Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?

An investigation that gives you the opportunity to make and justify predictions.

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Can you find any perfect numbers? Read this article to find out more...

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

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

56 406 is the product of two consecutive numbers. What are these two numbers?

An environment which simulates working with Cuisenaire rods.

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

Got It game for an adult and child. How can you play so that you know you will always win?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

Have a go at balancing this equation. Can you find different ways of doing it?

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

Factors and Multiples game for an adult and child. How can you make sure you win this game?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Can you work out some different ways to balance this equation?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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?

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?