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Cubes. Working systematically. Team-building. Visualising. Shape, space & measures - generally. Practical Activity. Tangram. Generalising. Interactivities. Compound transformations.

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

Stage: 1 and 2

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

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.

Right or Left?

Stage: 2 Challenge Level:

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

Hexagon Transformations

Stage: 2 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!

Endless Noughts and Crosses

Stage: 2 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.

Matchsticks

Stage: 2 Challenge Level:

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

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?

A Chain of Eight Polyhedra

Stage: 2 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?

World of Tan 18 - Soup

Stage: 2 Challenge Level:

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

Making Tangrams

Stage: 2 Challenge Level:

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

Turning Cogs

Stage: 2 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.

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?

World of Tan 15 - Millennia

Stage: 2 Challenge Level:

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

World of Tan 16 - Time Flies

Stage: 2 Challenge Level:

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

Put Yourself in a Box

Stage: 2 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.

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!

Cubic Conundrum

Stage: 2 Challenge Level:

Which of the following cubes can be made from these nets?

World of Tan 29 - the Telephone

Stage: 2 Challenge Level:

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

World of Tan 28 - Concentrating on Coordinates

Stage: 2 Challenge Level:

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

Trace the Edges

Stage: 2 Challenge Level:

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

Fractional Triangles

Stage: 2 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.

Jomista Mat

Stage: 2 Challenge Level:

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

Makeover

Stage: 1 and 2 Challenge Level:

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

World of Tan 27 - Sharing

Stage: 2 Challenge Level:

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

World of Tan 26 - Old Chestnut

Stage: 2 Challenge Level:

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

World of Tan 21 - Almost There Now

Stage: 2 Challenge Level:

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

World of Tan 20 - Fractions

Stage: 2 Challenge Level:

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

World of Tan 22 - an Appealing Stroll

Stage: 2 Challenge Level:

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

World of Tan 24 - Clocks

Stage: 2 Challenge Level:

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

World of Tan 25 - Pentominoes

Stage: 2 Challenge Level:

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

World of Tan 19 - Working Men

Stage: 2 Challenge Level:

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

World of Tan 9 - Animals

Stage: 2 Challenge Level:

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

Making Maths: Rolypoly

Stage: 1 and 2 Challenge Level:

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

Stage: 2 Challenge Level:

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

Move Those Halves

Stage: 2 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 ...

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

Stage: 1

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

World of Tan 1 - Granma T

Stage: 2 Challenge Level:

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

Folding Flowers 1

Stage: 2 Challenge Level:

Can you visualise what shape this piece of paper will make when it is folded?

Holes

Stage: 1 and 2 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?

Odd Squares

Stage: 2 Challenge Level:

Think of a number, square it and subtract your starting number. Is the number youâ€™re left with odd or even? How do the images help to explain this?

Circles, Circles

Stage: 1 and 2 Challenge Level:

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

Square it for Two

Stage: 1 and 2 Challenge Level:

Square It game for an adult and child. Can you come up with a way of always winning this game?

How Would We Count?

Stage: 1 and 2 Challenge Level:

An activity centred around observations of dots and how we visualise number arrangement patterns.

A Square in a Circle

Stage: 2 Challenge Level:

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

Folding, Cutting and Punching

Stage: 2 Challenge Level:

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

World of Tan 2 - Little Ming

Stage: 2 Challenge Level:

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

Folding Flowers 2

Stage: 2 Challenge Level:

Make a flower design using the same shape made out of different sizes of paper.

World of Tan 5 - Rocket

Stage: 2 Challenge Level:

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

World of Tan 7 - Gat Marn

Stage: 2 Challenge Level:

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