Resources tagged with: Visualising

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Broad Topics > Mathematical Thinking > Visualising

LOGO Challenge - Circles as Animals

Age 11 to 16 Challenge Level:

See if you can anticipate successive 'generations' of the two animals shown here.

Overlapping Again

Age 7 to 11 Challenge Level:

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

Part the Polygons

Age 7 to 11 Short Challenge Level:

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

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!

Regular Rings 2

Age 7 to 11 Challenge Level:

What shape is made when you fold using this crease pattern? Can you make a ring design?

LOGO Challenge - Triangles-squares-stars

Age 11 to 16 Challenge Level:

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

World of Tan 13 - A Storm in a Tea Cup

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of the convex shapes?

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.

Efficient Cutting

Age 11 to 14 Challenge Level:

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

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?

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?

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?

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.

Coin Cogs

Age 7 to 11 Challenge Level:

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

Square It

Age 11 to 16 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.

On the Edge

Age 11 to 14 Challenge Level:

If you move the tiles around, can you make squares with different coloured edges?

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.

Right or Left?

Age 7 to 11 Challenge Level:

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

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.

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!

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.

Rolling Around

Age 11 to 14 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?

Painted Faces

Age 7 to 11 Challenge Level:

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

Trice

Age 11 to 14 Challenge Level:

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

Framed

Age 11 to 14 Challenge Level:

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .

Tetra Square

Age 11 to 14 Challenge Level:

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

Playground Snapshot

Age 7 to 14 Challenge Level:

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

Coloured Edges

Age 11 to 14 Challenge Level:

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

Trace the Edges

Age 7 to 11 Challenge Level:

On which of these shapes can you trace a path along all of its edges, without going over any edge twice?

Zooming in on the Squares

Age 7 to 14

Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?

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.

Cube Paths

Age 11 to 14 Challenge Level:

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

The Old Goats

Age 11 to 14 Challenge Level:

A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't. . . .

Concrete Wheel

Age 11 to 14 Challenge Level:

A huge wheel is rolling past your window. What do you see?

World of Tan 3 - Mah Ling

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of Mah Ling?

An Unusual Shape

Age 11 to 14 Challenge Level:

Can you maximise the area available to a grazing goat?

Regular Rings 1

Age 7 to 11 Challenge Level:

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

World of Tan 25 - Pentominoes

Age 7 to 11 Challenge Level:

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

World of Tan 20 - Fractions

Age 7 to 11 Challenge Level:

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

World of Tan 30 - Logical Thinking

Age 7 to 11 Challenge Level:

Can you logically construct these silhouettes using the tangram pieces?

World of Tan 9 - Animals

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of the camel and giraffe?

World of Tan

Age 5 to 11 Challenge Level:

Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.

Polygon Pictures

Age 11 to 14 Challenge Level:

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

World of Tan 4 - Monday Morning

Age 7 to 11 Challenge Level:

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

World of Tan 5 - Dragon

Age 7 to 11 Challenge Level:

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

World of Tan 12 - All in a Fluff

Age 7 to 11 Challenge Level:

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

World of Tan 15 - Millennia

Age 7 to 11 Challenge Level:

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

World of Tan 1 - Granma T

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of Granma T?

World of Tan 24 - Clocks

Age 7 to 11 Challenge Level:

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

World of Tan 28 - Concentrating on Coordinates

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of the playing piece?