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?

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?

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?

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

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

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

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.

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?

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

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?

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

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?

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?

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

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

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

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?

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

"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 ...?

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?

How will you work out which numbers have been used to create this multiplication square?

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?

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!

Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.

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

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?

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

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

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

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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?

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

Number problems at primary level that may require resilience.

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

Can you make square numbers by adding two prime numbers together?

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?

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.

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

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

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?

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