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?

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?

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?

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?

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

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

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.

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

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

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

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

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. . . .

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

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.

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?

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

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

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.

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

In this problem, we're investigating the number of steps we would climb up or down to get out of or into the swimming pool. How could you number the steps below the water?

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?

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

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

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

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

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

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.

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?

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

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

"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 ...?

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

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?

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

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

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.

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

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?

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

A game for two people, who take turns to move the counters. The player to remove the last counter from the board wins.

Can you deduce the pattern that has been used to lay out these bottle tops?