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

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

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.

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.

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?

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. . . .

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?

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

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

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?

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?

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

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

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?

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

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?

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

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

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...

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

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

Can you find the area of a parallelogram defined by two vectors?

Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?

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?

Two ladders are propped up against facing walls. The end of the first ladder is 10 metres above the foot of the first wall. The end of the second ladder is 5 metres above the foot of the second. . . .

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

What is the same and what is different about these circle questions? What connections can you make?

If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at. . . .

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

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

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?

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

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. . . .

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

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

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

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?

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 napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed .

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

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

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.

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?