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?

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

Are these statements always true, sometimes true or never true?

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

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

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

"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 ...?

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?

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?

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?

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?

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?

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?

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

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?

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

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?

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

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

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?

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

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?

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?

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?

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?

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

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?

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

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

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

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

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

Number problems at primary level that may require resilience.

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

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.

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

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

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.

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?

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?

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

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?

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

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