Triangles
Stage: 5 Challenge Level:
Prove that the sum of the reciprocals of the first n triangular numbers is approximately equal to 2 when n is large and tends to 2 as n tends to infinity.
Golden Triangle
Stage: 5 Challenge Level:
Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.
Sangaku
Stage: 5 Challenge Level:
The square ABCD is split into three triangles by the lines BP and CP. Find the radii of the three inscribed circles to these triangles as P moves on AD.
Proof Sorter - the Square Root of 2 Is Irrational
Stage: 5 Challenge Level:
Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.
