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Broad Topics > Information and Communications Technology > Interactivities

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?

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. . . .

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.

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. . . .

Percentages for Key Stage 4

Stage: 4 Challenge Level:

A group of interactive resources to support work on percentages Key Stage 4.

Excel Interactive Resource: Number Grid Functions

Stage: 3 and 4 Challenge Level:

Use Excel to investigate the effect of translations around a number grid.

Excel Interactive Resource: Long Multiplication

Stage: 3 and 4 Challenge Level:

Use an Excel spreadsheet to explore long multiplication.

Excel Interactive Resource: Equivalent Fraction Bars

Stage: 3 and 4 Challenge Level:

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

Excel Interactive Resource: the up and Down Game

Stage: 3 and 4 Challenge Level:

Use an interactive Excel spreadsheet to explore number in this exciting game!

Excel Interactive Resource: Fraction Multiplication

Stage: 3 and 4 Challenge Level:

Use Excel to explore multiplication of fractions.

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?

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?

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?

Stage: 2, 3 and 4 Challenge Level:

A metal puzzle which led to some mathematical questions.

Scientific Measurement

Stage: 4 Challenge Level:

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

Shear Magic

Stage: 3 Challenge Level:

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

Tilted Squares

Stage: 3 Challenge Level:

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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.

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.

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

Excel Interactive Resource: Multiples Chain

Stage: 3 and 4 Challenge Level:

Use an interactive Excel spreadsheet to investigate factors and multiples.

Matter of Scale

Stage: 4 Challenge Level:

Prove Pythagoras' Theorem using enlargements and scale factors.

Excel Interactive Resource: Haitch

Stage: 3 and 4 Challenge Level:

An Excel spreadsheet with an investigation.

Excel Interactive Resource: Fraction Addition & Fraction Subtraction

Stage: 3 and 4 Challenge Level:

Use Excel to practise adding and subtracting fractions.

Excel Interactive Resource: Interactive Division

Stage: 3 and 4 Challenge Level:

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

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.

Just Rolling Round

Stage: 4 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?

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.

Guesswork

Stage: 4 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.

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?

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. . . .

Substitution Cipher

Stage: 3 Challenge Level:

Find the frequency distribution for ordinary English, and use it to help you crack the code.

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?

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...

More Number Pyramids

Stage: 3 and 4 Challenge Level:

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

Number Pyramids

Stage: 3 Challenge Level:

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

Napier's Location Arithmetic

Stage: 4 Challenge Level:

Have you seen this way of doing multiplication ?

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.

Proof Sorter - Quadratic Equation

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.

More Magic Potting Sheds

Stage: 3 Challenge Level:

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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?

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.

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?

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. . . .

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.

Card Game (a Simple Version of Clock Patience)

Stage: 4 Challenge Level:

Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in. . . .

Square It

Stage: 1, 2, 3 and 4 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.

Jam

Stage: 4 Challenge Level:

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

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.

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.