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.

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

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.

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.

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...