A starter is a short activity that is used to get a lesson off to a purposeful start by capturing students’ attention and introducing key concepts and vocabulary. Displaying a relevant puzzle (chosen using the Concepts index) on a projector as students arrive, or having worksheets waiting on each desk, is a good way to accomplish these objectives. Once students have had time to attempt to solve the puzzle, you can discuss the solution and the mathematical concepts that underpin it, and then lead into the main body of the lesson.

A plenary is an activity used at the end of a lesson to reinforce key concepts or vocabulary from the main body of the lesson. Many of the puzzles in this resource are ideal for use as plenaries, since they can be used to demonstrate an interesting or unusual application of what students have just learnt, helping students to link the concepts involved to other areas of maths or to ‘real-world’ situations.

If you often use the puzzles in this way, students may even begin to look forward to them. This makes them more likely to stay on-task during the lesson, because they want to make sure they have time for what they see as some welcome light relief.

Many of the puzzles are designed to encourage students to consider different strategies as they work towards a solution. By dividing students into pairs or small groups, you can encourage them to discuss alternatives with each other, giving them the opportunity to use mathematical vocabulary and to gain an insight into how others think.

Some puzzles, such as Fun with figures and Guess a friend’s age and birthday, have to be delivered in pairs or small groups. A good idea is to give each student in a pair or group a different puzzle in worksheet form, and let them take turns asking and answering the questions.

You can involve the whole class by displaying a puzzle (in PowerPoint format) on a projector or interactive whiteboard and trying to solve it together. This is a particularly good way to use the more open-ended puzzles, as well as challenging tasks where the whole class may need to collaborate to find a solution. Some of the spatial puzzles work well when used with an interactive whiteboard, as students can use the whiteboard’s annotation facility to attempt to draw their solution in front of the class, justifying their reasoning, and their work can be easily cleared for someone else to try if they are unsuccessful or if someone suggests an alternative approach.

Several of the puzzles in this resource can be used as a starting point for an extended investigation. Some examples are:

• The clever butcher
• The lucky farrier
• Match puzzles
• The merry table
• A milkman’s problem
• Shape-shifters
• The stupid gardener
• Tricky lines.

Suggestions for developing an investigation are given under the Extension heading on each relevant page.

The PDF worksheets can provide an interesting and unusual stimulus for use in maths clubs outside normal school hours. Once students have found a solution, they could be encouraged to try to come up with similar puzzles of their own for others to solve, or to demonstrate their understanding by thinking of a seemingly different question that expresses the same underlying mathematical concept.

Several of the puzzles require students to read the question very carefully in order to solve them correctly. This makes them good to use for exam preparation, as interpreting what is actually being asked is an important exam skill. Suitable puzzles for this include:

• From A to B
• Charlie and the signpost
• The curious 45
• Did he ride or walk?
• Going to St Ives
• The wayside inn
• In the desert
• Which vegetable?

You may wish to incorporate some of the puzzles into longer tests or quizzes, for example for an end-of-term quiz or a class, subject or whole school competition. To do this, simply open the relevant PowerPoint or PDF file, copy the text, and paste it into a word processing programme. Pictures and diagrams included in PowerPoint files can also be copied in this way.