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Broad Topics > Using, Applying and Reasoning about Mathematics > Visualising

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Change Around

Age 5 to 7 Challenge Level:

Move just three of the circles so that the triangle faces in the opposite direction.

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Overlaps

Age 5 to 7 Challenge Level:

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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Folding, Cutting and Punching

Age 7 to 11 Challenge Level:

Exploring and predicting folding, cutting and punching holes and making spirals.

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Take One Example

Age 5 to 11

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

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Horizontal Vertical

Age 5 to 7 Challenge Level:

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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Colour Wheels

Age 7 to 11 Challenge Level:

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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Alquerque II

Age 5 to 7 Challenge Level:

A variant on the game Alquerque

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Posting Triangles

Age 5 to 7 Challenge Level:

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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Red Even

Age 7 to 11 Challenge Level:

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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Making Maths: Rolypoly

Age 5 to 11 Challenge Level:

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

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One Big Triangle

Age 5 to 7 Challenge Level:

Make one big triangle so the numbers that touch on the small triangles add to 10.

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Making Tangrams

Age 7 to 11 Challenge Level:

Here's a simple way to make a Tangram without any measuring or ruling lines.

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World of Tan 27 - Sharing

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of Little Fung at the table?

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World of Tan 26 - Old Chestnut

Age 7 to 11 Challenge Level:

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

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World of Tan 28 - Concentrating on Coordinates

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

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World of Tan 29 - the Telephone

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of this telephone?

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Sea Defences

Age 7 to 14 Challenge Level:

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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World of Tan 30 - Logical Thinking

Age 7 to 11 Challenge Level:

Can you logically construct these silhouettes using the tangram pieces?

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Fractional Triangles

Age 7 to 11 Challenge Level:

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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L-ateral Thinking

Age 5 to 11 Challenge Level:

Try this interactive strategy game for 2

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Taking Steps

Age 7 to 11 Challenge Level:

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

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World of Tan 8 - Sports Car

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of this sports car?

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Cover the Camel

Age 5 to 7 Challenge Level:

Can you cover the camel with these pieces?

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Tessellate the Triominoes

Age 5 to 7 Challenge Level:

What happens when you try and fit the triomino pieces into these two grids?

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World of Tan 9 - Animals

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of this goat and giraffe?

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The Development of Spatial and Geometric Thinking: the Importance of Instruction.

Age 5 to 11

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

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Makeover

Age 5 to 11 Challenge Level:

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

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Turning Cogs

Age 7 to 11 Challenge Level:

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

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Seeing Squares

Age 5 to 11 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.

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Cubes Cut Into Four Pieces

Age 5 to 7 Challenge Level:

Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?

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World of Tan 25 - Pentominoes

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of these people?

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World of Tan 24 - Clocks

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of these clocks?

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Penta Play

Age 7 to 11 Challenge Level:

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

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Start Cube Drilling

Age 5 to 7 Challenge Level:

Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?

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World of Tan 15 - Millennia

Age 7 to 11 Challenge Level:

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

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World of Tan 14 - Celebrations

Age 7 to 11 Challenge Level:

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

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Hundred Square

Age 5 to 7 Challenge Level:

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

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Twice as Big?

Age 7 to 11 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.

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Shadow Play

Age 5 to 7 Challenge Level:

Here are shadows of some 3D shapes. What shapes could have made them?

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World of Tan 16 - Time Flies

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of the candle and sundial?

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Put Yourself in a Box

Age 7 to 11 Challenge Level:

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

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World of Tan 18 - Soup

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

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World of Tan 17 - Weather

Age 7 to 11 Challenge Level:

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

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Right or Left?

Age 7 to 11 Challenge Level:

Which of these dice are right-handed and which are left-handed?

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World of Tan 2 - Little Ming

Age 7 to 11 Challenge Level:

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

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Endless Noughts and Crosses

Age 7 to 11 Challenge Level:

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

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World of Tan 20 - Fractions

Age 7 to 11 Challenge Level:

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

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World of Tan 19 - Working Men

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

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World of Tan 21 - Almost There Now

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

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World of Tan 22 - an Appealing Stroll

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of the child walking home from school?