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?

How many different symmetrical shapes can you make by shading triangles or squares?

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.

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

A challenging activity focusing on finding all possible ways of stacking rods.

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?

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.?

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.

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

Use the clues about the symmetrical properties of these letters to place them on the grid.

What is the best way to shunt these carriages so that each train can continue its journey?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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?

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

An activity making various patterns with 2 x 1 rectangular tiles.

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

This activity investigates how you might make squares and pentominoes from Polydron.

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

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

In how many ways can you stack these rods, following the rules?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

These practical challenges are all about making a 'tray' and covering it with paper.

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

The pages of my calendar have got mixed up. Can you sort them out?

Find out about Magic Squares in this article written for students. Why are they magic?!

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Four small numbers give the clue to the contents of the four surrounding cells.

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?