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?

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

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

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

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

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?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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!

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

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....?

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

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

An environment which simulates working with Cuisenaire rods.

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

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

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

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

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

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

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

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?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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

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?

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 complete this jigsaw of the multiplication square?

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?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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

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

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

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?

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

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

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

An interactive activity for one to experiment with a tricky tessellation

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

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

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.

Exchange the positions of the two sets of counters in the least possible number of moves

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

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

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?

Stop the Clock game for an adult and child. How can you make sure you always win this game?

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

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?