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Mathematics - Foundation Level

Foundation Level Description

The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the...

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Foundation Level Content Descriptions

Number and Algebra

Number and place value
  1. Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from  any starting point (ACMNA001)
  2. Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002)
  3. Subitise small collections of objects (ACMNA003)
  4. Compare, order and make correspondences between collections, initially to 20, and explain reasoning (ACMNA289)
  5. Represent practical situations to model addition and sharing (ACMNA004)
Patterns and algebra
  1. Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings (ACMNA005)

Measurement and Geometry

Using units of measurement
  1. Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language (ACMMG006)
  2. Compare and order the duration of events using the everyday language of time (ACMMG007)
  3. Connect days of the week to familiar events and actions (ACMMG008)
Shape
  1. Sort, describe and name familiar two-dimensional shapes and three-dimensional objects in the environment (ACMMG009)
Location and transformation
  1. Describe position and movement (ACMMG010)

Statistics and Probability

Data representation and interpretation
  1. Answer yes/no questions to collect information (ACMSP011)

Foundation Level Achievement Standard

Number and Algebra

Students connect number names and numerals with sets of up to 20 elements, estimate the size of these sets, and use counting strategies to solve problems that involve comparing, combining and separating these sets. They match individual objects with counting sequences up to and back from 20. Students order the first 10 elements of a set.

Measurement and Geometry

Students identify measurement attributes in practical situations and compare lengths, masses and capacities of familiar objects. They order events, explain their duration, and match days of the week to familiar events. Students identify simple shapes in their environment and sort shapes by their common and distinctive features. They use simple statements and gestures to describe location.

Statistics and Probability

Students sort familiar categorical data into sets and use these to answer yes/no questions and make simple true/false statements about the data.

Foundation Level Work Samples

Mathematics - Level 1

Level 1 Description

The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the...

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Level 1 Content Descriptions

Number and Algebra

Number and place value
  1. Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero (ACMNA012)
  2. Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line (ACMNA013)
  3. Count collections to 100 by partitioning numbers using place value (ACMNA014)
  4. Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015)
Fractions and decimals
  1. Recognise and describe one-half as one of two equal parts of a whole. (ACMNA016)
Money and financial mathematics
  1. Recognise, describe and order Australian coins according to their value (ACMNA017)
Patterns and algebra
  1. Investigate and describe number patterns formed by skip counting and patterns with objects (ACMNA018)

Measurement and Geometry

Using units of measurement
  1. Measure and compare the lengths and capacities of pairs of objects using uniform informal units (ACMMG019)
  2. Tell time to the half-hour (ACMMG020)
  3. Describe duration using months, weeks, days and hours (ACMMG021)
Shape
  1. Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features (ACMMG022)
Location and transformation
  1. Give and follow directions to familiar locations (ACMMG023)

Statistics and Probability

Chance
  1. Identify outcomes of familiar events involving chance and describe them using everyday language such as ‘will happen’, ‘won’t happen’ or ‘might happen’ (ACMSP024)
Data representation and interpretation
  1. Choose simple questions and gather responses (ACMSP262)
  2. Represent data with objects and drawings where one object or drawing represents one data value. Describe the displays (ACMSP263)

Level 1 Achievement Standard

Number and Algebra

Students count to and from 100 and locate these numbers on a number line. They partition numbers using place value and carry out simple additions and subtractions, using counting strategies. Students recognise Australian coins according to their value. They identify representations of one half. Students describe number sequences resulting from skip counting by 2s, 5s and 10s. They continue simple patterns involving numbers and objects with and without the use of digital technology.

Measurement and Geometry

Students use informal units of measurement to order objects based on length and capacity. They tell time to the half-hour and explain time durations. Students describe two-dimensional shapes and three-dimensional objects. They use the language of distance and direction to move from place to place.

Statistics and Probability

Students describe data displays. They ask questions to collect data and draw simple data displays. Students classify outcomes of simple familiar events.

Level 1 Work Samples

Mathematics - Level 2

Level 2 Description

The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the...

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Level 2 Content Descriptions

Number and Algebra

Number and place value
  1. Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences. (ACMNA026)
  2. Recognise, model, represent and order numbers to at least 1000 (ACMNA027)
  3. Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028)
  4. Explore the connection between addition and subtraction (ACMNA029)
  5. Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030)
  6. Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031)
  7. Recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032)
Fractions and decimals
  1. Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
Money and financial mathematics
  1. Count and order small collections of Australian coins and notes according to their value (ACMNA034)
Patterns and algebra
  1. Describe patterns with numbers and identify missing elements (ACMNA035)
  2. Solve problems by using number sentences for addition or subtraction (ACMNA036)

Measurement and Geometry

Using units of measurement
  1. Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037)
  2. Compare masses of objects using balance scales (ACMMG038)
  3. Tell time to the quarter-hour, using the language of 'past' and 'to' (ACMMG039)
  4. Name and order months and seasons (ACMMG040)
  5. Use a calendar to identify the date and determine the number of days in each month (ACMMG041)
Shape
  1. Describe and draw two-dimensional shapes, with and without digital technologies (ACMMG042)
  2. Describe the features of three-dimensional objects (ACMMG043)
Location and transformation
  1. Interpret simple maps of familiar locations and identify the relative positions of key features (ACMMG044)
  2. Investigate the effect of one-step slides and flips with and without digital technologies (ACMMG045)
  3. Identify and describe half and quarter turns (ACMMG046)

Statistics and Probability

Chance
  1. Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ (ACMSP047)
Data representation and interpretation
  1. Identify a question of interest based on one categorical variable. Gather data relevant to the question (ACMSP048)
  2. Collect, check and classify data (ACMSP049)
  3. Create displays of data using lists, table and picture graphs and interpret them (ACMSP050)

Level 2 Achievement Standard

Number and Algebra

Students count to and from, and order numbers up to 1000. They perform simple addition and subtraction calculations, using a range of strategies. They find the total value of simple collections of Australian notes and coins. Students represent multiplication and division by grouping into sets and divide collections and shapes into halves, quarters and eighths. They recognise increasing and decreasing number sequences involving 2s, 3s, 5s and 10s, identify the missing element in a number sequence, and use digital technology to produce sequences by constant addition.

Measurement and Geometry

Students order shapes and objects, using informal units for a range of measures. They tell time to the quarter hour and use a calendar to identify the date, days, weeks and months included in seasons and other events. Students draw two-dimensional shapes, specify their features and explain the effects of one-step transformations. They recognise the features of three-dimensional objects. They interpret simple maps of familiar locations.

Statistics and Probability

Students collect data from relevant questions to create lists, tables and picture graphs with and without the use of digital technology. They interpret data in context. Students describe outcomes of familiar events using everyday language. 

Level 2 Work Samples

Mathematics - Level 3

Level 3 Description

The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the...

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Level 3 Content Descriptions

Number and Algebra

Number and place value
  1. Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051)
  2. Recognise, model, represent and order numbers to at least 10 000 (ACMNA052)
  3. Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053)
  4. Recognise and explain the connection between addition and subtraction (ACMNA054)
  5. Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)
  6. Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)
  7. Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057)
Fractions and decimals
  1. Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058)
Money and financial mathematics
  1. Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059)
Patterns and algebra
  1. Describe, continue, and create number patterns resulting from performing addition or subtraction (ACMNA060)

Measurement and Geometry

Using units of measurement
  1. Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)
  2. Tell time to the minute and investigate the relationship between units of time (ACMMG062)
Shape
  1. Make models of three-dimensional objects and describe key features (ACMMG063)
Location and transformation
  1. Create and interpret simple grid maps to show position and pathways (ACMMG065)
  2. Identify symmetry in the environment (ACMMG066)
Geometric reasoning
  1. Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064)

Statistics and Probability

Chance
  1. Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067)
Data representation and interpretation
  1. Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording (ACMSP068)
  2. Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies (ACMSP069)
  3. Interpret and compare data displays (ACMSP070)

Level 3 Achievement Standard

Number and Algebra

Students count and order numbers to and from 10 000. They recognise the connection between addition and subtraction, and solve problems using efficient strategies for multiplication with and without the use of digital technology. Students recall addition and multiplication facts for single-digit numbers. They represent money values in various ways and correctly count out change from financial transactions. Students model and represent unit fractions for halves, thirds, quarters, fifths and eighths, and multiples of these up to one. They classify numbers as either odd or even, continue number patterns involving addition or subtraction, and explore simple number sequences based on multiples.

Measurement and Geometry

Students use metric units for length, mass and capacity. They tell time to the nearest minute. Students identify symmetry in natural and constructed environments. They use angle size as a measure of turn in real situations and make models of three-dimensional objects. Students match positions on maps with given information and create simple maps.

Statistics and Probability

Students carry out simple data investigations for categorical variables. They interpret and compare data displays. Students conduct chance experiments, list possible outcomes and recognise variations in results.

Level 3 Work Samples

Mathematics - Level 4

Level 4 Description

The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the...

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Level 4 Content Descriptions

Number and Algebra

Number and place value
  1. Investigate and use the properties of odd and even numbers (ACMNA071)
  2. Recognise, represent and order numbers to at least tens of thousands (ACMNA072)
  3. Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)
  4. Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074)
  5. Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075)
  6. Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076)
Fractions and decimals
  1. Investigate equivalent fractions used in contexts (ACMNA077)
  2. Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078)
  3. Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)
Money and financial mathematics
  1. Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080)
Patterns and algebra
  1. Explore and describe number patterns resulting from performing multiplication (ACMNA081)
  2. Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082)
  3. Use equivalent number sentences involving addition and subtraction to find unknown quantities (ACMNA083)

Measurement and Geometry

Using units of measurement
  1. Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084)
  2. Compare objects using familiar metric units of area and volume (ACMMG290)
  3. Convert between units of time (ACMMG085)
  4. Use am and pm notation and solve simple time problems (ACMMG086)
Shape
  1. Compare the areas of regular and irregular shapes by informal means (ACMMG087)
  2. Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088)
Location and transformation
  1. Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090)
  2. Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091)
Geometric reasoning
  1. Compare angles and classify them as equal to, greater than or less than a right angle (ACMMG089)

Statistics and Probability

Chance
  1. Describe possible everyday events and order their chances of occurring (ACMSP092)
  2. Identify everyday events where one cannot happen if the other happens (ACMSP093)
  3. Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094)
Data representation and interpretation
  1. Select and trial methods for data collection, including survey questions and recording sheets (ACMSP095)
  2. Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values (ACMSP096)
  3. Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097)

Level 4 Achievement Standard

Number and Algebra

Students recall multiplication facts to 10 x 10 and related division facts. They choose appropriate strategies for calculations involving multiplication and division, with and without the use of digital technology, and estimate answers accurately enough for the context. Students solve simple purchasing problems with and without the use of digital technology. They locate familiar fractions on a number line, recognise common equivalent fractions in familiar contexts and make connections between fractions and decimal notations up to two decimal places. Students identify unknown quantities in number sentences. They use the properties of odd and even numbers and describe number patterns resulting from multiplication. Students continue number sequences involving multiples of single-digit numbers and unit fractions, and locate them on a number line.

Measurement and Geometry

Students compare areas of regular and irregular shapes, using informal units. They solve problems involving time duration. Students use scaled instruments to measure length, angle, area, mass, capacity and temperature of shapes and objects. They convert between units of time. Students create symmetrical simple and composite shapes and patterns, with and without the use of digital technology. They classify angles in relation to a right angle. Students interpret information contained in maps.

Statistics and Probability

Students describe different methods for data collection and representation, and evaluate their effectiveness. They construct data displays from given or collected data, with and without the use of digital technology. Students list the probabilities of everyday events. They identify dependent and independent events.

Level 4 Work Samples

Mathematics - Level 5

Level 5 Description

The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the...

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Level 5 Content Descriptions

Number and Algebra

Number and place value
  1. Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098)
  2. Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099)
  3. Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100)
  4. Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101)
  5. Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)
Fractions and decimals
  1. Compare and order common unit fractions and locate and represent them on a number line (ACMNA102)
  2. Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103)
  3. Recognise that the place value system can be extended beyond hundredths (ACMNA104)
  4. Compare, order and represent decimals (ACMNA105)
Money and financial mathematics
  1. Create simple financial plans (ACMNA106)
Patterns and algebra
  1. Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107)
  2. Use equivalent number sentences involving multiplication and division to find unknown quantities (ACMNA121)

Measurement and Geometry

Using units of measurement
  1. Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)
  2. Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109)
  3. Compare 12- and 24-hour time systems and convert between them (ACMMG110)
Shape
  1. Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111)
Location and transformation
  1. Use a grid reference system to describe locations. Describe routes using landmarks and directional language (ACMMG113)
  2. Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries (ACMMG114)
  3. Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original (ACMMG115)
Geometric reasoning
  1. Estimate, measure and compare angles using degrees. Construct angles using a protractor (ACMMG112)

Statistics and Probability

Chance
  1. List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)
  2. Recognise that probabilities range from 0 to 1 (ACMSP117)
Data representation and interpretation
  1. Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)
  2. Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119)
  3. Describe and interpret different data sets in context (ACMSP120)

Level 5 Achievement Standard

Number and Algebra

Students solve simple problems involving the four operations using a range of strategies including digital technology. They estimate to check the reasonableness of answers and approximate answers by rounding. Students identify and describe factors and multiples. They explain plans for simple budgets. Students order decimals and unit fractions and locate them on a number line. Students add and subtract fractions with the same denominator. They find unknown quantities in number sentences and continue patterns by adding or subtracting fractions and decimals.

Measurement and Geometry

Students use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. They convert between 12 and 24-hour time. Students use a grid reference system to locate landmarks. They estimate angles, and use protractors and digital technology to construct and measure angles. Students connect three-dimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry.

Statistics and Probability

Students pose questions to gather data and construct various displays appropriate for the data, with and without the use of digital technology. They compare and interpret different data sets. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities as a number from 0 to 1.

Level 5 Work Samples

Mathematics - Level 6

Level 6 Description

The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the...

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Level 6 Content Descriptions

Number and Algebra

Number and place value
  1. Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122)
  2. Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)
  3. Investigate everyday situations that use integers. Locate and represent these numbers on a number line (ACMNA124)
Fractions and decimals
  1. Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)
  2. Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126)
  3. Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127)
  4. Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)
  5. Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies (ACMNA129)
  6. Multiply and divide decimals by powers of 10 (ACMNA130)
  7. Make connections between equivalent fractions, decimals and percentages (ACMNA131)
Money and financial mathematics
  1. Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)
Patterns and algebra
  1. Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (ACMNA133)
  2. Explore the use of brackets and order of operations to write number sentences (ACMNA134)

Measurement and Geometry

Using units of measurement
  1. Connect decimal representations to the metric system (ACMMG135)
  2. Convert between common metric units of length, mass and capacity (ACMMG136)
  3. Solve problems involving the comparison of lengths and areas using appropriate units (ACMMG137)
  4. Connect volume and capacity and their units of measurement (ACMMG138)
  5. Interpret and use timetables (ACMMG139)
Shape
  1. Construct simple prisms and pyramids (ACMMG140)
Location and transformation
  1. Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)
  2. Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)
Geometric reasoning
  1. Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles (ACMMG141)

Statistics and Probability

Chance
  1. Describe probabilities using fractions, decimals and percentages (ACMSP144)
  2. Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)
  3. Compare observed frequencies across experiments with expected frequencies (ACMSP146)
Data representation and interpretation
  1. Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)
  2. Interpret secondary data presented in digital media and elsewhere (ACMSP148)

Level 6 Achievement Standard

Number and Algebra

Students recognise the properties of prime, composite, square and triangular numbers and determine sets of these numbers. They solve problems that involve all four operations with whole numbers and describe the use of integers in everyday contexts. Students locate fractions and integers on a number line and connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students calculate a simple fraction of a quantity and calculate common percentage discounts on sale items, with and without the use of digital technology. They make connections between the powers of 10 and the multiplication and division of decimals. Students add, subtract and multiply decimals and divide decimals where the result is rational. Students write number sentences using brackets and order of operations, and specify rules used to generate sequences involving whole numbers, fractions and decimals. They use ordered pairs of integers to represent coordinates of points and locate a point in any one of the four quadrants on the Cartesian plane.

Measurement and Geometry

Students relate decimals to the metric system and choose appropriate units of measurement to perform a calculation. They solve problems involving length and area, and make connections between capacity and volume. Students interpret a variety of everyday timetables. They solve problems using the properties of angles and investigate simple combinations of transformations in the plane, with and without the use of digital technology. Students construct simple prisms and pyramids.

Statistics and Probability

Students interpret and compare a variety of data displays, including displays for two categorical variables. They analyse and evaluate data from secondary sources. Students compare observed and expected frequencies of events, including those where outcomes of trials are generated with the use of digital technology. They specify, list and communicate probabilities of events using simple ratios, fractions, decimals and percentages.

Level 6 Work Samples

Mathematics - Level 7

Level 7 Description

The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the...

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Level 7 Content Descriptions

Number and Algebra

Number and place value
  1. Investigate index notation and represent whole numbers as products of powers of prime numbers (ACMNA149)
  2. Investigate and use square roots of perfect square numbers (ACMNA150)
  3. Apply the associative, commutative and distributive laws to aid mental and written computation (ACMNA151)
  4. Compare, order, add and subtract integers (ACMNA280)
Real numbers
  1. Compare fractions using equivalence. Locate and represent positive and negative fractions and mixed numbers on a number line (ACMNA152)
  2. Solve problems involving addition and subtraction of fractions, including those with unrelated denominators (ACMNA153)
  3. Multiply and divide fractions and decimals using efficient written strategies and digital technologies (ACMNA154)
  4. Express one quantity as a fraction of another, with and without the use of digital technologies (ACMNA155)
  5. Round decimals to a specified number of decimal places (ACMNA156)
  6. Connect fractions, decimals and percentages and carry out simple conversions (ACMNA157)
  7. Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies. (ACMNA158)
  8. Recognise and solve problems involving simple ratios (ACMNA173)
Money and financial mathematics
  1. Investigate and calculate 'best buys', with and without digital technologies (ACMNA174)
Patterns and algebra
  1. Introduce the concept of variables as a way of representing numbers using letters (ACMNA175)
  2. Create algebraic expressions and evaluate them by substituting a given value for each variable (ACMNA176)
  3. Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (ACMNA177)
Linear and non-linear relationships
  1. Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (ACMNA178)
  2. Solve simple linear equations (ACMNA179)
  3. Investigate, interpret and analyse graphs from authentic data (ACMNA180)

Measurement and Geometry

Using units of measurement
  1. Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving (ACMMG159)
  2. Calculate volumes of rectangular prisms (ACMMG160)
Shape
  1. Draw different views of prisms and solids formed from combinations of prisms (ACMMG161)
Location and transformation
  1. Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries (ACMMG181)
Geometric reasoning
  1. Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal (ACMMG163)
  2. Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning (ACMMG164)
  3. Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral (ACMMG166)
  4. Classify triangles according to their side and angle properties and describe quadrilaterals (ACMMG165)

Statistics and Probability

Chance
  1. Construct sample spaces for single-step experiments with equally likely outcomes (ACMSP167)
  2. Assign probabilities to the outcomes of events and determine probabilities for events (ACMSP168)
Data representation and interpretation
  1. Identify and investigate issues involving numerical data collected from primary and secondary sources (ACMSP169)
  2. Construct and compare a range of data displays including stem-and-leaf plots and dot plots (ACMSP170)
  3. Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (ACMSP171)
  4. Describe and interpret data displays using median, mean and range (ACMSP172)

Level 7 Achievement Standard

Number and Algebra

Students solve problems involving the order, addition and subtraction of integers. They make the connections between whole numbers and index notation and the relationship between perfect squares and square roots. They solve problems involving all four operations with fractions, decimals, percentages and their equivalences, and express fractions in their simplest form. Students compare the cost of items to make financial decisions, with and without the use of digital technology. They make simple estimates to judge the reasonableness of results. Students use variables to represent arbitrary numbers and connect the laws and properties of number to algebra and substitute numbers into algebraic expressions. They assign ordered pairs to given points on the Cartesian plane and interpret and analyse graphs of relations from real data. Students develop simple linear models for situations, make predictions based on these models, solve related equations and check their solutions.

Measurement and Geometry

Students use formulas for the area and perimeter of rectangles. They classify triangles and quadrilaterals and represent transformations of these shapes on the Cartesian plane, with and without the use of digital technology. Students name the types of angles formed by a transversal crossing parallel lines and solve simple numerical problems involving these lines and angles. They describe different views of three-dimensional objects, and use models, sketches and digital technology to represent these views. Students calculate volumes of rectangular prisms.

Statistics and Probability

Students identify issues involving the collection of discrete and continuous data from primary and secondary sources. They construct stem-and-leaf plots and dot-plots. Students identify or calculate mean, mode, median and range for data sets, using digital technology for larger data sets. They describe the relationship between the median and mean in data displays. Students determine the sample space for simple experiments with equally likely outcomes, and assign probabilities outcomes. 

Level 7 Work Samples

Mathematics - Level 8

Level 8 Description

The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the...

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Level 8 Content Descriptions

Number and Algebra

Number and place value
  1. Use index notation with numbers to establish the index laws with positive integral indices and the zero index (ACMNA182)
  2. Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies (ACMNA183)
Real numbers
  1. Investigate terminating and recurring decimals (ACMNA184)
  2. Investigate the concept of irrational numbers, including π (ACMNA186)
  3. Solve problems involving the use of percentages, including percentage increases and decreases, with and without digital technologies (ACMNA187)
  4. Solve a range of problems involving rates and ratios, with and without digital technologies (ACMNA188)
Money and financial mathematics
  1. Solve problems involving profit and loss, with and without digital technologies (ACMNA189)
Patterns and algebra
  1. Extend and apply the distributive law to the expansion of algebraic expressions (ACMNA190)
  2. Factorise algebraic expressions by identifying numerical factors (ACMNA191)
  3. Simplify algebraic expressions involving the four operations (ACMNA192)
Linear and non-linear relationships
  1. Plot linear relationships on the Cartesian plane with and without the use of digital technologies (ACMNA193)
  2. Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution (ACMNA194)

Measurement and Geometry

Using units of measurement
  1. Choose appropriate units of measurement for area and volume and convert from one unit to another (ACMMG195)
  2. Find perimeters and areas of parallelograms, trapeziums, rhombuses and kites (ACMMG196)
  3. Investigate the relationship between features of circles such as circumference, area, radius and diameter. Use formulas to solve problems involving circumference and area (ACMMG197)
  4. Develop the formulas for volumes of rectangular and triangular prisms and prisms in general. Use formulas to solve problems involving volume (ACMMG198)
  5. Solve problems involving duration, including using 12- and 24-hour time within a single time zone (ACMMG199)
Geometric reasoning
  1. Define congruence of plane shapes using transformations (ACMMG200)
  2. Develop the conditions for congruence of triangles (ACMMG201)
  3. Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning (ACMMG202)

Statistics and Probability

Chance
  1. Identify complementary events and use the sum of probabilities to solve problems (ACMSP204)
  2. Describe events using language of 'at least', exclusive 'or' (A or B but not both), inclusive 'or' (A or B or both) and 'and'. (ACMSP205)
  3. Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292)
Data representation and interpretation
  1. Investigate techniques for collecting data, including census, sampling and observation (ACMSP284)
  2. Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes (ACMSP206)
  3. Explore the variation of means and proportions of random samples drawn from the same population (ACMSP293)
  4. Investigate the effect of individual data values , including outliers, on the mean and median (ACMSP207)

Level 8 Achievement Standard

Number and Algebra

Students use efficient mental and written strategies to make estimates and carry out the four operations with integers, and apply the index laws to whole numbers. They identify and describe rational and irrational numbers in context. Students estimate answers and solve everyday problems involving profit and loss rates, ratios and percentages, with and without the use of digital technology. They simplify a variety of algebraic expressions and connect expansion and factorisation of linear expressions. Students solve linear equations and graph linear relationships on the Cartesian plane.

Measurement and Geometry

Students convert between units of measurement for area and for volume. They find the perimeter and area of parallelograms, rhombuses and kites. Students name the features of circles, calculate circumference and area, and solve problems relating to the volume of prisms. They make sense of time duration in real applications, including the use of 24-hour time. Students identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. They use tools, including digital technology, to construct congruent shapes.

Statistics and Probability

Students explain issues related to the collection of sample data and discuss the effect of outliers on means and medians of the data. They use various approaches, including the use of digital technology, to generate simple random samples from a population. Students model situations with Venn diagrams and two-way tables and explain the use of 'not', 'and' and 'or'. Students choose appropriate language to describe events and experiments. They determine complementary events and calculate the sum of probabilities. 

Level 8 Work Samples

Mathematics - Level 9

Level 9 Description

The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the...

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Level 9 Content Descriptions

Number and Algebra

Real numbers
  1. Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208)
  2. Apply index laws to numerical expressions with integer indices (ACMNA209)
  3. Express numbers in scientific notation (ACMNA210)
Money and financial mathematics
  1. Solve problems involving simple interest (ACMNA211)
Patterns and algebra
  1. Extend and apply the index laws to variables, using positive integer indices and the zero index (ACMNA212)
  2. Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate (ACMNA213)
Linear and non-linear relationships
  1. Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software (ACMNA214)
  2. Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software (ACMNA294)
  3. Sketch linear graphs using the coordinates of two points and solve linear equations (ACMNA215)
  4. Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations (ACMNA296)

Measurement and Geometry

Using units of measurement
  1. Calculate the areas of composite shapes (ACMMG216)
  2. Calculate the surface area and volume of cylinders and solve related problems (ACMMG217)
  3. Solve problems involving the surface area and volume of right prisms (ACMMG218)
  4. Investigate very small and very large time scales and intervals (ACMMG219)
Geometric reasoning
  1. Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar (ACMMG220)
  2. Solve problems using ratio and scale factors in similar figures (ACMMG221)
Pythagoras and trigonometry
  1. Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles (ACMMG222)
  2. Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles (ACMMG223)
  3. Apply trigonometry to solve right-angled triangle problems (ACMMG224)

Statistics and Probability

Chance
  1. List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events (ACMSP225)
  2. Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or' (ACMSP226)
  3. Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians (ACMSP227)
Data representation and interpretation
  1. Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (ACMSP228)
  2. Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’ (ACMSP282)
  3. Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread (ACMSP283)

Level 9 Achievement Standard

Number and Algebra

Students apply the index laws using integer indices to variables and numbers, express numbers in scientific notation, solve problems involving very small and very large numbers, and check the order of magnitude of calculations. They solve problems involving simple interest. Students use the distributive law to expand algebraic expressions, including binomial expressions, and simplify a range of algebraic expressions. They find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment using a range of strategies including the use of digital technology. Students sketch and draw linear and non-linear relations, solve simple related equations and explain the relationship between the graphical and symbolic forms, with and without the use of digital technology.

Measurement and Geometry

Students solve measurement problems involving perimeter and area of composite shapes, surface area and volume of rectangular prisms and cylinders, with and without the use of digital technology. They relate three-dimensional objects to two-dimensional representations. Students explain similarity of triangles, interpret ratios and scale factors in similar figures, and apply Pythagoras's theorem and trigonometry to solve problems involving angles and lengths in right-angled triangles.

Statistics and Probability

Students compare techniques for collecting data from primary and secondary sources, and identify questions and issues involving different data types. They construct histograms and back-to-back stem-and-leaf plots with and without the use of digital technology. Students identify mean and median in skewed, symmetric and bi-modal displays and use these to describe and interpret the distribution of the data. They calculate relative frequencies to estimate probabilities. Students list outcomes for two-step experiments and assign probabilities for those outcomes and related events. 

Level 9 Work Samples

Mathematics - Level 10

Level 10 Description

The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the...

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Level 10 Content Descriptions

Number and Algebra

Money and financial mathematics
  1. Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies (ACMNA229)
Patterns and algebra
  1. Factorise algebraic expressions by taking out a common algebraic factor (ACMNA230)
  2. Simplify algebraic products and quotients using index laws (ACMNA231)
  3. Apply the four operations to simple algebraic fractions with numerical denominators (ACMNA232)
  4. Expand binomial products and factorise monic quadratic expressions using a variety of strategies (ACMNA233)
  5. Substitute values into formulas to determine an unknown (ACMNA234)
Linear and non-linear relationships
  1. Solve problems involving linear equations, including those derived from formulas (ACMNA235)
  2. Solve linear inequalities and graph their solutions on a number line (ACMNA236)
  3. Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology (ACMNA237)
  4. Solve problems involving parallel and perpendicular lines (ACMNA238)
  5. Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate (ACMNA239)
  6. Solve linear equations involving simple algebraic fractions (ACMNA240)
  7. Solve simple quadratic equations using a range of strategies (ACMNA241)

Measurement and Geometry

Using units of measurement
  1. Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids (ACMMG242)
Geometric reasoning
  1. Formulate proofs involving congruent triangles and angle properties (ACMMG243)
  2. Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes (ACMMG244)
Pythagoras and trigonometry
  1. Solve right-angled triangle problems including those involving direction and angles of elevation and depression (ACMMG245)

Statistics and Probability

Chance
  1. Describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events. Investigate the concept of independence (ACMSP246)
  2. Use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language (ACMSP247)
Data representation and interpretation
  1. Determine quartiles and interquartile range (ACMSP248)
  2. Construct and interpret box plots and use them to compare data sets (ACMSP249)
  3. Compare shapes of box plots to corresponding histograms and dot plots (ACMSP250)
  4. Use scatter plots to investigate and comment on relationships between two numerical variables (ACMSP251)
  5. Investigate and describe bivariate numerical data where the independent variable is time (ACMSP252)
  6. Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data (ACMSP253)

Level 10 Achievement Standard

Number and Algebra

Students recognise the connection between simple and compound interest. They solve problems involving linear equations and inequalities, quadratic equations and pairs of simultaneous linear equations and related graphs, with and without the use of digital technology. Students substitute into formulas, find unknown values, manipulate linear algebraic expressions, expand binomial expressions and factorise monic and simple non-monic quadratic expressions, with and without the use of digital technology. They represent linear, quadratic and exponential functions numerically, graphically and algebraically, and use them to model situations and solve practical problems.

Measurement and Geometry

Students solve and explain surface area and volume problems relating to composite solids. They use parallel and perpendicular lines, angle and triangle properties, similarity, trigonometry and congruence to solve practical problems and develop proofs involving lengths, angles and areas in plane shapes. They use digital technology to construct and manipulate geometric shapes and objects, and explore symmetry and pattern in two dimensions.

Statistics and Probability

Students compare univariate data sets by referring to summary statistics and the shape of their displays. They describe bivariate data where the independent variable is time and use scatter-plots generated by digital technology to investigate relationships between two continuous variables. Students evaluate the use of statistics in the media. They list outcomes for multi-step chance experiments involving independent and dependent events, and assign probabilities for these experiments. 

Level 10 Work Samples

Mathematics - Level 10A

Level 10A Content Descriptions

Number and Algebra

Real numbers
  1. Define rational and irrational numbers and perform operations with surds and fractional indices (ACMNA264)
  2. Use the definition of a logarithm to establish and apply the laws of logarithms (ACMNA265)
Patterns and algebra
  1. Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems (ACMNA266)
Linear and non-linear relationships
  1. Solve simple exponential equations (ACMNA270)
  2. Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267)
  3. Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation (ACMNA268)
  4. Factorise monic and non-monic quadratic expressions and solve a wide range of quadratic equations derived from a variety of contexts (ACMNA269)

Measurement and Geometry

Using units of measurement
  1. Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids (ACMMG271)
Geometric reasoning
  1. Prove and apply angle and chord properties of circles (ACMMG272)
Pythagoras and trigonometry
  1. Establish the sine, cosine and area rules for any triangle and solve related problems (ACMMG273)
  2. Use the unit circle to define trigonometric functions, and graph them with and without the use of digital technologies (ACMMG274)
  3. Solve simple trigonometric equations (ACMMG275)
  4. Apply Pythagoras’ theorem and trigonometry to solving three-dimensional problems in right-angled triangles (ACMMG276)

Statistics and Probability

Chance
  1. Investigate reports of studies in digital media and elsewhere for information on their planning and implementation (ACMSP277)
Data representation and interpretation
  1. Calculate and interpret the mean and standard deviation of data and use these to compare data sets (ACMSP278)
  2. Use information technologies to investigate bivariate numerical data sets. Where appropriate use a straight line to describe the relationship allowing for variation (ACMSP279)
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