Explaining, convincing and proving

problem

Classifying Solids Using Angle Deficiency

Age

11 to 16

Challenge level

Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
problem

Where Are the Primes?

Age

11 to 16

Challenge level

What can we say about all the primes which are greater than 3?
problem

Three Consecutive Odd Numbers

Age

11 to 16

Challenge level

How many sets of three consecutive odd numbers can you find, in which all three numbers are prime?
problem

Adding Odd Numbers

Age

11 to 16

Challenge level

Is there a quick and easy way to calculate the sum of the first 100 odd numbers?
problem

Cyclic Quadrilaterals Proof

Age

11 to 16

Challenge level

Can you prove that the opposite angles of cyclic quadrilaterals add to $180^\circ$?
problem

Circumference Angles

Age

11 to 16

Challenge level

Can you prove the angle properties described by some of the circle theorems?
problem

Proof Sorter - Circumference Angles

Age

11 to 16

Challenge level
problem

Starting to Explore Four Consecutive Numbers

Age

11 to 16

Challenge level
game

Yih or Luk Tsut K'i or Three Men's Morris

Age

11 to 18

Challenge level

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and knot arithmetic.
problem

The Bridges of Konigsberg

Age

11 to 18

Challenge level

Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.