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?

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

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?

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

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.

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.

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?

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

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

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

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

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.

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

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

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

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?

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

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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?

"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 ...?

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?

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.

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

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?

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

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

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?

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?

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?

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.

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

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

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?

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

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

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

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

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. . . .

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

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?