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

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

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

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.

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?

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?

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

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

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

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?

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.

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Can you find the chosen number from the grid using the clues?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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?

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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.

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?

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

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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

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

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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

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?

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

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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?

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

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.

"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 ...?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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

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

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

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

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

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

If you have only four weights, where could you place them in order to balance this equaliser?

A game that tests your understanding of remainders.