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

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!

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.

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

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

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?

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

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

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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

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?

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?

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

Play this game and see if you can figure out the computer's chosen number.

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.

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?

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

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

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?

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

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

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?

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?

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

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 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?

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

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

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

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

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

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.

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

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

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

Number problems at primary level to work on with others.

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.

Number problems at primary level that may require resilience.

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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?