Resources tagged with: Visualising

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Broad Topics > Thinking Mathematically > Visualising

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?

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?

Building with Cubes

Age 5 to 7 Challenge Level:

Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?

How Many Pieces This Time?

Age 5 to 7 Challenge Level:

How many pieces of string have been used in these patterns? Can you describe how you know?

The Development of Spatial and Geometric Thinking: Co-ordinating Space in Drawings

Age 5 to 7

This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.

Triangular Faces

Age 7 to 11 Challenge Level:

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

A Puzzling Cube

Age 7 to 11 Challenge Level:

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

Green Cube, Yellow Cube

Age 7 to 11 Challenge Level:

How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 x 2 cube that is green all over AND a 2 x 2 x 2 cube that is yellow all over?

Holes

Age 5 to 11 Challenge Level:

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

More Building with Cubes

Age 7 to 11 Challenge Level:

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

How Many Pieces?

Age 5 to 7 Challenge Level:

How many loops of string have been used to make these patterns?

Dragons and Swans

Age 5 to 7 Challenge Level:

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

Move Those Halves

Age 7 to 11 Challenge Level:

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

Paper Patchwork 1

Age 5 to 7 Challenge Level:

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

Paper Patchwork 2

Age 5 to 7 Challenge Level:

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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?

Map Folding

Age 7 to 11 Challenge Level:

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Dramatic Mathematics

Age 5 to 11

This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.

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?

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.

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.

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?

Right or Left?

Age 7 to 11 Challenge Level:

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

Shadow Play

Age 5 to 7 Challenge Level:

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

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.

Reef and Granny

Age 7 to 11 Challenge Level:

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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?

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.

Sponge Sections

Age 7 to 11 Challenge Level:

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Construct-o-straws

Age 7 to 11 Challenge Level:

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

Skeleton Shapes

Age 5 to 7 Challenge Level:

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

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.

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?

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?

Jomista Mat

Age 7 to 11 Challenge Level:

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

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 7 - Golden Goose

Age 7 to 11 Challenge Level:

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

World of Tan 6 - Junk

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the silhouette of the junk?

World of Tan 18 - Soup

Age 7 to 11 Challenge Level:

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

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?

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 1 - Granma T

Age 7 to 11 Challenge Level:

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

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 20 - Fractions

Age 7 to 11 Challenge Level:

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

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 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

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.

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?

How Many?

Age 5 to 11 Challenge Level:

Have a look at these photos of different fruit. How many do you see? How did you count?

Folding, Cutting and Punching

Age 7 to 11 Challenge Level:

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