Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Can you complete this jigsaw of the multiplication square?

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

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

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

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

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

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

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

These interactive dominoes can be dragged around the screen.

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....?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

How many right angles can you make using two sticks?

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

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

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

An interactive activity for one to experiment with a tricky tessellation

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

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?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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?

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?

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

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

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

Train game for an adult and child. Who will be the first to make the train?

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

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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

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?

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

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?

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

Use the interactivity or play this dice game yourself. How could you make it fair?

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

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

Can you hang weights in the right place to make the equaliser balance?

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