S3 Mathematics Scope & Sequence
This scope and sequence is an example only, schools will need to make modifications as necessary dependent on school context and student needs.
The same scope and sequence can be used in Year 5 and Year 6. Each term is organised into two parts – Early Term (the first half of term) and Later Term (the second half of term) to provide
opportunities to develop deep knowledge and understanding.
Number and Algebra
Measurement and Geometry
Early Term 1
Whole Numbers
Addition and Subtraction
Multiplication and Division
Fractions and Decimals (relate to Length)
Later Term 1
Whole Numbers (relate to Multiplication and Division)
Addition and Subtraction
Multiplication and Division
Fractions and Decimals (relate to Addition and Subtraction)
Early Term 2
Addition and Subtraction
Multiplication and Division
Fractions and Decimals (relate to Length)
Later Term 2
Whole Numbers
Addition and Subtraction
Multiplication and Division
Fractions and Decimals (relate to Addition and Subtraction)
Patterns and Algebra
Early Term 3
Whole Numbers (relate to Multiplication and Division)
Addition and Subtraction
Multiplication and Division
Fractions and Decimals (relate to Length)
Patterns and Algebra
Area (relate to Fractions and
Later Term 3
Addition and Subtraction
Multiplication and Division
Fractions and Decimals (relate to Multiplication and Division)
(relate to Whole Numbers)
Decimals)
Early Term 4
Whole Numbers
Multiplication and Division
Fractions and Decimals (relate to Addition and Subtraction)
Later Term 4
Addition and Subtraction
Multiplication and Division
Fractions and Decimals
Patterns and Algebra
3D Space
Angles
Data (relate to Whole
(relate to Multiplication and
Division)
2D Space (relate to
Data
Time
Position
Length
Volume and Capacity (relate
3D Space
2D Space (relate to
to Multiplication and Division)
3D Space)
Mass (relate to Fractions and
2D Space
Angles
Data
Chance
Length
Time (relate to Whole Numbers)
2D Space (relate to
Chance (relate to
Angles)
Fractions and Decimals)
Position
Data
3D Space
Data
Chance (relate to
(relate to Fractions and
Decimals)
Area
Patterns and Algebra
(relate to Multiplication and
Division)
Decimals)
Volume and Capacity (relate
Angles
Time
Patterns and Algebra
Mass
(relate to Fractions and
Decimals)
Numbers)
Area)
to Fractions and Decimals)
Note: The concept of percentages first appears in Part 2 of Fractions and Decimals in Stage Three.
© Department of Education and Communities
Length
Statistics and
Probability
Fractions and Decimals)
2D Space
Angles (relate to 2D
Space)
Stage 3 Mathematics Scope & Sequence of key ideas
Number and Algebra
Whole Numbers
Read, write and order numbers of any size
Measurement and Geometry
Length
Use the kilometre to measure lengths and
distances
State the place value of digits in numbers of any size
Record numbers of any size using expanded notation
Early Term 1
Addition and Subtraction
Select and apply efficient mental, written and calculator strategies for
addition and subtraction of numbers of any size
Use estimation to check answers to calculations
Select and use appropriate instruments and
units to measure lengths
Record lengths and distances using the
abbreviations km, m, cm and mm
3D Space
Name prisms and pyramids according to the
shape of their ‘base’
Multiplication and Division
Use and record a range of mental and written strategies to multiply by one- Describe and compare properties of prisms and
and two-digit operators
pyramids in terms of their faces, edges and
vertices
Solve word problems and record the strategy used
Angles (relate to 3D Space)
Use estimation to check answers to calculations
Recognise the need for formal units to measure
angles
Fractions and Decimals (relate to Length)
Compare and order unit fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12
Measure, compare and estimate angles in
and 100
degrees (up to 360°)
Model and represent strategies to add and subtract fractions with the
same denominator
Express mixed numerals as improper fractions and vice versa
Patterns and Algebra (relate to Fractions and Decimals)
Identify, continue create and describe increasing and decreasing number
patterns with fractions, decimals and whole numbers
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Statistics and Probability
Data (relate to Whole Numbers)
Collect categorical and
numerical data by
observation and by survey
Construct data displays,
including tables, column
graphs, dot plots and line
graphs, appropriate for the
data type
Stage 3 Mathematics Scope & Sequence of key ideas
Number and Algebra
Whole Numbers (relate to Multiplication and Division)
Determine factors and multiples of whole numbers
Measurement and Geometry
Area (relate to Multiplication and Division)
Recognise the need for square kilometres and
hectares to measure area
Identify and describe prime and composite numbers
Record areas using the abbreviations km2 and ha
Later Term 1
Addition and Subtraction
Solve word problems and record the strategy
used, including problems involving money
Develop a strategy to find areas of rectangles
(including squares) and record the strategy in
words
Create a simple budget
Multiplication and Division
Use and record a range of mental and written strategies to
multiply by one- and two-digit operators
Interpret remainders in division problems
Fractions and Decimals (relate to Addition and Subtraction)
Determine, generate and record equivalent fractions
Model and represent strategies to add and subtract fractions
with the same denominator
Add and subtract fractions, included mixed numerals, with the
same or related denominators
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Time
Convert between 12- and 24-hour time
Determine and compare the duration of events
2D Space (relate to Area)
Compare and describe side properties of the
special quadrilaterals and special triangles
Classify and draw regular and irregular twodimensional shapes from descriptions of their
features
Position
Use grid-referenced maps to locate and describe
positions
Statistics and Probability
Data
Describe and interpret data
presented in tables, column
graphs, dot plots and line
graphs
Stage 3 Mathematics Scope & Sequence of key ideas
Early Term 2
Number and Algebra
Measurement and Geometry
Addition and Subtraction
Select and apply efficient mental, written and calculator
strategies for addition and subtraction of numbers of any size
Length
Find perimeters of common two-dimensional
shapes and record the strategy
Use estimation to check answers to calculations
Record lengths and distances using decimal
notation to three decimal places
Multiplication and Division
Use and record a range of mental and written strategies to divide Volume and Capacity (relate to Multiplication and
Division)
numbers with three or more digits by a one-digit operator,
Use cubic centimetres and cubic metres to measure
including problems that result in a remainder
and estimate volumes
Use the formal algorithm for multiplication by one- and two-digit
Select and use appropriate units to measure volume
operators
Fractions and Decimals (relate to Length)
Apply the place value system to represent thousandths as
decimals
Compare, order and represent decimals with up to three decimal
places
Patterns and Algebra (relate to Multiplication and Division)
Find missing numbers in number sentences involving
multiplication or division on one or both sides of the equals sign
Record volumes using the abbreviations cm3 and
m3
3D Space
Connect three-dimensional objects with their nets
2D Space (relate to 3D Space)
Identify, name and draw right-angled, equilateral,
isosceles and scalene triangles
Explore angle properties of the special
quadrilaterals and special triangles
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Statistics and Probability
Stage 3 Mathematics Scope & Sequence of key ideas
Later Term 2
Number and Algebra
Measurement and Geometry
Whole Numbers
Read, write and order numbers of any size
Mass (relate to Fractions and Decimals)
Recognise the need for tonnes to measure mass
State the place value of digits in numbers of any size
Record masses using the abbreviations t, kg and g
Record numbers of any size using expanded notation
Select and use appropriate instruments and units to
measure mass
Addition and Subtraction
Select and apply efficient mental, written and calculator
strategies to solve word problems and record the strategy
used
Multiplication and Division
Use and record a range of mental and written strategies to
divide numbers with three or more digits by a one-digit
operator, including problems that result in a remainder
Distinguish between ‘gross mass’ and ‘net mass’
Solve problems involving mass
2D Space
Use the terms ‘translate’, ‘reflect’ and ‘rotate’ to
describe transformations of shapes
Identify line and rotational symmetries
Use the formal algorithm for multiplication by one- and twodigit operators
Fractions and Decimals (relate to Addition and Subtraction)
Model and represent strategies to add and subtract fractions
with the same denominator
Write fractions in their ‘simplest form’
Add and subtract fractions, included mixed numerals, with
the same or related denominators
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Angles
Record angle measurements using the symbol for
degrees (°)
Construct angles using a protractor (up to 360°)
Describe angle size in degrees for each angle
classification
Statistics and Probability
Data
Construct data displays,
including tables,
column graphs, dot plots
and line graphs,
appropriate for the data
type
Describe and interpret data
presented in tables,
column graphs, dot plots
and line graphs
Chance
List outcomes of chance
experiments involving
equally likely outcomes
Represent probabilities
using fractions
Recognise that
probabilities range from 0
to 1
Stage 3 Mathematics Scope & Sequence of key ideas
Number and Algebra
Whole Numbers (relate to Multiplication and Division)
Determine factors and multiples of whole numbers
Measurement and Geometry
Length
Convert between kilometres, metres, centimetres and
millimetres
Identify and describe prime and composite numbers
Solve problems involving length and perimeter
Model and describe square and triangular numbers
Early Term 3
Addition and Subtraction
Select and apply efficient mental, written and calculator strategies
to solve word problems and record the strategy used
Use estimation to check answers to calculations
Multiplication and Division
Solve word problems and record the strategy used
Time (relate to Whole Numbers)
Interpret and use timetables
Draw and interpret timelines using a given scale
2D Space (relate to Angles)
Make and compare enlargements of shapes/pictures
Identify, use and describe combinations of
translations, reflections and rotations
Interpret remainders in division problems
Fractions and Decimals (related to Length)
Represent, compare and order fractions with denominators 2, 3, 4,
5, 6, 8, 10, 12 and 100
Multiply fractions by whole numbers
Find a simple fraction of a quantity
Use mental, written and calculator strategies to add and subtract
decimals with up to three decimal places
Patterns and Algebra
Continue, create, record and describe geometric and number
patterns in words
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Angles
Identify and name angle types formed by the
intersection of straight lines, including ‘angles on a
straight line’, ‘angles at a point’ and ‘vertically
opposite angles’
Statistics and Probability
Chance (relate to Fractions
and Decimals)
Compare observed
frequencies in chance
experiments with expected
frequencies
Represent probabilities
using fractions,
decimals and percentages
Stage 3 Mathematics Scope & Sequence of key ideas
Number and Algebra
Statistics and Probability
Addition and Subtraction
Select and apply efficient mental, written and calculator strategies
to solve word problems and record the strategy used
Area (relate to Fractions and Decimals)
Develop a strategy to find areas of triangles and
record the strategy in words
Data
Interpret and create twoway tables
Multiplication and Division
Select and apply efficient mental, written and calculator strategies
to solve word problems and record the strategy used
Solve problems involving areas of rectangles
(including squares) and triangles
Interpret side-by-side
column graphs
Use estimation to check answers to calculations
Later Term 3
Measurement and Geometry
Fractions and Decimals (relate to Multiplication and Division)
Use mental, written and calculator strategies to multiply decimals
by one- and two-digit whole numbers
Use mental, written and calculator strategies to divide decimals by
one-digit whole numbers
Multiply and divide decimals by 10, 100 and 1000
Patterns and Algebra (relate to Whole Numbers)
Determine the rule for geometric and number patterns in words
and use the rule to calculate values
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Position
Follow a sequence of directions, including
compass directions, to find a particular location
on a map
Describe routes using landmarks and directional
language
Stage 3 Mathematics Scope & Sequence of key ideas
Number and Algebra
Whole Numbers
Recognise the location of negative numbers in relation to zero on
a number line
Multiplication and Division
Recognise and use grouping symbols
Measurement and Geometry
Volume and Capacity (related to Fractions and
Decimals)
Connect volume and capacity and their units of
measurement
Record volumes and capacities using decimal
notation to three decimal places
Apply the order of operations in calculations
Early Term 4
Convert between millilitres and litres
Statistics and Probability
Data
Compare a range of data
displays to determine the
most appropriate display for
particular sets of data
Interpret and critically
evaluate data presented in
digital media and elsewhere
Solve word problems and record the strategy used
Fractions and Decimals (related to Addition and Subtraction)
Solve word problems involving fractions and decimals, including
money problems
Make connections between equivalent percentages, fractions and
decimals
Develop a strategy to find volumes of
rectangular prisms and record the strategy in
words
Time
Convert between 12- and 24-hour time
Determine and compare the duration of events
Use mental, written and calculator strategies to calculate 10%,
25% and 50% of quantities, including as discounts
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3D Space
Construct prisms and pyramids using a variety
of materials, and given drawings from different
views
Chance (related to Fractions and
Decimals)
Conduct chance experiments
with both small and large
numbers of trials
Represent probabilities using
fractions
Recognise that probabilities
range from 0 to 1
Stage 3 Mathematics Scope & Sequence of key ideas
Later Term 4
Number and Algebra
Measurement and Geometry
Addition and Subtraction
Select and apply efficient mental, written and calculator strategies
to solve word problems and record the strategy used
Mass (related to Fractions and Decimals)
Record mass using decimal notation to three
decimal places
Multiplication and Division
Select and apply efficient mental, written and calculator strategies
to solve word problems and record the strategy used
Convert between tonnes, kilograms and grams
Recognise and use grouping symbols
2D Space
Identify, describe, compare and draw diagonals
of two-dimensional shapes
Apply the order of operations in calculations
Identify and name parts of circles
Fractions and Decimals
Compare, order and represent decimals with up to three decimal
places
Angles (related to 2D Space)
Identify and name angle types formed by the
intersection of straight lines, including ‘angles
on a straight line’, ‘angles at a point’ and
‘vertically opposite angles’
Multiply fractions by whole numbers
Find a simple fraction of a quantity
Use mental, written and calculator strategies to add and subtract
decimals with up to three decimal places
Patterns and Algebra
Locate and record the coordinates of points in all four quadrants
of the Cartesian plane
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Use known angle results to find unknown
angles in diagrams
Statistics and Probability