# Minimum standards - numeracy

## 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 two-digit numbers.

Students meeting the minimum standard have typically developed computational fluency with addition and subtraction of small whole numbers. They generally add and subtract two-digit 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 three-digit 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 two-digit 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 two-digit numbers

• partition one- and two-digit 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 two-digit 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 alpha-numeric 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 pre-algebraic 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:

• recognise and continue a number pattern with a constant addition or subtraction of a small whole number

• identify the change between consecutive terms in a simple pattern.

### 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 one-to-one correspondence and read data presented in simple tables, two-way tables and pictographs with one-to-one or one-to-two 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 whole-number 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 two-way 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 strand-specific 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 problem-solving 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.

## 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 place-value 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 two-digit 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 one-digit 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 non-symmetrical 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, three-quarters and a full turn

### 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 one-step 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 one-step 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:

• read measures from simple whole-unit scales.

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:

• make predictions based on data.

Students read data presented in tables, bar graphs and simple two-way tables and make simple interpretations. For example, students can generally:

• read tabular and graphical displays involving simple whole-number 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 strand-specific 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 whole-number scales, tables, simple graphs and pictographs (one-to-one or one-to-two 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.

## 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 seven-digit 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:

• identify common 2D shapes that have specific properties.

#### 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 whole-number 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 non-linear 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 simple-worded 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:

• find the smallest number which satisfies a simple-worded problem in a familiar context

#### Patterns

Students recognise and continue linear and simple non-linear patterns presented as models or in tables. For example, students can generally:

• find the next term in a simple non-linear pattern presented visually or in a table or as a sequence

• recognise and extend simple number patterns to make predictions or to find subsequent terms.

### 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 12-hour and 24-hour 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:

• read time on analogue and digital clocks using 12- and 24-hour time.

#### 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:

• link different representations of the same data

• read and interpret data in a two-way table.

### Year 7: Working mathematically

In working mathematically, the emphasis is on the processes rather than strand-specific 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 problem-solving 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 problem-solving 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.

## 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 three-digit 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 multi-step 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:

• solve a word problem involving fractions

• solve routine problems involving simple ratios.

Students can form estimates and approximations. For example, students can generally:

• form estimates and approximations of rational and irrational numbers and simple expressions

• interpret and justify the reasons for making estimates and approximations.

### 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 alpha-numeric coordinates to specify locations on maps

• identify and use whole-number 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 non-linear 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:

• identify equivalent forms of simple algebraic expressions.

#### Patterns

Students can identify and continue patterns, and make predictions of future representations in patterns. For example, students can generally:

• identify and continue a number pattern from a given diagram or a table of values

• identify future term in visual representation of linear pattern.

### 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:

• find value of missing angle in a triangle, with access to a calculator.

#### 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:

• identify probability (expressed as fraction) of familiar random event.

#### 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 strand-specific 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 whole-number 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 problem-solving 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.