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Resources tagged with Interactivities similar to Weekly Problem 46 - 2009:

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Other tags that relate to Weekly Problem 46 - 2009
Squares. Visualising. Mathematical reasoning & proof. Generalising. Interactivities. Area. Logo. Circles. Pythagoras' theorem.

There are 221 results

Broad Topics > Information and Communications Technology > Interactivities

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?

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?

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?

Poly-puzzle

Stage: 3 Challenge Level:

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.

Muggles Magic

Stage: 3 Challenge Level:

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.

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. . . .

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?

Conway's Chequerboard Army

Stage: 3 Challenge Level:

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

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.

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.

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. . . .

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.

When Will You Pay Me? Say the Bells of Old Bailey

Stage: 3 Challenge Level:

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

Stage: 2, 3 and 4 Challenge Level:

A metal puzzle which led to some mathematical questions.

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. . . .

Simple Counting Machine

Stage: 3 Challenge Level:

Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?

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.

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.

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.

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?

The Triangle Game

Stage: 3 and 4 Challenge Level:

Can you discover whether this is a fair game?

Three Squares

Stage: 1 and 2 Challenge Level:

What is the greatest number of squares you can make by overlapping three squares?

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?

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

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.

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.

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?

Shuffle Shriek

Stage: 3 Challenge Level:

Can you find all the 4-ball shuffles?

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?

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?

Number Pyramids

Stage: 3 Challenge Level:

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

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?

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.

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...

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.

Instant Insanity

Stage: 3, 4 and 5 Challenge Level:

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.

Triangle Pin-down

Stage: 2 Challenge Level:

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Diamond Mine

Stage: 3 Challenge Level:

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

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?

Round Peg Board

Stage: 1 and 2 Challenge Level:

A generic circular pegboard resource.

Shuffles Tutorials

Stage: 3 Challenge Level:

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

Train

Stage: 2 Challenge Level:

A train building game for 2 players.

Fault-free Rectangles

Stage: 2 Challenge Level:

Find out what a "fault-free" rectangle is and try to make some of your own.

How Random!

Stage: 2 Challenge Level:

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

Number Differences

Stage: 2 Challenge Level:

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Coin Cogs

Stage: 2 Challenge Level:

Can you work out what is wrong with the cogs on a UK 2 pound coin?

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.

Teddy Town

Stage: 1, 2 and 3 Challenge Level:

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?

Fraction and Percentage Card Game

Stage: 3 and 4 Challenge Level:

Match the cards of the same value.

World of Tan 26 - Old Chestnut

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?