Minimum standards  numeracy
Year 3  Year 5  Year 7  Year 9 
Year 3
Year 3: Number
In number, students at the minimum standard at Year 3 generally recognise, compare and order whole numbers with up to three digits, recognising standard representations and different ways of partitioning one and twodigit numbers.
Students meeting the minimum standard have typically developed computational fluency with addition and subtraction of small whole numbers. They generally add and subtract twodigit numbers, add the value of coins and use partitioning and grouping to solve simple problems.
Whole numbers
Students read, recognise and count with whole numbers up to three digits. For example, students can generally:

recognise threedigit numbers in words and symbols

recognise odd and even numbers

make given numbers larger or smaller by 1, by 10 or by 100

count forwards and backwards by 1s, 2s, 5s and 10s

skip count by 2s, 5s and 10s.
Students compare and order whole twodigit numbers. They use place value knowledge up to the hundreds to interpret different representations of whole numbers. For example, students can generally:

compare and order twodigit numbers

partition one and twodigit numbers in different ways

recognise different standard representations of numbers in hundreds, tens and ones.
Fractions and decimals
Students halve small amounts and recognise a half and a quarter in familiar contexts. They start to interpret decimals in a money context. For example, students can generally:

recognise a half and find half of discrete quantities or amounts

find half of a symmetrical object

interpret key decimals in money contexts as dollars and cents.
Calculating
Students recall basic number facts with small numbers and use them to complete addition and subtraction calculations. They recognise situations involving making equal groups. For example, students can generally:

recall and use addition and subtraction facts to 20

use partitioning to assist addition and subtraction of one and twodigit numbers

interpret repeated addition as multiplication

form equal groups of objects, given a visual support

count and record the total value of coins in dollars and cents (up to $5).
Applying number
Students generally identify situations and problems that require addition or subtraction with small numbers. For example, students can generally:

use addition or subtraction to solve routine problems

start to link the correct mathematical terms to the relevant operations (e.g. sum, difference, equal groups or equal sharing)

recognise situations involving a single operation.
Year 3: Space
In space, students at the minimum standard generally recognise basic 2D shapes and their properties such as length of sides, and size of angles or areas. They typically recognise and visualise familiar 2D shapes such as triangles, squares and circles, and common 3D objects such as cubes, prisms, cylinders and cones. They also recognise standard 2D representations of common 3D objects, line of symmetry and single turns. They generally follow simple directions to find locations on grids and informal maps.
Classification and properties of shapes
Students typically recognise and describe familiar 2D shapes and common 3D objects. They identify them within sketches, diagrams or photographs. For example, students can generally:

identify familiar 2D shapes such as squares, rectangles, triangles and circles

identify families of common 3D objects such as prisms, cones, cylinders

recognise models and 2D diagrams of common 3D objects

differentiate between 2D shapes and 3D objects

recognise angles in shapes, objects and in turns

visualise simple objects made of cubes.
Transformations
Students recognise line of symmetry in simple 2D shapes. They recognise simple transformations of familiar shapes. For example, students can generally:

use folding or other techniques to identify a line of symmetry

recognise the effect of a single flip, slide or turn

use symmetry or transformations to continue patterns.
Location and movement
Students identify pathways and specific locations on simple informal maps, grids and plans. For example, students can generally:

identify the key features of simple informal maps, grids and plans

use alphanumeric coordinates to locate position on simple grids

interpret informal maps or grids of familiar environments

follow directions for moving from one point to another using the language of turns.
Year 3: Algebra, function and pattern
In algebra, function and pattern, students at the minimum standard have prealgebraic skills and concepts that relate mostly to number sense. They relate known facts to simple number sentences and number patterns.
Students at the minimum standard can typically complete addition or subtraction number sentences involving small numbers correctly. They can model familiar situations with addition or subtraction number sentences. Students can identify relationships between consecutive terms in number patterns with constant addition or subtraction of small numbers.
Equivalence
Students at the minimum standard level recognise equivalences in a variety of ways. For example, students can generally:

recognise a familiar correspondence between two sets of objects

order objects according to a common criterion

follow a short sequence of instructions

recognise an equivalent form of a number or a simple expression

identify the same attribute in measurement or spatial contexts.
Patterns
Students identify and continue patterns and sequences that show increase, decrease and repetition. For example, students can generally:
Year 3: Measurement, chance and data
In measurement, chance and data, students at the minimum standard at Year 3 are generally able to visually compare by length ordered objects and to choose the instrument that measures length. Students can also calculate areas or volumes by counting whole units. They are able to read and tell key times on digital and analogue clocks.
Students meeting the minimum standard record data using onetoone correspondence and read data presented in simple tables, twoway tables and pictographs with onetoone or onetotwo correspondence.
Measures
Students identify and distinguish the attributes of shapes and objects with respect to length, area, volume and mass. They start to use informal units to compare, measure and order a set of objects according to a specified attribute. For example, students can generally:

understand the language used to describe length in familiar contexts

measure length using informal units

compare and order objects according to a specific attribute  length, capacity or area.
Students choose and use standard metric units such as metre, centimetre, litre and kilogram. They estimate and compare measurements, and choose appropriate instruments to measure to the nearest unit. For example, students can generally:

decide whether containers hold less, about the same or more than a litre

use informal units to estimate length, volume and mass of familiar objects

use some relationships between standard units, e.g. 1h = 60 min, 1m = 100 cm

read wholenumber scales with all calibrations shown.
Students read times and dates using clocks and calendars. For example, students can generally:

read half and quarter hour times on analogue clocks

read time on digital clocks in hours and minutes

recognise the time half an hour before or after a given time.
Data
Students read data present in tallies and simple tables. They make statements about familiar events that are likely or unlikely to happen. For example, students can generally:

read and interpret data presented in lists, tallies, tables, pictographs (1:1 or 1:2 correspondence) or simple column graphs and twoway tables

make qualitative judgements about data in frequency tables

identify variation of data in tables and graphs.
Year 3: Working mathematically
In working mathematically, the emphasis is on the processes rather than strandspecific content. In working mathematically, students at the minimum standard at Year 3 can generally recognise and respond to routine questions addressing known facts in familiar contexts.
Students recall basic facts, terms, procedures or properties of numbers and recognise simple shapes in familiar contexts. For example, students can generally:

recall names of familiar shapes, symbols and notations

recognise images of familiar 2D shapes and 3D objects, and equivalent forms of whole numbers and simple number sentences

calculate with small numbers and coins

retrieve information from simple tables, graphs and pictographs

group shapes, objects or numbers according to a common attribute or property

compare shapes and objects by lengths, areas and masses.
Students’ ability to apply known problemsolving strategies and procedures to solve routine problems is essential for their progress and for their cognitive development. For example, students can generally:

select the correct operation or a number sentence for a given situation

compare information presented in familiar forms

interpret simple diagrams and tables

construct number sentences by using known facts

follow simple instructions

solve routine problems involving one or two steps.
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Year 5
Year 5: Number
In number, students at the minimum standard at Year 5 typically understand and recognise relationships between numbers and perform simple calculations with the four operations.
Students meeting the minimum standard have developed number sense of whole numbers with up to three digits, and use the understanding of the four operations to solve routine problems in familiar contexts. They generally interpret the symbols for common fractions and decimals, and they add and subtract decimals with the same number of decimal places.
Whole numbers
Students recognise, read, compare, and order whole numbers up to four digits.For example, students can generally:

recognise different representations of a whole number

use place value to compare, order or locate numbers on a number line

multiply or divide by 10 or 100 in placevalue contexts.
Fractions and decimals
Students recognise equivalent forms of common fractions and link unit fractions to familiar situations. For example, students can generally:

identify and use equal partitions, and name the parts

recognise different representations of simple fractions

compare decimals with the same number of decimal places

use common unit fractions to solve routine problems.
Calculating
Students recall addition and subtraction facts with one and twodigit numbers and link to routine multiplication and related division facts. They add and subtract whole numbers to hundreds and decimal fractions with the same number of decimal places, and multiply onedigit numbers. For example, students can generally:

recall addition and subtraction facts of small numbers

identify and use known number facts to assist calculations

multiply small whole numbers

complete operations with coins and record amounts of money in decimals

add or subtract common fractions with the same denominators.
Applying number
Students recognise situations that require the use of addition, subtraction, multiplication or division. For example, students can generally:

recognise the use of a single operation in familiar contexts

use addition or subtraction to solve routine problems

solve routine problems involving a single operation

add or subtract decimals in money/measurement contexts

estimate the value of simple computations

link the four operations to routine situations.
Year 5: Space
In space, students at the minimum standard at Year 5 identify familiar 2D shapes and recognise simple representations of common 3D objects that illustrate the essential features.
They generally identify symmetrical and nonsymmetrical shapes and recognise spatial patterns and tessellations. They interpret conventions used in simple maps, grids and plans.
Classification and properties of shapes
Students identify common properties of 2D shapes or 3D objects and use the correct mathematical terms to describe them. For example, students can generally:

identify features of common shapes and objects

summarise features of groups of common shapes or objects

interpret the spatial language used in describing common shapes and objects.
Students recognise common shapes and objects presented in drawings and diagrams. For example, students can generally:

interpret drawings of shapes or objects that reflect the size and significant features

recognise different orientations of a shape or different perspectives of an object

identify shapes or objects with given features

visualise simple objects made of unit cubes.
Transformations
Students identify shapes and designs that are symmetrical or asymmetrical. They recognise a single transformation used in patterns or arrangements including tessellations. For example, students can generally:

identify symmetrical shapes and designs

identify the result of a single transformation of a simple shape

identify common shapes that tessellate.
Location and movement
Students interpret key symbols and conventions used in maps, grids and plans. For example, students can generally:

interpret the symbols for the key compass directions

link the four major compass points to a quarter, half, threequarters and a full turn

interpret and follow directions.
Year 5: Algebra, function and pattern
In algebra, function and pattern, students at the minimum standard at Year 5 complete number sentences with whole numbers involving addition or subtraction.
They generally recognise number patterns involving one operation and they select the correct rule used in a given pattern.
Relationships
Students recognise number relationships in familiar contexts. For example, students can generally:

identify a familiar criterion used in arranging and sorting shapes or objects

recognise and describe simple relationships

use simple tables or graphs to predict change.
Students make links between arithmetic operations based on familiar properties. For example, students can generally:

make links between routine multiplication and division facts

use known facts to work out related calculations

make changes to computations that maintain equivalence.
Equivalence
Students solve simple number sentences arising from familiar situations. For example, students can generally:

recognise the number sentence that matches a familiar situation

recognise equivalence in familiar contexts (e.g. balance scales)

solve onestep number sentences involving simple calculations.
Patterns
Students recognise and describe numerical and spatial patterns. For example, students can generally:

recognise different representations of the same pattern

recognise a single relationship between consecutive terms

continue number patterns requiring onestep calculations.
Year 5: Measurement, chance and data
In measurement, chance and data, students at the minimum standard at Year 5 use standard units such as centimetres and metres to measure lengths, grams and kilograms to measure mass, and litres to measure capacity.
Students meeting the minimum standard identify the possible outcomes for familiar events and make predictions. They read data in tables and simple graphs, and check simple statements.
Measures
Students compare, measure, and order lengths, areas, volumes, angles and masses selecting and using suitable standard units and appropriate measuring instruments and scales. For example, students can generally:

choose the appropriate attribute to compare objects

measure and compare areas of shapes on grids counting whole and half units

measure and compare volumes counting informal units

arrange measurements in order of magnitude

make reasonable estimates of a quantity using known measures.
Students recognise different recordings of metric measures. They understand relationships between perimeters of familiar shapes and the lengths of their sides. For example, students can generally:
Students read times on digital clocks and key times on analogue clocks, and they calculate durations of specific events. Students use calendars and simple timetables and timelines to sequence events. For example, students can generally:

recognise key times on analogue clocks and read times on digital clocks

identify equivalent forms of saying and recording a key time

use calendars and timetables to seek specific information.
Data
Students identify the possible outcomes for familiar events and predict their comparative likelihood. For example, students can generally:
Students read data presented in tables, bar graphs and simple twoway tables and make simple interpretations. For example, students can generally:

read tabular and graphical displays involving simple wholenumber scales

check statements or predictions against data

identify variation within a set of data.
Year 5: Working mathematically
In working mathematically, the emphasis is on the processes rather than strandspecific content. In working mathematically, students at the minimum standard at Year 5 can generally recognise and respond to routine questions involving known facts in familiar contexts.
Students at the minimum standard recall number facts, terms, properties of common shapes and recognise common objects in simple diagrams. For example, students can generally:

recall properties of numbers, common fractions, measures, familiar shapes and objects

recognise diagrams of common shapes and objects, equivalent forms of whole numbers, common fractions, decimals and simple expressions

calculate with whole numbers, common fractions with the same denominators and decimals

read and interpret information from wholenumber scales, tables, simple graphs and pictographs (onetoone or onetotwo correspondence)

measure length, area, mass and capacity using standard units

group shapes, objects or numbers according to a familiar attribute.
Students at the minimum standard apply simple strategies to solve routine problems. For example, students can generally:

select the correct operation or the missing number in a number sentence

construct and complete number sentence involving one operation

interpret a situation presented in diagrams, tables or simple graphs

follow simple instructions and procedures

analyse patterns to identify the rule

solve routine problems in familiar contexts.
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Year 7
Year 7: Number
In number students at the minimum standard at Year 7 identify, represent, compare and order integers and common fractions using a variety of methods. They perform calculations using all four operations (addition, subtraction, multiplication and division), both with and without the access to a calculator.
Students meeting the minimum standard can solve routine problems involving simple rates and proportions, and they can use strategies to form reasonable estimations.
Rational numbers
Students represent, describe and order integers, common fractions and decimals. For example, students can generally:

order and locate integers, mixed numbers or common fractions on a suitably scaled number line

recall decimal equivalence of common fractions

recognise different representations of a common fraction.
Calculating
Students use mental and written methods with addition, subtraction, multiplication and division. They use a calculator to assist with more complex calculations.
For example, students can generally:

solve simple problems in familiar contexts involving addition or subtraction of integers

use knowledge of place value to multiply and divide decimals by 10 and 100

perform calculations involving key percentages or addition and subtraction of decimal numbers with the same number of decimal places.
Applying number
Students form estimates and make approximations. They interpret and solve practical problems using appropriate operations. For example, students can generally:

round sevendigit numbers to the nearest thousand

solve simple rate problems involving time and distance

select an appropriate approximation to a calculation involving money

interpret and solve practical problems involving division, with access to a calculator.
Year 7: Space
In space students at the minimum standard at Year 7 identify, describe and classify common 2D shapes and 3D objects. They recognise lines of symmetry of irregular shapes.
Students, meeting the minimum standard, can read and interpret maps and plans and they use compass points to follow directions and find locations.
Classification and properties of shapes
Students identify, describe and classify 2D shapes and 3D objects. For example, students can generally:
Transformations
Students recognise symmetry and congruence in 2D shapes. They visualise simple translations of objects in space. For example, students can generally:

identify an increase or a decrease of a shape or object

identify lines of symmetry in regular and irregular shapes

visualise possible results of joining objects made from cubes.
Location and movement
Students interpret maps and plans using compass points and directions. For example, students can generally:

locate and describe positions on maps or plans using the major compass points

interpret wholenumber scales to estimate real distance between objects

follow directions on informal and formal maps using compass points (including NE NW SE SW).
Year 7: Algebra, function and pattern
In algebra, function and pattern, students at the minimum standard at Year 7 begin to recognise and interpret simple algebraic relationships. They can model familiar situations with informal linear equations and number sentences.
Students, meeting the minimum standard, can use visual images to identify attributes of equivalence, and continue and describe linear and simple nonlinear number patterns.
Relationships
Students recognise simple relationships presented visually as models or numerically in tables. For example, students can generally:

recognise and extend a linear relationship in a practical context

construct and interpret tables and graphs of simple functions

use the links between the four operations in familiar contexts.
Equivalence
Students solve simpleworded problems and number sentences. They can recognise and complete equivalences modelled visually. Students begin to identify inequalities involving the use of minimum (at least) or maximum (at most). For example, students can generally:
Patterns
Students recognise and continue linear and simple nonlinear patterns presented as models or in tables. For example, students can generally:
Year 7: Measurement, chance and data
In measurement, chance and data, students at the minimum standard at Year 7 use both formal and informal methods to measure and compare lengths, areas, volumes or angles. They identify and use relationships between standard units and read and record measurements from simple scales. Students can read and compare 12hour and 24hour time displays, and they calculate elapsed time.
Students, meeting the minimum standard, can identify more/less/equally likely events and calculate simple numerical probabilities. They read and interpret data presented in graphs and tables.
Measures
Students measure and compare lengths, areas, volumes and angles. They read calibrated scales, and make conversions between metric units. For example, students can generally:
Chance and data
Students identify more/less/equally likely events and calculate probabilities in simple familiar contexts. They use and interpret a range of graphs and tables. For example, students can generally:
Year 7: Working mathematically
In working mathematically, the emphasis is on the processes rather than strandspecific content. In working mathematically students at the minimum standard at Year 7 can generally recall known number facts, procedures and properties of whole rational numbers. They can solve routine questions in familiar contexts using known problemsolving strategies.
Students recall known number facts, concepts and procedures. For example, students can generally:

recall properties of whole numbers, fractions, decimals and common 2D shapes

recognise equivalent forms of common fractions and number sentences

calculate with whole numbers, decimals and key percentages using written methods

read and interpret information from tables, lists, pictographs and a range of graphs

group shapes, objects or numbers according to a common property.
Students' ability to apply known problemsolving strategies and procedures to solve routine problems is essential for the students' progress. For example, students can generally:

select the correct set of operations or relationships for a given situation

represent situations using tables, graphs, informal number sentences, etc.

construct number sentences involving at least two operations for a situation

follow a sequence of mathematics operations, instructions and procedures

recognise and extend number patterns

solve routine problems involving the four operations, with or without access to a calculator.
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Year 9
Year 9: Number
In number, students at the minimum standard at Year 9 identify, compare and order integers, decimals, key percentages and common fractions. They can identify equivalent representations of common fractions, key percentages and decimals.
Students, meeting the minimum standard, can apply common strategies to calculate simple proportions, percentages and simple rates used in familiar practical situations. They can use common methods to form estimates and approximations of rational and irrational numbers and simple expressions.
Rational and irrational numbers
Students identify and represent rational and some irrational numbers and compare and order them in respect to their properties. For example, students can generally:

identify a rational expression with the same value as a given fraction

identify range within which the square root of a threedigit number lies

identify the rational number that is a solution to a routine word problem, with access to a calculator

compare and order rational and irrational numbers, with access to a calculator.
Calculating
Students calculate with four operations using integers, key percentages, decimals and common fractions. For example, students can generally:

solve a problem involving addition and subtraction of decimal numbers with different number of decimal places

use simple ratios in familiar practical situations

identify solutions of multistep word problems involving common fractions or key percentages.
Applying number
Students calculate proportions, key percentages and simple rates involving money, time and measurements. For example, students can generally:
Students can form estimates and approximations. For example, students can generally:
Year 9: Space
In space, students at the minimum standard at Year 9 can identify, describe and classify common 2D shapes and 3D objects. Students can recognise symmetry and congruence and relate them to transformations and patterns.
Students meeting the minimum standard can interpret and use maps to specify locations and movements.
Classification and properties of shapes
Students can classify 2D shapes and 3D objects according to common properties including angles, sides, perimeters, areas and surface. For example, students can generally:

visualise nets of prisms or pyramids

identify the net of a cube using criteria about opposite faces

interpret 2D representations of 3D objects made from cubes and calculate their surface area.
Transformations
Students can recognise symmetry and congruence and relate these to transformations and patterns. For example, students can generally:

identify points and lines of symmetry in complex 2D shapes and specify these in terms of reflection, centre of rotation and angle of rotation

identify lines and planes of symmetry of common 2D shapes and 3D objects

use and modify congruent shapes to produce tessellations.
Location and movement
Students can interpret and use maps and plans to specify locations and follow directions to move from one location to another. For example, students can generally:

use alphanumeric coordinates to specify locations on maps

identify and use wholenumber scales

follow instructions for moving from one location to another, with reference to distances, directions and angles.
Year 9: Algebra, function and pattern
In algebra, function and pattern, students at the minimum standard at Year 9 can recognise relationships and evaluate simple algebraic expressions to establish equivalences. They can construct tables of values for functions following or using simple rules and graph the corresponding set of ordered pairs.
Students, meeting the minimum standard, can identify and continue patterns and predict future representations in patterns.
Relationships
Students can construct tables of values of functions given by simple rules. For example, students can generally:

identify the linear rule that generates a specific pattern

identify the graph of a simple nonlinear function given a table of values

read and interpret a range of graphs.
Equivalence
Students can evaluate simple algebraic expressions. For example, students can generally:

evaluate simple algebraic expressions with one variable

identify solution of simple formal and informal linear equations, unknown on one side only.
Students can establish equivalence between algebraic expressions. For example, students can generally:
Patterns
Students can identify and continue patterns, and make predictions of future representations in patterns. For example, students can generally:
Year 9: Measurement, chance and data
In measurement, chance and data, students at the minimum standard at Year 9 can use SI units to measure and compare, and they can apply simple measurement formulae in familiar practical situations.
Students meeting the minimum standard can interpret empirical estimates of probabilities and compare theoretical probabilities with sample data. They can summarise sample data from a population and make informal inferences in response to questions and hypotheses.
Measures
Students can use SI units to measure and compare lengths, areas, surfaces areas, volumes, angles, masses, times and temperatures. They can apply measurement formulae and use them in familiar practical situations. For example, students can generally:
Chance
Students can make and interpret empirical estimates of probabilities in familiar situations and compare theoretical probabilities to data obtained from trials. For example, students can generally:
Data
Students can represent and summarise sample data from a given population and can use data to make inferences. For example, students can generally:

calculate the average (mean) of a set of data

interpret data presented in a simple bivariate graph

interpret variation between sets of data and the effects of variation.
Year 9: Working mathematically
In working mathematically, the emphasis is on the processes rather than strandspecific content. In working mathematically students at the minimum standard at Year 9 can generally recall known facts, procedures and properties of rational numbers and solve routine questions in familiar contexts.
Students recall known facts, procedures or properties of rational numbers and interpret and use diagrams incorporating features of 2D shapes and 3D objects. For example, students can generally:

recall key concepts, properties of numbers and figures and symbolic or specific notations (e.g. a × b = ab, a + a + a = 3a)

interpret diagrams showing features of 2D shapes and 3D objects

calculate with whole numbers, fractions, decimals and integers using the four operations and approximate numbers to estimate computations

carry out routine algebraic procedures

read and interpret graphs, tables or other sources, read and use simple wholenumber scales

measure lengths, areas, volumes, masses, time, surface areas of basic shapes and objects

group or order numbers or objects by a given attribute or property.
Students’ ability to apply known problemsolving strategies and procedures to solve routine problems is essential for their progress and for their cognitive development. For example, students can generally:

choose appropriate set of operations or a strategy for solving routine problems

represent and interpret data in familiar tabular and graphical forms

model a familiar situation with a diagram or an equation

draw or identify common figures and shapes, given specifications

solve routine problems.
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