Follow this recipe for sieving numbers and see what interesting patterns emerge.

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

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?

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

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?

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

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 many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

Given the products of adjacent cells, can you complete this Sudoku?

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

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.

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

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?

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

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.

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

A game that tests your understanding of remainders.

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

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

Number problems at primary level to work on with others.

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

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?

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

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

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

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.

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!

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?

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

There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?

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

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

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

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

I put eggs into a basket in groups of 7 and noticed that I could easily have divided them into piles of 2, 3, 4, 5 or 6 and always have one left over. How many eggs were in the basket?

Can you find what the last two digits of the number $4^{1999}$ are?

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.

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?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

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

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?

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?

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

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