Pascal's Triangle is a wonderful starting point for introducing or discovering lots of number patterns including the triangle numbers, the Fibonacci sequence, the doubling sequence and many more. There are 20 pieces which need assembling to make 16 rows of the triangle with spare pieces for extra rows. Each piece needs cutting out and ideally laminating. It would make a fun activity to just piece it together! It can be printed out on A3 paper to fill a display board or on A4 paper for a smaller version. The title and questions are also included.

How many people do you need to have in the same room before it is more likely than not that two people share the same birthday? The answer is surprisingly counter intuitive and in fact it is only 23! This 21 slide power point presentation explains the mathematics behind this answer. Pupils only really need to know how to calculate basic probabilities to appreciate this presentation.

This is a selection of questions which involve calculating the angle between the hands of a clock. Used for 13+ Scholarship mathematics, it has some interesting problems.

This is a worksheet which describes how to generate mathematical palindromes - numbers which read the same backwards as forwards. It requires accuracy and patience!

This explains how Public Key Cyphers work and includes a problem to solve. Very helpful as part of a code-breaking course. The solution is also provided. Designed for bright 13 year olds and upwards.

Two A4 sheets which show a way to remember the names of all the horizontal and vertical lines as well as y = x and y = -x.

This is a fun method of teaching substitution. The answers are put in the outer rim of the wheel and the variables can be easily made harder. The worksheet has four wheels with the final wheel having negative values of x and y.

This was a very brief introduction to mathematical proofs, including a (false) proof as to how you can prove that 1 = 2! It includes some questions at the end.

This is a brief power point presentation to demonstrate the solution to the well know rope around the earth problem: if a rope goes all the way around the equator, how much more rope is needed to lift the rope exactly one metre above the surface of the earth? The answer is an extraordinary and completely counter-intuitive one! It is in fact just 6.28 metres and it is exactly the same answer, whether the question is talking about a football or the earth!

This is an 8 page booklet which takes the pupils through the maths of calculating the number of ways an Enigma machine can be set up, using both permutations (the order of the rotors does matter) and combinations, where the order in which the plug board is set up doesn't matter. The first two pages lead the pupils through the various calculations leading to the answer of approximately 158 million billion ways or 158,962,555,217,826,360,000 ways to be precise! The remaining six pages explain the difference between permutations and combinations.

This is a poster of six images of Pascal's Triangle with a number pattern highlighted in each image: The Fibonacci Sequence, The Doubling Sequence, The Odds and Evens and Multiples of 3, 5 and 7. It would make a very good poster for the wall or for students to have in their books - the six sheets can be printed out onto one sheet of A4 paper for a mini version.

A wonderful starter lesson for 2022 finding how to make the numbers 1 to 25 with the four digits 2022 and mathematical symbols and it is actually possible! Bonus marks can be given for using the four digits in the order 2022 and an extension idea is included which involves continuing the problem to find the numbers 26 - 50. It is possible to find at least 15 of these 25 numbers. This works well as a full class activity and pupils can initially work on their own, then share their solutions in pairs and then finally see if the whole class has found the 25 solutions between them.

This is a fun introduction to Pascal’s Triangle or reminder to those who have seen it before with a Christmassy theme! Can your pupils work out how the triangle works and what the different colours represent?

For display in the classroom - the square, cubic and triangular numbers. You can print them out twice and stick them back to back, laminate them and either create a mobile or hang them on a string across the classroom.

This is for pupils learning about cubic numbers. It is a very clever cross number which requires the pupils not only to work out the answers but also to work out where the dark squares must go. Any clue must have a dark square both before it and after it (unless it starts or finishes at the edge of the cross number). When complete, it reveals the 11 distinct nets of a cube.