Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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

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

A game in which players take it in turns to choose a number. Can you block your opponent?

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!

Use the interactivities to complete these Venn diagrams.

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

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

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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

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.

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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

A game that tests your understanding of remainders.

Can you complete this jigsaw of the multiplication square?

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?

A challenge that requires you to apply your knowledge of the properties of numbers. Can you fill all the squares on the board?

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

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

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?

Given the products of diagonally opposite 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.

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.

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

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. . . .

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?"

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

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?

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?

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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?

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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

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

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

Can you find a way to identify times tables after they have been shifted up?

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

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?

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

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.

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.