This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

These two group activities use mathematical reasoning - one is numerical, one geometric.

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

A game for 2 players. Practises subtraction or other maths operations knowledge.

A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!

Find all the numbers that can be made by adding the dots on two dice.

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

Find your way through the grid starting at 2 and following these operations. What number do you end on?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?