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

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

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?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

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?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

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

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

How would you count the number of fingers in these pictures?

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

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?

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

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

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .

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?

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

There were 22 legs creeping across the web. How many flies? How many spiders?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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

Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?

I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

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?

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

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?

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

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?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

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

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