Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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

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

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?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

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

Dotty Six is a simple dice game that you can adapt in many ways.

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?

Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?

How many starfish could there be on the beach, and how many children, if I can see 28 arms?

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

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.

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

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?

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?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

Use these head, body and leg pieces to make Robot Monsters which are different heights.

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

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?

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?

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

Can you substitute numbers for the letters in these sums?

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

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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?

Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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

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!

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

Try out this number trick. What happens with different starting numbers? What do you notice?

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?

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

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

This task follows on from Build it Up and takes the ideas into three dimensions!

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

Got It game for an adult and child. How can you play so that you know you will always win?