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

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

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

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.

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?

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

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

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?

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

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?

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

Explore the effect of reflecting in two parallel mirror lines.

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?

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?

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

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".

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. . . .

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?

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.

Explore the effect of combining enlargements.

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?

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...

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

The clues for this Sudoku are the product of the numbers in adjacent squares.

Use the differences to find the solution to this Sudoku.

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

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

There are lots of different methods to find out what the shapes are worth - how many can you find?

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 to. . . .

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?

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

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

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?

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?

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

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 country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Can all unit fractions be written as the sum of two unit fractions?

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?

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

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?