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?

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

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?

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

Can you complete this jigsaw of the multiplication square?

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?"

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

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?

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?

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

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

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?

Given the products of diagonally opposite cells - can you complete this Sudoku?

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?

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?

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.

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?

A game that tests your understanding of remainders.

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 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.

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

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

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.

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?

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

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

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

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?

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

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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

An environment which simulates working with Cuisenaire rods.

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.

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

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.

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A

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

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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

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.

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

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

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