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.

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?

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

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

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

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

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?

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?

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?

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

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.

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

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?

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?

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.

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

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?

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

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

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.

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?

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

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

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?

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

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

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

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?

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

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

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?

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

Investigate what happens when you add house numbers along a street in different ways.

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?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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?

This challenge is about finding the difference between numbers which have the same tens digit.

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

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?

This dice train has been made using specific rules. How many different trains can you make?