How can we as teachers begin to introduce 3D ideas to young
children? Where do they start? How can we lay the foundations for a
later enthusiasm for working in three dimensions?
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . .
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?
Explore the properties of oblique projection.
Here are four cubes joined together. How many other arrangements of
four cubes can you find? Can you draw them on dotty paper?
Can you mentally fit the 7 SOMA pieces together to make a cube? Can
you do it in more than one way?
The challenge for you is to make a string of six (or more!) graded
You have 27 small cubes, 3 each of nine colours. Use the small
cubes to make a 3 by 3 by 3 cube so that each face of the bigger
cube contains one of every colour.
Find all the ways to cut out a 'net' of six squares that can be
folded into a cube.
Can you make a 3x3 cube with these shapes made from small cubes?
Explore the properties of isometric drawings.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Here are some pictures of 3D shapes made from cubes. Can you make
these shapes yourself?
In this investigation, you must try to make houses using cubes. If
the base must not spill over 4 squares and you have 7 cubes which
stand for 7 rooms, what different designs can you come up with?
Explore the properties of perspective drawing.
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
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 tennis ball is served from directly above the baseline (assume
the ball travels in a straight line). What is the minimum height
that the ball can be hit at to ensure it lands in the service area?
This article, written for teachers, looks at the different kinds of
recordings encountered in Primary Mathematics lessons and the
importance of not jumping to conclusions!
This article (the first of two) contains ideas for investigations.
Space-time, the curvature of space and topology are introduced with
some fascinating problems to explore.
This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.