Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

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...

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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.

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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

What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .

Can you describe this route to infinity? Where will the arrows take you next?

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Explore the effect of reflecting in two parallel mirror lines.

Explore the effect of combining enlargements.

How many different symmetrical shapes can you make by shading triangles or squares?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

A game for 2 or more people, based on the traditional card game Rummy. Players aim to make two `tricks', where each trick has to consist of a picture of a shape, a name that describes that shape, and. . . .

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

Start with two numbers. This is the start of a sequence. The next number is the average of the last two numbers. Continue the sequence. What will happen if you carry on for ever?

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try. . . .

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

Can you see how to build a harmonic triangle? Can you work out the next two rows?

A decorator can buy pink paint from two manufacturers. What is the least number he would need of each type in order to produce different shades of pink.

A jigsaw where pieces only go together if the fractions are equivalent.

Is it always possible to combine two paints made up in the ratios 1:x and 1:y and turn them into paint made up in the ratio a:b ? Can you find an efficent way of doing this?

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?