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. . . .
What can you see? What do you notice? What questions can you ask?
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?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Try this interactive strategy game for 2
Can you make a 3x3 cube with these shapes made from small cubes?
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?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
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
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
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,. . . .
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
A variant on the game Alquerque
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Exchange the positions of the two sets of counters in the least possible number of moves
This second article in the series refers to research about levels
of development of spatial thinking and the possible influence of
A game for two players. You'll need some counters.
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.
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!
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Which of these dice are right-handed and which are left-handed?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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?
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?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
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.
Move just three of the circles so that the triangle faces in the
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
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. . . .
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
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?
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 toy has a regular tetrahedron, a cube and a base with triangular
and square hollows. If you fit a shape into the correct hollow a
bell rings. How many times does the bell ring in a complete game?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back