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

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

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

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

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?

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

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?

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

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

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

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

Can you complete this jigsaw of the multiplication square?

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

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

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

An environment which simulates working with Cuisenaire rods.

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

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

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

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?

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

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

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

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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

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

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....?

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?

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?

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

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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

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

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

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

An interactive activity for one to experiment with a tricky tessellation