E-book Code:
REA
U0013
REAU0013
Ready-Ed
Publications
The Shapes & Spaces Series
Book 3 - F
or 10 Y
ears+
For
Years+
Shapes and Spaces
for UPPER Primary
Students
BY JANE BOURKE
Written by Jane Bourke. Illustrated by Melinda Parker. © Ready-Ed Publications - 1999.
PubLished by Ready-Ed Publications (1999) PO Box 276 Greenwood Perth Australia 6024
E-mail: [email protected]
Web Site: www.readyed.com.au
COPYRIGHT NOTICE
Permission is granted for the purchaser to photocopy sufficient copies for non-commercial
educational purposes. However, this permission is not transferable and applies only to the
purchasing individual or institution.
ISBN 1 87397 228 5
Page 2
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CONTENTS
Teachers’ Notes ....................................................... 4
Neighbourhood Network ......................................... 5
Where am I?............................................................. 6
Networks .................................................................. 7
Traversable Networks ............................................... 8
Symmetry in 2 D Shapes 1 ...................................... 9
Symmetry in 2 D Shapes 2 ....................................10
Symmetry and Regular Polygons ..........................11
Point Symmetry of 2D Shapes ............................... 12
Rotational Symmetry .............................................. 13
Features of 2 D Shapes .........................................14
Patterns in Shapes ................................................ 15
Tessellating Shapes ...............................................16
Tessellations .......................................................... 17
The Tangram .........................................................18
Tangram Pictures ...................................................19
Prisms ....................................................................20
Pyramids ................................................................ 21
Cylinders and Cones .............................................22
Spheres .................................................................23
Properties of 3D Shapes........................................ 24
Cross Sections of Shapes 1 .................................. 25
Cross Sections of Shapes 2 .................................. 26
Regular Polyhedrons .............................................27
Nets for 3D Models
The Cube ............................................................... 28
The Cube Networks ............................................... 29
The Tetrahedron ..................................................... 30
The Hexahedron .................................................... 31
Square Based Pyramid ......................................... 32
Hexagonal & Octagonal Pyramid .......................... 33
Rectangular Based Pyramid .................................. 34
Irregular Pyramid ................................................... 34
Rectangular Prism ................................................. 35
Triangular Prism ..................................................... 36
Triangular Prism Nets ............................................ 37
Hexagonal Prism ................................................... 38
Cylinder and Cone ................................................. 39
Pentagonal Prism .................................................. 40
The Octahedron .................................................... 41
The Dodecahedron ............................................... 42
The Icosahedron.................................................... 43
Reflectional Symmetry ........................................... 44
Rotational Symmetry ............................................. 45
Answers ................................................................. 46
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Page 3
TEACHERS’ NOTES
This book is designed to complement the spatial maths component of the curriculum. It provides a
basic introduction to new concepts as well as activities that will consolidate the skills and ideas
associated with 2D and 3D shapes.
The book contains a set of networks for constructing models of prisms, pyramids and various polyhedra.
Ideally, these nets should be copied onto card to allow students to make a solid shape that will last for
the duration of this unit of maths.
Specific activities include identifying traversable networks, studying the properties and features of 2D
and 3D shapes, exploring reflectional and rotational symmetry, looking at cross sections of 3D
shapes and creating tessellations with a number of regular and irregular 2D shapes.
It is intended that the activities be completed sequentially as certain learning concepts need to be
mastered in order to complete some of the later activities. Also, it is assumed that the ideas in this
book will be explored in class prior to completing the activities as they are not designed as a
complete maths programme.
Using this book
When starting on the section concerning 3D models, use the nets to construct the shapes prior to
using the worksheets. Students can then refer to these shapes when they are needed.
Additional Materials
It is a good idea to have the following materials on hand for all Shape and Space lessons.
Stiff card - photocopy the 3D nets onto card. This will allow the students to fit the models together
more easily. Once arranged either sticky-tape or glue can be used. Provide students with a plastic bag
in which they can store all their models as the models will be used in many activities.
Tracing paper - useful for tracing shapes and then copying them to card, particularly for the sheets
concerned with tessellations.
Grid paper - for 2D Drawings.
Isometric paper - very handy for drawing 3D models. Students can draw models and then paste
them onto the worksheet.
Geoboards are great for allowing students to experiment with networks and 2D shapes.
Straws and Plasticine can be used to construct 3D models. This kind of activity makes it easy for
students to see how shapes fit together and how edges and vertices are formed.
Math-o-Mat - these are particularly useful for making tessellations as well as measuring angles.
Mira - useful for checking symmetry of 2D shapes.
Attribute Blocks - useful for making tessellations.
Page 4
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NEIGHBOURHOOD NETWORK
Using the grid below, draw a detailed map of where you live in relation to your school. Include
roads and other buildings such as friends’ houses, shops and parks.
Draw your diagram to scale. For example one square could equal 100 metres, or if you live
further away, one square could equal one kilometre.
Scale: 1 square = .................
ÏN
Highlight the route you take to get to school each morning, either by vehicle, bike or walking.
Describe in words the path you would take to get to your friend’s house from your school.
.........................................................................................................................................................
.........................................................................................................................................................
.........................................................................................................................................................
.........................................................................................................................................................
.........................................................................................................................................................
.........................................................................................................................................................
Challenge:
Find the location of your house in a street directory and ask your teacher if you can
photocopy the page. Highlight the different routes you could take to get to your school.
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Page 5
WHERE AM I?
In each grid below I am visiting a certain house. Start at the arrow and follow the directions
given underneath. Circle the mystery house I visit in each grid.
1.
2.
Ï
Ï
E, E, E, S, E, S, W, N, W, S, W, W.
4.
Ï
Ï
3.
N, N, N, E, S, E, E, N, N, W, S, S, S, S, E.
5.
Ï
S, S, E, E, E, N, W, S, S, E, S, N
W, W, N, E, N, N, W, S, W, W, N, E, N, W
6.
Ï
W, W, W, S, W, S, S, E, E, S, W, N, N
Page 6
E, E, N, N, W, W, N, W, N, E, S, S, S
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NETWORKS
A network contains paths, regions and intersections.
In the diagram below a network is formed between the friends’ houses and the school.
Jacinta
Roger
School
Fiona
Donelle
Anthony
With your pencil can you find a way to visit every house and the school without travelling over
any path twice?
Hint: You may visit the same house more than once, and you must travel over every line.
This network has five intersections.
Can you find a way to go over every line
once without going over any line twice
and without lifting your pencil?
A network is traversable if the whole route can be walked without retracing the steps, or
traced without going over the same line twice.
Circle the networks below that are traversable.
a.
e.
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b.
c.
f.
d.
g.
Page 7
TRAVERSABLE NETWORKS
1. All the networks below are traversable. Try them and see.
2. Check to see if these networks below are traversable.
In the network below the vertices have been labelled. A vertex is a point where two or more lines
meet to form an angle.
E
This network has six vertices.
The vertices marked with an E have an even
number of lines joining while those marked
with O have an odd number.
E
E
E
O
O
The Swiss mathematician, Leonard Euler, discovered that a network can only be
traversable without retracing if it has all even vertices or if it only has two odd vertices.
Go back to the networks above and check this idea by looking at the number of even and
odd vertices.
3. Decide whether the following networks are traversable by counting the odd and even vertices.
Check to see if your decision is correct.
a.
b.
c.
d.
Challenge: Use a geoboard to make some networks of your own. Check the vertices to
see if they are traversable. What other rules can you find?
Hint: Look at the vertex that you start with. Is it odd or even?
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SYMMETRY IN 2 D SHAPES 1
A shape has line symmetry if both its parts match when it is folded along a line.
The shapes below have line symmetry.
In two of the shapes above, another line of symmetry can be drawn. Mark these lines onto the shapes.
Show all the lines of symmetry on each of the shapes below.
Mark the lines of symmetry onto the irregular shapes below.
Some lines have been marked on these shapes, yet only one line is the line of symmetry. Trace
over the correct line in red.
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Page 9
SYMMETRY IN 2 D SHAPES 2
Circle the shapes where the dotted line represents the line of symmetry.
Complete the diagrams below by drawing the missing half.
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SYMMETRY AND
REGULAR POLYGONS
Draw all the lines of symmetry on the polygons below.
equilateral triangle
heptagon
square
octagon
pentagon
nonagon
hexagon
decagon
Complete the table.
Shape
Number of sides
Number of lines of symmetry
Use a mira to determine whether these shapes are symmetrical.
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Page 11
POINT SYMMETRY OF 2D SHAPES
A shape has point symmetry if it can be rotated around a point to create the same image.
.
.
Which of the shapes below have point symmetry? Mark the point on the shape.
a.
b.
c.
d.
e.
f.
i.
j.
g.
k.
h.
l.
Alphabet Symmetry
Which of the letters below have lines of symmetry? Draw them in.
You may like to use a mira to help you with this activity.
ABCDEFGHI
JKLMNOPQ
RSTUVWXYZ
Which of the above letters have point symmetry? Mark the point using a red pen.
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ROTATIONAL SYMMETRY
If the circle below is rotated 90° to the right, it will still look the same. It can also be rotated 180°.
2.
1.
1.
4.
3.
2.
4.
3.
Which of the following shapes have rotational symmetry?
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
Design your own patterns in the shapes below so that if they were rotated 90° to the right they
would show the same pattern.
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Page 13
FEATURES OF 2 D SHAPES
1. In the shapes below draw a line from the vertex J to other points in the shape.
J
J
J
J
J
J
J
2. Complete the table below. (One has been done for you.)
Polygon
J
J
Number of sides
Diagonals leaving J
4
1
Triangle
Diamond
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Write a rule about what you found.
.................................................................................................................................................
.................................................................................................................................................
3. On a scrap piece of paper trace around triangular shaped blocks to make some regular
polygons. This will only work with isosceles or equilateral triangles.
Study one of the shapes you have made. How many sides does it have? ...............
What is the size of the centre angle of each triangle? ......................................... °
What did you find? ................................................................................................
....................................................................................................
Do you find the same results if you make
another polygon using a different shaped triangle? ...........................................................................
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PATTERNS IN SHAPES
In the hexagon below the pattern has been formed by drawing diagonals from each point to
all other points. Identify some of the shapes that can be seen.
Colour an irregular quadrilateral blue.
Colour a scalene triangle red.
Colour an isosceles triangle green.
Colour a kite shape in yellow.
How many rectangles can you see?
How many diamonds can you find?
How many equilateral triangles can you see?
Draw in the diagonals in the shapes below and then colour in a symmetrical design.
Draw two identical polygons on separate pieces of tracing paper. Place one on top of the
other and study the shapes that can be made in the overlap. Try this with three other pairs of
polygons.
What did you find?
Perfect Pentagon. Construct a regular pentagon by
using a strip of ticker tape. Tie a knot loosely in the paper
and then tighten and press down flat. Cut off the left over
paper and you should be left with a regular pentagon.
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Page 15
TESSELLATING SHAPES
A tessellation is formed when one or more shapes fit together without leaving gaps or overlapping.
Examples of tessellations can be seen in brick and tile work and in honeycombs.
A tessellation with one shape
A tessellation
using two shapes
Which of the shapes below will tessellate? Cut out a copy of the shape from a piece of card
and then trace around it on a piece of blank paper to see if it will tessellate.
Which of the following pairs of shapes will tessellate?
a.
b.
d.
c.
e.
f.
Make copies of these shapes and tessellate them.
Extra! Visit your library and find some books about M.C. Escher, one of the most famous tessellators!
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TESSELLATIONS
Some irregular polygons will also tessellate.
Make a unique tessellation by designing a shape on a square piece of card. First draw a
line of any shape through a square. Cut along this line and then slide one half over the other.
Use the shape on the right as a template to make a tessellation on the back of this page.
1
1
1
2
2
1
2
3
2
3
new shape
Challenge: If the original square you used had sides of 5 cm, what will be the area of the
new shape you have made?
Some shapes will not tessellate on their own unless additional shapes are used. These are
known as semi-regular tessellations.
Create a semi-regular tessellation by copying a number of shapes onto card and then tracing
around them. Experiment on the back of this page with pairs of shapes and groups of three
or more shapes. Create a tiling pattern in the box below and colour the shapes in.
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Page 17
THE TANGRAM
Copy the tangram onto card and cut out the shapes. Number your shapes as they appear in the
tangram below.
Using your tangram shapes complete the following.
2
1
7
5
In what way are shapes 3, 4 and 5 the same?
6
4
Using pieces 6 and 7 make the shape of 3.
Using the same pieces make the shape of 4
and then make the shape of 5.
.................................................................................
3
Make the shapes below by arranging your tangram pieces.
Extra:
Make a unique shape of your own using all 7 pieces. Trace around your shape, with the
help of a ruler and then swap your outline with a friend to see if they can solve the puzzle.
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TANGRAM PICTURES
Can you arrange all seven pieces of the tangram into the outlines below?
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Page 19
PRISMS
3D shapes are known as solids and are often referred to as polyhedra. There are three main
types of polyhedra; prisms, pyramids and shapes with curved surfaces.
A prism has two bases which are similar and parallel. The sides of prisms are known as
parallelograms as the corresponding edges are parallel.
A cereal box is an example of a rectangular prism.
base
base
Some brands of chocolate such as Toblerone®
come in a triangular prism shaped box.
base
parallelogram
parallelogram
base
Using the shapes below draw a model of the prisms.
a.
b.
c.
d.
e.
f.
How many sides does each prism have?
a. .............
b. .............
c. .............
d. .............
e..............
f................
Is a cube a prism? .....................
List some examples of different prisms that you see every day. ...............................................
........................................................................................................................................................
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PYRAMIDS
A pyramid is a solid shape which has only one base while all the other faces are triangular.
The base can be made from any shape that has more than two sides.
A square based pyramid.
A tetrahedron
(triangular pyramid)
1. Draw models of pyramids using the shapes below as the base.
2. The pyramids of Egypt are probably the most famous pyramids in the world.
What is the base shape of these pyramids? ..................................
3. List some pyramid shaped objects that you see around you. ....................................................
.........................................................................................................................................................
4. Is a cone also a pyramid? ................ Give reasons for your answer. .........................................
.........................................................................................................................................................
5. If you sliced a triangular pyramid in half by cutting from the point to the base, what shapes would be formed?
.........................................................................................................................................................
6. What shape would be formed at the cross-section if other pyramids (e.g. rectangular-based)
were cut in the same way?
.........................................................................................................................................................
Challenge: Find out the name of the 3D shape that is formed
when two square-based pyramids are joined together at their bases?
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Page 21
CYLINDERS AND CONES
Cylinders and cones are 3D shapes with curved surfaces. A cylinder is made up from two
congruent circles and a curved rectangular face. Draw some more cylinders in the space below.
List some examples of cylindrical objects that are seen in everyday surroundings.
Cones
Cones have only one vertex and one edge and are made from a circular base and
one curved surface. Draw models of cones using the shapes below as the base.
Cross sections of cones and cylinders
Draw the approximate shape of the plane made by the cuts in the following diagrams.
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SPHERES
A sphere is a perfectly round 3D shape. It has no vertices and no edges.
The Earth is a sphere. The southern half of the Earth is known as the southern hemisphere.
In a sphere every single point on the curved surface is exactly the same distance away from the centre.
A basketball is a sphere.
Name some other sports that use a spherical ball.
.........................................................................................................................................................
Cross Sections
Under each sphere below, draw the approximate shape of the plane that is made if the
sphere is cut along the dotted line.
Challenge: Find out how the following words relate to a sphere.
e.g. Atmosphere - the gaseous layer that surrounds the earth and other celestial bodies.
Biosphere: ......................................................................................................................................
Bathysphere: ..................................................................................................................................
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Page 23
PROPERTIES OF 3D SHAPES
Construct models of the 3D shapes using the nets in this book. Study the shapes and their attributes.
Complete the table below.
Shape
Cube
Tetrahedron
Hexahedron
Square pyramid
Hexagonal pyramid
Octagonal pyramid
Rectangular pyramid
Pentagonal pyramid
Rectangular prism
Triangular prism
Hexagonal prism
Pentagonal prism
Octahedron
Number of Faces
6
Number of Vertices
8
Number of Edges
12
What patterns can you find? ............................................................................................................
.........................................................................................................................................................
Take another look at the 3D models and fill in this table.
Prisms
Faces other than the two ends Number of Vertices
Cube
4
8
Triangular
Rectangular
Square
Hexagonal
Pentagonal
Number of Edges
12
Describe all the patterns you found for both the prisms and the pyramids.
· ........................................................................................................................................................
· ........................................................................................................................................................
· ........................................................................................................................................................
· ........................................................................................................................................................
· ........................................................................................................................................................
· ........................................................................................................................................................
· ........................................................................................................................................................
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CROSS SECTIONS OF SHAPES 1
If you were to cut a rectangular pyramid in half as shown below, what shape would be made across the plane?
Would the shape be a triangle or a rectangle?
.....................................................................
2. What shape has
been made? .............
Cut
This shape is known
as the cross section.
Draw the shape that would be made if the following 3D shapes were cut into two sections at
the dotted line.
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Page 25
CROSS SECTIONS OF SHAPES 2
In the following cross sections, circle the shapes that would be circular, mark a cross under
the shapes that would be rectangular, tick the shapes that would have a triangular cross
section and write the name of the shape for all the others that are left.
a.
b.
c.
d.
e.
f.
g.
i.
j.
Page 26
h.
k.
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REGULAR POLYHEDRONS
1. Look at a model of a cube.
Are all of the faces the same size?
...................................................
2. Are the angles at the vertices
the same size? ..........................
A cube is a regular polyhedron.
There are only five regular polyhedrons. A tetrahedron can be a regular polyhedron because all faces
are congruent. Some pyramids are not regular as the base is usually a different shape to the sides.
3. Which of the following objects represent regular polyhedra?
Tetrahedron
Cube
Icosahedron
Octahedron
Dodecahedron
Hexagonal prism
4. Complete the table below. You may like to look at the models you have made.
Shape
Faces
Edges
Vertices
Tetrahedron
4
6
4
Regular or Irregular
Cube
Octagonal pyramid
Dodecahedron
Hexagonal prism
Octahedron
Icosahedron
5. Fill in the missing words.
a. A tetrahedron is made up of ........... equilateral ................................. .
b. A cube is made up of .............................. .
c. An octahedron is made up of .........
.......................................... triangles.
d. A ............................................................... is made of 12 regular pentagons.
e. An icosahedron is made up of 20.....................
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.................................. .
Page 27
THE CUBE
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THE CUBE NETWORKS
Which of these nets can be made into cubes? Tick the ones that work.
a.
b.
c.
d.
Design five nets of your own that can be made to form a cube.
Look at the sides of your cube. What do you notice about each of the faces?
Make a different sized cube by cutting out the net below. Use sticky tape to hold it together.
Compare this cube with the larger cube.
Are the two cubes congruent or similar?
..............................
Explain whether the cubes would be
described as congruent or similar.
.................................................................
.................................................................
Extra! Sometimes shapes are known as regular polyhedra as their faces are congruent. If
a shape has faces that are not congruent, it is known as an irregular shape.
Is there such a thing as an irregular cube? ...............................
What is another name for a cube? H................................................... .
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THE TETRAHEDRON
A tetrahedron is a triangular pyramid with four faces, four vertices and six edges.
If we were to join two tetrahedrons together, how many sides would the new shape have?
What do you think this shape might be called? ................................................
Make a tetrahedron using the net below.
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THE HEXAHEDRON
A hexahedron is a 3D solid shape that has six sides.
A cube is a regular hexahedron as all sides are congruent.
The shape drawn here is also known as a hexahedron as it has
six sides. It can be made by joining two tetrahedra together.
Draw a different shaped hexahedron in this space.
Did you know?
A pentagonal pyramid has six sides and
can be known as an irregular hexahedron.
Make a hexahedron using the net below.
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Page 31
SQUARE BASED PYRAMID
Page 32
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HEXAGONAL
PYRAMID
OCTAGONAL
PYRAMID
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RECTANGULAR BASED PYRAMID
IRREGULAR PYRAMID
You can use any quadrilateral as the base.
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TRIANGULAR PRISM
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TRIANGULAR PRISM NETS
Tick the networks below that can be made into triangular prisms.
In the space provided, design three nets that will form a triangular prism. Use your ruler and a
pencil and then copy your nets onto card so that they can be constructed.
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RECTANGULAR PRISM
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HEXAGONAL PRISM
Page 38
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CYLINDER
CONE
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PENTAGONAL PRISM
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THE OCTAHEDRON
An octahedron is an eight sided
figure where each face is identical.
Each face on a regular octahedron
is an equilateral triangle.
Use the net below to construct
a regular octahedron.
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Page 41
THE DODECAHEDRON
A dodecahedron is a twelve sided figure where each face is identical.
Each face on a regular dodecahedron is a regular pentagon.
Use the net below to construct
a regular dodecahedron.
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THE ICOSAHEDRON
An icosahedron is a twenty sided figure where each face is identical. Each face on a regular
icosahedron is an equilateral triangle.
Use the net below to construct an icosahedron.
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Page 43
REFLECTIONAL SYMMETRY
In a 2D shape a figure can have a reflectional image around a line of symmetry, where each
point on one side of the line corresponds with a point on the other side with both points being
the exact same distance from the line.
In 3D shapes an image has reflectional symmetry around a plane of symmetry.
Look at some of the planes of symmetry for the shapes below.
Draw the plane of symmetry for these shapes. If they have more than one plane of symmetry
use different coloured pencils.
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ROTATIONAL SYMMETRY
A figure has rotational symmetry if it can be matched by rotating it a full turn or half a turn.
For example, in the shape below the shapes have been turned to the right by 90°. Note the
position of the .
Some 3D shapes can be rotated around an axis of symmetry.
If the shape is rotated 90° to the left, the shape’s appearance is the same.
Which of these shapes can be rotated 90° around an axis and still look the same?
a.
c.
d.
b.
Draw three 3D shapes below and place a dotted line to represent the axis of symmetry.
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Page 45
ANSWERS
Where Am I? (page 6)
1.
2.
3.
Ï
Ï
4.
Ï
Ï
Ï
Ï
5.
6.
Networks (page 7)
Traversable: d, e, f, g.
Traversable Networks (page 8)
2. Only the first network is traversable. 3. b. and d. are traversable.
Symmetry in 2 D Shapes 1 (page 9)
Check Diagrams.
Symmetry in 2 D Shapes 2 (pages 10)
Check Diagrams.
Symmetry and Regular Polygons (page 11)
Check table.
Point Symmetry of 2D Shapes (page 12)
a, b, f.
Alphabet Symmetry - These letters have lines of symmetry: A, B, C, D, E, H, I, M, O, T, U, V, W, X, Y.
These letters have point symmetry - I, N, O, S, X, Z.
Rotational Symmetry (page 13)
a, b, c, g, h, j.
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Features of 2 D Shapes (page 14)
1. Check diagrams; 2.
Polygon
Triangle
Diamond
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Number of sides
3
4
5
6
7
8
9
10
Diagonals leaving J
0
1
2
3
4
5
6
7
3. Students should find that the size of the centre angle of the triangle they use multiplied by the
number of sides of the regular polygon made is equal to 360°.
Patterns in Shapes (page 15)
Check diagram.
Tessellating Shapes (page 16)
1. rectangle, triangle, diamond, equilateral triangle.
2. a, c.
Tessellations (page 17)
Challenge: 25m²
Answers will vary.
The Tangram (page 18)
Shapes 3, 4 and 5 have the exact same area.
Prisms (page 20)
Sides - a. 6, b. 8, c. 10, d. 6, e. 7, f. 6.
A cube is a prism.
Pyramids (page 21)
1. Check diagrams, 2. square, 3. Answers will vary, 4. A cone is not a pyramid as it has a curved
face instead of triangular faces. 5. You would create two more pyramids although they would be
irregular. The cross-section shape would be triangular. 6. The cross section would always be a
triangular shape.
Challenge: Octahedron.
Cylinders and Cones (page 22)
Check diagrams.
Spheres (page 23)
Check diagrams.
Properties of 3D Shapes (page 24)
Shape
Cube
Tetrahedron
Hexahedron
Square pyramid
Hexagonal pyramid
Octagonal pyramid
Rectangular pyramid
Pentagonal pyramid
Rectangular prism
Triangular prism
Hexagonal prism
Pentagonal prism
Octahedron
Ready-Ed Publications
Faces
6
4
6
5
7
9
5
5
6
5
8
7
8
Vertices
8
4
5
5
7
9
5
6
8
6
12
10
12
Edges
12
6
9
8
12
16
8
9
12
9
18
15
18
Page 47
Students should be able to find that the sum of the number of faces and vertices is always
two less than the number of edges.
Prisms
Triangular
Cube
Rectangular
Hexagonal
Pentagonal
Faces other than the two ends
3
4
4
6
5
Number of Vertices
6
8
8
12
10
Number of Edges
9
12
12
18
15
Cross Sections of Shapes 1 (page 25)
1. rectangle, 2. ellipse/circle. Check diagrams.
Cross Sections of Shapes 2 (page 26)
a. decagon; b. rectangle; c. square; d. rectangle; e. triangle; f. rectangle; g. pentagon;
h. square; i. oval; j. square; k. triangle.
Regular Polyhedrons (page 27)
1. yes, 2. yes, 3. Tetrahedron, octahedron, icosahedron, cube, dodecahedron.
4.
Shape
Faces
Vertices Edges
Regular or Irregular
Tetrahedron
4
6
4
regular
Cube
6
8
12
regular
Octagonal pyramid 9
9
16
irregular
Dodecahedron
12
20
30
regular
Hexagonal prism
8
12
18
irregular
Octahedron
8
12
18
regular
Icosahedron
20
12
30
regular
5. a. 3 triangles; b. 6 squares; c. 8 equilateral; d. dodecahedron; e. equilateral triangles.
The Cube Networks (page 28)
a, c. Extra! - hexahedron.
Reflectional Symmetry (page 44)
Check diagrams.
Rotational Symmetry (page 45)
Check diagrams.
Page 48
Ready-Ed Publications