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

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 ...?

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.

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

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

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?

Use the interactivities to complete these Venn diagrams.

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

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?

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 make square numbers by adding two prime numbers together?

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

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?

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.

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?

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

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

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?

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

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

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

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?

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

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 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?

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

Can you work out some different ways to balance this equation?

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?

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?

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?

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.

Can you complete this jigsaw of the multiplication square?

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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

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

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?

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

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

Number problems at primary level that may require determination.

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

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

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