This problem explores loci. A dog stands between a fire hydrant and a tree, twice as far from the hydrant as the tree. He runs in a way so that he is always twice as far from the hydrant. What is the shape of the dog's path?

Eight pieces of origami paper are shown after they have fallen on the floor. The challenge is to establish the order in which the papers fell on the floor.

In this challenge students have to establish the minimum number of fish tanks needed for six fish to live in harmony, as some fish cannot be placed in the same tanks as others safely.

In this puzzle four pieces of information are given about five children in a family. The challenge is to establish the age order of the five siblings.

Imagine a cube-frame made out of infinitely stretchy wire that could be flattened to make a 2D shape, what would it look like? In this puzzle students are given three such 2D representation of 3D shapes and have to name them.

The front face of four cards are shown, together with some statements about what could be on the reverse side. The challenge is to work out how many cards must be turned over to establish if the statements are true.

Four children make statements about their relative ages but one child is lying. The challenge is to order the children from the youngest to the oldest.

A diagram is shown with horses arranged in fields around a rectangle. There are four challenges to move the horses to fulfill given criteria. A worksheet is also included for students to record their answers.

The magic of…is a collection of four resources, produced by Queen Mary College at the University of London, designed for teachers to use in the classroom with the intention of making learning engaging and entertaining. The four resources are all linked to the relevant curricula and provide inspiration when teaching...

A series of books about detectives Stanley, Charlotte, Gertie, and Felix who solve crimes with maths.

This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the aeronautical industry. Students are given a scenario which involves the recovery of stranded mountaineers by a rescue helicopter and the considerations required for a successful outcome. Trigonometry, formula...

A floor plan is shown from a museum. The challenge is to place two security guards so that they will be able to keep watch on the whole museum

This puzzle provides an introduction to simultaneous equations in three variables. Three combinations of coins are shown, together with the total value for each pair. The challenge is to calculate the value of each coin.

This task is designed to assess how well students understand various aspects of the number system.

There are a series of short tasks on using a calculator, working with fractions, directed numbers, and extending a multiplication fact.

As an example:

12345679 x 27 = 333 333 333

and...

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.