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?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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

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?

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

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

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!

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?

Can you complete this jigsaw of the multiplication square?

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

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

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

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?

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?

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....?

How many right angles can you make using two sticks?

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

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

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?

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?

How many different rhythms can you make by putting two drums on the wheel?

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

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

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?

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

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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

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?

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?

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?

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?

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

Make one big triangle so the numbers that touch on the small triangles add to 10.

Move just three of the circles so that the triangle faces in the opposite direction.

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

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?

How many different triangles can you make on a circular pegboard that has nine pegs?

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?

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

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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

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

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

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