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

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

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

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

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

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

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

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

A job needs three men but in fact six people do it. When it is finished they are all paid the same. How much was paid in total, and much does each man get if the money is shared as Fred suggests?

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. . . .

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. . . .

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

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

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?

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

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?

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

The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?

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

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. . . .

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

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

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 ?

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

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. . . .

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

Make some loops out of regular hexagons. What rules can you discover?

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

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

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}.

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

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.

Can you figure out how sequences of beach huts are generated?

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

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.

Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .

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

What is the total number of squares that can be made on a 5 by 5 geoboard?

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?

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

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?

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

Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.

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

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

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.