NSW Curriculum and Learning Innovation Centre
Exploring Early Arithmetical Strategies
(EAS)
Building capacity with the new syllabuses
Early Arithmetical Strategies (EAS)
Early Arithmetical Strategies (EAS) refers to the range of
counting strategies that are used to solve addition and
subtraction problems.
Arithmetical learning develops through two
complementary processes, counting and grouping.
The transition from count-by-one strategies to grouping
strategies underpins the structure of the Early
Arithmetical Strategies (EAS) framework.
NSW Curriculum and Learning Innovation Centre
The Early Arithmetical Strategies (EAS) Stages
EAS Stages
describing
count-byone
strategies
Emergent
Perceptual
EAS Stage
describing
grouping
strategies
Facile
(Flexible)
Figurative
Countingon-andback
NSW Curriculum and Learning Innovation Centre
Emergent counting
Stage
description
The student
cannot count
visible items.
The student either
does not know
the number words
or cannot
correctly
coordinate
number words
with items when
counting.
Videos
These videos
show students
attempting a
counting task.
Click on an image to
view the video
Syllabus
outcomes
Key ideas in
the syllabus
Working towards:
MAe-4NA
Counts to 30, and
orders, reads and
represents numbers
in the range 0 to 20
Working towards:
Count forwards to
30 and backwards
from a number in
the range 0 to 20
Working towards:
MAe-5NA
Combines,
separates and
compares
collections of
objects, describes
using everyday
language, and
records using
informal methods
Compare, order,
read and
represent
numbers to 10,
then 20
Combine two
groups of objects
to model addition
Take part of a
group away to
model subtraction
Sample related
content
Connect number
names, numerals
and quantities to
10
Recognise
numbers in a
variety of
contexts
Compare order
and make
collections to 10
then to 20
Recognise dice
and domino
patterns
NSW Curriculum and Learning Innovation Centre
Perceptual counting
Stage
description
The student is
able to count
visible items.
The student builds
numbers by using
materials or
fingers to
represent each
number when
solving addition
and subtraction
questions.
The materials
must always be
present during the
counting.
Videos
Syllabus
outcomes
These videos
show students
using a
perceptual
counting
strategy.
MAe-5NA
Combines,
separates and
compares
collections of
objects,
describes using
everyday
language, and
records using
informal methods
Click on an image
to view the video
Key ideas in
the syllabus
Combine two or
more groups to
model addition
Take part of a
group away to
model subtraction
Compare two
groups to
determine ‘how
many more’
Record addition
and subtraction
informally
Sample related
content
Use concrete
materials or fingers
to model and solve
simple addition and
subtraction problems
Use visual
representations of
numbers, e.g. ten
frames, to solve
addition and
subtraction problems
Create and recognise
combinations of
numbers to at least
10
NSW Curriculum and Learning Innovation Centre
Figurative counting
Stage
description
Videos
The student is
able to count
concealed items
by visualising the
items but always
starts counting
from “one”.
These videos show
students mentally
solving an
addition question
using a figurative
counting strategy.
The student may
sub-vocalise when
counting.
Click on an image to view
the video
Syllabus
outcomes
Key ideas in
the syllabus
MA1-5NA
Uses a range
of strategies
and informal
recording
methods for
addition and
subtraction
involving oneand two-digit
numbers
Use and record a
range of mental
strategies for
addition and
subtraction of
one- and twodigit numbers
Solve word
problems
involving addition
and subtraction
Sample related
content
Create, record and
recognise
combinations for
numbers from 11 up
to and including 20
Model and record
number patterns for
individual numbers
Use the terms add,
plus, equals, is equal
to, take away, minus
and the difference
between
NSW Curriculum and Learning Innovation Centre
Counting-on-and-back
Stage
description
The student
counts-on or
counts-back
from one of the
numbers rather
than counting
from “one” to
solve addition
and subtraction
problems .
The student
understands that
one of the
numbers takes
the place of a
completed
count.
Videos
This video
shows a
student
counting on
to solve
addition
questions.
Click on the image
to view the video
Syllabus
outcomes
MA1-5NA
Uses a range of
strategies and
informal
recording
methods for
addition and
subtraction
involving oneand two-digit
numbers
Key ideas in
the syllabus
Use and record a
range of mental
strategies for
addition and
subtraction of
one- and twodigit numbers
Solve word
problems
involving addition
and subtraction
Make connections
between addition
and subtraction
Sample related
content
Use a range of mental
strategies to solve
addition and subtraction
problems involving oneand two-digit numbers
including:
- counting-on from
the larger number to
find the total of two
numbers
- counting-back from
a number to find the
number remaining
- counting-on or
counting-back to
find the difference
between two
numbers.
NSW Curriculum and Learning Innovation Centre
Facile (flexible) number knowledge
Stage
description
Videos
Syllabus
outcomes
Key ideas in the
syllabus
Sample related
content
The student
uses known
facts, number
structure and
other grouping
strategies to
solve addition
and
subtraction
problems.
This video
shows a
student using
a facile
counting
strategy.
MA1-5NA
Uses a range of
strategies and
informal recording
methods for
addition and
subtraction
involving one- and
two-digit numbers
Recognise and recall
number combinations
that add to numbers up
to 20.
Model and apply the
commutative property
and associative
property for addition.
Use the inverse
operation to check
addition and
subtraction
calculations.
Use and record a range
of mental strategies for
addition and
subtraction of one-,
two-, three- and fourdigit numbers.
Use a range of
mental strategies
to solve addition
and subtraction
problems
including:
- using doubles
or near
doubles
- combining
numbers that
add to 10
- bridging to 10
- partitioning
numbers to at
least 20.
Click on the image
to view the video
MA2-5NA
Uses mental and
written strategies
for addition and
subtraction
involving two-,
three- and fourdigit numbers
NSW Curriculum and Learning Innovation Centre
Where to next?
Consider
Look
Plan
Consider assessing each student to determine where he or
she is on the Early Arithmetical Strategies aspect.
Look at the associated syllabus outcomes as indicated on
the numeracy continuum.
The syllabus content associated with each outcome will help
you to plan a teaching program aimed at progressing each
student to the next level along the continuum.
NSW Curriculum and Learning Innovation Centre