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

These interactive dominoes can be dragged around the screen.

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

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

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.

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?

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

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

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

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

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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?

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?

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

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

How many right angles can you make using two sticks?

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

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

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

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

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?

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

Can you complete this jigsaw of the multiplication square?

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?

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

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?

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

Use the number weights to find different ways of balancing the equaliser.

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

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

Sort the houses in my street into different groups. Can you do it in any other ways?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Can you sort these triangles into three different families and explain how you did 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?

Work out the fractions to match the cards with the same amount of money.

What happens when you try and fit the triomino pieces into these two grids?

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?

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?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?