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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > Information and Communications Technology > Interactivities

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Rollin' Rollin' Rollin'

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Two circles of equal radius touch 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?

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Khun Phaen Escapes to Freedom

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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A Resource to Support Work on Transformations

Stage: 4 Challenge Level: Challenge Level:1

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

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Overlaid

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

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

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Overlap

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

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Attractive Tablecloths

Stage: 4 Challenge Level: Challenge Level:1

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?

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Bow Tie

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

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Cubic Rotations

Stage: 4 Challenge Level: Challenge Level:1

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?

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Conway's Chequerboard Army

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Drips

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

An animation that helps you understand the game of Nim.

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Napoleon's Theorem

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

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Poly-puzzle

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Teddy Town

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

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?

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Zodiac

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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Disappearing Square

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

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Online

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

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.

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Jam

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

To avoid losing think of another very well known game where the patterns of play are similar.

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Sliding Puzzle

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

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.

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Icosian Game

Stage: 3 Challenge Level: Challenge Level:1

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

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Game of PIG - Sixes

Stage: 2, 3, 4 and 5 Challenge Level: Challenge Level:1

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

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Fifteen

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

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Colour in the Square

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

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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Muggles Magic

Stage: 3 Challenge Level: Challenge Level:1

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.

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Inside Out

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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Nine Colours

Stage: 3 and 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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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.

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Instant Insanity

Stage: 3, 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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Cogs

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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Excel Interactive Resource: Fraction Multiplication

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

Use Excel to explore multiplication of fractions.

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Power Crazy

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Diagonal Dodge

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

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.

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Got It

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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Factor Lines

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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A Tilted Square

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Tilting Triangles

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Nim-interactive

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

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.

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Partitioning Revisited

Stage: 3 Challenge Level: Challenge Level:1

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

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Conversion Sorter

Stage: 4 Challenge Level: Challenge Level:1

Can you break down this conversion process into logical steps?

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Scientific Measurement

Stage: 4 Challenge Level: Challenge Level:1

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

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Mixed up Mixture

Stage: 4 Challenge Level: Challenge Level:1

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

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Dilution Series Calculator

Stage: 4 Challenge Level: Challenge Level:1

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

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Balancing 1

Stage: 3 Challenge Level: Challenge Level:1

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

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Exact Dilutions

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Countdown

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

Here is a chance to play a version of the classic Countdown Game.

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Advent Calendar 2009

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

A collection of our favourite pictorial problems, one for each day of Advent.

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First Connect Three for Two

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Square it for Two

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

Square It game for an adult and child. Can you come up with a way of always winning this game?

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See the Light

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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White Box

Stage: 2, 3, 4 and 5 Challenge Level: Challenge Level:1

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

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Dice and Spinners Environment

Stage: 1, 2, 3, 4 and 5 Challenge Level: Challenge Level:1

A tool for generating random integers.