Year 3
Mathematics
ASMATY3
Year 3 Mathematics Achievement Standard
18 statements aligned to content descriptors and elaborations
Achievement standard (as ACARA publishes it)
Achievement standard
Click any sentence to jump to its statement and linked content descriptors.
By the end of Year 3, students order and represent natural numbers beyond 10 000. They partition, rearrange and regroup two- and three-digit numbers in different ways to assist in calculations. Students extend and use single-digit addition and related subtraction facts and apply additive strategies to model and solve problems involving two- and three-digit numbers. They use mathematical modelling to solve practical problems involving single-digit multiplication and division, recalling multiplication facts for twos, threes, fours, fives and tens, and using a range of strategies. Students represent unit fractions and their multiples in different ways. They make estimates and determine the reasonableness of financial and other calculations. Students find unknown values in number sentences involving addition and subtraction. They create algorithms to investigate numbers and explore simple patterns.
Students use familiar metric units when estimating, comparing and measuring the attributes of objects and events. They identify angles as measures of turn and compare them to right angles. Students estimate and compare measures of duration using formal units of time. They represent money values in different ways. Students make, compare and classify objects using key features. They interpret and create two-dimensional representations of familiar environments.
Students conduct guided statistical investigations involving categorical and discrete numerical data and interpret their results in terms of the context. They record, represent and compare data they have collected. Students use practical activities, observation or experiment to identify and describe outcomes and the likelihood of everyday events explaining reasoning. They conduct repeated chance experiments and discuss variation in results.
The 18 achievement standard statements
Open a statement to see the content descriptors ACARA links to it, then open a descriptor's elaborations.
By the end of Year 3, students order and represent natural numbers beyond 10 000.
Content descriptorAC9M3N01 Number
recognise, represent and order natural numbers using naming and writing conventions for numerals beyond 10 000
Elaborations (5)
- Elaboration moving materials from one place to another on a place value model to show renaming of numbers; for example, 1574 can be shown as one thousand, 5 hundreds, 7 tens and 4 ones, or as 15 hundreds, 7 tens and 4 ones
- Elaboration using the repeating pattern of place value names and spaces within sets of 3 digits to name and write larger numbers: ones, tens, hundreds, ones of thousands, tens of thousands, hundreds of thousands, ones of millions, tens of millions; writing, for example, four hundred and twenty-five thousand as 425 000
- Elaboration predicting and naming the number that is one more than 99, 109, 199, 1009, 1099, 1999, 10 009 ... 99 999 and discussing what will change when one, one ten and one hundred is added to each
- Elaboration comparing the Hindu-Arabic numeral system to other numeral systems; for example, investigating the Japanese numeral system, 一、十、百、千、万
- Elaboration comparing, reading and writing the numbers involved in the more than 60 000 years of First Peoples of Australia’s presence on the Australian continent through time scales relating to pre-colonisation and post-colonisation
They partition, rearrange and regroup two- and three-digit numbers in different ways to assist in calculations.
Content descriptorAC9M3A01 Algebra
recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences
Elaborations (3)
- Elaboration partitioning numbers using materials, part-part-whole diagrams or bar models, and recording addition and subtraction facts for each representation, explaining how each fact is connected to the materials, diagrams or models; for example, 16 + 8 = 24, 24\space – \space8 = 16, 8 = 24 \space–\space 16
- Elaboration using the inverse relationship between addition and subtraction to find unknown values with a calculator; for example, representing the problem, “Peter had some money and then spent \$375, now he has \$158 left. How much did Peter have to start with?” as \square – \$375 = \$158 and solving the problem using \$375 + \$158 = \$533; solving 27 + \square = 63 using subtraction, \square = 63\space – \space27 or by counting on; 27, 37, 47, 57, 60, 63, so add 3 tens and 6 ones, so \square = 36
- Elaboration exploring First Nations Australians’ stories and dances that show the connection between addition and subtraction, representing this as a number sentence and discussing how this conveys important information about balance in processes on Country/Place
Content descriptorAC9M3M06 Measurement
recognise the relationships between dollars and cents and represent money values in different ways
Elaborations (3)
- Elaboration investigating the relationship between dollars and cents, using physical or virtual materials to make different combinations of the same amount of money
- Elaboration representing money amounts in different ways using knowledge of part-part-whole relationships; for example, knowing that \$1 is equal to 100 cents; representing \$1.85 as \$1 + 50c + 20c + 10c + 5c or 50c + 50c + 50c + 10c + 10c + 10c + 5c; when calculating change from buying an item for \$1.30 from \$2, starting from \$1.30 add 20c and 50c which gives \$2
- Elaboration representing money values in multiple ways when role-playing money transactions; for example, using play money to represent the coins and dollars you could use to pay for items
Content descriptorAC9M3N03 Number
add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator
Elaborations (6)
- Elaboration using partitioning and part-part-whole models and the inverse relationship between addition and subtraction to solve addition or subtraction problems, making informal written “jottings” to keep track of the numbers if necessary
- Elaboration using physical or virtual grouped materials or diagrams to make proportional models of numbers to assist in calculations; for example, to calculate 214 + 325 representing 214 as 2 groups of 100, one group of 10 and 4 ones and 325 as 3 groups of 100, 2 groups of 10 and 5 ones resulting in 5 groups of 100, 3 groups of 10 and 9 ones which is 539
- Elaboration choosing between standard and non-standard place value partitions to assist with calculations; for example, to solve 485 + 365, thinking of 365 as 350 + 15, then adding the parts, 485 + 15 = 500, 500 + 350 = 850
- Elaboration solving subtraction problems efficiently by adding or subtracting a constant amount to both numbers to create an easier calculation; for example, 534 \space– \space395 adding 5 to both numbers to make 539 \space – \space400 = 139
- Elaboration justifying choices about partitioning and regrouping numbers in terms of their usefulness for particular calculations when solving problems
- Elaboration applying knowledge of place value to assist in calculations when solving problems involving larger numbers; for example, calculating the total crowd numbers for an agricultural show that lasts a week
Students extend and use single-digit addition and related subtraction facts and apply additive strategies to model and solve problems involving two- and three-digit numbers.
Content descriptorAC9M3A02 Algebra
extend and apply knowledge of addition and subtraction facts to 20 to develop efficient mental strategies for computation with larger numbers without a calculator
Elaborations (3)
- Elaboration partitioning using materials and part-part-whole diagrams to develop subtraction facts related to addition facts, such as 8 + 7 = 15 therefore, 15 \space–\space 7 = 8 and 15\space – \space 8 = 7
- Elaboration using partitioning to develop and record facts systematically; for example, “How many ways can 12 monkeys be spread among 2 trees?”, 12 = 12 + 0, 12 = 11 + 1, 12 = 10 + 2, 12 = 9 + 3, …; explaining how they know they have found all possible partitions
- Elaboration understanding basic addition and related subtraction facts and using extensions to these facts; for example, 6 + 6 = 12, 16 + 6 = 22, 6 + 7 = 13, 16 + 7 = 23, and 60 + 60 = 120, 600 + 600 = 1200
Content descriptorAC9M3N03 Number
add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator
Elaborations (6)
- Elaboration using partitioning and part-part-whole models and the inverse relationship between addition and subtraction to solve addition or subtraction problems, making informal written “jottings” to keep track of the numbers if necessary
- Elaboration using physical or virtual grouped materials or diagrams to make proportional models of numbers to assist in calculations; for example, to calculate 214 + 325 representing 214 as 2 groups of 100, one group of 10 and 4 ones and 325 as 3 groups of 100, 2 groups of 10 and 5 ones resulting in 5 groups of 100, 3 groups of 10 and 9 ones which is 539
- Elaboration choosing between standard and non-standard place value partitions to assist with calculations; for example, to solve 485 + 365, thinking of 365 as 350 + 15, then adding the parts, 485 + 15 = 500, 500 + 350 = 850
- Elaboration solving subtraction problems efficiently by adding or subtracting a constant amount to both numbers to create an easier calculation; for example, 534 \space– \space395 adding 5 to both numbers to make 539 \space – \space400 = 139
- Elaboration justifying choices about partitioning and regrouping numbers in terms of their usefulness for particular calculations when solving problems
- Elaboration applying knowledge of place value to assist in calculations when solving problems involving larger numbers; for example, calculating the total crowd numbers for an agricultural show that lasts a week
Content descriptorAC9M3N06 Number
use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation
Elaborations (5)
- Elaboration modelling practical additive situations, choosing whether to use an addition, subtraction or both when representing the problem as a number sentence, and explaining how each number in their number sentence is connected to the situation
- Elaboration modelling additive problems using a bar model to represent the problem; for example, “I had 75 tomatoes and then picked some more, now I have 138. How many did I pick?”
- Elaboration modelling practical multiplicative situations using materials or a diagram to represent the problem; for example, if 4 tomato plants each have 6 tomatoes, deciding whether to use an addition or multiplication number sentence, explaining how each number in their number sentence is connected to the situation
- Elaboration modelling and solving practical division problems involving unknown numbers of groups or finding how much is in each group by representing the problem with both division and multiplication number sentences; explaining how the 2 number sentences are connected to the problem
- Elaboration modelling the problem of deciding how to share an amount equally; for example, 48 horses into 2, 4, 6 or 8 paddocks, representing the shares with a division and a multiplication number sentence, and counting the number in each share to check the solutions
They use mathematical modelling to solve practical problems involving single-digit multiplication and division, recalling multiplication facts for twos, threes, fours, fives and tens, and using a range of strategies.
Content descriptorAC9M3A03 Algebra
recall and demonstrate proficiency with multiplication facts for 3, 4, 5 and 10; extend and apply facts to develop the related division facts
Elaborations (4)
- Elaboration using concrete or virtual manipulatives, groups and repeated addition to recognise patterns and establish the 3, 4, 5 and 10 multiplication facts; ; using the language of “3 groups of 2 equals 6” to develop into “3 twos are 6” and extend to establish the 3 \times 10 multiplication facts and related division facts
- Elaboration recognising that when they multiply a number by 5, the resulting number will either end in a 5 or a zero; using a calculator or spreadsheet to generate a list of the multiples of 5 to develop the multiplication and related division facts for fives
- Elaboration practising calculating and deriving multiplication facts for 3, 4, 5 and 10, explaining and recalling the patterns in them and using them to derive related division facts
- Elaboration systematically exploring algorithms used for repeated addition, comparing and describing what is happening, and using them to establish the multiplication facts for 3, 4, 5 and 10; for example, following the sequence of steps, the decisions being made and the resulting solution, recognising and generalising any emerging patterns
Content descriptorAC9M3N04 Number
multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies
Elaborations (4)
- Elaboration applying knowledge of numbers and the properties of operations using a variety of ways to represent multiplication or division number sentences; for example, using a Think Board to show different ways of visualising 8 \times 4, such as an array, a diagram and as a worded problem
- Elaboration using part-part-whole and comparative models to visually represent multiplicative relationships and choosing whether to use multiplication or division to solve problems
- Elaboration matching or creating a problem scenario or story that can be represented by a given number sentence involving multiplication and division; for example, using given number sentences to create worded problems for others to solve
- Elaboration formulating connected multiplication and division expressions by representing situations from First Nations Australians’ cultural stories and dances about how they care for Country/Place such as turtle egg gathering using number sentences
Content descriptorAC9M3N06 Number
use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation
Elaborations (5)
- Elaboration modelling practical additive situations, choosing whether to use an addition, subtraction or both when representing the problem as a number sentence, and explaining how each number in their number sentence is connected to the situation
- Elaboration modelling additive problems using a bar model to represent the problem; for example, “I had 75 tomatoes and then picked some more, now I have 138. How many did I pick?”
- Elaboration modelling practical multiplicative situations using materials or a diagram to represent the problem; for example, if 4 tomato plants each have 6 tomatoes, deciding whether to use an addition or multiplication number sentence, explaining how each number in their number sentence is connected to the situation
- Elaboration modelling and solving practical division problems involving unknown numbers of groups or finding how much is in each group by representing the problem with both division and multiplication number sentences; explaining how the 2 number sentences are connected to the problem
- Elaboration modelling the problem of deciding how to share an amount equally; for example, 48 horses into 2, 4, 6 or 8 paddocks, representing the shares with a division and a multiplication number sentence, and counting the number in each share to check the solutions
Students represent unit fractions and their multiples in different ways.
Content descriptorAC9M3N02 Number
recognise and represent unit fractions including 1/2, 1/3, 1/4, 1/5 and 1/10 and their multiples in different ways; combine fractions with the same denominator to complete the whole
Elaborations (4)
- Elaboration recognising that unit fractions represent equal parts of a whole; for example, one-third is one of 3 equal parts of a whole
- Elaboration representing unit fractions and their multiples in different ways; for example, using a Think Board to represent three-quarters using a diagram, concrete materials, a situation and fraction notation
- Elaboration cutting objects such as oranges, sandwiches or playdough into halves, quarters or fifths and reassembling them to demonstrate; for example, two-halves make a whole, four-quarters make a whole, counting the fractions as they go
- Elaboration sharing collections of objects, such as pop sticks or counters, between 3, 4 and 5 people and connecting division with fractions; for example, sharing between 3 people gives 1/3 of the collection to each and sharing between 5 people gives 1/5 of the collection to each
They make estimates and determine the reasonableness of financial and other calculations.
Content descriptorAC9M3M01 Measurement
identify which metric units are used to measure everyday items; use measurements of familiar items and known units to make estimates
Elaborations (4)
- Elaboration examining the packaging on supermarket items to determine the metric unit used to describe the mass or capacity of the contents
- Elaboration identifying items that have a mass of one kilogram or 500 grams, or a capacity of one litre or 500 millilitres and using these benchmarks to estimate the mass or capacity of other things, explaining their reasoning
- Elaboration estimating the height of a tree by comparing it to the height of their friend and quoting the result as “the tree is about 3 times as tall”; estimating the capacity of a fish tank by using a litre milk carton as a benchmark
- Elaboration choosing and using metres to estimate the dimensions of the classroom
Content descriptorAC9M3M06 Measurement
recognise the relationships between dollars and cents and represent money values in different ways
Elaborations (3)
- Elaboration investigating the relationship between dollars and cents, using physical or virtual materials to make different combinations of the same amount of money
- Elaboration representing money amounts in different ways using knowledge of part-part-whole relationships; for example, knowing that \$1 is equal to 100 cents; representing \$1.85 as \$1 + 50c + 20c + 10c + 5c or 50c + 50c + 50c + 10c + 10c + 10c + 5c; when calculating change from buying an item for \$1.30 from \$2, starting from \$1.30 add 20c and 50c which gives \$2
- Elaboration representing money values in multiple ways when role-playing money transactions; for example, using play money to represent the coins and dollars you could use to pay for items
Content descriptorAC9M3N05 Number
estimate the quantity of objects in collections and make estimates when solving problems to determine the reasonableness of calculations
Elaborations (4)
- Elaboration estimating how much space a grid paper representation of a large number such as 20 200 will take up on the wall and how much paper will be required
- Elaboration estimating the number of people in a large gathering; for example, school assembly, using known numbers, such as how many students per class
- Elaboration choosing which place value they would estimate to for different situations; for example, they would estimate to the nearest 10 when estimating how many dots on a ladybird or they would estimate to the nearest 1000 when estimating crowd sizes at a venue
- Elaboration checking the reasonableness of an addition calculation by using two- and three-digit numbers to the nearest 10 or hundred to estimate; for example, using 200 + 400 = 600 to estimate and check the solution to the calculation 219 + 385
Content descriptorAC9M3N06 Number
use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation
Elaborations (5)
- Elaboration modelling practical additive situations, choosing whether to use an addition, subtraction or both when representing the problem as a number sentence, and explaining how each number in their number sentence is connected to the situation
- Elaboration modelling additive problems using a bar model to represent the problem; for example, “I had 75 tomatoes and then picked some more, now I have 138. How many did I pick?”
- Elaboration modelling practical multiplicative situations using materials or a diagram to represent the problem; for example, if 4 tomato plants each have 6 tomatoes, deciding whether to use an addition or multiplication number sentence, explaining how each number in their number sentence is connected to the situation
- Elaboration modelling and solving practical division problems involving unknown numbers of groups or finding how much is in each group by representing the problem with both division and multiplication number sentences; explaining how the 2 number sentences are connected to the problem
- Elaboration modelling the problem of deciding how to share an amount equally; for example, 48 horses into 2, 4, 6 or 8 paddocks, representing the shares with a division and a multiplication number sentence, and counting the number in each share to check the solutions
Students find unknown values in number sentences involving addition and subtraction.
Content descriptorAC9M3A01 Algebra
recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences
Elaborations (3)
- Elaboration partitioning numbers using materials, part-part-whole diagrams or bar models, and recording addition and subtraction facts for each representation, explaining how each fact is connected to the materials, diagrams or models; for example, 16 + 8 = 24, 24\space – \space8 = 16, 8 = 24 \space–\space 16
- Elaboration using the inverse relationship between addition and subtraction to find unknown values with a calculator; for example, representing the problem, “Peter had some money and then spent \$375, now he has \$158 left. How much did Peter have to start with?” as \square – \$375 = \$158 and solving the problem using \$375 + \$158 = \$533; solving 27 + \square = 63 using subtraction, \square = 63\space – \space27 or by counting on; 27, 37, 47, 57, 60, 63, so add 3 tens and 6 ones, so \square = 36
- Elaboration exploring First Nations Australians’ stories and dances that show the connection between addition and subtraction, representing this as a number sentence and discussing how this conveys important information about balance in processes on Country/Place
They create algorithms to investigate numbers and explore simple patterns.
Content descriptorAC9M3N07 Number
follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any emerging patterns
Elaborations (4)
- Elaboration following or creating an algorithm to generate number patterns formed by doubling and halving using technology to assist where appropriate; identifying and describing emerging patterns
- Elaboration following or creating an algorithm that determines whether a given number is a multiple of 2, 5 or 10, identifying and discussing emerging patterns
- Elaboration creating an algorithm as a set of instructions that a classmate can follow to generate multiples of 3 using the rule “To multiply by 3 you double the number and add on one more of the number”; for example, for 3 threes you double 3 and add on 3 to get 9, for 3 fours you double 4 and add one more 4 to get 12 ...
- Elaboration creating a sorting algorithm that will sort a collection of 5 cent and 10 cent coins and providing the total value of the collection by applying knowledge of multiples of 5 and 10
Students use familiar metric units when estimating, comparing and measuring the attributes of objects and events.
Content descriptorAC9M3M01 Measurement
identify which metric units are used to measure everyday items; use measurements of familiar items and known units to make estimates
Elaborations (4)
- Elaboration examining the packaging on supermarket items to determine the metric unit used to describe the mass or capacity of the contents
- Elaboration identifying items that have a mass of one kilogram or 500 grams, or a capacity of one litre or 500 millilitres and using these benchmarks to estimate the mass or capacity of other things, explaining their reasoning
- Elaboration estimating the height of a tree by comparing it to the height of their friend and quoting the result as “the tree is about 3 times as tall”; estimating the capacity of a fish tank by using a litre milk carton as a benchmark
- Elaboration choosing and using metres to estimate the dimensions of the classroom
Content descriptorAC9M3M02 Measurement
measure and compare objects using familiar metric units of length, mass and capacity, and instruments with labelled markings
Elaborations (5)
- Elaboration making a measuring tape using metric units of length and using it to measure and compare things; for example, the girth of a tree; explaining that the lines on a ruler show the beginning and end of each unit
- Elaboration using a strip of centimetre grid paper to measure and compare the length of objects, connecting this with centimetre units on a ruler and using fractions of a graduation to give a more accurate measure
- Elaboration discussing how the capacity of a container or object usually refers to the amount of liquid it can hold, measured in millilitres and litres; comparing the capacity of different sizes of familiar drinks; for example, 600 millilitres, one litre, 2 litre and 3 litre milk containers
- Elaboration measuring and comparing the mass of objects and capacity of containers, using measuring jugs and kitchen or other scales and standard metric units of millilitres, litres, grams and kilograms; interpreting and explaining what the lines on the measuring jug or scales mean
- Elaboration comparing the capacity of different beakers used in science lessons and using the numbered graduations to measure out different capacities of liquid
Content descriptorAC9M3M03 Measurement
recognise and use the relationship between formal units of time including days, hours, minutes and seconds to estimate and compare the duration of events
Elaborations (5)
- Elaboration estimating how long it would take to read a set passage of text, and sharing this information to demonstrate understanding of formal units of duration of time
- Elaboration planning a sequence of events based on estimates of the duration of each event; for example, planning a set of activities for a class party by estimating how long each game or activity will take
- Elaboration reading or setting the time on digital devices to the minute or second; for example, setting an online timing device to count down from a set time; or setting the time on a digital clock
- Elaboration using sand timers and digital timers to measure and check estimates of short durations of time, such as one minute, 3 minutes and 5 minutes
- Elaboration exploring how cultural accounts of First Nations Australians explain cycles of time that involve the sun, moon and stars
They identify angles as measures of turn and compare them to right angles.
Content descriptorAC9M3M05 Measurement
identify angles as measures of turn and compare angles with right angles in everyday situations
Elaborations (4)
- Elaboration using quarter, half and three-quarter turns and comparing them to a right angle; for example, a quarter turn is the same as a right angle; a half a turn is greater than a right angle and is the same as 2 right angles; a three-quarter turn is greater than a right angle and is the same as 3 right angles
- Elaboration recognising that right angles occur at the corners of many everyday objects; for example, books, windows, table tops and whiteboards
- Elaboration identifying angles that are bigger than, smaller than and the same as a right angle in the environment; for example, opening doors partially and fully and comparing the angles created to a right angle
- Elaboration exploring First Nations Australian children’s instructive games to investigate angles as measures of turn; for example, the game Waayin from the Datiwuy People in the northern part of the Northern Territory
Students estimate and compare measures of duration using formal units of time.
Content descriptorAC9M3M03 Measurement
recognise and use the relationship between formal units of time including days, hours, minutes and seconds to estimate and compare the duration of events
Elaborations (5)
- Elaboration estimating how long it would take to read a set passage of text, and sharing this information to demonstrate understanding of formal units of duration of time
- Elaboration planning a sequence of events based on estimates of the duration of each event; for example, planning a set of activities for a class party by estimating how long each game or activity will take
- Elaboration reading or setting the time on digital devices to the minute or second; for example, setting an online timing device to count down from a set time; or setting the time on a digital clock
- Elaboration using sand timers and digital timers to measure and check estimates of short durations of time, such as one minute, 3 minutes and 5 minutes
- Elaboration exploring how cultural accounts of First Nations Australians explain cycles of time that involve the sun, moon and stars
Content descriptorAC9M3M04 Measurement
describe the relationship between the hours and minutes on analog and digital clocks, and read the time to the nearest minute
Elaborations (3)
- Elaboration representing and reading the time on an analog clock using the markings and the positions of the hands, to the nearest minute mark or five-minute interval
- Elaboration reading and connecting analog and digital time, interpreting times, recognising and using the language of time; for example, 12:15 as a quarter past 12, or 15 minutes past 12, 12:45 as a quarter to one or 15 minutes before one o’clock and 10:05 as 5 minutes past 10
- Elaboration reading analog clocks throughout the day, and noticing and connecting the position of the hour hand and the distance the minute hand has travelled during the current hour
They represent money values in different ways.
Content descriptorAC9M3M06 Measurement
recognise the relationships between dollars and cents and represent money values in different ways
Elaborations (3)
- Elaboration investigating the relationship between dollars and cents, using physical or virtual materials to make different combinations of the same amount of money
- Elaboration representing money amounts in different ways using knowledge of part-part-whole relationships; for example, knowing that \$1 is equal to 100 cents; representing \$1.85 as \$1 + 50c + 20c + 10c + 5c or 50c + 50c + 50c + 10c + 10c + 10c + 5c; when calculating change from buying an item for \$1.30 from \$2, starting from \$1.30 add 20c and 50c which gives \$2
- Elaboration representing money values in multiple ways when role-playing money transactions; for example, using play money to represent the coins and dollars you could use to pay for items
Students make, compare and classify objects using key features.
Content descriptorAC9M3SP01 Space
make, compare and classify objects, identifying key features and explaining why these features make them suited to their uses
Elaborations (6)
- Elaboration classifying a collection of geometric objects, including cylinders, spheres, prisms and pyramids according to key features such as the shape and number of faces and/or surfaces, edges and vertices
- Elaboration making and comparing objects built out of cubic blocks and discussing key features; for example, comparing the amount of space objects occupy by counting how many blocks it takes to build different rectangular prisms that have the same height but different bases
- Elaboration making geometric objects in solid form out of connecting cubes, in skeleton form with straws, and constructing objects using dynamic geometric software, recognising, comparing and discussing the features of the objects using the different representations
- Elaboration using familiar shapes and objects to build or construct models and compare the suitability of different shapes and objects for aspects of the model; for example, building rectangular towers out of connecting cubes and recognising that the taller the tower, the less stable it becomes unless the base is increased; building bridges out of straws bent into different shapes and comparing the strength of different designs
- Elaboration identifying, classifying and comparing common objects found on Country/Place as cubes, rectangular prisms, cylinders, cones and spheres
- Elaboration investigating and explaining how First Nations Australians’ dwellings are oriented in the environment to accommodate climatic conditions
They interpret and create two-dimensional representations of familiar environments.
Content descriptorAC9M3SP02 Space
interpret and create two-dimensional representations of familiar environments, locating key landmarks and objects relative to each other
Elaborations (6)
- Elaboration designing the layout of a space; for example, a proposed games room or the classroom using a blank sheet of paper as the boundary and cut outs of shapes to represent furniture from a top view perspective
- Elaboration locating themselves within a space such as a basketball court, an oval, stage or assembly hall, guided by a simple hand-held plan indicating the different positions of the participants in the activity
- Elaboration sketching a map within the classroom indicating where they have hidden an object, swapping maps with partners and then providing feedback about what was helpful and what was confusing in the map
- Elaboration identifying differences in the representation of a place on a map, in an aerial photograph, in a street view and in a satellite image and discussing the different information the representations can give
- Elaboration creating a two-dimensional plan of the school on a floor mat, representing key buildings and landmarks, then programming a robot to move to different locations within the space
- Elaboration exploring land maps or cultural maps used by First Nations Australians to locate, identify and position important landmarks such as waterholes
Students conduct guided statistical investigations involving categorical and discrete numerical data and interpret their results in terms of the context.
Content descriptorAC9M3ST01 Statistics
acquire data for categorical and discrete numerical variables to address a question of interest or purpose by observing, collecting and accessing data sets; record the data using appropriate methods including frequency tables and spreadsheets
Elaborations (5)
- Elaboration using efficient ways to collect and record data; for example, written surveys, online surveys, polling the class using interactive digital mediums, and representing and reporting the results of investigations
- Elaboration developing questions of interest and using surveys, observations or experiments to collect categorical, discrete numerical or qualitative data sets and discussing what kind of data can be used to help inform or answer the question in a statistical investigation
- Elaboration using lists, tallies, symbols and digital data tables to record and display data collected during a chance experiment for interpretation
- Elaboration using different online sources to access data; for example, using online query interfaces to select and retrieve data from an online database such as weather records, Google Trends or the World Health Organization
- Elaboration using software to sort and calculate data when solving problems; for example, sorting discrete numerical and categorical data in ascending or descending order and automating simple arithmetic calculations using nearby cells and the Sum function in spreadsheets to calculate total frequencies of collected data
Content descriptorAC9M3ST02 Statistics
create and compare different graphical representations of data sets including using software where appropriate; interpret the data in terms of the context
Elaborations (4)
- Elaboration comparing various student-generated data representations and describing their similarities and differences
- Elaboration using digital tools, including generative artificial intelligence tools or graphing software, to construct graphs of data acquired through experiments or observation and interpreting the data and making inferences; for example, graphing data from a science experiment and interpreting the results
- Elaboration selecting appropriate formats or layout styles to present data as information, depending on the type of data and the audience; for example, lists, tables, graphs and infographics
- Elaboration using newspapers or magazines to find examples of different displays of data, interpreting and describing the information they present
Content descriptorAC9M3ST03 Statistics
conduct guided statistical investigations involving the collection, representation and interpretation of data for categorical and discrete numerical variables with respect to questions of interest
Elaborations (5)
- Elaboration creating a poster, flowchart or infographic that describes the process of statistical investigation, and the components, the tools and the types of data that can be collected, represented and interpreted for a purpose
- Elaboration collaboratively working through a whole class investigation by choosing a question of interest, using an efficient collection method and recording collected data; interpreting the data in terms of the question
- Elaboration planning and carrying out investigations that involve collecting data; for example, narrowing the focus of a question such as, “Which is the most popular breakfast cereal?” to “Which is the most popular breakfast cereal among Year 3 students in our class?”
- Elaboration conducting a whole class statistical investigation into the best day to hold an open day for parents by creating a simple survey; collecting the data by asking the parents, representing and interpreting the results, and deciding as a class which day would be best
- Elaboration investigating seasonal calendars of First Nations Australians by collecting data and creating frequency tables and spreadsheets based on environmental indicators; creating one-to-one data displays about frequency of environmental indicators for the current season
They record, represent and compare data they have collected.
Content descriptorAC9M3ST01 Statistics
acquire data for categorical and discrete numerical variables to address a question of interest or purpose by observing, collecting and accessing data sets; record the data using appropriate methods including frequency tables and spreadsheets
Elaborations (5)
- Elaboration using efficient ways to collect and record data; for example, written surveys, online surveys, polling the class using interactive digital mediums, and representing and reporting the results of investigations
- Elaboration developing questions of interest and using surveys, observations or experiments to collect categorical, discrete numerical or qualitative data sets and discussing what kind of data can be used to help inform or answer the question in a statistical investigation
- Elaboration using lists, tallies, symbols and digital data tables to record and display data collected during a chance experiment for interpretation
- Elaboration using different online sources to access data; for example, using online query interfaces to select and retrieve data from an online database such as weather records, Google Trends or the World Health Organization
- Elaboration using software to sort and calculate data when solving problems; for example, sorting discrete numerical and categorical data in ascending or descending order and automating simple arithmetic calculations using nearby cells and the Sum function in spreadsheets to calculate total frequencies of collected data
Content descriptorAC9M3ST02 Statistics
create and compare different graphical representations of data sets including using software where appropriate; interpret the data in terms of the context
Elaborations (4)
- Elaboration comparing various student-generated data representations and describing their similarities and differences
- Elaboration using digital tools, including generative artificial intelligence tools or graphing software, to construct graphs of data acquired through experiments or observation and interpreting the data and making inferences; for example, graphing data from a science experiment and interpreting the results
- Elaboration selecting appropriate formats or layout styles to present data as information, depending on the type of data and the audience; for example, lists, tables, graphs and infographics
- Elaboration using newspapers or magazines to find examples of different displays of data, interpreting and describing the information they present
Students use practical activities, observation or experiment to identify and describe outcomes and the likelihood of everyday events explaining reasoning.
Content descriptorAC9M3P01 Probability
identify practical activities and everyday events involving chance; describe possible outcomes and events as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ explaining reasoning
Elaborations (4)
- Elaboration predicting what could happen next in practical activities that involve an element of chance, considering possible outcomes and using terms such as “likely” or “unlikely” to explain their predictions
- Elaboration classifying a list of everyday events or sorting a set of event cards according to how likely they are to happen, using the language of chance and giving reasons for classifications; discussing how impossible outcomes cannot ever happen, uncertain outcomes are affected by chance as they may or may not happen whereas certain events must always happen, so they are not affected by chance
- Elaboration making predictions and testing what would happen; for example, if 10 names were put in a box, and names were then drawn out one at a time and replaced after each selection, discussing how likely it would be after 10 selections that all 10 names were drawn from the box or that one name was drawn multiple times
- Elaboration role-playing being a chatbot or virtual assistant responding to a user about the likelihood of events; for example, using preset questions on cards relating to the likelihood of events, role-playing in pairs responding as a virtual assistant, giving reasons for their response
Content descriptorAC9M3P02 Probability
conduct repeated chance experiments; identify and describe possible outcomes, record the results, recognise and discuss the variation
Elaborations (3)
- Elaboration identifying the possible outcomes of a chance experiment, creating a tally chart to record results, carrying out a few trials and tallying the results for each trial; responding to the questions: “How did your results vary for each trial?” and “How do the results vary across the class?”
- Elaboration conducting repeated trials of chance experiments such as tossing a coin, throwing a dice, drawing a coloured or numbered ball from a bag, using a coloured spinner with equal partitions, and identifying the variation in the number of heads/fives/reds between trials
- Elaboration discussing how the process of conducting repeated chance experiments is crucial in the training of artificial intelligence applications like recommendation systems; for example, if they were building a recommendation system for an online shopping website, they could conduct repeated experiments by tracking user interactions over time
They conduct repeated chance experiments and discuss variation in results.
Content descriptorAC9M3P02 Probability
conduct repeated chance experiments; identify and describe possible outcomes, record the results, recognise and discuss the variation
Elaborations (3)
- Elaboration identifying the possible outcomes of a chance experiment, creating a tally chart to record results, carrying out a few trials and tallying the results for each trial; responding to the questions: “How did your results vary for each trial?” and “How do the results vary across the class?”
- Elaboration conducting repeated trials of chance experiments such as tossing a coin, throwing a dice, drawing a coloured or numbered ball from a bag, using a coloured spinner with equal partitions, and identifying the variation in the number of heads/fives/reds between trials
- Elaboration discussing how the process of conducting repeated chance experiments is crucial in the training of artificial intelligence applications like recommendation systems; for example, if they were building a recommendation system for an online shopping website, they could conduct repeated experiments by tracking user interactions over time
This achievement standard describes the expected learning for Year 3 Mathematics. Use it to plan teaching and assessment with the Australian Curriculum v9.
At a Glance
| Strand | Substrand | CDs | Elaborations |
|---|---|---|---|
| Algebra | — | 3 | 10 |
| Measurement | — | 6 | 24 |
| Number | — | 7 | 32 |
| Probability | — | 2 | 7 |
| Space | — | 2 | 12 |
| Statistics | — | 3 | 14 |
| Total | 23 | 99 | |
Frequently Asked Questions
What should students know by the end of Year 3 Mathematics?
By the end of Year 3, students order and represent natural numbers beyond 10 000. They partition, rearrange and regroup two- and three-digit numbers in different ways to assist in calculations. Read the full standard
How many Content Descriptors support this standard?
23 Content Descriptors support this Achievement Standard (Algebra: 3, Measurement: 6, Number: 7, Probability: 2, Space: 2, Statistics: 3).
How does this compare to Year 2?
The Year 2 Mathematics standard (ASMATY2) covers the preceding curriculum level. Standards build progressively, with Year 3 expectations extending what was introduced in Year 2.
Is this from the latest Australian Curriculum?
Yes, this Achievement Standard is from the Australian Curriculum version 9.0 (AC v9), the most current version published by ACARA.