During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Try this matching game which will help you recognise different ways of saying the same time interval.

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

In this matching game, you have to decide how long different events take.

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

Try out the lottery that is played in a far-away land. What is the chance of winning?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

My coat has three buttons. How many ways can you find to do up all the buttons?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

What happens when you try and fit the triomino pieces into these two grids?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

This challenge extends the Plants investigation so now four or more children are involved.

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Can you find out in which order the children are standing in this line?

Use these head, body and leg pieces to make Robot Monsters which are different heights.

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

How many different triangles can you make on a circular pegboard that has nine pegs?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

Can you find all the different ways of lining up these Cuisenaire rods?

Find out what a "fault-free" rectangle is and try to make some of your own.

How many trains can you make which are the same length as Matt's, using rods that are identical?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?