TOWNSVILLE CATHOLIC EDUCATION OFFICE
Measurement and Geometry Scope & Sequence
The Australian Curriculum v4.0
Prep
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Compares objects
directly by placing
one object against
another to determine
which is longer,
hefting to determine
which is heavier or
pours to determine
which holds more,
and uses terms such
as “tall, taller” “holds
more, holds less”
(ACMMG006)
Measures and
compares the lengths
and capacities of pairs
of objects using
uniform informal
units (ACMMG019)
Compares and orders
several shapes and
objects based on
length, area, volume
and capacity using
appropriate uniform
informal units eg.
(length) finger length,
hand span, string,
(area) palm of your
hand, counters,
(volume) containers
(ACMMG037)
Measures, orders and
compares objects
using centimetres and
metres, grams and
kilograms and
milliliters and liters.
Recognises the
importance of using
common units of
measurement
(ACMMG061)
Uses graduated
scaled instruments to
measure and
compare lengths,
masses, capacities
and temperatures
(ACMMG084)
Chooses appropriate
units of measurement
for length, area,
volume, capacity and
mass, recognising
that some units of
measurement are
better suited for
some tasks than
others, for example,
km rather than m to
measure the distance
between two towns
(ACMMG108)
Connects decimal
representations to
the metric system
(recognises the
equivalence of
measurements such
as 1.25m and 125 cm)
(ACMMG135)
Establishes the
formulas for areas of
rectangles, triangles
and parallelograms
and usea these in
problem solving
(ACMMG159)
TIMESMG10
Converts between
common metric units
of length, mass and
capacity (identifying
and using the correct
operations when
converting units
including millimetres,
centimetres, metres,
kilometres,
milligrams, grams,
kilograms, tonnes,
millilitres, litres,
kilolitres and megalitres (ACMMG136)
TIMESMG10
Calculates volumes of
rectangular prisms
(ACMMG160)
TIMESMG11
Chooses appropriate
units of measurement
for area and volume
and converts from
one unit to another.
Recognises that the
conversion factors for
area of units are the
squares of those for
the corresponding
linear units and for
volume, units are the
cubes of those for the
corresponding linear
units (ACMMG195)
Using Units Usof Measurement
Compares and orders
the duration of
events using the
everyday language of
time (ACMMG007)
TIMESMG03
Tells time to the halfhour using analogue
and digital clocks
(ACMMG020)
TIMESMG03
Describes duration
using months, weeks,
days and hours
(ACMMG021)
TIMESMG03
Knows and identifies
the days of the week
and links specific days
to familiar events and
actions
(ACMMG 008)
Compares masses of
objects using balance
scales eg. find out
how many marbles
are used to balance
an object
(ACMMG038)
Tells time to the
minute and
investigates the
relationship between
units of time, for
example, there are
60 minutes in an hour
and 60 seconds in a
minute (ACMMG062)
TIMESMG03
Tells time to the
quarter-hour, using
the language of 'past'
and 'to' (ACMMG039)
TIMESMG03
Names and orders
months and seasons
(ACMMG040)
TIMESMG03
Compares objects
using familiar metric
units of area (grid
paper) and volume
(centicubes)
(ACMMG290)
Converts between
units of time
(ACMMG085)
TIMESMG03
Uses am and pm
notation and solve
simple time problems
for example,
determining arrival
time given departure
time, calculating the
time spent at school
during a normal
school day)
(ACMMG086)
TIMESMG03
Uses a calendar to
identify the date and
determine the
number of days in
each month
(ACMMG041)
TIMESMG03
Calculates the
perimeter and area of
rectangles using
familiar metric units.
Explores efficient
ways of calculating
perimeters by adding
the length and width
together and
doubling the result
(ACMMG109)
Compares 12- and 24hour time systems
using and convert
between them
(ACMMG110)
TIMESMG03
Uses units of hours,
minutes and seconds
(ACMMG110)
TIMESMG03
Find perimeters and
areas of
parallelograms,
rhombuses and kites
(ACMMG196)
TIMESMG11
Investigates the
relationship between
features of circles
such as
circumference,
area, radius and
diameter. Uses
formulas to solve
problems involving
circumference and
area (ACMMG197)
TIMESMG17
Recognises the
significance of the
prefixes in the units
of measurements eg:
milli = 1000th,
mega = one million
kilo= 1000th, centi =
100th, etc
(ACMMG136)
Solves problems
involving the
comparison of
lengths and areas
using appropriate
units (ACMMG137)
Develops the
formulas for volumes
of rectangular and
triangular prisms and
prisms in general.
Uses formulas to
solve problems
involving volume
(ACMMG198)
TIMESMG11
Connects volume and
capacity and their
units of measurement
(eg: recognise that
1mL is equivalent to
1cm3 (ACMMG138)
Solves problems
involving duration,
including using 12and 24-hour time
within a single
time zone
(ACMMG199)
TIMESMG03
Shape
Interprets and uses
timetables
(ACMMG139)
TIMESMG03
Sorts, describes and
names squares,
circles, triangles,
rectangles, spheres
and cubes
(ACMMG009)
Recognises and
classifies familiar two
dimensional
shapes including
squares, circles and
triangles, and three
dimensional shapes
using obvious
features
Describes and draws
two-dimensional
shapes, with and
without digital
technologies
(ACMMG042)
Identifies key features
of squares,
Makes models of
three dimensional
Objects (prisms and
pyramids) and
describes key
features
(ACMMG063)
Compares the areas
of regular and
irregular shapes by
using metric units
such as counting the
number of square
centimeters required
to cover two areas
and by overlaying the
Connects threedimensional objects
(prisms and pyramids)
with their nets and
other twodimensional
representations
(ACMMG111)
Construcst simple
prisms and pyramids
from nets
(ACMMG140)
Draws different views
of prisms and solids
formed from
combinations of
prisms (ACMMG161)
Year 9
Calculates the areas
of composite shapes
(ACMMG216)
Calculates the surface
area and volume of
cylinders and solves
related problems
(ACMMG217)
TIMESMG12
Solves problems
involving the surface
area and volume of
right prisms
(ACMMG218)
TIMESMG12
Investigates very
small and very large
time scales and
intervals
(ACMMG219)
Year 10
Year 10 A
Solves problems
involving surface area
and volume for a
range of prisms,
cylinders and
composite solids
(ACMMG242)
TIMESMG12
Solves problems
involving surface area
and volume of right
pyramids, right cones,
spheres and related
composite solids.
Uses formulas to
solve problems
including authentic
situations
(ACMMG271)
TIMESMG12
using terms such as
“corners”, “edges”
and “faces”
(ACMMG022)
rectangles, triangles,
kites, rhombuses and
circles such as
straight lines or
curved lines and
counting the edges
and corners
(ACMMG042)
area with a grid of
centimeter squares
(ACMMG087)
Compares and
describes two
dimensional shapes
that result from
combining and
splitting common
shapes, for example,
identifying common
2-D shapes that are
part of a composite
shape by re-creating
it from these shapes
(ACMMG088)
Describes the
features of three
dimensional objects
by identifying
features such as
faces, vertices or
edges (ACMMG043)
Location and Transformation
Describes position
and movement.
Interprets the
everyday language of
location and
direction, such as
“between”, “near”,
“next to”, “forwards”
and “towards”
(ACMMG010)
Gives and follows
directions to familiar
locations.
Understands that
people need to give
and follow directions
to and from a place
and that this involves
turns, direction and
distance
(ACMMG023)
Understands terms
such as “clockwise”,
“anticlockwise”,
“forward” and
“under” when giving
and following
directions
(ACMMG023)
Interprets simple
maps of familiar
locations and
identifies the relative
positions of key
features
(ACMMG044)
Investigates the effect
of one-step
slides and flips with
and without digital
technologies.
Understands that
changing position
does not alter an
objects size or
features
(ACMMG045)
Identifies and
describes half and
quarter turns
(ACMMG046)
Creates and
interprets simple
grid maps to show
position and
pathways
(ACMMG065)
Uses simple scales,
legends and
directions to interpret
information
contained in basic
maps (ACMMG090)
Identifies symmetry
in the environment
(ACMMG066)
Creates symmetrical
patterns, pictures
and shapes with and
without digital
technologies
(ACMMG091)
Uses a grid reference
system to describe
locations. Describe
routes using
landmarks and
directional language
(ACMMG113)
Describes
translations,
reflections and
rotations of twodimensional shapes.
(ACMMG114)
Identifies line and
rotational symmetries
by manually cutting,
folding and turning
shapes (ACMMG114)
Applies the
enlargement
transformation
to familiar two
dimensional shapes
and explores the
properties of the
resulting image
compared with the
original using a grid
system or digital
technologies
(ACMMG115)
Investigates
combinations of
translations,
reflections and
rotations, with and
without the use of
digital technologies.
Understands that
translations, rotations
and reflections can
change the position
and orientation of
shapes and objects
but not their
geometric features or
size (ACMMG142)
Introduces the
Cartesian coordinate
system using all four
quadrants
(ACMMG143)
Cartesian coordinate
system. Two
intersecting number
lines intersecting at
right angles at their
origins to form the
axes of the coordinate
system. The plane is
divided into four
quadrants by these
perpendicular axes
called the x-axis
(horizontal line) and
the y-axis (vertical
line). The position of
any point in the plane
can be represented by
an ordered pair of
numbers (x, y). These
ordered pairs are
called the coordinates
of the point
Describes
translations,
reflections in an axis,
and rotations of
multiples of 90° on
the Cartesian plane
using coordinates.
Identifies line and
rotational
symmetries.
Understands
transformations
(translation,
reflection, rotation)
to help identify the
movement of shapes
and rotational and
line symmetry
(ACMMG181)
Identifies angles as
measures of
turn and compares
angle sizes
in everyday situations
for example, opening
doors partially and
fully and comparing
the size of the angles
created (ACMMG064)
Compares angles and
classifies them as
equal to, greater than
or less than a
right angle
(ACMMG089)
Estimates, measures
and compares angles
using degrees.
Constructs angles
using both a 180° and
360° protractor
(ACMMG112)
Investigates, with and
without digital
technologies, angles
on a straight line
, angles at a
point
and
vertically opposite
angles
. Uses
results to find
unknown angles.
Defines acute,
obtuse, reflex and
right angles.
Identifies that angles
have arms and a
vertex and that the
angle size is the
amount of turn
required for one arm
to coincide with the
other. (ACMMG141)
TIMESMG09
Classifies triangles
according to their
side and angle
properties of scalene,
isosceles, right-angled
and obtuse-angled
triangles
(ACMMG165)
TIMESMG13
Describes squares,
rectangles,
rhombuses,
parallelograms, kites
and trapeziums
(ACMMG165)
TIMESMG13
TIMESMG20
TIMESMG21
Demonstrates that
the angle sum of a
triangle is 180°
and uses this to find
the angle sum of a
quadrilateral
(ACMMG166)
TIMESMG09
Geometric Reasoning
Identifies
corresponding
,
alternate
and cointerior
angles
when two parallel
straight lines are
crossed by a
transversal. Defines
and classifies angles
such as acute, right,
obtuse, straight,
reflex and revolution,
and pairs of angles
such as
complimentary ,
supplementary
, adjacent and
vertically opposite
(ACMMG163)
TIMESMG09
Investigates
conditions for two
lines to be parallel
and solves simple
numerical problems
using reasoning.
Defines and identifies
alternate
,
corresponding and
allied (co-interior)
angles and the
relationships
between them for a
pair of parallel lines
cut by a transversal
(ACMMG164)
TIMESMG09
Defines congruence
of plane shapes using
transformations.
Establishes that two
figures are congruent
if one shape lies
exactly on top of the
other after one or
more transformations
(translation,
reflection, rotation)
(ACMMG200)
TIMESMG14
Develops the
conditions for
congruence of
triangles. Investigates
the minimal
conditions needed for
the unique
construction of
triangles leading to
the establishment of
the conditions for
congruence (SSS, SAS,
ASA and RHS) and
demonstrates in
which conditions do
not prescribe
congruence (ASS and
AAA) (ACMMG201)
TIMESMG14
TIMESMG22
Establishes properties
of quadrilaterals
using congruent
triangles and angle
properties, and solves
related numerical
problems using
reasoning
(ACMMG202)
TIMESMG14
TIMESMG20
TIMESMG22
Uses the enlargement
transformation to
explain similarity and
develop the
conditions for
triangles to be similar.
Establishes the
conditions of
similarity of two
triangles and
compare this to the
conditions of
congruence
(ACMMG220)
TIMESMG22
Solves problems using
ratio and scale factors
in similar figures
(ACMMG221)
TIMESMG22
Formulates proofs
involving congruent
triangles and angle
properties
(ACMMG243)
TIMESMG22
Applies logical
reasoning, including
the use of
congruence and
similarity, to proofs
and numerical
exercises involving
plane shapes.
Performs a sequence
of steps to determine
an unknown angle
giving a justification
for each step
(ACMMG244)
TIMESMG20
TIMESMG21
TIMESMG22
Proves and applies
angle and chord
properties of circles
(ACMMG272)
TIMESMG26
Pythagoras and
Trigonometry
Investigates
Pythagoras’ Theorem
and its application to
solving simple
problems involving
right angled triangles
that generate results
that can be integral,
fractional or irrational
numbers
(ACMMG222)
TIMESMG15
Uses similarity to
investigate the
constancy
of the sine, cosine
and tangent ratios for
a given angle in rightangled triangles
(ACMMG223)
TIMESMG22
TIMESMG23
Applies trigonometry
to solve right-angled
triangle problems.
Understands the
terminology
“adjacent” and
“opposite” sides and
hypotenuse in right
angled triangles.
Uses trigonometric
ratios to find
unknown sides and
angles in right-angled
triangles
(ACMMG224)
TIMESMG23
Solves right-angled
triangle problems
including those
involving direction
and angles of
elevation and
depression
(ACMMG245)
TIMESMG23
Establishes the sine,
cosine and area rules
for any triangle and
solves related
problems
(ACMMG273)
TIMESMG24
Uses the unit circle to
define trigonometric
functions, and graphs
them with and
without the use of
digital technologies
(ACMMG274)
TIMESMG25
Solves simple
trigonometric
equations
(ACMMG275)
TIMESMG25
Applis Pythagoras’
theorem and
trigonometry to
solving threedimensional problems
in right-angled
triangles
(ACMMG276)
TIMESMG24