These assessment pointers are for judging standards of student performance in Year 6 Mathematics.
They are examples of what students may demonstrate rather than being a checklist of everything
they should do. For reporting, they are used to make on-balance judgements about achievement,
based on what has been taught and assessed during the reporting period. They can also be used to
guide the pitch of assessment tasks, develop marking keys and inform assessment feedback.
JUDGING STANDARDS IN YEAR 6 MATHEMATICS
Reporting against the Achievement Standard
YEAR 6 MATHEMATICS ACHIEVEMENT STANDARD
By the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the use of integers in everyday contexts. They solve
problems involving all four operations with whole numbers. Students connect fractions, decimals and percentages as different representations of the same number. They solve
problems involving the addition and subtraction of related fractions. Students make connections between the powers of 10 and the multiplication and division of decimals.
They describe rules used in sequences involving whole numbers, fractions and decimals. Students connect decimal representations to the metric system and choose
appropriate units of measurement to perform a calculation. They make connections between capacity and volume. They solve problems involving length and area. They
interpret timetables. Students describe combinations of transformations. They solve problems using the properties of angles. Students compare observed and expected
frequencies. They interpret and compare a variety of data displays including those displays for two categorical variables. They evaluate secondary data displayed in the media.
Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity. They add, subtract and multiply decimals and divide decimals where the
result is rational. Students calculate common percentage discounts on sale items. They write correct number sentences using brackets and order of operations. Students locate
an ordered pair in any one of the four quadrants on the Cartesian plane. They construct simple prisms and pyramids. Students list and communicate probabilities using simple
fractions, decimals and percentages.
YEAR 6 MATHEMATICS ASSESSMENT POINTERS
Number and Algebra
A
B
C
D
E
Excellent achievement
High achievement
Satisfactory achievement
Limited achievement
Very low achievement
Investigates and describes the
relationships between prime,
composite, square and
triangular numbers.
2013/37234v7 [PDF 2013/37706] Published: 20 July, 2015
Applies properties of prime,
composite, square and
triangular numbers to solve
problems, e.g. represents
composites as a product of their
primes, for instance
24 = 2 x 2 x 2 x 3.
Identifies the properties of
prime, composite, square and
triangular numbers, e.g. factor
trees.
Identifies some key features of
prime and composite numbers,
e.g. that all prime numbers
except 2 are odd numbers.
Recalls multiples up to 10 x 10.
Number and Algebra
A
B
C
D
E
Excellent achievement
High achievement
Satisfactory achievement
Limited achievement
Very low achievement
Evaluates and applies efficient
strategies to solve problems
involving any of the four
operations, with whole
numbers, and justifies the use of
the chosen strategies.
Selects and applies appropriate
strategies to solve problems
involving any of the four
operations, with whole
numbers.
Uses mental and written
strategies to solve problems
involving any of the four
operations, with whole
numbers, e.g. completes a
sequence, creates an ordered
list.
Uses given strategies to solve
problems involving any of the
four operations, with small
numbers, e.g. guess and check.
Calculates addition and
subtraction to solve problems.
Investigates everyday situations
that involve integers and solves
related problems, using a
number line, e.g. changes in
temperature.
Solves everyday additive
problems involving integers,
using a number line.
Describes the use of integers in
everyday situations, and locates
integers on a number line, e.g.
temperatures above and below
zero.
Completes number lines
involving zero and positive
integers.
Completes number lines
involving whole numbers.
Compares related fractions by
demonstrating their equivalence
using a number line. Solves
multi-step addition and/or
subtraction word problems
involving related fractions, e.g. If
2
3
of a group wore red and
5
10
wore green, what fraction wore
another colour?
Compares fraction families on a
number line. Estimates before
solving problems involving the
addition and/or subtraction of
related fractions.
Locates fractions on a number
line. Solves problems involving
the addition and/or subtraction
of related fractions, e.g.
1 5 5 3 8
+ = + = .
Represents fractions by drawing
diagrams. Adds fractions with a
common denominator, e.g.
4
2 6
+ = .
Completes arrangements or
drawings to represent a unit
fraction. Adds unit fractions with
common denominators, e.g.
1 1 2
+ = .
Solves problems by identifying
and applying simple fractions of
a quantity, e.g. finds two-thirds
of a cake cut into nine pieces:
2
2
9
of 9 = x = 6.
Calculates simple fractions of a
quantity and finds equivalent
fractions of the same quantity,
1
1 9
e.g. of 9 = x = 3.
Calculates simple fractions of a
quantity, where the result is a
whole number, e.g. one third of
nine is the same as 9 ÷ 3 = 3.
Models and calculates fractions
with drawings and diagrams.
Models and calculates unit
fractions with drawings and
diagrams.
Solves problems involving
decimals by recognising the
operation to be performed,
where results are rational. Uses
estimation and rounding to
check the reasonableness of
answers.
Adds, subtracts, multiplies and
divides decimals, where results
are terminating. Applies
rounding to estimate a result
before calculating.
Adds and subtracts decimals and
makes connections between the
powers of 10 and the
multiplication and division of
decimals, where the results are
rational, e.g. 2.05 x 100 = 205.
Adds and subtracts decimals.
Adds and subtracts whole
numbers.
3
3
3
3
1
3
9
9
9
7
7
7
9
7
7
7
1
Number and Algebra
Measurement and
Geometry
A
B
C
D
E
Excellent achievement
High achievement
Satisfactory achievement
Limited achievement
Very low achievement
Solves problems by selecting
and applying appropriate
equivalent decimals, fractions
and percentages.
Converts between equivalent
decimals, fractions and
percentages.
Connects fractions, decimals and
percentages as different
representations of the same
number.
Connects unit fractions,
decimals and simple
percentages.
Connects unit fractions and
decimals.
Solves problems involving the
calculation and comparison of
percentage discounts on items.
Finds the total cost of given
quantities and prices per item,
after application of percentage
discounts.
Calculates common percentage
discounts, e.g. calculates
discounts of 10%, 25% and 50%.
Calculates discounts of 10% and
50%.
Calculates discounts of 10% and
50% only with digital
technologies.
Solves problems involving an
additive or multiplicative
pattern, to predict a given term
in a sequence, e.g. finds a
specific missing term such as the
18th house in the street from
house number 43.
Identifies sequence/s involving
whole numbers, fractions
and/or decimals represented in
a pattern, and describes the rule
used to create the sequence.
Describes rules used in
sequences involving whole
numbers, fractions and/or
decimals.
Completes sequences involving
whole numbers, unit fractions or
decimals.
Follows given sequences.
Applies order of operations to
solve problems involving more
than two operations.
Applies order of operations to
solve problems involving up to
two operations.
Writes number sentences using
brackets and order of
operations, e.g. (20 x 6) + 15 =
135.
Writes number sentences with
any combination of addition,
subtraction, multiplication and
division.
Writes number sentences with
combinations of addition and
subtraction.
Converts and calculates to solve
problems involving the
comparison of length, mass,
area, volume and capacity, using
the correct operations.
Converts units and calculates
measurements of length, mass,
area, volume and capacity.
Compares lengths and areas to
solve problems, e.g. given the
area, finds possible lengths of
sides.
Connects decimals to the metric
system, e.g. 1.5 m = 150 cm.
Chooses appropriate units of
measurement to perform
calculations. Makes connections
between capacity and volume.
Solves problems involving length
and area.
Converts between standard
metric units for length and
mass.
Applies standard metric units to
measure length.
Interprets timetables and uses
timetables for planning, e.g.
plans a day trip involving a bus
and a train.
Interprets timetables and uses a
timetable to schedule events.
Interprets timetables.
Identifies events and their start
and finish times.
Identifies the starting time of a
given event.
Creates nets to construct prisms
and pyramids, satisfying given
criteria.
Creates nets to construct prisms
and pyramids, comparing
features.
Constructs simple prisms and
pyramids, e.g. from given nets.
Models simple prisms and
pyramids, e.g. using play dough.
Distinguishes between prisms
and pyramids.
Measurement and
Geometry
Statistics and Probability
A
B
C
D
E
Excellent achievement
High achievement
Satisfactory achievement
Limited achievement
Very low achievement
Applies combinations of
translations, reflections and
rotations to change the position
and orientation of shapes, e.g.
designs a logo.
Draws and describes the
transformation of one shape, i.e.
reflects, translates or rotates,
and identifies the new position.
Describes combinations of
transformations, e.g. uses terms
such as flip/reflect,
slide/translate, turn/rotate.
Describes one transformation of
a regular shape, e.g. identifies a
triangle was flipped.
Identifies line and rotational
symmetry.
Applies and explains
combinations of transformations
of shapes on the Cartesian
plane, maintaining shape and
size.
Provides instructions to locate
and draw a shape on the
Cartesian plane.
Locates an ordered pair in any
one of the four quadrants on the
Cartesian plane.
Identifies 𝑥 and 𝑦 axes on the
Cartesian plane and plots
coordinates.
Misplaces 𝑥 and 𝑦 values.
Solves problems involving
unknown angles. Measures
angles of two-dimensional
regular shapes and writes a
relationship, e.g. the three
angles of a triangle add to 180°.
Compares angles and classifies
them according to size, i.e. as
acute, right, obtuse, straight or
reflex angles.
Solves problems using the
properties of angles, e.g. finds a
missing angle.
Measures angles using a
protractor.
Identifies angles in relation to a
right angle, i.e. as greater than,
less than or the same as.
Designs and conducts a chance
experiment to investigate
probabilities of changed
conditions, such as a 50%
increase in the proportion of a
spinner that is red, and lists the
probabilities.
Matches statements of
probability and numerical
expressions in fractions,
decimals and percentages.
Lists the probabilities of all
possible outcomes using simple
fractions, decimals and
percentages, e.g. assesses the
various probabilities with an
unequally coloured spinner.
Lists probabilities of outcomes
using a range from 0 to 1 in
simple fractions.
States the probability of
outcomes as likely or unlikely.
Interprets the similarities and
differences between expected
outcomes and actual results of
both small and large numbers of
trials.
Compares observed results in
trials with expected outcomes,
using an appropriate expression,
e.g. in 30 rolls of a six-sided die,
a two was rolled 7/30, when it
was expected to be rolled 5/30.
Compares observed and
expected frequencies, e.g. when
rolling a six-sided die 12 times, a
one was expected to come up
two times but it was rolled four
times.
Conducts trials and records
results.
Records the results of a trial.
Statistics and Probability
A
B
C
D
E
Excellent achievement
High achievement
Satisfactory achievement
Limited achievement
Very low achievement
Evaluates data in complex
displays with multi-layered
information. Evaluates
secondary data displayed in the
media by validating its accuracy,
identifying potentially
misleading representations and
explaining possible reasons for
specific representations, e.g. to
emphasise a point of view.
Interprets data in complex
displays with multi-layered
information. Evaluates
secondary data displayed in the
media by validating its accuracy
and identifying potentially
misleading representations, e.g.
graphics not drawn to scale.
Interprets and compares data
displayed in a variety of ways,
including displays for two
categorical variables, e.g.
identifies the value of the
symbol in a graph to display the
populations of different cities.
Evaluates secondary data
displayed in the media by
assessing its usefulness, e.g.
consults web-based rainfall data
to decide the best month for an
overseas holiday.
Identifies information from a
range of data displays. Makes
literal statements about
secondary data displayed in the
media, e.g. there was 4 mm of
rain overnight.
Identifies information from
simple data displays, e.g.
displays for one categorical
variable.