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?

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

How many trains can you make which are the same length as Matt's, using rods that are identical?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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

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'.

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?

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?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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?

How many different sets of numbers with at least four members can you find in the numbers in this box?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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

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?

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

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?

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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 smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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

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

"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 ...?

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

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

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

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

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?

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

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

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

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?

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?

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?

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?

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

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

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

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

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?