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

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

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

Prove Pythagoras' Theorem using enlargements and scale factors.

Use Excel to explore multiplication of fractions.

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Explore displacement/time and velocity/time graphs with this mouse motion sensor.

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Can you explain the strategy for winning this game with any target?

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

Work out how to light up the single light. What's the rule?

Which dilutions can you make using 10ml pipettes and 100ml measuring cylinders?

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .

A metal puzzle which led to some mathematical questions.

Which exact dilution ratios can you make using only 2 dilutions?

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?

Can you fill in the mixed up numbers in this dilution calculation?

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

Can you work out which spinners were used to generate the frequency charts?

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

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

Can you break down this conversion process into logical steps?

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

Use Excel to investigate the effect of translations around a number grid.

An Excel spreadsheet with an investigation.

Use an interactive Excel spreadsheet to explore number in this exciting game!

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

Find the frequency distribution for ordinary English, and use it to help you crack the code.

Use an Excel spreadsheet to explore long multiplication.

A group of interactive resources to support work on percentages Key Stage 4.

Use Excel to practise adding and subtracting fractions.

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

Use an interactive Excel spreadsheet to investigate factors and multiples.

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?