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

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Poly Plug Pattern

Age 5 to 7 Challenge Level:

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

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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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Hexpentas

Age 5 to 11 Challenge Level:

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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L-ateral Thinking

Age 5 to 11 Challenge Level:

Try this interactive strategy game for 2

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Shape Mapping

Age 7 to 11 Challenge Level:

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

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Stringy Quads

Age 7 to 11 Challenge Level:

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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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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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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28 and It's Upward and Onward

Age 7 to 11 Challenge Level:

Can you find ways of joining cubes together so that 28 faces are visible?

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Rearrange the Square

Age 5 to 7 Challenge Level:

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

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Flip

Age 7 to 11 Challenge Level:

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

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Let Us Reflect

Age 7 to 11 Challenge Level:

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

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Peg Rotation

Age 7 to 11 Challenge Level:

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

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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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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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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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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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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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World of Tan 4 - Monday Morning

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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Fred the Class Robot

Age 7 to 11 Challenge Level:

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

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World of Tan 5 - Rocket

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of the rocket?

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Multiplication Series: Illustrating Number Properties with Arrays

Age 5 to 11

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

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World of Tan 13 - A Storm in a Tea Cup

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of these convex shapes?

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World of Tan 7 - Gat Marn

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of this plaque design?

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Dragons and Swans

Age 5 to 7 Challenge Level:

A game for two players. You'll need some counters.

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Ten Hidden Squares

Age 7 to 11 Challenge Level:

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

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World of Tan 12 - All in a Fluff

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of these rabbits?

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World of Tan 11 - the Past, Present and Future

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of the telescope and microscope?

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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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Cut Nets

Age 7 to 11 Challenge Level:

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

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A Chain of Eight Polyhedra

Age 7 to 11 Challenge Level:

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

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Hexagon Transformations

Age 7 to 11 Challenge Level:

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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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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Matchsticks

Age 7 to 11 Challenge Level:

Reasoning about the number of matches needed to build squares that share their sides.

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Redblue

Age 7 to 11 Challenge Level:

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

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Construct-o-straws

Age 7 to 11 Challenge Level:

Make a cube out of straws and have a go at this practical challenge.

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Tangram Paradox

Age 7 to 11 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!

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Tricky Triangles

Age 5 to 7 Challenge Level:

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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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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Tangram Tangle

Age 5 to 7 Challenge Level:

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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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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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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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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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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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 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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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?