Play this game and see if you can figure out the computer's chosen number.

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Follow this recipe for sieving numbers and see what interesting patterns emerge.

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

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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?

In how many ways can you fit all three pieces together to make shapes with line symmetry?

How much of the square is coloured blue? How will the pattern continue?

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

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

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?

A triomino is a flat L shape made from 3 square tiles. A chess board is marked into squares the same size as the tiles and just one square, anywhere on the board, is coloured red. Can you cover the board with trionimoes so that only the square is exposed?

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

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

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

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

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?

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?

L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?

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?

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

Can you explain the surprising results Jo found when she calculated the difference between square numbers?