Year 6 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 6, students use integers to represent points on a number line and in the Cartesian plane. They solve problems using the properties of prime, composite and square numbers. Students order common fractions, giving reasons, and add and subtract fractions with related denominators. They use all 4 operations with decimals and connect decimal representations of measurements to the metric system. Students solve problems involving finding a fraction, decimal or percentage of a quantity and use estimation to find approximate solutions to problems involving rational numbers and percentages. They use mathematical modelling to solve financial and other practical problems involving percentages and rational numbers, formulating and solving the problem, and justifying choices. Students find unknown values in numerical equations involving combinations of arithmetic operations. They identify and explain rules used to create growing patterns. Students create and use algorithms to generate sets of numbers, using a rule.
They interpret and use timetables. Students convert between common units of length, mass and capacity. They use the formula for the area of a rectangle and angle properties to solve problems. Students identify the parallel cross-section for right prisms. They create tessellating patterns using combinations of transformations. Students locate an ordered pair in any one of the 4 quadrants on the Cartesian plane.
They compare distributions of discrete and continuous numerical and ordinal categorical data sets as part of their statistical investigations, using digital tools. Students critique arguments presented in the media based on statistics. They assign probabilities using common fractions, decimal and percentages. Students conduct simulations using digital tools, to generate and record the outcomes from many trials of a chance experiment. They compare observed frequencies to the expected frequencies of the outcomes of chance experiments.
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 6, students use integers to represent points on a number line and in the Cartesian plane.
Content descriptorAC9M6N01 Number
recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane
Elaborations (5)
- Elaboration extending the number line in the negative direction to locate and represent integers, recognising the difference in location between (-2) and (+2) and their relationship to zero as -2< 0< 2
- Elaboration using integers to represent quantities in financial contexts, including the concept of profit and loss for a planned event
- Elaboration using horizontal and vertical number lines to represent and find solutions to everyday problems involving locating and ordering integers around zero; for example, elevators, above and below sea level; distinguishing a location by referencing to the 4 quadrants of the Cartesian plane
- Elaboration recognising that the sign (positive or negative) indicates a direction in relation to zero; for example, 30 metres left of the admin block is (-30) and 20 metres right of the admin block is (+20); programming robots to move along a number line which is either horizontal or vertical but not both at the same time
- Elaboration representing the temperatures of the different planets in the solar system, using a diagram of a thermometer that models a vertical number line
Content descriptorAC9M6SP02 Space
locate points in the 4 quadrants of a Cartesian plane; describe changes to the coordinates when a point is moved to a different position in the plane
Elaborations (6)
- Elaboration understanding that the Cartesian plane provides a graphical or visual way of describing location with respect to a fixed origin
- Elaboration understanding that the axes are number lines that can have different scales, including fractions and decimals, depending on purpose
- Elaboration understanding that the horizontal coordinate is written first and is changed if there is a move to the left or right, whereas a move up or down will change the vertical coordinate
- Elaboration using the Cartesian plane to draw lines and polygons, listing co-ordinates in the correct order to complete a polygon
- Elaboration exploring how coordinates can be used to input positional data for artificial intelligence systems to locate positions in an image or other two-dimensional space
- Elaboration investigating and connecting land or star maps used by First Nations Australians with the Cartesian plane through a graphical or visual way of describing location
They solve problems using the properties of prime, composite and square numbers.
Content descriptorAC9M6N02 Number
identify and describe the properties of prime, composite and square numbers and use these properties to solve problems and simplify calculations
Elaborations (5)
- Elaboration using the definition of a prime number to explain why one is not a prime number
- Elaboration testing numbers by using division to distinguish between prime and composite numbers, recording the results on a number chart to identify any patterns
- Elaboration representing composite numbers as a product of their factors, including prime factors when necessary and using this form to simplify calculations involving multiplication such as 15 \times 16 as 5 \times 3 \times 4 \times 4 which can be rearranged to simplify calculation to 5 \times 4 \times 3 \times 4 = 20 \times 12
- Elaboration identifying and describing the product of a number with itself as square; for example, 3 \times 3 is the same as 3^2
- Elaboration using spreadsheets to list all the numbers that have up to 3 factors, using combinations of only the first 3 prime numbers, recognise any emerging patterns, making conjectures and experimenting with other combinations
Students order common fractions, giving reasons, and add and subtract fractions with related denominators.
Content descriptorAC9M6N03 Number
apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order
Elaborations (4)
- Elaboration applying factors and multiples to fraction denominators, such as halves with quarters, eighths and twelfths, and thirds with sixths, ninths and twelfths to determine equivalent representations of fractions in order to make comparisons
- Elaboration representing fractions on the same number line, paying attention to relative position, and using this to explain relationships between denominators
- Elaboration explaining equivalence and order between fractions using number lines, drawings and models
- Elaboration comparing and ordering fractions by placing cards on a string line across the room and referring to benchmark fractions to justify their position; for example, 5/8 is greater than 1/2 can be written as 5/8>1/2, because half of 8 is 4; 1/6 is less than 1/4, because 6 > 4 and can be written 1/6 < 1/4
Content descriptorAC9M6N05 Number
solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions
Elaborations (4)
- Elaboration representing addition and subtraction of fractions, using an understanding of equivalent fractions and methods such as jumps on a number line, or diagrams of fractions as parts of shapes
- Elaboration determining the lowest common denominator using an understanding of prime and composite numbers to find equivalent representation of fractions when solving addition and subtraction problems
- Elaboration calculating the addition or subtraction of fractions in the context of realistic problems; for example, using part cups or spoons in a recipe; using the understanding of equivalent fractions
- Elaboration understanding the processes for adding and subtracting fractions with related denominators and fractions as an operator, in preparation for calculating with all fractions; for example, using fraction overlays and number lines to give meaning to adding and subtracting fractions with related and unrelated denominators
They use all 4 operations with decimals and connect decimal representations of measurements to the metric system.
Content descriptorAC9M6M01 Measurement
convert between common metric units of length, mass and capacity; choose and use decimal representations of metric measurements relevant to the context of a problem
Elaborations (3)
- Elaboration recognising the significance of the prefixes in units of measurement
- Elaboration identifying and using the correct operations when converting between units including millimetres, centimetres, metres, kilometres, milligrams, grams, kilograms, tonnes, millilitres, litres, kilolitres and megalitres
- Elaboration recognising the equivalence of measurements, such as 1.25 metres is the same as 125 centimetres
Content descriptorAC9M6N04 Number
apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answers
Elaborations (4)
- Elaboration applying estimation strategies to addition and subtraction of decimals to at least thousandths before calculating answers or when a situation requires just an estimation
- Elaboration applying whole-number strategies; for example, using basic facts, place value, partitioning and the inverse relationship between addition and subtraction, and properties of operations to develop meaningful mental strategies for addition and subtraction of decimal numbers to at least hundredths
- Elaboration working additively with linear measurements expressed as decimals up to 2 and 3 decimal places; for example, calculating how far off the world record the athletes were at the last Olympic games in the women’s long jump or shot-put and comparing school records to the Olympic records
- Elaboration deciding to use a calculator as a calculation strategy for solving additive problems involving decimals that vary in their number of decimal places beyond hundredths; for example, 1.0 - 0.0035 or 2.345 + 1.4999
Content descriptorAC9M6N06 Number
multiply and divide decimals by multiples of powers of 10 without a calculator, applying knowledge of place value and proficiency with multiplication facts; using estimation and rounding to check the reasonableness of answers
Elaborations (3)
- Elaboration applying place value knowledge, including that the value of the digit is 10 times smaller each time a place is moved to the right, and known multiplication facts, to multiply and divide a decimal by powers of 10
- Elaboration applying and explaining estimation strategies in multiplicative situations involving a decimal greater than one that is multiplied by a two- or three-digit number, using a multiple of 10 or 100 when the situation requires just an estimation
- Elaboration explaining the effect of multiplying or dividing a decimal by 10, 100, 1000 … in terms of place value and not the decimal point shifting
Students solve problems involving finding a fraction, decimal or percentage of a quantity and use estimation to find approximate solutions to problems involving rational numbers and percentages.
Content descriptorAC9M6N04 Number
apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answers
Elaborations (4)
- Elaboration applying estimation strategies to addition and subtraction of decimals to at least thousandths before calculating answers or when a situation requires just an estimation
- Elaboration applying whole-number strategies; for example, using basic facts, place value, partitioning and the inverse relationship between addition and subtraction, and properties of operations to develop meaningful mental strategies for addition and subtraction of decimal numbers to at least hundredths
- Elaboration working additively with linear measurements expressed as decimals up to 2 and 3 decimal places; for example, calculating how far off the world record the athletes were at the last Olympic games in the women’s long jump or shot-put and comparing school records to the Olympic records
- Elaboration deciding to use a calculator as a calculation strategy for solving additive problems involving decimals that vary in their number of decimal places beyond hundredths; for example, 1.0 - 0.0035 or 2.345 + 1.4999
Content descriptorAC9M6N06 Number
multiply and divide decimals by multiples of powers of 10 without a calculator, applying knowledge of place value and proficiency with multiplication facts; using estimation and rounding to check the reasonableness of answers
Elaborations (3)
- Elaboration applying place value knowledge, including that the value of the digit is 10 times smaller each time a place is moved to the right, and known multiplication facts, to multiply and divide a decimal by powers of 10
- Elaboration applying and explaining estimation strategies in multiplicative situations involving a decimal greater than one that is multiplied by a two- or three-digit number, using a multiple of 10 or 100 when the situation requires just an estimation
- Elaboration explaining the effect of multiplying or dividing a decimal by 10, 100, 1000 … in terms of place value and not the decimal point shifting
Content descriptorAC9M6N07 Number
solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies and using digital tools where appropriate
Elaborations (5)
- Elaboration explaining how 1/3 of a quantity can be achieved by dividing by 3, and how knowledge of 1/3 of a quantity can be used to find 2/3 or 4/3 of the same quantity using situations involving money, length, duration, mass or capacity
- Elaboration investigating percentage discounts of 15%, 30% and 45% in an online toy sale, using their equivalent decimal representations of 0.15, 0.3 and 0.45 to calculate the amount of discount on sale items, with and without digital tools
- Elaboration linking percentages to their decimal equivalent of tenths and hundredths and using these to determine percentage discounts; for example, finding 30% discount by using its equivalence to 0.3, dividing by 10 and multiplying the result by 3 to give 30%
- Elaboration explaining the equivalence between percentages and fractions; for example, 33 1/3% and 1/3; keeping to percentages that are equivalent to fractions with small denominators such as 66 2/3% and 12.5%
- Elaboration representing a situation with a mathematical expression; for example, numbers and symbols such as 1/4\times24, that involve finding a familiar fraction or percentage of a quantity; using mental strategies or a calculator and explaining the result in terms of the situation in question
Content descriptorAC9M6N08 Number
approximate numerical solutions to problems involving rational numbers and percentages, including financial contexts, using appropriate estimation strategies
Elaborations (6)
- Elaboration using familiar fractions, decimals and percentages to approximate calculations, such as, 0.3 of 180 is about a 1/3 of 180 or 52% is about a 1/2
- Elaboration choosing appropriate estimation strategies including rounding to the nearest whole number, knowledge of multiples of 2, 5 or 10 and partitioning numbers in contexts such as measuring or cost per unit
- Elaboration recognising the effect of rounding on calculations involving fractions or decimals and saying what numbers the answer will be between
- Elaboration recognising the usefulness of estimation to check calculations for contexts such as dividing wood into a number of lengths, calculating cost per unit, reducing a recipe or dividing the cost of dinner for a group into individual amounts
- Elaboration verifying solutions by estimating percentages in suitable contexts such as discounts using common percentages of 10%, 25%, 30%, 50% and 1%
- Elaboration investigating estimation strategies to make decisions about steam cooking in ground ovens by First Nations Australians, including catering for different numbers of people and resources needed for cooking
They use mathematical modelling to solve financial and other practical problems involving percentages and rational numbers, formulating and solving the problem, and justifying choices.
Content descriptorAC9M6N09 Number
use mathematical modelling to solve practical problems involving natural and rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and efficient calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, justifying the choices made
Elaborations (3)
- Elaboration modelling practical situations involving percentages using efficient calculation strategies to find solutions, such as mental calculations, spreadsheets, calculators or a variety of informal jottings, and interpreting the results in terms of the situation; for example, purchasing items during a sale
- Elaboration modelling situations involving earning money and budgeting, asking questions such as, “Can I afford it?”, “Do I need it?”, “How much do I need to save for it?”, and developing a savings plan or budget for an upcoming event or personal purchase
- Elaboration modelling and solving the problem of creating a budget for a class excursion or family holiday, using the internet to research costs and expenses, and representing the budget in a spreadsheet, creating and using formulas to calculate totals
Students find unknown values in numerical equations involving combinations of arithmetic operations.
Content descriptorAC9M6A02 Algebra
find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations
Elaborations (4)
- Elaboration using brackets and the order of operations to write number sentences and appreciating the need for an agreed set of rules to complete multiple operations within the same number sentence; for example, for 40 ÷ 2 \times (4 + 6) = \square, you solve what is in the brackets first then complete the number sentence from left to right as there is no hierarchy between division and multiplication
- Elaboration constructing equivalent number sentences involving brackets and combinations of the 4 operations; explaining the need to have shared agreement on the order of operations when solving problems involving more than one operation to have unique solutions
- Elaboration finding pairs of unknown values in numerical equations that make the equation hold true; for example, listing possible combinations of natural numbers that make this statement true: 6+4\times8\;=\;6\times\bigtriangleup+\square
- Elaboration applying knowledge of inverse operations and number properties to create equivalent number sentences; removing one of the numbers and replacing it with a symbol, then swapping with a classmate to find the unknown values
They identify and explain rules used to create growing patterns.
Content descriptorAC9M6A01 Algebra
recognise and use rules that generate visually growing patterns and number patterns involving rational numbers
Elaborations (5)
- Elaboration investigating patterns such as the number of tiles in a geometric pattern, or the number of dots or other shapes in successive repeats of a strip or border pattern; looking for patterns in the way the numbers increase/decrease
- Elaboration using a calculator or spreadsheet to experiment with number patterns that result from multiplying or dividing; for example, 1 ÷ 9, 2 ÷ 9, 3 ÷ 9…, 210 \times 11, 211 \times 11, 212 \times 11…, 111 \times 11, 222 \times 11, 333 \times 11…, or 100 ÷ 99, 101 ÷ 99, 102 ÷ 99…
- Elaboration creating an extended number sequence that represents an additive pattern using decimals; for example, representing the additive pattern formed as students pay their \$2.50 for an incursion as 2.50, 5.00, 7.50, 10.00, 12.50, 15.00, 17.50 …
- Elaboration investigating the number of regions created by successive folds of a sheet of paper: one fold, 2 regions; 2 folds, 4 regions; 3 folds, 8 regions, and describing the pattern using everyday language
- Elaboration creating a pattern sequence with materials, writing the associated number sequence and then describing the sequence with a rule so someone else can replicate it with different materials; for example, using matchsticks or toothpicks to create a growing pattern of triangles using 3 for one triangle, 5 for 2 triangles, 7 for 3 triangles and describing the pattern as, “Multiply the number of triangles by 2 and then add one for the extra toothpick in the first triangle”
Students create and use algorithms to generate sets of numbers, using a rule.
Content descriptorAC9M6A03 Algebra
create and use algorithms involving a sequence of steps and decisions that use rules to generate sets of numbers; identify, interpret and explain emerging patterns
Elaborations (3)
- Elaboration using an algorithm to create extended number sequences involving rational numbers, using a rule and digital tools, explaining any emerging patterns
- Elaboration designing an algorithm to model operations, using the concept of input and output, describing and explaining relationships and any emerging patterns; for example, using function machines to model operations and recognising and comparing additive and multiplicative relationships
- Elaboration designing an algorithm or writing a simple program to generate a sequence of numbers based on the user’s input and a chosen operation, discussing any emerging patterns; for example, generating a sequence of numbers and comparing how quickly the sequences are growing in comparison to each other using the rule adding 2 to the input number compared to multiplying the input number by 2
They interpret and use timetables.
Content descriptorAC9M6M03 Measurement
interpret and use timetables and itineraries to plan activities and determine the duration of events and journeys
Elaborations (3)
- Elaboration planning a trip involving one or more modes of public transport
- Elaboration developing a timetable of daily activities for a planned event; for example, a sports carnival
- Elaboration investigating different ways duration is represented in timetables and using different timetables to plan a journey
Students convert between common units of length, mass and capacity.
Content descriptorAC9M6M01 Measurement
convert between common metric units of length, mass and capacity; choose and use decimal representations of metric measurements relevant to the context of a problem
Elaborations (3)
- Elaboration recognising the significance of the prefixes in units of measurement
- Elaboration identifying and using the correct operations when converting between units including millimetres, centimetres, metres, kilometres, milligrams, grams, kilograms, tonnes, millilitres, litres, kilolitres and megalitres
- Elaboration recognising the equivalence of measurements, such as 1.25 metres is the same as 125 centimetres
They use the formula for the area of a rectangle and angle properties to solve problems.
Content descriptorAC9M6M02 Measurement
establish the formula for the area of a rectangle and use it to solve practical problems
Elaborations (4)
- Elaboration using one centimetre grid paper to construct a variety of rectangles, recording the side lengths and the related areas of the rectangles in a table to establish the formula for the area of a rectangle by recognising the relationship between the length of the sides and its calculated area
- Elaboration using the relationship between the length and area of square units and the array structure to derive a formula for calculating the area of a rectangle from the lengths of its sides
- Elaboration solving problems involving the comparison of lengths and areas using appropriate units
- Elaboration investigating the connection between the perimeters of different rectangles with the same area and between the areas of rectangles with the same perimeter
Content descriptorAC9M6M04 Measurement
identify the relationships between angles on a straight line, angles at a point and vertically opposite angles; use these to determine unknown angles, communicating reasoning
Elaborations (3)
- Elaboration using protractors or dynamic geometry software to measure and generalise about the size of angles formed when lines are crossed, and combinations of angles that meet at a point, including combinations that form right or straight angles
- Elaboration demonstrating the meaning of language associated with properties of angles, including right, complementary, complement, straight, supplement, vertically opposite, and angles at a point
- Elaboration using the properties of supplementary and complementary angles to represent spatial situations with number sentences and solving to find the size of unknown angles
Students identify the parallel cross-section for right prisms.
Content descriptorAC9M6SP01 Space
compare the parallel cross-sections of objects and recognise their relationships to right prisms
Elaborations (6)
- Elaboration using objects made of foam or polystyrene, slice along different cross-sections, and record the different shapes of faces that result; comparing cross-sections of different objects
- Elaboration using different pieces of fruit, slicing across different cross-sections, drawing the cross-section; reporting back to the class the results of the investigation
- Elaboration observing and drawing the shapes resulting from different ways of slicing through familiar objects; for example, slicing carrots at different angles or cutting through playdough models of objects; using playdough models, fruit or similar to establish which objects can be cut in such a way that the cross-section will always be the same shape
- Elaboration understanding that right prisms are objects where parallel cross-sections to the base of the prism are the same shape and size
- Elaboration connecting different right prisms to the shape of their parallel cross-sections, such as a triangular prism which can be described as a stack of the same sized triangles, and a cube or square prism, which can be described as a stack of the same sized squares
- Elaboration investigating the design of First Nations Australians’ dwellings, exploring the relationship between the cross-sections and the dwellings’ construction
They create tessellating patterns using combinations of transformations.
Content descriptorAC9M6SP03 Space
recognise and use combinations of transformations to create tessellations and other geometric patterns, using dynamic geometric software where appropriate
Elaborations (5)
- Elaboration using digital tools to create tessellations of shapes, including paver and tiling patterns, describing the transformations used and discussing why these shapes tessellate; identifying shapes or combinations of shapes that will or will not tessellate, answering questions such as, “Do all triangles tessellate
- Elaboration designing a school or brand logo using the transformation of one or more shapes and describing the transformations used
- Elaboration using dynamic geometric software and digital tools to experiment with transformations; for example, to demonstrate when the order of transformations produces different results; experimenting with transformations and their application to fractals
- Elaboration designing an algorithm as a set of instructions to transform a shape, including getting back to where you started from; for example, programming a robot to move around the plane using instructions for movements, such as 2 down, 3 to the right, and combinations of these to transform shapes
- Elaboration investigating symmetry, transformation and tessellation in different shapes on Country/Place, including rock formations, insects, and land and sea animals, discussing the purpose or role symmetry plays in their physical structure
Students locate an ordered pair in any one of the 4 quadrants on the Cartesian plane.
Content descriptorAC9M6N01 Number
recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane
Elaborations (5)
- Elaboration extending the number line in the negative direction to locate and represent integers, recognising the difference in location between (-2) and (+2) and their relationship to zero as -2< 0< 2
- Elaboration using integers to represent quantities in financial contexts, including the concept of profit and loss for a planned event
- Elaboration using horizontal and vertical number lines to represent and find solutions to everyday problems involving locating and ordering integers around zero; for example, elevators, above and below sea level; distinguishing a location by referencing to the 4 quadrants of the Cartesian plane
- Elaboration recognising that the sign (positive or negative) indicates a direction in relation to zero; for example, 30 metres left of the admin block is (-30) and 20 metres right of the admin block is (+20); programming robots to move along a number line which is either horizontal or vertical but not both at the same time
- Elaboration representing the temperatures of the different planets in the solar system, using a diagram of a thermometer that models a vertical number line
Content descriptorAC9M6SP02 Space
locate points in the 4 quadrants of a Cartesian plane; describe changes to the coordinates when a point is moved to a different position in the plane
Elaborations (6)
- Elaboration understanding that the Cartesian plane provides a graphical or visual way of describing location with respect to a fixed origin
- Elaboration understanding that the axes are number lines that can have different scales, including fractions and decimals, depending on purpose
- Elaboration understanding that the horizontal coordinate is written first and is changed if there is a move to the left or right, whereas a move up or down will change the vertical coordinate
- Elaboration using the Cartesian plane to draw lines and polygons, listing co-ordinates in the correct order to complete a polygon
- Elaboration exploring how coordinates can be used to input positional data for artificial intelligence systems to locate positions in an image or other two-dimensional space
- Elaboration investigating and connecting land or star maps used by First Nations Australians with the Cartesian plane through a graphical or visual way of describing location
They compare distributions of discrete and continuous numerical and ordinal categorical data sets as part of their statistical investigations, using digital tools.
Content descriptorAC9M6ST01 Statistics
interpret and compare data sets for ordinal and nominal categorical, discrete and continuous numerical variables using comparative displays or visualisations and digital tools; compare distributions in terms of mode, range and shape
Elaborations (4)
- Elaboration determining the range for a numerical data set by finding the difference between the highest and the lowest value in the set and comparing the range for different data sets
- Elaboration representing acquired numerical data sets using side-by-side column graphs, comparing the spread of each data set using the range, the highest frequency for each data set using the mode, and discussing the shape
- Elaboration representing ordinal data collected through surveys, using visualisation tools including dot plots and bar charts, and discussing the distribution of data in terms of shape
- Elaboration using technology to access data sets and graphing software to construct side-by-side column graphs or stacked line graphs; comparing data sets that are grouped by gender, year level, age group or other variables and discussing findings
Content descriptorAC9M6ST03 Statistics
plan and conduct statistical investigations by posing and refining questions or identifying a problem and collecting relevant data; analyse and interpret the data and communicate findings within the context of the investigation
Elaborations (6)
- Elaboration selecting and using appropriate peripherals; for example, using a scientific probe to collect data about changing soil moisture for plants, interpreting the data and sharing the results as a digital chart
- Elaboration using a spreadsheet to record and analyse data, recognising the difference between cell formats in spreadsheets; for example, changing the default general format to numerical, text or date as needed
- Elaboration investigating the daily water usage by a student in the home compared to the World Health Organization claim of 50 litres of clean water allocated per person per day
- Elaboration collecting sample sets of “discrete numerical data”; for example, the number of cars or pets in a household, where the class is surveyed, then other classes are surveyed, and data is analysed and compared, discussing findings
- Elaboration collecting ordinal categorical data through the use of a survey; for example, surveying each member of the class where they are asked to indicate their preference on a five-point scale for a particular graphic and colour combination of a proposed school logo
- Elaboration collecting ordinal data for ranking nominees for school captain with respect to several criteria, contrasting the use of a five-point scale compared with using a four-point scale
Students critique arguments presented in the media based on statistics.
Content descriptorAC9M6ST02 Statistics
identify statistically informed arguments presented in traditional and digital media; discuss and critique methods, data representations and conclusions
Elaborations (4)
- Elaboration investigating data representations in the media and discussing what they illustrate and the messages the people who created them might want to convey
- Elaboration evaluating reports and secondary data relating to the distribution and use of non-renewable resources around the world
- Elaboration identifying potentially misleading data representations in the media; for example, graphs with broken axes or non-linear scales, graphics not drawn to scale, data not related to the population about which the claims are made and pie charts in which the whole pie does not represent the entire population about which the claims are made
- Elaboration investigating both traditional and digital media relating to First Nations Australians, identifying and critiquing statistically informed arguments
They assign probabilities using common fractions, decimal and percentages.
Content descriptorAC9M6P01 Probability
recognise that probabilities lie on numerical scales of 0 – 1 or 0% – 100% and use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimals
Elaborations (6)
- Elaboration recognising that the probability of an event occurring can be represented numerically as either a number ranging from zero to one or a percentage from 0% to 100% where zero or 0% means it won’t happen and one or 100% means it is certain to happen
- Elaboration using a scale of zero to one or 0% to 100% to estimate chances of events
- Elaboration listing the different possible outcomes for rolling a dice and using a scale to locate the relative probability by considering the chance of more or less than for each possible event; for example, the probability of getting a number greater than 4
- Elaboration recognising the language used to describe situations involving uncertainty, such as what it means to be lucky, a 75% chance of rain or a 1-in-100 years flood
- Elaboration exploring how probabilities are used in artificial intelligence for machine learning and decision-making; for example, when choosing a video on a streaming service or travelling in a self-driving autonomous car, where artificial intelligence algorithms estimate the probability of a pedestrian crossing the road, which helps the autonomous car make decisions about when to stop or slow down
- Elaboration exploring First Nations Australian children’s instructive games, such as Weme from the Warlpiri Peoples of Central Australia, to investigate and assign probabilities that events will occur, indicating their estimated likelihood
Students conduct simulations using digital tools, to generate and record the outcomes from many trials of a chance experiment.
Content descriptorAC9M6P02 Probability
conduct repeated chance experiments and run simulations with an increasing number of trials using digital tools; compare observations with expected results and discuss the effect on variation of increasing the number of trials
Elaborations (4)
- Elaboration using digital tools to simulate multiple tosses of a coin or dice and comparing the relative frequency of an outcome as the number of trials increases; identifying the variation between trials and realising that the results tend to the prediction with larger numbers of trials
- Elaboration using online simulations of repeated random events to recognise emerging patterns, discussing and comparing expected results to the actual results
- Elaboration investigating the relative frequencies of all outcomes for a chance experiment and verifying that their sum equals one
- Elaboration systematically recording the outcome of large numbers of spins on a spinner and analysing the relative frequencies of outcomes, representing these as percentages
They compare observed frequencies to the expected frequencies of the outcomes of chance experiments.
Content descriptorAC9M6P02 Probability
conduct repeated chance experiments and run simulations with an increasing number of trials using digital tools; compare observations with expected results and discuss the effect on variation of increasing the number of trials
Elaborations (4)
- Elaboration using digital tools to simulate multiple tosses of a coin or dice and comparing the relative frequency of an outcome as the number of trials increases; identifying the variation between trials and realising that the results tend to the prediction with larger numbers of trials
- Elaboration using online simulations of repeated random events to recognise emerging patterns, discussing and comparing expected results to the actual results
- Elaboration investigating the relative frequencies of all outcomes for a chance experiment and verifying that their sum equals one
- Elaboration systematically recording the outcome of large numbers of spins on a spinner and analysing the relative frequencies of outcomes, representing these as percentages
This achievement standard describes the expected learning for Year 6 Mathematics. Use it to plan teaching and assessment with the Australian Curriculum v9.
At a Glance
| Strand | Substrand | CDs | Elaborations |
|---|---|---|---|
| Algebra | — | 3 | 12 |
| Measurement | — | 4 | 13 |
| Number | — | 9 | 39 |
| Probability | — | 2 | 10 |
| Space | — | 3 | 17 |
| Statistics | — | 3 | 14 |
| Total | 24 | 105 | |