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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
Interactivities. Visualising. Generalising. Pythagoras' theorem. Squares. Area. smartphone. Logo. Mathematical reasoning & proof.

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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?

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.

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.

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.

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?

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.

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. . . .

Number Pyramids

Stage: 3 Challenge Level:

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

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?

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?

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.

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

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.

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?

Conway's Chequerboard Army

Stage: 3 Challenge Level:

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

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.

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. . . .

Twice as Big?

Stage: 2 Challenge Level:

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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?

Three Squares

Stage: 1 and 2 Challenge Level:

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

Stage: 2 Challenge Level:

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

The Triangle Game

Stage: 3 and 4 Challenge Level:

Can you discover whether this is a fair game?

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?

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?

Nine Colours

Stage: 3 Challenge Level:

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

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?

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.

Shuffle Shriek

Stage: 3 Challenge Level:

Can you find all the 4-ball shuffles?

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.

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. . . .

Online

Stage: 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.

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?

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.

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.

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 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?

Makeover

Stage: 1 and 2 Challenge Level:

Exchange the positions of the two sets of counters in the least possible number of moves

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.

Noughts and Crosses

Stage: 2 Challenge Level:

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

Coin Cogs

Stage: 2 Challenge Level:

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

World of Tan 15 - Millennia

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the workmen?

World of Tan 17 - Weather

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

Domino Numbers

Stage: 2 Challenge Level:

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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.

Stage: 2, 3 and 4 Challenge Level:

A metal puzzle which led to some mathematical questions.

Fault-free Rectangles

Stage: 2 Challenge Level:

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

The Path of the Dice

Stage: 2 Challenge Level:

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

World of Tan 14 - Celebrations

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

Shuffles Tutorials

Stage: 3 Challenge Level:

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