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Tablecloth

Stage: 4 Challenge Level:

Colour the squares of the square tablecloth so that each square is the same colour as all the symmetrically placed squares and a different colour from the rest of the squares.

Conway's Chequerboard Army

Stage: 3 Challenge Level:

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

Roundabout

Stage: 3 Challenge Level:

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Overlaid

Stage: 2, 3 and 4 Challenge Level:

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

Nine Colours

Stage: 3 Challenge Level:

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

Khun Phaen Escapes to Freedom

Stage: 3 Challenge Level:

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

Square Coordinates

Stage: 3 Challenge Level:

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?

Muggles Magic

Stage: 3 Challenge Level:

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

Diagonal Dodge

Stage: 2 and 3 Challenge Level:

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

Picturing Triangle Numbers

Stage: 3 Challenge Level:

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

Triangles and Petals

Stage: 4 Challenge Level:

An equilateral triangle rotates polygons with equal length sides and produces an outline like a flower. What is its perimeter?

When Will You Pay Me? Say the Bells of Old Bailey

Stage: 3 Challenge Level:

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

Konigsberg Plus

Stage: 3 Challenge Level:

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.

100 Percent

Stage: 3 Challenge Level:

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100 percent.

Rollin' Rollin' Rollin'

Stage: 3 Challenge Level:

Two circles of equal radius kiss at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

You Owe Me Five Farthings, Say the Bells of St Martin's

Stage: 3 Challenge Level:

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

Cubic Rotations

Stage: 4 Challenge Level:

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?

Cogs

Stage: 3 Challenge Level:

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. . . .

Cushion Ball

Stage: 4 Challenge Level:

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

A Resource to Support Work on Coordinates

Stage: 4 Challenge Level:

This resource contains a range of problems and interactivities on the theme of coordinates in two and three dimensions.

Shuffle Shriek

Stage: 3 Challenge Level:

Can you find all the 4-ball shuffles?

Ratio Pairs 3

Stage: 3 and 4 Challenge Level:

Match pairs of cards so that they have equivalent ratios.

Excel Interactive Resource: Fraction Multiplication

Stage: 3 and 4 Challenge Level:

Use Excel to explore multiplication of fractions.

Garfield's Proof

Stage: 4 Challenge Level:

Rotate a copy of the trapezium about the centre of the longest side of the blue triangle to make a square. Find the area of the square and then derive a formula for the area of the trapezium.

Sliding Puzzle

Stage: 1, 2, 3 and 4 Challenge Level:

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

Got It! Article

Stage: 2 and 3

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

A Resource to Support Work on Transformations

Stage: 4 Challenge Level:

This resources contains a series of interactivities designed to support work on transformations at Key Stage 4.

Inside Out

Stage: 4 Challenge Level:

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. . . .

Loci Resources

Stage: 4 Challenge Level:

This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.

Volume of a Pyramid and a Cone

Stage: 3

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

Partitioning Revisited

Stage: 3 Challenge Level:

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

Cushion Ball Interactivity

Stage: 4 Challenge Level:

The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"

Number Tricks

Stage: 3 Challenge Level:

Think of a number add 3 double add 4 halve take away the number you started with ? What did you end up with? Now try again starting with a different number. Try again? Try starting with a fraction. . . .

Zodiac

Stage: 4 Challenge Level:

Shuffles Tutorials

Stage: 3

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

More Number Pyramids

Stage: 3 Challenge Level:

Are there any patterns within the pyramid? Can you explain why you only get multiples of 4 at the top when you start with an integer in the bottom left hand corner?

Number Pyramids

Stage: 3 Challenge Level:

Using the same starter numbers 2, 1, 4 and 6 can you get a larger total at the top of the pyramid? What is the largest total you can get?

Isosceles Triangles

Stage: 3 Challenge Level:

Draw some isosceles triangles with an area of 9 cm squared and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

A Tilted Square

Stage: 4 Challenge Level:

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

Squaring the Circle and Circling the Square

Stage: 4 Challenge Level:

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

An Unhappy End

Stage: 3 Challenge Level:

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

Tessellation Interactivity

Stage: 2, 3 and 4 Challenge Level:

An environment that enables you to investigate tessellations of regular polygons

Diamond Mine

Stage: 3 Challenge Level:

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

Tracking Points

Stage: 4 Challenge Level:

Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?

Multiplication Tables - Matching Cards

Stage: 1, 2, 3 and 4 Challenge Level:

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

Online - a Game for Two Players

Stage: 3 Challenge Level:

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

Fifteen

Stage: 3 Challenge Level:

Fifteen is a game for two players that you can play anywhere, anytime. Players take it in turns to select a number from 1 to 9. The aim is to choose 3 numbers that total 15.

Archery

Stage: 3 Challenge Level:

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

Thank Your Lucky Stars

Stage: 4 Challenge Level:

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

First Connect Three

Stage: 2 and 3 Challenge Level:

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?