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Broad Topics > Information and Communications Technology > Interactivities

### Proof Sorter - Sum of an AP

##### Age 16 to 18 Challenge Level:

Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing

### Proof Sorter - Quadratic Equation

##### Age 14 to 18 Challenge Level:

This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.

### Direct Logic

##### Age 16 to 18 Challenge Level:

Can you work through these direct proofs, using our interactive proof sorters?

### Proof Sorter - Geometric Series

##### Age 16 to 18 Challenge Level:

Can you correctly order the steps in the proof of the formula for the sum of a geometric series?

### The Triangle Game

##### Age 11 to 16 Challenge Level:

Can you discover whether this is a fair game?

### Matter of Scale

##### Age 14 to 16 Challenge Level:

Prove Pythagoras' Theorem using enlargements and scale factors.

### Attractive Tablecloths

##### Age 14 to 16 Challenge Level:

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?

### Napoleon's Hat

##### Age 16 to 18 Challenge Level:

Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?

### Interactive Number Patterns

##### Age 14 to 16 Challenge Level:

How good are you at finding the formula for a number pattern ?

### Cyclic Triangles

##### Age 16 to 18 Challenge Level:

Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.

### Sliding Puzzle

##### Age 11 to 16 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.

### Jam

##### Age 14 to 16 Challenge Level:

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

### Polycircles

##### Age 14 to 16 Challenge Level:

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

### Nine Colours

##### Age 11 to 16 Challenge Level:

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

### A Tilted Square

##### Age 14 to 16 Challenge Level:

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

### Colour in the Square

##### Age 7 to 16 Challenge Level:

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?

##### Age 14 to 16 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. . . .

### Squaring the Circle and Circling the Square

##### Age 14 to 16 Challenge Level:

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

### Magic W

##### Age 14 to 16 Challenge Level:

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

### Got a Strategy for Last Biscuit?

##### Age 11 to 16 Challenge Level:

Can you beat the computer in the challenging strategy game?

### Olympic Magic

##### Age 14 to 16 Challenge Level:

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

### Factors and Multiples Game

##### Age 7 to 16 Challenge Level:

A game in which players take it in turns to choose a number. Can you block your opponent?

### Euclid's Algorithm I

##### Age 16 to 18

How can we solve equations like 13x + 29y = 42 or 2x +4y = 13 with the solutions x and y being integers? Read this article to find out.

### Graphical Interpretation

##### Age 14 to 16 Challenge Level:

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

### Solving with Euclid's Algorithm

##### Age 14 to 18 Challenge Level:

A java applet that takes you through the steps needed to solve a Diophantine equation of the form Px+Qy=1 using Euclid's algorithm.

### Matrix Countdown

##### Age 16 to 18 Challenge Level:

Play countdown with matrices

### Loci Resources

##### Age 14 to 16 Challenge Level:

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

### Crossword 1

##### Age 16 to 18 Challenge Level:

A mathematically themed crossword.

### Guesswork

##### Age 14 to 16 Challenge Level:

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

### Changing Places

##### Age 14 to 16 Challenge Level:

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

### Square It

##### Age 11 to 16 Challenge Level:

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

### Red or Black Spinner

##### Age 3 to 16 Challenge Level:

A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .

### Trigonometric Protractor

##### Age 14 to 16 Challenge Level:

An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.

### Fractions and Percentages Card Game

##### Age 11 to 16 Challenge Level:

Match the cards of the same value.

### Just Rolling Round

##### Age 14 to 16 Challenge Level:

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

### Complex Countdown

##### Age 16 to 18 Challenge Level:

Play a more cerebral countdown using complex numbers.

### Excel Interactive Resource: Haitch

##### Age 11 to 16 Challenge Level:

An Excel spreadsheet with an investigation.

### Using the Haemocytometer

##### Age 14 to 16 Challenge Level:

Practise your skills of proportional reasoning with this interactive haemocytometer.

### Countdown Fractions

##### Age 11 to 16 Challenge Level:

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

### Spinners Environment

##### Age 5 to 18 Challenge Level:

A tool for generating random integers.

### White Box

##### Age 7 to 18 Challenge Level:

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

### Interactive Workout - Mathmo

##### Age 16 to 18 Short Challenge Level:

Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!

### Lottery Simulator

##### Age 7 to 16 Challenge Level:

Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.

### Power Match

##### Age 16 to 18 Challenge Level:

Can you locate these values on this interactive logarithmic scale?

### Flower

##### Age 16 to 18 Challenge Level:

Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.

### Proof Sorter - the Square Root of 2 Is Irrational

##### Age 16 to 18 Challenge Level:

Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.

### Excel Interactive Resource: Fraction Addition & Fraction Subtraction

##### Age 11 to 16 Challenge Level:

Use Excel to practise adding and subtracting fractions.

### Ratio Pairs 3

##### Age 11 to 16 Challenge Level:

Match pairs of cards so that they have equivalent ratios.

### Cushion Ball Interactivity

##### Age 14 to 16 Challenge Level:

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

### Tessellation Interactivity

##### Age 7 to 16 Challenge Level:

An environment that enables you to investigate tessellations of regular polygons