This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view. . . .
This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?
A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.
Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.
A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.
This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .
I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?
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?
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?
Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.
Can you find a way of representing these arrangements of balls?
What is the shape of wrapping paper that you would need to completely wrap this model?
What can you see? What do you notice? What questions can you ask?
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.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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.
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you fit the tangram pieces into the outlines of the workmen?
Which of these dice are right-handed and which are left-handed?
Can you fit the tangram pieces into the outlines of the candle and sundial?
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!
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of the chairs?
Here's a simple way to make a Tangram without any measuring or ruling lines.
Make a cube out of straws and have a go at this practical challenge.
Which of the following cubes can be made from these nets?
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?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
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.
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Can you fit the tangram pieces into the outline of Little Ming?
Can you fit the tangram pieces into the outline of Granma T?
This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.
Make a flower design using the same shape made out of different sizes of paper.
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?
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?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
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 ...