Each puzzle develops one or more mathematical concepts, ie key mathematical ideas. To search for puzzles relating to a particular concept, see the Concepts index.

Where applicable, puzzles are referenced to the National Curriculum for Key Stages 3 and 4. To search for puzzles relating to a particular part of the curriculum, see the KS3 and KS4 curriculum indexes.

Most of the puzzles are presented as both PDF (portable document format) worksheets and PowerPoint presentations. The only exceptions are where one format is not suitable, eg because the puzzle is too long to fit conveniently on PowerPoint slides.

The PDF worksheets are designed to be printed out and distributed to students. As most of the puzzles are quite short, the majority are arranged with two copies on an A4 page and need to be cut in half before use. The worksheets look best when printed in colour, but can be used in black and white as well.

To use the PowerPoint presentations, you will need a projector or interactive whiteboard. When using them in lessons, it is recommended that you do not open them directly from the puzzles’ individual pages, because the teaching notes and solution may be visible to the students. Instead, you can do one of the following:

• Save the files to a suitable location on your network (see Using digital files for instructions).
• Open the files in the folder called digital_files on the disc, rather than through this interface.
• Open the files using the links on the Digital files page in the Resources section.

Where a puzzle has a visual solution, this is also included in the PowerPoint file. Solutions are preceded by a warning slide saying ‘Solution’ to help you avoid displaying them by accident.

For further guidance on using PowerPoint and PDF files, see Using digital files.

Some puzzles are very short. These may be better delivered verbally, or simply written on the board, rather than via a worksheet or presentation, although PowerPoint presentations and PDF worksheets are still provided to use if you wish.

The teaching notes provide general guidance on using the puzzles in your teaching. This can include:

• suggested approaches to finding a solution
• hints to help students get started if they are struggling
• common pitfalls
• ideas for discussion
• types of teaching to which the puzzles are especially suited, eg group work or whole class teaching
• links to other subjects.

It is a good idea to familiarise yourself with a puzzle before using it with students so that you can anticipate any questions or difficulties that might arise. This includes reading the teaching notes.

Answers to the puzzles are provided, with full working where appropriate. Depending on the puzzle and the situation, you may wish to print out a copy of the solution to a puzzle before you use it with students, so that you can work through each step together.

Note that not all puzzles have a solution – some (particularly in the Optical illusions section) are ‘just for fun’, intended as a starting point for discussion rather than a test of students’ abilities.

Some puzzles lead naturally into further exploration of the mathematical ideas involved. The extension activities suggested can range from simple follow-up questions to starting points for a full investigation. By using these ideas (or others of your own) you can develop a single puzzle into a whole lesson, or in some cases several lessons. Alternatively, you might use them to stretch more able students, or to encourage students to think about a particular topic in more depth.

The extension activities are chiefly intended as pointers towards how the ideas behind a puzzle can be developed or applied to other situations, rather than additional questions. For this reason, many of them are deliberately open-ended and full solutions are not provided.