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

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

How will you go about finding all the jigsaw pieces that have one peg and one hole?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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?

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?

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

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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?

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

How long does it take to brush your teeth? Can you find the matching length of time?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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?

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?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Can you find all the different triangles on these peg boards, and find their angles?

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

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

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....?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

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

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

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

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

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?

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

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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. . . .

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

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.

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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

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

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

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.

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

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.?