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?

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 find different ways of creating paths using these paving slabs?

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

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

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?

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?

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

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?

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

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?

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?

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

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.

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.

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

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

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?

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?

Number problems at primary level to work on with others.

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

Number problems at primary level that may require resilience.

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

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?

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

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

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?

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

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

Can you complete this jigsaw of the multiplication square?

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?

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?

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

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.

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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

Can you sort numbers into sets? Can you give each set a name?

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

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

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

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?

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?