Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .

Here are three 'tricks' to amaze your friends. But the really clever trick is explaining to them why these 'tricks' are maths not magic. Like all good magicians, you should practice by trying. . . .

If you know the perimeter of a right angled triangle, what can you say about the area?

Kyle and his teacher disagree about his test score - who is right?

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

How good are you at finding the formula for a number pattern ?

Surprising numerical patterns can be explained using algebra and diagrams...

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

The sums of the squares of three related numbers is also a perfect square - can you explain why?

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible.

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.

A task which depends on members of the group noticing the needs of others and responding.

Where should you start, if you want to finish back where you started?

Account of an investigation which starts from the area of an annulus and leads to the formula for the difference of two squares.

Can you explain what is going on in these puzzling number tricks?

Can you explain why a sequence of operations always gives you perfect squares?

The Number Jumbler can always work out your chosen symbol. Can you work out how?

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

What is special about the difference between squares of numbers adjacent to multiples of three?

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?

A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . .

There are unexpected discoveries to be made about square numbers...

A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees. . . .

Play around with the Fibonacci sequence and discover some surprising results!

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

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 figure out how sequences of beach huts are generated?

Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?

Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I. . . .

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

Attach weights of 1, 2, 4, and 8 units to the four attachment points on the bar. Move the bar from side to side until you find a balance point. Is it possible to predict that position?

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?