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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

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

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.

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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

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?

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

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

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?

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

Can you use the information to find out which cards I have used?

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?

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

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

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

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

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

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

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

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?

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?

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

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

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?

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?

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....?

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?

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

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

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?

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

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.

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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

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

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?

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?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

Using the statements, can you work out how many of each type of rabbit there are in these pens?