Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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?

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

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

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

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. . . .

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

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

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

First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...

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

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

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

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

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

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. . . .

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

Choose any four consecutive even numbers. Multiply the two middle numbers together. Multiply the first and last numbers. Now subtract your second answer from the first. Try it with your own. . . .

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

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. . . .

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. . . .

The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 � 1 [1/3]. What other numbers have the sum equal to the product and can this be so. . . .

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

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

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

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

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. . . .

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.

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

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

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

How many winning lines can you make in a three-dimensional version of noughts and crosses?

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

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?

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 ?

What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

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.

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?