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

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?

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

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?

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

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?

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

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?

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

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?

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

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.

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

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

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

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?

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

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

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?

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?

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?

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

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

Ben’s class were making 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?

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

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

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?

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.

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?

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?

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?

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

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?

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

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?

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

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

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.

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

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

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.

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 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?