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?

"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 ...?

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

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?

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 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.

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

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

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?

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?

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?

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

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

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?

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.

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?

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

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.

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?

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

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

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

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

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

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

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?

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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?

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?

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

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?

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

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.

Number problems at primary level to work on with others.

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?

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

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

Number problems at primary level that may require resilience.

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?

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

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

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?

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?