Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?

While musing about the difficulties children face in comprehending number structure, notation, etc., it occured to the author that there is a vast array of occasions when numbers and signs are used. . . .

Buzzy Bee was building a honeycomb. She decorated the honeycomb with a pattern using numbers. Can you discover Buzzy's pattern and fill in the empty cells for her?

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?

This article for pupils explores what makes numbers special or lucky, and looks at the numbers that are all around us every day.

25 students are queuing in a straight line. How many are there between Julia and Jenny?

This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.

Helen Joyce interviews the neuropsychologist Brian Butterworth whose research has shown that we are all born with a "built-in" sense of cardinal number.

How many legs do each of these creatures have? How many pairs is that?

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

What could these drawings, found in a cave in Spain, represent?

Ruth Trundley outlines her doctoral research and concludes that development of an understanding of cardinality is a crucial element of counting that can be overlooked.

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

What do you see as you watch this video? Can you create a similar video for the number 12?

Daisy and Akram were making number patterns. Daisy was using beads that looked like flowers and Akram was using cube bricks. First they were counting in twos.

Here is a version of the game 'Happy Families' for you to make and play.

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

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?

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

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

How could you estimate the number of pencils/pens in these pictures?

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

Can you work out how many apples there are in this fruit bowl if you know what fraction there are?

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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

You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?

Nim-7 game for an adult and child. Who will be the one to take the last counter?

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

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

Can you find a path from a number at the top of this network to the bottom which goes through each number from 1 to 9 once and once only?

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

Can you work out how to win this game of Nim? Does it matter if you go first or second?

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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?

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

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?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.