If you have only four weights, where could you place them in order to balance this equaliser?

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?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Can you complete this jigsaw of the multiplication square?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Here is a chance to play a version of the classic Countdown Game.

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

An environment which simulates working with Cuisenaire rods.

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?

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

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

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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....?

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

Use the interactivities to complete these Venn diagrams.

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

Work out how to light up the single light. What's the rule?

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

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 different ways of lining up these Cuisenaire rods?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

An interactive activity for one to experiment with a tricky tessellation

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?