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Broad Topics > Information and Communications Technology > Interactivities

Proof Sorter - Geometric Series

Stage: 5 Challenge Level:

This is an interactivity in which you have to sort into the correct order the steps in the proof of the formula for the sum of a geometric series.

Tri-split

Stage: 4 Challenge Level:

A point P is selected anywhere inside an equilateral triangle. What can you say about the sum of the perpendicular distances from P to the sides of the triangle? Can you prove your conjecture?

Polycircles

Stage: 4 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?

The Triangle Game

Stage: 3 and 4 Challenge Level:

Can you discover whether this is a fair game?

Got a Strategy for Last Biscuit?

Stage: 3 and 4 Challenge Level:

Can you beat the computer in the challenging strategy game?

Direct Logic

Stage: 5 Challenge Level:

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

A Number Sequences Resource

Stage: 4 Challenge Level:

This resource contains interactive problems to support work on number sequences at Key Stage 4.

Changing Places

Stage: 4 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. . . .

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.

Nim-interactive

Stage: 3 and 4 Challenge Level:

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.

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.

Jam

Stage: 4 Challenge Level:

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

Stage: 4 and 5 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.

Cellular

Stage: 2, 3 and 4 Challenge Level:

Cellular is an animation that helps you make geometric sequences composed of square cells.

Flower

Stage: 5 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.

Cyclic Triangles

Stage: 5 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.

Pentagon

Stage: 4 Challenge Level:

Find the vertices of a pentagon given the midpoints of its sides.

Vector Racer

Stage: 2, 3 and 4 Challenge Level:

The classic vector racing game brought to a screen near you.

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. . . .

Matrix Countdown

Stage: 5 Challenge Level:

Play countdown with matrices

Proof Sorter - the Square Root of 2 Is Irrational

Stage: 5 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.

Stage: 5 Challenge Level:

With red and blue beads on a circular wire; 'put a red bead between any two of the same colour and a blue between different colours then remove the original beads'. Keep repeating this. What happens?

Proof Sorter - Sum of an AP

Stage: 5 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

Vector Countdown

Stage: 5 Challenge Level:

Play countdown with vectors.

Game of PIG - Sixes

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

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

Red or Black Spinner

Stage: Early years, 1, 2, 3 and 4 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. . . .

Tilting Triangles

Stage: 4 Challenge Level:

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?

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. . . .

Magic W

Stage: 4 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.

Excel Interactive Resource: Fraction Multiplication

Stage: 3 and 4 Challenge Level:

Use Excel to explore multiplication of fractions.

Attractive Tablecloths

Stage: 4 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?

Colour in the Square

Stage: 2, 3 and 4 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?

Square it for Two

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

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

Complex Countdown

Stage: 5 Challenge Level:

Play a more cerebral countdown using complex numbers.

Weekly Challenge 44: Prime Counter

Stage: 5 Challenge Level:

A weekly challenge concerning prime numbers.

Interactive Number Patterns

Stage: 4 Challenge Level:

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

Stage: 2, 3 and 4 Challenge Level:

A metal puzzle which led to some mathematical questions.

Loci Resources

Stage: 4 Challenge Level:

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

Dice and Spinners Environment

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

A tool for generating random integers.

Power Match

Stage: 5 Challenge Level:

Can you locate these values on this interactive logarithmic scale?

Stage: 2, 3 and 4 Challenge Level:

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

Using the Haemocytometer

Stage: 4 Challenge Level:

Practise your skills of proportional reasoning with this interactive haemocytometer.

Fraction and Percentage Card Game

Stage: 3 and 4 Challenge Level:

Match the cards of the same value.

Olympic Magic

Stage: 4 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?

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?

More Number Pyramids

Stage: 3 and 4 Challenge Level:

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

Lottery Simulator

Stage: 2, 3 and 4 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.

Interactive Workout - Mathmo

Stage: 5 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!

Mesh

Stage: 5 Challenge Level:

A spherical balloon lies inside a wire frame. How much do you need to deflate it to remove it from the frame if it remains a sphere?

White Box

Stage: 2, 3, 4 and 5 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.