Year 4
Mathematics
ASMATY4
Year 4 Mathematics Achievement Standard
20 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 4, students use their understanding of place value to represent tenths and hundredths in decimal form and to multiply natural numbers by multiples of 10. They use mathematical modelling to solve financial and other practical problems , formulating the problem using number sentences, solving the problem choosing efficient strategies and interpreting the results in terms of the situation. Students use their proficiency with addition and multiplication facts to add and subtract, multiply and divide numbers efficiently. They choose rounding and estimation strategies to determine whether results of calculations are reasonable. Students use the properties of odd and even numbers. They recognise equivalent fractions and make connections between fraction and decimal notations. Students count and represent fractions on a number line. They find unknown values in numerical equations involving addition and subtraction. Students follow and create algorithms that generate sets of numbers and identify emerging patterns.
They use scaled instruments and appropriate units to measure length, mass, capacity and temperature. Students measure and approximate perimeters and areas. They convert between units of time when solving problems involving duration. Students compare angles relative to a right angle using angle names. They represent and approximate shapes and objects in the environment. Students create and interpret grid references. They identify line and rotational symmetry in plane shapes and create symmetrical patterns.
Students create many-to-one data displays, assess the suitability of displays for representing data and discuss the shape of distributions and variation in data. They use surveys and digital tools to generate categorical or discrete numerical data in statistical investigations and communicate their findings in context. Students order events or the outcomes of chance experiments in terms of likelihood and identify whether events are independent or dependent. They conduct repeated chance experiments and describe the variation in results.
The 20 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 4, students use their understanding of place value to represent tenths and hundredths in decimal form and to multiply natural numbers by multiples of 10.
Content descriptorAC9M4N01 Number
recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals
Elaborations (6)
- Elaboration using a bar to represent the whole, dividing it into 10 equal pieces with each piece representing 0.1 or a tenth of the whole length and understanding that 2 pieces are 0.2 or two-tenths of the whole
- Elaboration using materials to show the multiplicative relationship between the whole, tenths and hundredths; for example, using a bundle of 10 straws to represent the whole, one straw as the tenth and cutting the tenth into 10 parts to show the hundredths; using “Decipipes” to represent tenths
- Elaboration recognising that one is the same as ten-tenths and one-tenth is the same as 10 hundredths and using this relationship to rename decimals; for example, renaming 0.25 as two-tenths and five-hundredths or twenty-five hundredths
- Elaboration making models of measurement attributes to show the relationship between the base unit and parts of the unit; for example, 1.5 metres is one metre and five-tenths of the next metre; 1.75 units is one unit and seventy-five hundredths of the next unit
- Elaboration counting large quantities of mixed notes and coins, writing the total using dollars and cents, and recognising the cents as parts of the next dollar
- Elaboration comparing the way money and measures are read and said, and explaining how they are the same and different; for example, \$2.75 is said, “two dollars seventy-five” and 2.75 metres is said “two point seven five metres”; recognising that the 7 means seven-tenths and the 5 means five-hundredths in both
Content descriptorAC9M4N05 Number
solve problems involving multiplying or dividing natural numbers by multiples and powers of 10 without a calculator, using the multiplicative relationship between the place value of digits
Elaborations (3)
- Elaboration using physical or virtual materials to demonstrate the multiplicative relationship between the places
- Elaboration using materials such as place value charts, numeral expanders or sliders to recognise and explain why multiplying by 10 moves the digits one place to the left and dividing by 10 moves digits one place to the right
- Elaboration using a calculator or other digital tools to recognise and develop an understanding of the effect of multiplying or dividing numbers by 10s, 100s and 1000s, recording sequences in a place value chart, in a table or spreadsheet, generalising the patterns noticed and applying them to solve multiplicative problems without a calculator
They use mathematical modelling to solve financial and other practical problems , formulating the problem using number sentences, solving the problem choosing efficient strategies and interpreting the results in terms of the situation.
Content descriptorAC9M4N06 Number
develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder
Elaborations (7)
- Elaboration using and choosing efficient calculation strategies for addition and subtraction problems involving larger numbers; for example, place value partitioning, inverse relationship, compatible numbers, jump strategies, bridging tens, splitting one or more numbers, extensions to basic facts, algorithms and digital tools where appropriate
- Elaboration using physical or virtual materials to demonstrate doubling and halving strategies for solving multiplication problems; for example, for 5 \times 18, using the fact that double 5 is 10 and half of 18 is 9; or using 10 \times 18 = 180 and halve 180 is 90; applying the associative property of multiplication, where 5 \times18 becomes 5 \times 2 \times 9, then 5 \times 2 \times 9 = 10 \times 9 = 90 so that 5 \times 18 = 90
- Elaboration using an array to represent a multiplication problem, connecting the idea of how many groups and how many in each group with the rows and columns of the array, and writing an associated number sentence
- Elaboration using materials or a diagram to solve a multiplication or division problem, by writing a number sentence, and explaining what each of the numbers within the number sentence refers to
- Elaboration representing a multiplicative situation using materials, array diagrams and/or a bar model, and writing multiplication and/or division number sentences, based on whether the number of groups, the number per group or the total is missing, and explaining how each number in their number sentence is connected to the situation
- Elaboration using place value partitioning, basic facts and an area or region to represent and solve multiplication problems, such as 16 \times 4, thinking 10 \times 4 and 6 \times 4, 40 + 24 = 64 or a double, double strategy where double 16 is 32, double this is 64, so 16 \times 4 is 64
- Elaboration using materials or diagrams to develop and explain division strategies; for example, finding thirds, using the inverse relationship to turn division into a multiplication
Content descriptorAC9M4N08 Number
use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems using number sentences and choose efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation
Elaborations (5)
- Elaboration modelling and solving a range of practical additive problems using materials, part-part-whole diagrams and/or a bar model, and writing addition and/or subtraction number sentences, based on whether a part or the whole is missing; explaining how each number in their number sentence is connected to the situation
- Elaboration modelling practical problems with division, interpreting and representing the situation using a diagram or array to represent what is unknown (the number of groups, or the number per group); writing a division number sentence to represent the situation and choosing an efficient calculation strategy
- Elaboration modelling practical problems involving money, such as a budget for a large event, as requiring either addition, subtraction, multiplication or division and justifying the choice of operation in relation to the situation
- Elaboration modelling and solving multiplication problems involving money, such as buying 5 toy scooters for \$96 each, using efficient mental strategies and written jottings to keep track if needed; for example, rounding \$96 up to \$100 and subtracting 5 \times\$4 = \$20, so 5 \times\$96 is the same as 5\times\$100 less \$20, giving the answer \$500 \space–\space \$20 = \$480
- Elaboration modelling situations by formulating comparison problems using number sentences, comparison models and arrays; for example, “Ariana read 16 books for the readathon; Maryam read 4 times as many books. How many books did Maryam read?” using the expression 4 \times 16 and using place value partitioning, basic facts and an array, thinking 4 \times 10 = 40 and 4 \times 6 = 24, so 4 \times 16 can be written as 40 + 24 = 64
Students use their proficiency with addition and multiplication facts to add and subtract, multiply and divide numbers efficiently.
Content descriptorAC9M4A02 Algebra
recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator
Elaborations (6)
- Elaboration using arrays on grid paper or created with blocks or counters to develop, represent and explain patterns in the 10 \times 10 multiplication facts; using the arrays to explain the related division facts
- Elaboration using materials or diagrams to develop and record multiplication strategies such as doubling, halving, commutativity, and adding one more or subtracting from a group to reach a known fact; for example, creating multiples of 3 on grid paper and doubling to find multiples of 6; recording and explaining the connections to the \times3 and \times6 multiplication facts: 3, 6, 9, … doubled is 6, 12, 18, …
- Elaboration using known multiplication facts for 2, 3, 5 and 10 to establish multiplication facts for 4, 6, 7, 8 and 9 in different ways; for example, using multiples of 10 to establish the multiples of 9 as “to multiply a number by 9 you multiply by 10 then take the number away”; 9 \times 4 = 10 \times 4\space – \space4, so 9 \times 4 is 40 \space– \space4 = 36; using multiple of 3 as “to multiply a number by 9 you multiply by 3, and then multiply the result by 3 again”
- Elaboration using arrays and known multiplication facts for twos and fives to develop the multiplication facts for sevens, applying the distributive property of multiplication; for example, when finding 6 \times 7, knowing that 7 is made up of 2 and 5, and using an array to show that 6 \times 7 is the same as 6 \times 2 + 6 \times 5 = 12 + 30 which is 42
- Elaboration using known multiplication facts up to 10 \times 10 and the inverse relationship of multiplication and division to establish corresponding division facts
- Elaboration designing, creating and playing instructive card games that involve the recall, recognition and explanation of the 10 \times 10 multiplication facts and related division facts
Content descriptorAC9M4N06 Number
develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder
Elaborations (7)
- Elaboration using and choosing efficient calculation strategies for addition and subtraction problems involving larger numbers; for example, place value partitioning, inverse relationship, compatible numbers, jump strategies, bridging tens, splitting one or more numbers, extensions to basic facts, algorithms and digital tools where appropriate
- Elaboration using physical or virtual materials to demonstrate doubling and halving strategies for solving multiplication problems; for example, for 5 \times 18, using the fact that double 5 is 10 and half of 18 is 9; or using 10 \times 18 = 180 and halve 180 is 90; applying the associative property of multiplication, where 5 \times18 becomes 5 \times 2 \times 9, then 5 \times 2 \times 9 = 10 \times 9 = 90 so that 5 \times 18 = 90
- Elaboration using an array to represent a multiplication problem, connecting the idea of how many groups and how many in each group with the rows and columns of the array, and writing an associated number sentence
- Elaboration using materials or a diagram to solve a multiplication or division problem, by writing a number sentence, and explaining what each of the numbers within the number sentence refers to
- Elaboration representing a multiplicative situation using materials, array diagrams and/or a bar model, and writing multiplication and/or division number sentences, based on whether the number of groups, the number per group or the total is missing, and explaining how each number in their number sentence is connected to the situation
- Elaboration using place value partitioning, basic facts and an area or region to represent and solve multiplication problems, such as 16 \times 4, thinking 10 \times 4 and 6 \times 4, 40 + 24 = 64 or a double, double strategy where double 16 is 32, double this is 64, so 16 \times 4 is 64
- Elaboration using materials or diagrams to develop and explain division strategies; for example, finding thirds, using the inverse relationship to turn division into a multiplication
Content descriptorAC9M4N08 Number
use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems using number sentences and choose efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation
Elaborations (5)
- Elaboration modelling and solving a range of practical additive problems using materials, part-part-whole diagrams and/or a bar model, and writing addition and/or subtraction number sentences, based on whether a part or the whole is missing; explaining how each number in their number sentence is connected to the situation
- Elaboration modelling practical problems with division, interpreting and representing the situation using a diagram or array to represent what is unknown (the number of groups, or the number per group); writing a division number sentence to represent the situation and choosing an efficient calculation strategy
- Elaboration modelling practical problems involving money, such as a budget for a large event, as requiring either addition, subtraction, multiplication or division and justifying the choice of operation in relation to the situation
- Elaboration modelling and solving multiplication problems involving money, such as buying 5 toy scooters for \$96 each, using efficient mental strategies and written jottings to keep track if needed; for example, rounding \$96 up to \$100 and subtracting 5 \times\$4 = \$20, so 5 \times\$96 is the same as 5\times\$100 less \$20, giving the answer \$500 \space–\space \$20 = \$480
- Elaboration modelling situations by formulating comparison problems using number sentences, comparison models and arrays; for example, “Ariana read 16 books for the readathon; Maryam read 4 times as many books. How many books did Maryam read?” using the expression 4 \times 16 and using place value partitioning, basic facts and an array, thinking 4 \times 10 = 40 and 4 \times 6 = 24, so 4 \times 16 can be written as 40 + 24 = 64
They choose rounding and estimation strategies to determine whether results of calculations are reasonable.
Content descriptorAC9M4N07 Number
choose and use estimation and rounding to check and explain the reasonableness of calculations including the results of financial transactions
Elaborations (3)
- Elaboration using proficiency with basic facts to estimate the result of a calculation and say what amounts the answer will be between; for example, 5 packets of biscuits at \$2.60 each will cost between \$10 and \$15 as 5 \times \$2 =\$10 and 5\times\$3=\$15
- Elaboration using rounded amounts to complete an estimated budget for a shopping trip or an excursion, explaining why overestimating the amounts is appropriate
- Elaboration recognising the effect of rounding in addition and multiplication calculations; rounding both numbers up, both numbers down and one number up and one number down, and explaining which is the best approximation and why
Students use the properties of odd and even numbers.
Content descriptorAC9M4N02 Number
explain and use the properties of odd and even numbers
Elaborations (4)
- Elaboration identifying even numbers and explaining why all numbers that end in the digits 0, 2, 4, 6 and 8 are even and that numbers ending in 1, 3, 5, 7 and 9 are odd
- Elaboration explaining why some materials can be shared evenly between 2 people without leaving a remainder and some cannot
- Elaboration explaining the patterns involved in adding, subtracting and multiplying odd and even numbers; for example, even + even = even, odd + even = odd, odd + odd = even and using this to decide whether answers to addition, subtraction and multiplication calculations are correct or not
- Elaboration following an algorithm consisting of a flow chart with a series of instructions and decisions to determine whether a number is even or odd; using the algorithm to identify which elements of a set of numbers are divisible by 2
They recognise equivalent fractions and make connections between fraction and decimal notations.
Content descriptorAC9M4N01 Number
recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals
Elaborations (6)
- Elaboration using a bar to represent the whole, dividing it into 10 equal pieces with each piece representing 0.1 or a tenth of the whole length and understanding that 2 pieces are 0.2 or two-tenths of the whole
- Elaboration using materials to show the multiplicative relationship between the whole, tenths and hundredths; for example, using a bundle of 10 straws to represent the whole, one straw as the tenth and cutting the tenth into 10 parts to show the hundredths; using “Decipipes” to represent tenths
- Elaboration recognising that one is the same as ten-tenths and one-tenth is the same as 10 hundredths and using this relationship to rename decimals; for example, renaming 0.25 as two-tenths and five-hundredths or twenty-five hundredths
- Elaboration making models of measurement attributes to show the relationship between the base unit and parts of the unit; for example, 1.5 metres is one metre and five-tenths of the next metre; 1.75 units is one unit and seventy-five hundredths of the next unit
- Elaboration counting large quantities of mixed notes and coins, writing the total using dollars and cents, and recognising the cents as parts of the next dollar
- Elaboration comparing the way money and measures are read and said, and explaining how they are the same and different; for example, \$2.75 is said, “two dollars seventy-five” and 2.75 metres is said “two point seven five metres”; recognising that the 7 means seven-tenths and the 5 means five-hundredths in both
Content descriptorAC9M4N03 Number
find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation
Elaborations (5)
- Elaboration extending fraction families within collections of materials; for example, by seeing 3/4 as 3 in each 4, showing this within related fractions like 6/8 or seeing that 2/5 means 2 in each 5 so it can be shown within 4/10
- Elaboration creating models of equivalent fractions by subdividing capacity measures into smaller fractions; for example, half a cup of flour could be shown as two-quarters or four-eighths of a cup of flour
- Elaboration folding paper to show equivalence between different fractions; for example, folding A4 paper in half and half again, repeating to form eighths and demonstrating that 4/8 = 2/4 = 1/2; folding paper strips into fifths and tenths, and recording as both fractions and decimals
- Elaboration identifying and using the connection between fractions of metres and decimals; for example, finding 1/4 of a metre and connecting this to 0.25 metres or 25 centimetres, or finding 1/10 of a metre and connecting this with 0.10 metres or 10 centimetres
- Elaboration using array diagrams to show the relationship between fractions and division and multiplication of natural numbers; for example, 3 \times 4 = 12, 12 ÷ 4 = 3, 1/4 of 12 is 3, 1/3 of 12 is 4
Students count and represent fractions on a number line.
Content descriptorAC9M4N04 Number
count by fractions including mixed numerals; locate and represent these fractions as numbers on number lines
Elaborations (4)
- Elaboration cutting objects such as oranges or sandwiches into quarters and counting by quarters to find the total number, and saying the counting sequence: one-quarter, two-quarters, three-quarters, four-quarters or one-whole, five-quarters or one-and-one-quarter, six-quarters or one-and-two-quarters… eight-quarters or two-wholes...
- Elaboration subdividing the sections between whole numbers on parallel number lines so that one shows halves, another shows quarters and one other shows thirds; counting the fractions by jumping along the number lines, and noticing when the count is at the same position on the parallel lines
- Elaboration converting mixed numerals into improper fractions and vice versa and representing mixed numerals on a number line
- Elaboration using a number line to represent and count in tenths, recognising that 10 tenths is equivalent to one
They find unknown values in numerical equations involving addition and subtraction.
Content descriptorAC9M4A01 Algebra
find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations
Elaborations (4)
- Elaboration demonstrating the commutative properties of addition using materials, diagrams and number lines; for example, using number lines to demonstrate that 5 + 2 = 2 + 5, demonstrating that 2 + 2 + 3 = 7 and 2 + 3 + 2 = 7 and 3 + 2 + 2 = 7
- Elaboration using balance scales and informal uniform units to create addition or subtraction number sentences showing equivalence, such as 7 + 8 = 6 + 9, and to find unknowns in equivalent number sentences, such as 6 + 8 = \square + 10
- Elaboration using relational thinking and knowledge of equivalent number sentences to explain whether equations involving addition or subtraction are true; for example, explaining that 27 \space– \space 14 = 17\space – \space4 is true and using a number line to show the common difference is 13
- Elaboration using part-part-whole diagrams or bar models to recognise and explain the inverse relationship between addition and subtraction, using this to make calculations easier; for example, solving 27 + \square = 63 using subtraction, \square = 63\space – \space27
Students follow and create algorithms that generate sets of numbers and identify emerging patterns.
Content descriptorAC9M4N09 Number
follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns
Elaborations (3)
- Elaboration creating an algorithm that will generate number sequences involving multiples of one to 10 using digital tools to assist, identifying and explaining emerging patterns, recognising that number sequences can be extended indefinitely
- Elaboration creating a basic flow chart that represents an algorithm that will generate a sequence of numbers using multiplication by a constant term; using a calculator to model and follow the algorithm, and record the sequence of numbers generated; checking results and describing any emerging patterns
- Elaboration using a multiplication formula in a spreadsheet and the “fill down” function to generate a sequence of numbers; for example, entering the number one in the cell A1, using “fill down” to cell A100, entering the formula “ = A1*4 “ in the cell B1 and using the “fill down” function to generate a sequence of 100 numbers; describing emerging patterns
They use scaled instruments and appropriate units to measure length, mass, capacity and temperature.
Content descriptorAC9M4M01 Measurement
interpret unmarked and partial units when measuring and comparing attributes of length, mass, capacity, duration and temperature, using scaled and digital instruments and appropriate units
Elaborations (7)
- Elaboration reading the mass of objects measured with digital and analog kitchen scales and explaining what unit of mass the lines on the analog scales refer to
- Elaboration deciding on which attribute, unit and measuring instrument to use to compare the length and mass of various things, such as the distance travelled by an object in a science investigation; explaining the use of units such as grams or millimetres to give accurate measures when needed
- Elaboration using scaled instruments such as tape measures, measuring jugs, kitchen scales and thermometers, recording measures using whole units; for example, 560 millimetres, or whole and part units; for example, 5.25 metres, 1.75 litres, 2.5 kilograms, 28.5° Celsius
- Elaboration reading and interpreting the scale of an analog clock without marked minutes to estimate the time to the nearest minute and to determine the duration of time between events
- Elaboration using the timer or alarm function of a clock to alert when a specified duration has elapsed from a given starting time; for example, the different activities of an exercise routine
- Elaboration making a scaled measuring instrument such as a tape measure, ruler, sand timer, sun dial or measuring cup using scaled instruments and direct comparisons
- Elaboration exploring the different types of scaled instruments used by First Nations Ranger Groups and other groups to make decisions about caring for Country/Place, and modelling these in local contexts
Students measure and approximate perimeters and areas.
Content descriptorAC9M4M02 Measurement
recognise ways of measuring and approximating the perimeter and area of shapes and enclosed spaces, using appropriate formal and informal units
Elaborations (5)
- Elaboration recognising that perimeter is the sum of the lengths that form the boundary of a shape or enclosed space; choosing suitable units from a range of objects to measure around the boundary of a shape such as a garden bed; comparing the results to say which unit was an appropriate choice for the context; using a piece of string or rope to measure the perimeter of irregular shapes and enclosed spaces, including those that have curved sections
- Elaboration creating a range of rectangles representing “paddocks” on grid paper and establishing different methods of working out the length of the boundary fences; explaining that the more efficient methods involve adding the side lengths rather than counting squares
- Elaboration recognising that area is the space enclosed by the boundary of a shape or the surface of an object; measuring and comparing the area of shapes, using an array of paper tiles or mosaic squares, including part units to fill gaps at the edge of the shapes; comparing the total areas by combining the fractional parts to make whole units
- Elaboration demonstrating how to use one unit repeatedly to measure the area of a shape; for example, using one paper square to measure and compare the area of a rectangle and a triangle; recording and explaining how they used part units to give a more accurate measure, and why they needed to ensure there were no gaps or overlaps
- Elaboration investigating the ways First Nations Ranger Groups and other groups measure areas of land to make decisions about fire burns to care for Country/Place
They convert between units of time when solving problems involving duration.
Content descriptorAC9M4M03 Measurement
solve problems involving the duration of time including situations involving “am” and “pm” and conversions between units of time
Elaborations (3)
- Elaboration calculating the amount of time between 2 events, such as the start and finish of a movie, a bus journey or a flight, including cases where the starting and finishing times are written using “am” and “pm” notation
- Elaboration converting units of time using relationships between units, such as 60 minutes in an hour and 60 seconds in a minute, to solve problems; for example, creating a daily timetable for an activity such as an athletics carnival or planning an exercise routine with activities and rests
- Elaboration exploring First Nations Australians’ explanations of the passing of time through cultural accounts about cyclic phenomena involving sun, moon and stars
Students compare angles relative to a right angle using angle names.
Content descriptorAC9M4M04 Measurement
estimate and compare angles using angle names including acute, obtuse, straight angle, reflex and revolution, and recognise their relationship to a right angle
Elaborations (4)
- Elaboration classifying the interior angles of a range of shapes, using examples of angles to identify acute, obtuse, right and reflex angles
- Elaboration identifying angles within the environment and estimating whether they are acute, obtuse right or reflex
- Elaboration creating a right-angle template using cardboard or a double-folded piece of paper and using it to compare angles in the environment, commenting on whether they are smaller than or greater than a right angle
- Elaboration using different measuring tools such as a spirit level or set squares to determine whether lines or objects are straight, square or perpendicular (at right angles)
They represent and approximate shapes and objects in the environment.
Content descriptorAC9M4SP01 Space
represent and approximate composite shapes and objects in the environment, using combinations of familiar shapes and objects
Elaborations (4)
- Elaboration identifying common shapes that form part of a composite shape by re-creating these shapes using physical or virtual materials
- Elaboration physically or virtually using cubes to make three-dimensional models that approximate real objects; for example, building a virtual environment by using a computer software program to construct objects out of cubes
- Elaboration approximating complex shapes and objects in the environment with familiar shapes and objects; for example, drawing cartoon animals by combining familiar shapes
- Elaboration recognising how familiar shapes and objects are used in logos and other graphics to represent more complex shapes and creating logos using graphic design software
Students create and interpret grid references.
Content descriptorAC9M4SP02 Space
create and interpret grid reference systems using grid references and directions to locate and describe positions and pathways
Elaborations (5)
- Elaboration interpreting a grid reference map of a familiar location of interest, such as a map of the showgrounds, a food festival, a botanical garden, a park in the local area or a train station, and writing instructions using grid references for a friend to find them at a specified location
- Elaboration recognising that a spreadsheet uses a grid reference system, locating and entering data in cells and using a spreadsheet to record data collected through observations or experiments
- Elaboration comparing and contrasting, describing and locating landmarks, people or things in a bird’s eye picture of a busy scene, such as people in a park, initially without a transparent grid reference system overlaid on the picture, and then with the grid overlaid; noticing how the grid helps to pinpoint things quickly and easily
- Elaboration using different sized grids as a tool to enlarge an image or artwork
- Elaboration simulating the actions of autonomous or robotic vehicles moving to different positions within a grid, using grid references and directional language to describe positions and pathways; for example, imitating an autonomous mobile warehouse robot moving stock to different aisles, using grid reference systems to locate positions
They identify line and rotational symmetry in plane shapes and create symmetrical patterns.
Content descriptorAC9M4SP03 Space
recognise line and rotational symmetry of shapes and create symmetrical patterns and pictures, using dynamic geometric software where appropriate
Elaborations (4)
- Elaboration identifying rotational symmetry of shapes by tracing around various shapes and objects to create an image, and using the image to test and record which different rotations result in the same image
- Elaboration using dynamic geometric software or generative artificial intelligence tool to manipulate shapes and create symmetrical patterns; for example, creating tessellation patterns that are symmetrical and discussing any line or rotational symmetries
- Elaboration using stimulus materials such as the motifs in Central Asian textiles, Tibetan artefacts, Indian lotus designs and Islamic artwork to investigate and discuss line and rotational symmetry
- Elaboration exploring the natural environment on Country/Place to investigate and discuss patterns and symmetry of shapes and objects such as in flowers, plants and landscapes
Students create many-to-one data displays, assess the suitability of displays for representing data and discuss the shape of distributions and variation in data.
Content descriptorAC9M4ST01 Statistics
acquire data for categorical and discrete numerical variables to address a question of interest or purpose, using digital tools; represent data using many-to-one pictographs, column graphs and other displays or visualisations; interpret and discuss the information that has been created
Elaborations (6)
- Elaboration investigating many-to-one data displays using digital tools and graphical software, interpreting and discussing key features
- Elaboration understanding that data can be represented with one symbol representing more than one piece of data, and that it is important to read all information about a representation before making judgements
- Elaboration constructing graphs of data collected through observation during science experiments, recording, interpreting and discussing the results in terms of the scientific study
- Elaboration co-creating an online poll to survey students in their school about a topic of interest, exploring how online platforms use generative artificial intelligence to make word clouds, quizzes, polls and graphical representations of the collected data
- Elaboration acquiring samples of data using practical activities, observations or repeated chance experiments, recording data using tally charts, digital tables or spread sheets, graphing, discussing and comparing the results using a column graph
- Elaboration using secondary data of fire burns to construct data displays that assist First Nations Ranger Groups and other groups to care for Country/Place
Content descriptorAC9M4ST02 Statistics
analyse the effectiveness of different displays or visualisations in illustrating and comparing data distributions, then discuss the shape of distributions and the variation in the data
Elaborations (4)
- Elaboration suggesting questions that can be answered by a given data display and using the display to answer these questions
- Elaboration interpreting data representations in the media and other forums where symbols represent one-to-many relationships and how this can be challenging when the representations use part-whole representations
- Elaboration comparing different student generated diagrams, tables and graphs, describing their similarities and differences and commenting on the usefulness of each representation for interpreting the data
- Elaboration discussing how analysing data distributions and visualising data is a fundamental step in data preparation for AI developers
They use surveys and digital tools to generate categorical or discrete numerical data in statistical investigations and communicate their findings in context.
Content descriptorAC9M4ST01 Statistics
acquire data for categorical and discrete numerical variables to address a question of interest or purpose, using digital tools; represent data using many-to-one pictographs, column graphs and other displays or visualisations; interpret and discuss the information that has been created
Elaborations (6)
- Elaboration investigating many-to-one data displays using digital tools and graphical software, interpreting and discussing key features
- Elaboration understanding that data can be represented with one symbol representing more than one piece of data, and that it is important to read all information about a representation before making judgements
- Elaboration constructing graphs of data collected through observation during science experiments, recording, interpreting and discussing the results in terms of the scientific study
- Elaboration co-creating an online poll to survey students in their school about a topic of interest, exploring how online platforms use generative artificial intelligence to make word clouds, quizzes, polls and graphical representations of the collected data
- Elaboration acquiring samples of data using practical activities, observations or repeated chance experiments, recording data using tally charts, digital tables or spread sheets, graphing, discussing and comparing the results using a column graph
- Elaboration using secondary data of fire burns to construct data displays that assist First Nations Ranger Groups and other groups to care for Country/Place
Content descriptorAC9M4ST03 Statistics
conduct statistical investigations, collecting data through survey responses and other methods; record and display data using digital tools; interpret the data and communicate the results
Elaborations (3)
- Elaboration creating a survey to collect class responses to a preferred movie choice, and recording data responses using spreadsheets; graphing data using a column graph or other appropriate representations and interpreting the results of the survey reporting findings back to the class
- Elaboration conducting a statistical investigation and acquiring data from different online sources; 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 investigating different contexts in which statistical investigations can take place and the types of questions to ask to collect data relevant to the context; for example, investigating supermarket customer complaints that breakfast cereals with the most sugar are positioned at children’s eye level, discussing what questions they would need to ask and answer
Students order events or the outcomes of chance experiments in terms of likelihood and identify whether events are independent or dependent.
Content descriptorAC9M4P01 Probability
describe possible everyday events and the possible outcomes of chance experiments and order outcomes or events based on their likelihood of occurring; identify independent or dependent events
Elaborations (8)
- Elaboration using lists of events familiar to students and ordering them from “least likely” to “most likely” to occur; considering and discussing why the order of some events might be different for different students
- Elaboration predicting the outcome of a coin toss after 5 heads have been flipped in a row, discussing the assertion that because so many heads came up, it is more likely that a tail rather than a head will come up next; discussing with reasons why the assumption is correct or incorrect
- Elaboration predicting how likely, from least likely to most likely, of selecting a red ball from a bag containing 10 red balls and 5 white balls, a bag containing 20 of each, or one that has 25 red balls and 20 white balls, justifying their decision
- Elaboration identifying school activities where the chance of them taking place is affected by the chance of other events occurring; for example, given that there is a high chance of a storm on Friday, there is only a small chance that the coastal dune planting project will go ahead
- Elaboration listing the outcomes of everyday chance situations and identifying where one cannot happen if the other happens; for example, discussing that it cannot be hot and cold at the same time; selecting a card from a deck and discussing if it is red it cannot be a spade or a club
- Elaboration identifying different dependent events where the chance of one outcome occurring will be affected by the occurrence of other outcomes and different independent events where the chance of one outcome occurring will not be affected by the occurrence of other outcome(s)
- Elaboration exploring how ordering outcomes based on their likelihood of occurring is an essential component of early warning systems that use artificial intelligence to make decisions, such as natural disaster warning systems
- Elaboration discussing how likelihood relates to the decisions an artificial intelligence tool makes when generating predictive text; for example, discussing which word would most likely come next in a sentence, then refining the decision as the first letter is revealed
They conduct repeated chance experiments and describe the variation in results.
Content descriptorAC9M4P02 Probability
conduct repeated chance experiments to observe relationships between outcomes; identify and describe the variation in results
Elaborations (4)
- Elaboration playing games such as Noughts and Crosses or First to 20 and deciding if it makes a difference who goes first and whether you can use a particular strategy to increase your chances of winning
- Elaboration recording and ordering the outcomes of experiments using different physical or virtual random generators such as coins, dice and a variety of spinners, and discussing how AI systems use random generators to train algorithms
- Elaboration experimenting with tossing 2 coins at the same time, recording and commenting on the chance of outcomes after a number of tosses
- Elaboration shuffling a set of cards, drawing a card at random, and recording whether it was a spade, club, diamond or heart, picture card or numbered; repeating the experiment a number of times and discussing the results
This achievement standard describes the expected learning for Year 4 Mathematics. Use it to plan teaching and assessment with the Australian Curriculum v9.
At a Glance
| Strand | Substrand | CDs | Elaborations |
|---|---|---|---|
| Algebra | — | 2 | 10 |
| Measurement | — | 4 | 19 |
| Number | — | 9 | 40 |
| Probability | — | 2 | 12 |
| Space | — | 3 | 13 |
| Statistics | — | 3 | 13 |
| Total | 23 | 107 | |
Frequently Asked Questions
What should students know by the end of Year 4 Mathematics?
By the end of Year 4, students use their understanding of place value to represent tenths and hundredths in decimal form and to multiply natural numbers by multiples of 10. Read the full standard
How many Content Descriptors support this standard?
23 Content Descriptors support this Achievement Standard (Algebra: 2, Measurement: 4, Number: 9, Probability: 2, Space: 3, Statistics: 3).
How does this compare to Year 3?
The Year 3 Mathematics standard (ASMATY3) covers the preceding curriculum level. Standards build progressively, with Year 4 expectations extending what was introduced in Year 3.
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.