With just one fold of a square piece of paper, is it possible to make a triangle and a quadrilateral? Two quadrilaterals? A triangle and a pentagon? A further challenge asks students to explore the combination of shapes that can be made by using two folds of a square.

This puzzle provides a gentle introduction to simultaneous equations. Three pictures are given that show different combinations of three items from a menu, together with the total price for each meal. The challenge is to work out the cost of each item.

This problem looks at fencing chickens using pens. The challenge is to work out how many lengths are needed to create six separate pens for the roosters.

This combination problem builds up from combinations of three socks to six socks. Can students find a pattern and use it to work out how many socks would be needed to ensure a different pair was available each day for a month?

A sheet is shown containing six calculations that have been partially obscured by juice spilled on the sheet. The challenge is to work out what the calculations were, and their solutions.

This problem provides a gentle introduction to simultaneous equations. Three bags of shopping are shown: two have prices and one does not. The challenge is to find out the price of the final bag of shopping.

After thinking of a number, a series of steps is given that result in an answer that is independent of the initial number. There is scope to use fractions and directed numbers in the problem....

These activities, from the Association of Teachers of Mathematics (ATM) publication ‘Thinking for Ourselves’, provide a variety of contexts in which students are encouraged to think for themselves.

Activity 1: In the bag – More or less requires students to record how many more or...

This resource, produced by the Centre for Teaching Mathematics at the University of Plymouth, contains ten ‘puzzles to get the brain working!’

Each puzzle is designed to make students think laterally, consider the question carefully and not give the most obvious answer. The puzzles could be used as lesson...

These resources, produced by The National Centre for Excellence in the Teaching of Mathematics (NCETM), have been designed to encourage distinctive ways of thinking and learning as part of the NCETM professional development package.

Analysing reasoning and...

The This is Engineering: Entertainment STEM resource explores the essential role that engineers play in the entertainment industry.

This is Engineering: Entertainment asks young learners to express and share their thoughts and ideas, to be curious, experiment, find their own passions and interests, and to...

Some of the biggest challenges we face stem from how we interact with our environment, and engineering is essential to finding sustainable solutions. From renewable power to recycling, to making our homes more energy efficient, and tackling how we feed a growing population, engineering is a vital field.
 ...

Some of the biggest challenges we face stem from how we interact with our environment, and engineering is at the heart of finding sustainable solutions. Working with water is particularly important when thinking about the environment because water sustains all life and is essential to the survival of the planet....

In this Nuffield probability activity students play a bingo-style game. To maximize their chances of winning, students must decide which numbers are most likely to occur when three dice are thrown and the scores are added.

A photograph of three cubes is presented. The faces of the cubes are decorated with patterns. The challenge is to determine which box is different from the other two. This resource is suitable for Key Stage 3 and could be used as an extension when teaching nets for cubes.

• ...