Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

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

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.

An investigation that gives you the opportunity to make and justify predictions.

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

"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 ...?

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

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?

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

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.

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!

How many different sets of numbers with at least four members can you find in the numbers in this box?

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

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

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?

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

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?

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

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

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 some different ways to balance this equation?

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

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

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?

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

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

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.

Use the interactivities to complete these Venn diagrams.

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?

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?

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?

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?

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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

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?

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?

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

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.

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.

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?

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?"

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

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

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?

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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

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

A game that tests your understanding of remainders.