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Broad Topics > Information and Communications Technology > Interactivities

Semi-regular Tessellations

Stage: 3 Challenge Level:

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

Number Pyramids

Stage: 3 Challenge Level:

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

Cosy Corner

Stage: 3 Challenge Level:

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?

Subtended Angles

Stage: 3 Challenge Level:

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

Triangles in Circles

Stage: 3 Challenge Level:

How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?

Cops and Robbers

Stage: 2 and 3 Challenge Level:

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

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

Balancing 2

Stage: 3 Challenge Level:

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

Stars

Stage: 3 Challenge Level:

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?

Got It

Stage: 2 and 3 Challenge Level:

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.

Balancing 1

Stage: 3 Challenge Level:

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.

Multiplication Tables - Matching Cards

Stage: 1, 2 and 3 Challenge Level:

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

Bow Tie

Stage: 3 Challenge Level:

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.

Shuffles Tutorials

Stage: 3 Challenge Level:

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

Fifteen

Stage: 2 and 3 Challenge Level:

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

Isosceles Triangles

Stage: 3 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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?

Lost

Stage: 3 Challenge Level:

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

Diamond Mine

Stage: 3 Challenge Level:

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

Drips

Stage: 2 and 3 Challenge Level:

An animation that helps you understand the game of Nim.

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...

Balancing 3

Stage: 3 Challenge Level:

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.

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?

Two's Company

Stage: 3 Challenge Level:

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

Flip Flop - Matching Cards

Stage: 1, 2 and 3 Challenge Level:

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

Flippin' Discs

Stage: 3 Challenge Level:

Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?

Rolling Around

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?

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.

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.

Speeding Up, Slowing Down

Stage: 3 Challenge Level:

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

How Far Does it Move?

Stage: 3 Challenge Level:

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

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?

Rollin' Rollin' Rollin'

Stage: 3 Challenge Level:

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?

Tessellation Interactivity

Stage: 2, 3 and 4 Challenge Level:

An environment that enables you to investigate tessellations of regular polygons

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?

Online

Stage: 2 and 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.

Jam

Stage: 4 Challenge Level:

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

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?

First Connect Three for Two

Stage: 2 and 3 Challenge Level:

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.

Overlap

Stage: 3 Challenge Level:

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. . . .

Up and Across

Stage: 3 Challenge Level:

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

Disappearing Square

Stage: 3 Challenge Level:

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. . . .

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.

See the Light

Stage: 2 and 3 Challenge Level:

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

Top Coach

Stage: 3 Challenge Level:

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

Conway's Chequerboard Army

Stage: 3 Challenge Level:

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

Countdown

Stage: 2 and 3 Challenge Level:

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

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.

Shuffle Shriek

Stage: 3 Challenge Level:

Can you find all the 4-ball shuffles?

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. . . .