Reasoning, convincing and proving

interactivity
Proof sorter - the square root of 2 is irrational

Age

16 to 18

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.
interactivity
Proof sorter - geometric sequence

Age

16 to 18

Challenge level

Can you correctly order the steps in the proof of the formula for the sum of the first n terms in a geometric sequence?
interactivity
Proof sorter - quadratic equation

Age

14 to 18

Challenge level

This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.
game

The triangle game

Age

11 to 16

Challenge level

Can you discover whether this is a fair game?
game

Online

Age

7 to 11

Challenge level

Can you end up with all the occurrences of the same letter in this two-player game?
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
Anti-magic square

Age

11 to 14

Challenge level

You may have met Magic Squares, now meet an Anti-Magic Square. Its properties are slightly different - can you still solve it?
problem
Exponential intersection

Age

16 to 18

Challenge level

Can the pdfs and cdfs of an exponential distribution intersect?
problem
Next-door numbers

Age

5 to 7

Challenge level

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?
problem
Angles inside

Age

11 to 14

Challenge level

Draw some angles inside a rectangle. What do you notice? Can you prove it?