Exploring
Three-Dimensional
Shapes
3 DIMENSIONAL SHAPES
PRISMS are solid shapes with parallel ends of the same shape and size
(parallel equal polygons)
All the other faces are rectangles.
A prism has a uniform cross section
A CUBE is a rectangular prism
with six square faces, all
of the same size.
A CUBOID is a rectangular
prism with six rectangular faces.
Opposite faces are the same
HEXAGONAL
PRISM
TRIANGULAR
PRISM
OCTAGONAL
PRISM
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A CYLINDER has two equal parallel circular ends. It is
sometimes referred to as a circular prism.
A PYRAMID has a straight edged base and sloping
triangular faces meeting at a point (the apex).
A square based
pyramid
A pentagonal
pyramid
A CONE has a flat circular base and
a curved surface coming to a point
(apex). A cone is sometimes referred
to as a circular pyramid.
A SPHERE is a solid with a surface on which every
point is the same distance from the centre of the
solid.
(pictures by Rita Thompson)
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THE FIVE REGULAR SOLIDS
There are five known regular solid shapes which are sometimes referred to as the
Platonic solids.
The faces of each of these are all regular and equal shapes.
four
equilateral
triangles
six equal
squares
cube
tetrahedron
eight
equilateral
triangles
Octahedron
dodecahedron
icosahedron
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Exploring the Properties of Three-Dimensional
Shapes
A.
Using Junk Materials
•
Sorting empty/full containers in a variety of ways: allow children to set their own
criteria and find appropriate forms of recording. Encourage a focus on the shape of the
container to develop ideas of what is similar/different and the properties of shapes.
•
Set up displays where the children are invited to find mathematical equipment/objects
from the environment which are the same shape as the junk boxes.
•
Make buildings from. junk materials eg:
-
-
What is the tallest free-standing building you can make using these 6
containers?
What is the smallest building you can make using the same 6 containers?
Considering why various things are packaged in particular containers?
•
Using junk materials to print patterns or pictures. This helps to develop the mental
imagery of 3D-2D and vice versa.
•
Opening up junk packaging to explore NETS of 3D shapes.
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•
Looking at a box and trying to draw its net
initially without opening up the
box.
•
The above investigations of nets can lead to forms of recording which illustrates the links
between 3D and 2D.
Number of each 2D shape used to make the following 3D shapes
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B.
Using Clixi/Polydron
N.B. It’s important that children of all ages have sufficient time to explore materials
through ‘play’ before they are given specific structured activities. Unstructured play
allows children to familiarise themselves with the properties of, and relationships
between, the materials.
•
Investigate how many different prisms you can make.
•
-
Which shapes did you use for each prism?
-
What do their nets look like?
-
Can you recreate one of your prisms from card?
How many different pyramids can you build?
-
•
How many pieces did you use for each pyramid?
Make an open cube from 5 Clixi/Polydron squares. Now make a cuboid
which is double the length of your cube.
-
What is the volume of the cuboid compared to the cube?
-
What would happen to the volume of the cuboid if you doubled all
three dimensions of the cube?
•
Make a house from Clixi (see grid for one way of recording this activity).
•
Try making each of the five regular solid shapes.
•
Investigate the relationship between the number of faces, vertices and edges of
the closed shapes that you have made. What do you notice?
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CLIXI HOUSE GRID
With Clixi make house of some sort.
Record the number of shapes you used for your house on
the grid.
red
blue green yellow
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C)
Using Poleidoblocs (set G)
•
Sorting the blocks in a variety of ways e.g.
•
Constructing buildings and recording, in appropriate ways, the number and types of
blocks used.
Can you draw your building as it looks from the side/front? What does you building
look like from above?
-
•
Work in pairs but screened off. Agree on the blocks to be used and each take the same
number of blocks. Make a construction with the blocks while describing to your
partner exactly what you are doing. Your partner must attempt to copy your
construction by listening to your instructions. Discuss your result.
•
Building towers (see Poleidobloc Game)
•
‘I’m thinking of a shape...’ games.
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Poleidobloc Game
(for 2 players)
Take turns to
spin
Pick up that colour
poleidobloc
Build the tallest tower
you can
Are some colours better
for building than others?
Are some shapes better
for building than others?
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I’m Thinking of a Shape...
It has these properties
It could be...


 .


 it’s probably a...
‘



 .

 it’s probably a...
‘



 .

 it’s probably a...
‘
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D)
Constructing 3 Dimensional Shapes
•
ATM Tiles
•
Construction Straws -. these enable children to focus on the edges and vertices
of polyhedra.
.
•
Use of Clixi/Polydron
•
Making nets for boxes - these enable children to focus on the faces of polyhedra.
N.B. Children of all ages need a wide variety of experiences of ‘opening up’
boxes before attempting to construct their own. More complicated
polyhedra will necessitate a sophisticated level of understanding of
angles, and the use of compasses and/or protractors.
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E).
Symmetry of 3D Shapes
When a shape can be cut in half by a plane (flat surface) so that one half is the reflection of
the other half in the plane, the shape has a plane of symmetry.
•
Junk materials can be used and cut up for children to investigate planes of symmetry
these allow the children to test their theories by matching the reflected pieces.
•
Shapes can be made out of plasticine and cut to investigate planes of symmetry.
•
Multilink cubes are a useful resource to explore planes of symmetry. eg
-
-
Make this shape using 12 cubes
How many planes of symmetry can you
find?
-
-
-
Use 16 cubes to make a cuboid. How many planes of symmetry can you find in
the cuboid?
Use 8 cubes to make a larger cube. How many planes of symmetry can you find
in the larger cube?
Build half a shape.
its mirror image to
Ask a friend to construct
complete the shape.
Mirrors will prove useful for all of the activities in this section
DD/CA
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Multilink Buildings
How many different buildings can you make using 6
multilink each time? Choose some to draw so that
someone else could copy your buildings.
Here are the left side, right side, front and top
views of a building. Can you build it from the
drawings?
Use 8 cubes and make any building you like but keep
this hidden from your partner. Describe the shape to
your partner who must now copy your building from this
description.
Check are they the same? Reverse roles and try again!
—
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