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Organisation of content into year levels is advisory. Teachers will continue to make professional
judgements about when to introduce content based on children’s prior learning and achievement.
*National Consistency in Curriculum Outcomes, Statement of Learning
Early adolescence: Mathematics/Space – Students describe and analyse mathematically the spatial features of objects, environments and
movements.
Typical sequence of content:
Year 8
Year 9
Year 10
Represent spatial ideas
Represent location
Directional language
Directional language and symbols
Directional language, symbols and methods
 instructions for moving and locating objects
(eg distance, direction and common map grids)
 directional language for paths, regions and
locations (eg equidistant, bisect, parallel and
perpendicular)
 directional language, symbols and methods of
representation in maps and plans (eg degrees of
turn, compass directions, keys, bearings, distance,
scale and coordinates)
Interpret and make maps which represent distance
and direction, showing a sense of scale
Interpret and make maps and plans representing
size and position accurately
Interpret and make maps using bearings and
precise measurement
 key features on a map or path so that others can
use them (eg providing a tour map of their school
for visitors)
 following and providing directions from one location
to another on a variety of maps and plans with
reference to key features, distance and orientation*
(Mathematics) (eg writing a set of directions to
assist a visually-impaired peer find his or her way
around a part of the yard)
 more precision in map making including use of
bearings from 0 to 360
 interpreting maps to find their way around the
actual environment (eg using a plan of the library
to find a particular book)
 using drawing equipment when representing paths
and regions* (ICT) (eg computer software,
templates, protractors, compasses and rulers)
 sketching paths and regions, given a set of special
constraints (eg a path traced out by the valve of a
bicycle wheel)
 using grids and coordinates, scale, and true
bearings to read, interpret and follow maps*
(Mathematics) (eg orienteering)
 solving problems involving a series of distances
and bearings
© Department of Education and Training Western Australia, Early adolescence: Mathematics/Space scope and sequence, December 2007
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Organisation of content into year levels is advisory. Teachers will continue to make professional
judgements about when to introduce content based on children’s prior learning and achievement.
*National Consistency in Curriculum Outcomes, Statement of Learning
Typical sequence of content:
Year 8
Year 9
Year 10
Represent arrangements
Represent orientation through topological
diagrams
Produce diagrams with essential features of
location and orientation
Visualise and sketch own networks and use
networks to determine best path
 drawing and using topological maps to show place
and position but not distance (eg stations on a
railway line)
 paths and regions described in everyday language
(eg shading the region mowed when the electric
draw cord is x metres)
 why distance is not represented on a network
(eg explaining that they cannot tell from their
network which drink fountains are closer)
 tracing pathways through networks (eg a milk
round)
 drawing and using diagrams to represent and
analyse relationships* (Mathematics)
(eg The Konigsberg Bridge Problem)
 drawing and using networks that represent
information from a variety of real life situations
(eg delivery routes)
 network diagrams usually do not show distance or
direction, unlike conventional maps
 network diagrams show the order of, and paths
between locations
 investigating the traversablility of a network
 using network diagrams available within their
community (eg using an airline map to plan a tour
of the north-west by a country and western singer)
 ‘best’ paths and locations (eg finding the best
location for a recycling depot)
Represent shape
Shape and structure to make simple 3D models
Precision in producing models
Make complex models based on drawings
 matching the faces of an object with parts of its net
(eg finding the number opposite a six on the net of
a die)
 what the essential details are when constructing
figures and objects (eg matching lengths and
angles)
 making models from oblique, orthogonal and
isometric drawings
 making a box to match a provided wooden block by
drawing around each of its faces to make a net
 designing nets or constructing 3D objects from
isometric diagrams* (Mathematics) (eg a soccer
ball from the net of its stitching pattern involving a
tessellation of pentagons and hexagons)
© Department of Education and Training Western Australia, Early adolescence: Mathematics/Space scope and sequence, December 2007
2
Organisation of content into year levels is advisory. Teachers will continue to make professional
judgements about when to introduce content based on children’s prior learning and achievement.
*National Consistency in Curriculum Outcomes, Statement of Learning
Typical sequence of content:
Year 8
Year 9
Year 10
Represent shape (continued)
 cutting suitable lengths to make a skeleton of a
provided 3D shape (eg cutting straws to the correct
lengths to make a triangular prism)
 distinguishing suitable nets for various polyhedra
from a random set* (Mathematics)
 copying lengths and angles and constructing
parallels, perpendiculars, angle and line bisectors
and various angles* (Mathematics)
 drawing cross-sections of prisms, pyramids and
spheres* (Mathematics)
Common conventions for drawing angles,
2D shapes and 3D objects
Conventions to produce orthogonal, oblique,
perspective and isometric drawings
Use geometric tools and technology to make
accurate drawings
 drawing polyhedra, prisms, pyramids, cylinders and
cones* (Mathematics) (eg showing front, side and
top views and cross-sections)
 conventions for oblique or perspective drawings
when drawing common 3D shapes*
(Mathematics/ICT)
 using geometric equipment to construct accurate
drawings (eg parallel, perpendicular, various
angles and bisectors construct polygons, circles,
and ellipses from diagrams or given dimensions)
 drawing polyhedra, prisms, pyramids, cylinders and
cones and composite shapes formed from them
 constructing accurate two-dimensional
representations of three dimensional objects using
geometric shapes* (Mathematics/ICT) (eg an
isometric drawing or front-side-top view or a single
point perspective drawing of an hourglass)
 drawing a figure from a different position or
orientation without the aid of a model
 drawing two-dimensional shapes in terms of
boundary, angle and scale* (Mathematics)
 determining which properties are preserved by the
representation and which are not* (Mathematics)
(eg angle, length and area)
 using drawing equipment or computer drawing
software to copy and design (eg using logotypes
and other patterns)
 using compass and ruler and computer software in
constructions (eg constructing the bisector of an
angle)
 using geometric tools and techniques, such as
mirrors, templates and computer software, to make
accurate drawings* (Mathematics/ICT)
 using mathematical properties to check accuracy
(eg checking the lengths of the diagonals of a
rectangle)
© Department of Education and Training Western Australia, Early adolescence: Mathematics/Space scope and sequence, December 2007
3
Organisation of content into year levels is advisory. Teachers will continue to make professional
judgements about when to introduce content based on children’s prior learning and achievement.
*National Consistency in Curriculum Outcomes, Statement of Learning
Typical sequence of content:
Year 8
Year 9
Year 10
Represent transformations
Recognise and visualise transformation and
symmetry and produce spatial sequences
Combine two transformations and produce
symmetrical patterns
Describe properties of transformations to
reproduce drawings and complex patterns
 the language of transformation (eg ‘Rotate it at
right angles around the centre and slide it to the
left’)
 producing symmetrical designs* (Mathematics/ICT)
(eg folding paper or using mirrors or computer
graphics)
 carrying out a translation, rotation or reflection
using coordinates, tracing paper, geometric
drawing equipment or a computer package
(eg rotate triangle ABC about B, 60° clockwise)
 translation, rotation or reflection can affect the
position or orientation of a shape or object
 the effect of a translation, rotation, reflection,
dilation and distortion on the shape of an object*
(Mathematics)
 producing a reflection, translation or rotation of a
figure on a coordinate grid and describing it
(eg ‘I reflected it using the line that passes through
[0, 3] and [4, 0] as the mirror line’)
 representing dilations and distortions of a shape or
object by a whole number or unit fraction scale
factor (eg doubling width but not height)
 finding the centres, axes and planes of symmetry
in shapes or objects* (Mathematics)
 using properties of transformations to accurately
produce a symmetric arrangement (eg reflecting a
figure through a mirror line oblique to it)
 using transformations to design tessellations
 technologies which employ transformation
language or properties* (ICT) (eg swings or
projectors)
 finding the centres, axes and planes of symmetry
in figures
Enlargements and reductions
Predict the effects of enlargements and reductions
 using a grid to enlarge and reduce a figure and to
make distortions (eg doubling widths but not
heights)
 enlarging and reducing figures using projections
 enlarging models made with cubes to a small
whole number scale (eg given a model made of
6 cubes, produce one enlarged by a scale factor
of 3)
© Department of Education and Training Western Australia, Early adolescence: Mathematics/Space scope and sequence, December 2007
4
Organisation of content into year levels is advisory. Teachers will continue to make professional
judgements about when to introduce content based on children’s prior learning and achievement.
*National Consistency in Curriculum Outcomes, Statement of Learning
Typical sequence of content:
Year 8
Year 9
Year 10
Reason geometrically
Geometric language
Geometric language to refine descriptions
Geometric language to solve problems
 appropriate geometric language (eg using face and
edge rather than side)
 identifying, describing and classifying a broad range
of 2D shapes and 3D objects* (Mathematics)
 properties of shapes to produce informal
arguments about tessellations, symmetry and
transformations (eg all triangles tessellate since a
triangle and its reflection form a parallelogram
and all parallelograms tessellate)
 parallel and perpendicular lines and planes in figures
and objects (eg in a triangular prism)
 using counter-examples to test descriptions
Generate and classify shapes
Generate and classify shapes based on geometric
properties
Identify and use properties of triangles,
rectangles and circles
 identifying polygons, circles and ellipses*
(Mathematics)
 identifying different representations of three
dimensional shapes and objects* (Mathematics)
(eg cylinders, cones, platonic solids, packages and
containers)
 testing descriptions by using counter-examples
(eg ‘polygons with four equal sides are squares’
becomes ‘four-sided polygons with equal sides
and equal angles are squares’)
 classifying triangles and quadrilaterals in terms of
side, diagonal and angle* (Mathematics)
 showing front, side and top views of cross-sections
of three-dimensional shapes* (Mathematics/ICT)
 using congruent and similar triangles to solve
geometric problems* (Mathematics)
 similarity and congruence to solve mathematical
and practical problems (eg ‘I know that this side
equals this side – what else do I need to know in
order to say that the two triangles are
congruent’?)
© Department of Education and Training Western Australia, Early adolescence: Mathematics/Space scope and sequence, December 2007
5
Organisation of content into year levels is advisory. Teachers will continue to make professional
judgements about when to introduce content based on children’s prior learning and achievement.
*National Consistency in Curriculum Outcomes, Statement of Learning
Typical sequence of content:
Year 8
Year 9
Year 10
Reason geometrically (continued)
Make simple conjectures about familiar shapes
Informal arguments about familiar shapes
Generalisations about triangles
 why certain types of shapes will or will not
tessellate (eg ‘We think that all parallelograms will
tile. This is because you can always slide them
together to make long strips and then push the
strips together’)
 making deductions related to geometric properties
of shapes* (Mathematics) (eg when two straight
lines intersect, opposite angles are equal)
 generalising conditions for congruent triangles
 exploring demonstrations and informal proofs of
general propositions* (Mathematics) (eg the sum of
angles in a plane triangle is always 180°; if
corresponding angles are equal then alternate
angles are equal)
 applying tests for congruent triangles
Classify angles
Explore and use angle relationships
Identify and use angle relationships
 recognising and describing acute, obtuse, right and
straight angles
 applying angle properties related to parallel,
perpendicular and transversal lines* (Mathematics)
 angles which are congruent, supplementary and
complementary, and using angle relationships in
intersecting, parallel and perpendicular lines and
triangles to find the size of angles
 practical checks for whether lines and surfaces are
parallel, perpendicular, vertical or horizontal
(eg checking that two walls are parallel, that the
diagonals of a rectangle are congruent and bisect
each other)
© Department of Education and Training Western Australia, Early adolescence: Mathematics/Space scope and sequence, December 2007
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