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 two players. You'll need some counters.
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?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
Move just three of the circles so that the triangle faces in the opposite direction.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
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!
Exchange the positions of the two sets of counters in the least possible number of moves
How many different triangles can you make on a circular pegboard that has nine pegs?
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
A variant on the game Alquerque
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
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,. . . .
Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Square It game for an adult and child. Can you come up with a way of always winning this game?
Can you fit the tangram pieces into the outlines of the workmen?
Here's a simple way to make a Tangram without any measuring or ruling lines.
Can you find a way of representing these arrangements of balls?
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
Can you fit the tangram pieces into the outline of this goat and giraffe?
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?
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?
Can you fit the tangram pieces into the outline of this sports car?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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.
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
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?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
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.
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
Can you fit the tangram pieces into the outlines of the candle and sundial?
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 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?
Here are shadows of some 3D shapes. What shapes could have made them?
Which of these dice are right-handed and which are left-handed?