Year 8 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 8, students recognise irrational numbers and terminating or recurring decimals. They apply the exponent laws to calculations with numbers involving positive integer exponents. Students solve problems involving the 4 operations with integers and positive rational numbers. They use mathematical modelling to solve practical problems involving ratios, percentages and rates in measurement and financial contexts. Students apply algebraic properties to rearrange, expand and factorise linear expressions. They graph linear relations and solve linear equations with rational solutions and one-variable inequalities, graphically and algebraically. Students use mathematical modelling to solve problems using linear relations, interpreting and reviewing the model in context. They make and test conjectures involving linear relations using digital tools.
Students use appropriate metric units when solving measurement problems involving the perimeter and area of composite shapes, and volume of right prisms. They use Pythagoras’ theorem to solve measurement problems involving unknown lengths of right-angle triangles. Students use formulas to solve problems involving the area and circumference of circles. They solve problems of duration involving 12- and 24-hour cycles across multiple time zones. Students use 3 dimensions to locate and describe position. They identify conditions for congruency and similarity in shapes and create and test algorithms designed to test for congruency and similarity. Students apply the properties of quadrilaterals to solve problems.
They conduct statistical investigations and explain the implications of obtaining data through sampling. Students analyse and describe the distribution of data. They compare the variation in distributions of random samples of the same and different size from a given population with respect to shape, measures of central tendency and range. Students represent the possible combinations of 2 events with tables and diagrams, and determine related probabilities to solve practical problems. They conduct experiments and simulations using digital tools to determine related probabilities of compound events.
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 8, students recognise irrational numbers and terminating or recurring decimals.
Content descriptorAC9M8M03 Measurement
solve problems involving the circumference and area of a circle using formulas and appropriate units
Elaborations (4)
- Elaboration deducing that the area of a circle is between 2 radius squares and 4 radius squares, and using 3\timesradius^2 as a rough estimate for the area of a circle
- Elaboration investigating the area of circles using a square grid or by rearranging a circle divided into smaller and smaller sectors or slices to resemble a close approximation of a rectangle
- Elaboration applying the formulas for the area and circumference of a circle to solve practical problems, and using one of the measures of radius, diameter, circumference or area to deduce the value of the other measures; for example, determining the length of material needed to edge a round table, given its dimensions as the area of the tabletop
- Elaboration exploring traditional weaving designs by First Nations Australians and investigating the significance and use of circles
Content descriptorAC9M8N01 Number
recognise irrational numbers in applied contexts, including square roots and π
Elaborations (4)
- Elaboration recognising that the real number system includes irrational numbers which can be approximately located on the real number line; for example, the value of π lies somewhere between 3.141 and 3.142 that is, 3.141 < π < 3.142
- Elaboration using digital tools to systematically explore contexts or situations that use irrational numbers, such as finding the length of the hypotenuse in a right-angled triangle with the other 2 sides having lengths of one metre or 2 metres and one metre; or given the area of a square, finding the length of the side where the result is irrational; or finding ratios involved with the side lengths of paper sizes A0, A1, A2, A3 and A4
- Elaboration investigating the golden ratio in art and design, and historical approximations to π in different societies
- Elaboration connecting the ratio between the circumference and diameter of any circle to the irrational value of π using circular objects and string or dynamic drawing software
Content descriptorAC9M8N03 Number
recognise terminating and recurring decimals, using digital tools as appropriate
Elaborations (2)
- Elaboration identifying when a fraction has a terminating decimal expansion from the prime factorisation of its denominator; for example, 7/24\;=\;0.291\overset\_6 does not have a terminating decimal expansion, while 7/25\;=\;0.28 does
- Elaboration identifying terminating, recurring and non-terminating decimals and choosing their appropriate representations such as 1/3 is represented as 0.\overset\_3
They apply the exponent laws to calculations with numbers involving positive integer exponents.
Content descriptorAC9M8N02 Number
establish and apply the exponent laws with positive integer exponents and the zero-exponent, using exponent notation with numbers
Elaborations (4)
- Elaboration recognising the connection between exponent form and expanded form with the exponent laws of product of powers rule, quotient of powers rule, and power of a power rule; for example, 2^3\times2^2 can be represented as (2\times2\times2)\times(2\times2)=2^5 and connecting the result to the addition of exponents
- Elaboration applying the exponent laws of the product of powers rule, quotient of powers rule, power of a power rule and zero exponent individually and in combination; for example, using exponents to determine the effect on the volume of a 2 centimetre cube when the cube is enlarged to a 6 centimetre cube, 6^3/2^3\;=\;2^3\times3^3/2^3\;=\;3^3, so the volume is increased by a factor of 27
- Elaboration using digital tools to systematically explore the application of the exponent laws; observing that the bases need to be the same
- Elaboration using examples such as 3^4/3^4\;=\;1, and 3^{4-4}\;=\;3^0 to illustrate the necessity that for any non-zero natural number n,\;n^0\;=\;1
Students solve problems involving the 4 operations with integers and positive rational numbers.
Content descriptorAC9M8N04 Number
use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate
Elaborations (3)
- Elaboration using patterns to assist in establishing the rules for the multiplication and division of integers
- Elaboration applying and explaining efficient strategies such as using the commutative or associative property for regrouping, partitioning, place value, patterning, multiplication or division facts to solve problems involving positive and negative integers, fractions and decimals
- Elaboration recognising the effect of sign in the multiplication of integers; for example, (-1)^4\;=\;1 and (-1)^5\;= -1
They use mathematical modelling to solve practical problems involving ratios, percentages and rates in measurement and financial contexts.
Content descriptorAC9M8M05 Measurement
recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure
Elaborations (5)
- Elaboration identifying examples of rates in the real world, including constant rates, rate of pay, cost per kilogram, recipes, simple interest and average rates
- Elaboration applying rates to solve problems involving the conversion between different units of measure; for example, using a conversion rate to convert distances from miles into kilometres; using currency exchange rates to determine the price of items
- Elaboration applying rates to calculate solutions to problems in different contexts; for example, required run rates in cricket, dilution of concentrated chemicals and comparing the petrol consumption rates of different vehicles
- Elaboration using taxation tables to calculate an individual's annual income tax
- Elaboration investigating the application of rates in First Nation Australians’ land management practices, including the rate of fire spread under different environmental conditions such as fuel types, wind speed, temperature and relative humidity; the conservation of water by First Nations Australians by estimating rates of water evaporation based on surface area and climatic conditions
Content descriptorAC9M8M07 Measurement
use mathematical modelling to solve practical problems involving ratios and rates, including financial contexts; formulate problems; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model
Elaborations (5)
- Elaboration modelling and solving problems related to situations such as scales on maps and plans, the mixing of chemicals or ingredients, or calculating magnification factors applying relevant ratios and proportions
- Elaboration modelling problems involving converting money amounts using different exchange rates and applying them when planning and budgeting for overseas travel
- Elaboration modelling situations involving financial contexts; for example, income tax, using taxation rates on annual income, comparing different taxation brackets and rates of pay; comparing the benefits of different phone plans using different call rates and associated fees to determine the best plan
- Elaboration modelling situations involving the use of ratios in radiocarbon dating methods, including the ratio of carbon-14 to carbon-12 isotopes in organisms, to measure dates of First Peoples of Australia’s habitation on the Australian continent
- Elaboration modelling situations involving ratio and its application in the making of string and cordage by First Nations Australians, including the ratio of length to the mass of a rope, the strength of the ply in proportion to a rope’s pulling force, and the proportion of fibre for the length of string required
Content descriptorAC9M8N04 Number
use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate
Elaborations (3)
- Elaboration using patterns to assist in establishing the rules for the multiplication and division of integers
- Elaboration applying and explaining efficient strategies such as using the commutative or associative property for regrouping, partitioning, place value, patterning, multiplication or division facts to solve problems involving positive and negative integers, fractions and decimals
- Elaboration recognising the effect of sign in the multiplication of integers; for example, (-1)^4\;=\;1 and (-1)^5\;= -1
Content descriptorAC9M8N05 Number
use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; formulate problems, choosing efficient calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model
Elaborations (4)
- Elaboration modelling situations involving weather and environmental contexts including temperature or sea depths by applying operations to positive and negative rational numbers; for example, involving average temperature increases and decreases
- Elaboration modelling situations that involve percentage increases or decreases and explaining why it is an increase or decrease, such as mark-ups, discounts, Goods and Services Tax, changes in populations or recycling rates
- Elaboration modelling situations involving personal income tax, interpreting tax tables to determine income tax at various levels of income, including overall percentage of income allocated to tax
- Elaboration modelling situations involving percentage increase or decrease such as market trends, effects on population, or effects on the environment over extended time periods
Students apply algebraic properties to rearrange, expand and factorise linear expressions.
Content descriptorAC9M8A01 Algebra
create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties
Elaborations (3)
- Elaboration rearranging and simplifying linear expressions involving variables with integer coefficients and constants; using manipulatives such as algebra tiles to support calculations; for example, using manipulatives to demonstrate that 2x+4\;=\;2(x+2),\;3(a-b)=3a -3b, or 5(m+2n)+3m-4n\;=\;5m+10n+3m-4n\;=\;8m+6n
- Elaboration demonstrating the relationship between factorising and expanding linear expressions using manipulatives, such as algebra tiles or area models, and describing with mathematical language
- Elaboration using the distributive, associative, commutative, identity and inverse properties to expand and factorise algebraic expressions using strategies such as the area model
They graph linear relations and solve linear equations with rational solutions and one-variable inequalities, graphically and algebraically.
Content descriptorAC9M8A02 Algebra
graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution
Elaborations (6)
- Elaboration recognising that in a table of values, if the first difference between consecutive values of the dependent variable is constant, then it is a linear relation
- Elaboration graphing linear functions and relations of the form x\;=\;a,\;y\;=\;a,\;x\;\leq\;a,\;x\;>\;a,\;y\leq\;a,\;y>\;a on the Cartesian plane for known values of a
- Elaboration completing a table of values, plotting the resulting points on the Cartesian plane and determining whether the relationship is linear
- Elaboration graphing the linear relationship ax+b\;=\;c for given values of a, b and c and identifying from the graph where ax+b\;<\;c or where ax+b\;>\;c
- Elaboration solving linear equations of the form ax+b\;=\;c and one-variable inequalities of the form ax+b\;<\;c or ax+b\;>\;c where a>0 using inverse operations and digital tools, and checking solutions by substitution
- Elaboration solving linear equations such as 3x+7\;=\;6x-9, representing these graphically, and verifying solutions by substitution
Students use mathematical modelling to solve problems using linear relations, interpreting and reviewing the model in context.
Content descriptorAC9M8A01 Algebra
create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties
Elaborations (3)
- Elaboration rearranging and simplifying linear expressions involving variables with integer coefficients and constants; using manipulatives such as algebra tiles to support calculations; for example, using manipulatives to demonstrate that 2x+4\;=\;2(x+2),\;3(a-b)=3a -3b, or 5(m+2n)+3m-4n\;=\;5m+10n+3m-4n\;=\;8m+6n
- Elaboration demonstrating the relationship between factorising and expanding linear expressions using manipulatives, such as algebra tiles or area models, and describing with mathematical language
- Elaboration using the distributive, associative, commutative, identity and inverse properties to expand and factorise algebraic expressions using strategies such as the area model
Content descriptorAC9M8A02 Algebra
graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution
Elaborations (6)
- Elaboration recognising that in a table of values, if the first difference between consecutive values of the dependent variable is constant, then it is a linear relation
- Elaboration graphing linear functions and relations of the form x\;=\;a,\;y\;=\;a,\;x\;\leq\;a,\;x\;>\;a,\;y\leq\;a,\;y>\;a on the Cartesian plane for known values of a
- Elaboration completing a table of values, plotting the resulting points on the Cartesian plane and determining whether the relationship is linear
- Elaboration graphing the linear relationship ax+b\;=\;c for given values of a, b and c and identifying from the graph where ax+b\;<\;c or where ax+b\;>\;c
- Elaboration solving linear equations of the form ax+b\;=\;c and one-variable inequalities of the form ax+b\;<\;c or ax+b\;>\;c where a>0 using inverse operations and digital tools, and checking solutions by substitution
- Elaboration solving linear equations such as 3x+7\;=\;6x-9, representing these graphically, and verifying solutions by substitution
Content descriptorAC9M8A03 Algebra
use mathematical modelling to solve applied problems involving linear relations, including financial contexts; formulate problems with linear functions, choosing a representation; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model
Elaborations (4)
- Elaboration modelling situations involving linear functions, including practical contexts such as taxi fares involving flag fall fees, motion in a straight line at a constant speed, trade quotes involving call out fees, cooking that includes resting or cooling times, or water leakage from water tanks, interpreting the constant rate of change and initial value in context, and identifying when values of a model lie within a given range
- Elaboration modelling problems in practical situations and interpreting solutions within the context of the problem, including giving attention to all units of measure and whether results are suitable; for example, once a water tank is empty no more water can flow from it
- Elaboration modelling financial problems involving pay rates, using a table of values to represent the pay amounts and hours worked using an hourly rate of pay, and graphing the relationship to make inferences
- Elaboration modelling patterns on Country/Place and exploring their connections and meaning to linear equations, using the model as a predictive tool and critiquing results by connecting back to Country/Place
They make and test conjectures involving linear relations using digital tools.
Content descriptorAC9M8A02 Algebra
graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution
Elaborations (6)
- Elaboration recognising that in a table of values, if the first difference between consecutive values of the dependent variable is constant, then it is a linear relation
- Elaboration graphing linear functions and relations of the form x\;=\;a,\;y\;=\;a,\;x\;\leq\;a,\;x\;>\;a,\;y\leq\;a,\;y>\;a on the Cartesian plane for known values of a
- Elaboration completing a table of values, plotting the resulting points on the Cartesian plane and determining whether the relationship is linear
- Elaboration graphing the linear relationship ax+b\;=\;c for given values of a, b and c and identifying from the graph where ax+b\;<\;c or where ax+b\;>\;c
- Elaboration solving linear equations of the form ax+b\;=\;c and one-variable inequalities of the form ax+b\;<\;c or ax+b\;>\;c where a>0 using inverse operations and digital tools, and checking solutions by substitution
- Elaboration solving linear equations such as 3x+7\;=\;6x-9, representing these graphically, and verifying solutions by substitution
Content descriptorAC9M8A04 Algebra
experiment with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patterns
Elaborations (4)
- Elaboration using graphing software to investigate the effect of systematically varying parameters of linear functions on the corresponding graphs, making and testing conjectures; for example, making a conjecture that if the co-efficient of x is negative, then the line will slope down from left to right
- Elaboration using graphing software to systematically contrast the graphs of y\;=\;2x, -y\;=\;2x, y\;=\;-2x and -y\;=\;-2x with those of y<2x, -y<2x, y<-2x and -y<-2x and those of y>2x, -y>2x, y>-2x and -y>-2x, making and testing conjectures about sign and direction of the inequality
- Elaboration using digital tools to investigate integer solutions to equations such as 2x+3y\;=\;48
- Elaboration exploring how linear functions are used in linear regression models as a statistical technique in machine learning of artificial intelligence agents; for example, linear functions are used to model the relationship between input variables and a target variable, to predict stock or house prices in the financial and real-estate sectors
Students use appropriate metric units when solving measurement problems involving the perimeter and area of composite shapes, and volume of right prisms.
Content descriptorAC9M8M01 Measurement
solve problems involving the area and perimeter of irregular and composite shapes using appropriate units
Elaborations (3)
- Elaboration determining the area of composite shapes by composing or decomposing shapes
- Elaboration using arrays and rectangles to approximate the area of irregular shapes in situations such as a council needing to work out how much mosquito spray to use for a swamp area or a farmer needing to work out how much seed, fertilizer and herbicide are required to cover a paddock
- Elaboration determining the perimeter and area of irregular shapes by sums of increasingly accurate covering measurements, such as line segments and grids; for example, using millimetres or square millimetres as opposed to centimetres or square centimetres
Content descriptorAC9M8M02 Measurement
solve problems involving the volume and capacity of right prisms using appropriate units
Elaborations (4)
- Elaboration using models to demonstrate the number of cubic centimetres in a cubic metre and relating this to capacities of millilitres and litres, recognising that one millilitre is equivalent to one cm^3
- Elaboration solving practical problems involving volume and capacity; for example, optimal packaging and production
- Elaboration choosing which measurements are useful to consider when solving practical problems in context; for example, when purchasing a new washing machine, the dimensions are useful when determining whether it will fit in the available space in the laundry and its capacity is useful when considering the maximum washing load it can carry
- Elaboration investigating, reasoning and finding solutions to measurement problems involving dimensions, rates, volume and capacity of objects; for example, given the dimensions of a pool and the rate of flow from a tap, determining how long it will take to fill the pool to its normal capacity
Content descriptorAC9M8N04 Number
use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate
Elaborations (3)
- Elaboration using patterns to assist in establishing the rules for the multiplication and division of integers
- Elaboration applying and explaining efficient strategies such as using the commutative or associative property for regrouping, partitioning, place value, patterning, multiplication or division facts to solve problems involving positive and negative integers, fractions and decimals
- Elaboration recognising the effect of sign in the multiplication of integers; for example, (-1)^4\;=\;1 and (-1)^5\;= -1
They use Pythagoras’ theorem to solve measurement problems involving unknown lengths of right-angle triangles.
Content descriptorAC9M8M06 Measurement
use Pythagoras’ theorem to solve problems involving the side lengths of right-angled triangles
Elaborations (5)
- Elaboration discussing and comparing different applications, demonstrations and proofs of Pythagoras’ theorem, from Egypt and Mesopotamia, Greece, India and China with other historical and contemporary applications and proofs
- Elaboration using Pythagoras’ theorem to determine unknown lengths of sides in right-angled triangles and finding lengths of sides of right-angled triangles in practical applications
- Elaboration recognising the relationship between the squares of lengths of sides for different types of triangles: right-angled, acute or obtuse
- Elaboration identifying Pythagorean triples, such as (3,4,5), (5,12,13), (7, 24, 25) and (8,15, 17)
- Elaboration investigating how Pythagoras' theorem can be applied to determine the distance between two points in the plane, and how this can be used by predictive algorithms to navigate autonomous vehicles
Students use formulas to solve problems involving the area and circumference of circles.
Content descriptorAC9M8M03 Measurement
solve problems involving the circumference and area of a circle using formulas and appropriate units
Elaborations (4)
- Elaboration deducing that the area of a circle is between 2 radius squares and 4 radius squares, and using 3\timesradius^2 as a rough estimate for the area of a circle
- Elaboration investigating the area of circles using a square grid or by rearranging a circle divided into smaller and smaller sectors or slices to resemble a close approximation of a rectangle
- Elaboration applying the formulas for the area and circumference of a circle to solve practical problems, and using one of the measures of radius, diameter, circumference or area to deduce the value of the other measures; for example, determining the length of material needed to edge a round table, given its dimensions as the area of the tabletop
- Elaboration exploring traditional weaving designs by First Nations Australians and investigating the significance and use of circles
Content descriptorAC9M8N04 Number
use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate
Elaborations (3)
- Elaboration using patterns to assist in establishing the rules for the multiplication and division of integers
- Elaboration applying and explaining efficient strategies such as using the commutative or associative property for regrouping, partitioning, place value, patterning, multiplication or division facts to solve problems involving positive and negative integers, fractions and decimals
- Elaboration recognising the effect of sign in the multiplication of integers; for example, (-1)^4\;=\;1 and (-1)^5\;= -1
They solve problems of duration involving 12- and 24-hour cycles across multiple time zones.
Content descriptorAC9M8M04 Measurement
solve problems involving duration, including using 12- and 24-hour time across multiple time zones
Elaborations (3)
- Elaboration using digital tools to investigate time zones around the world and convert from one zone to another, such as time in Perth, Western Australia compared to Suva in Fiji or Toronto in Canada
- Elaboration recognising the challenges of planning regular virtual meeting times for a company that has both international staff and staff within different states and territories, and the impact daylight savings has due to multiple time zones, explaining the mathematical language used to communicate current time such as Coordinated Universal Time (UTC)+8, AEST, ACST and AWST
- Elaboration planning an international travel itinerary that covers destinations in different time zones across Asia
Students use 3 dimensions to locate and describe position.
Content descriptorAC9M8SP03 Space
describe the position and location of objects in 3 dimensions in different ways, including using a three-dimensional coordinate system with the use of dynamic geometric software and other digital tools
Elaborations (6)
- Elaboration locating aircraft/drones using latitude, longitude and altitude as a three-dimensional coordinate system
- Elaboration constructing three-dimensional objects using 3D printers or designing software that uses a three-dimensional coordinate system
- Elaboration comparing and contrasting two-dimensional and three-dimensional coordinate systems by highlighting what is the same and what is different, including virtual maps versus street views
- Elaboration using dynamic geometry software to construct shapes and objects within the first octant of a three-dimensional coordinate system
- Elaboration interpreting three-dimensional coordinate locations for objects in multi-storey car parks; playing games based on three-dimensional coordinate systems such as three-dimensional Noughts and Crosses (Tic-Tac-Toe)
- Elaboration exploring position and transformation through geospatial technologies used by First Nations Australians’ communities
They identify conditions for congruency and similarity in shapes and create and test algorithms designed to test for congruency and similarity.
Content descriptorAC9M8SP01 Space
identify the conditions for congruence and similarity of triangles and explain the conditions for other sets of common shapes to be congruent or similar, including those formed by transformations
Elaborations (6)
- Elaboration developing an understanding of what it means for shapes to be congruent or similar
- Elaboration using the enlargement transformation and digital tools to develop sets of similar shapes
- Elaboration investigating sufficient conditions to establish that 2 triangles are congruent
- Elaboration applying logical reasoning and tests for congruence and similarity, to problems and proofs involving plane shapes
- Elaboration comparing angle and side measurements of shapes under transformation to answer questions such as “What changes?” and “What stays the same?”
- Elaboration establishing that 2 shapes are congruent if one lies exactly on top of the other after one or more transformations including translations, reflections and rotations, and recognising that the matching sides and the matching angles are equal
Content descriptorAC9M8SP04 Space
design, create and test algorithms involving a sequence of steps and decisions that identify congruency or similarity of shapes, and describe how the algorithm works
Elaborations (3)
- Elaboration listing the properties or criteria necessary to determine if shapes are similar or congruent
- Elaboration using the conditions for congruence of triangles and similarity of triangles to develop a sorting algorithm; for example, creating a flow chart
- Elaboration evaluating algorithms for accuracy in classifying and distinguishing between similar and congruent triangles
Students apply the properties of quadrilaterals to solve problems.
Content descriptorAC9M8SP02 Space
establish properties of quadrilaterals using congruent triangles and angle properties, and solve related problems explaining reasoning
Elaborations (3)
- Elaboration establishing the properties of squares, rectangles, parallelograms, rhombuses, trapeziums and kites using geometric properties and proof, such as the sum of the exterior angles of a polygon is equal to a complete turn or 360°
- Elaboration identifying properties of quadrilaterals related to side lengths, parallel sides, angles, diagonals and symmetry
- Elaboration applying the properties of triangles and quadrilaterals to construction designs such as car jacks, scissor lifts, folding umbrellas, toolboxes and cherry pickers
They conduct statistical investigations and explain the implications of obtaining data through sampling.
Content descriptorAC9M8ST01 Statistics
investigate techniques for data collection including census, sampling, experiment and observation, and explain the practicalities and implications of obtaining data through these techniques
Elaborations (5)
- Elaboration identifying situations where data can be collected by census and those where a sample is appropriate
- Elaboration investigating the practicalities and implications of obtaining data through sampling, using a variety of investigative processes; for example, investigating situations when random sampling or non-random sampling is used to collect data and the implication of each sampling method
- Elaboration discussing how observations, experiments and sampling methods can be impacted by bias; for example, recognising that a sampling bias occurs when certain members of a population are more likely to be selected in a sample than others, such as a survey conducted at a shopping centre; recognising that environmental conditions may bias the results of scientific investigations if experiments are conducted at different times or under different conditions
- Elaboration using digital tools such as simulations and digital measuring devices to observe, measure and record qualitative and quantitative data, discussing precision and the implications of error
- Elaboration investigating how decisions concerning sampling relate to the training of artificial intelligence systems, recognising the need to mitigate any potential bias that may lead to the development of biased models
Content descriptorAC9M8ST02 Statistics
analyse and report on the distribution of data from primary and secondary sources using random and non-random sampling techniques to select and study samples
Elaborations (4)
- Elaboration investigating different methods of sampling used to collect data, considering the source and size of samples
- Elaboration comparing the sampling methods of simple random, systematic, stratified, quota, clustered or convenience, or judgement, and discussing the reliability of conclusions about the context that could be drawn
- Elaboration defining and distinguishing between probabilistic terms such as random, sample space, sample and sample distribution
- Elaboration investigating primary and secondary data sources relating to reconciliation between First Nations Australians and non-Indigenous Australians, analysing and reporting on findings
Content descriptorAC9M8ST03 Statistics
compare variations in distributions and proportions obtained from random samples of the same size drawn from a population and recognise the effect of sample size on this variation
Elaborations (6)
- Elaboration comparing the proportion of students in favour of a proposal for a change in school uniform between different random samples of 50 students from the school population
- Elaboration using digital tools to simulate repeated sampling of the same population, such as heights or arm spans of students, recording and comparing means, median and range of data between samples
- Elaboration using relative frequencies from historical data to predict proportions and the likely number of outcomes in situations such as weather forecasting or the countries of origin of visitors to tourist attractions
- Elaboration investigating the effect that adding or removing data from a data set has on measures of central tendency and spread
- Elaboration investigating First Nations Ranger Groups and other groups’ use of sampling techniques to track biodiversity of species
- Elaboration exploring how the comparison of variations in distributions and proportions from the same population applies to data-driven decision-making and how this relates to training of artificial intelligence systems
Content descriptorAC9M8ST04 Statistics
plan and conduct statistical investigations involving samples of a population; use ethical and fair methods to make inferences about the population and report findings, acknowledging uncertainty
Elaborations (3)
- Elaboration using data such as electricity consumption to draw conclusions about the impacts of events, such as pandemics, on households or business
- Elaboration identifying situations where the collection of data from a sample is necessary due to efficiency, cost or restricted time for collection of data, and sufficiently reliable for making inferences about a population
- Elaboration exploring progress in reconciliation between First Nations Australians and non-Indigenous Australians, investigating and evaluating sampling techniques and methods to gather relevant data to measure progress
Students analyse and describe the distribution of data.
Content descriptorAC9M8ST02 Statistics
analyse and report on the distribution of data from primary and secondary sources using random and non-random sampling techniques to select and study samples
Elaborations (4)
- Elaboration investigating different methods of sampling used to collect data, considering the source and size of samples
- Elaboration comparing the sampling methods of simple random, systematic, stratified, quota, clustered or convenience, or judgement, and discussing the reliability of conclusions about the context that could be drawn
- Elaboration defining and distinguishing between probabilistic terms such as random, sample space, sample and sample distribution
- Elaboration investigating primary and secondary data sources relating to reconciliation between First Nations Australians and non-Indigenous Australians, analysing and reporting on findings
They compare the variation in distributions of random samples of the same and different size from a given population with respect to shape, measures of central tendency and range.
Content descriptorAC9M8ST03 Statistics
compare variations in distributions and proportions obtained from random samples of the same size drawn from a population and recognise the effect of sample size on this variation
Elaborations (6)
- Elaboration comparing the proportion of students in favour of a proposal for a change in school uniform between different random samples of 50 students from the school population
- Elaboration using digital tools to simulate repeated sampling of the same population, such as heights or arm spans of students, recording and comparing means, median and range of data between samples
- Elaboration using relative frequencies from historical data to predict proportions and the likely number of outcomes in situations such as weather forecasting or the countries of origin of visitors to tourist attractions
- Elaboration investigating the effect that adding or removing data from a data set has on measures of central tendency and spread
- Elaboration investigating First Nations Ranger Groups and other groups’ use of sampling techniques to track biodiversity of species
- Elaboration exploring how the comparison of variations in distributions and proportions from the same population applies to data-driven decision-making and how this relates to training of artificial intelligence systems
Students represent the possible combinations of 2 events with tables and diagrams, and determine related probabilities to solve practical problems.
Content descriptorAC9M8P01 Probability
recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts
Elaborations (4)
- Elaboration understanding that knowing the probability of an event allows the probability of its complement to be found, including for those events that are not equally likely, such as getting a specific novelty toy in a supermarket promotion
- Elaboration using the relationship that for a single event A, Pr(A)+Pr(\;not\;A)\;=\;1; for example, if the probability that it rains on a particular day is 80\%, the probability that it does not rain on that day is 20\%, or the probability of not getting a 6 on a single roll of a fair dice is 1-1/6=5/6
- Elaboration using the sum of probabilities to solve problems, such as the probability of starting a game by throwing a 5 or 6 on a dice is 1/3 and probability of not throwing a 5 or 6 is 2/3
- Elaboration investigating how various applications of artificial intelligence use the probability of complementary events when assessing the likelihood of favourable and unfavourable outcomes and making informed decisions based on these probabilities; for example, in binary classification problems where data is classified into one of two categories, such as spam or not spam, fraud or not fraud
Content descriptorAC9M8P02 Probability
determine all possible combinations for 2 events, using two-way tables, tree diagrams and Venn diagrams, and use these to determine probabilities of specific outcomes in practical situations
Elaborations (4)
- Elaboration describing events using language of “at least”, exclusive “or” (A or B but not both), inclusive “or” (A or B or both) and “and”
- Elaboration using the relation Pr(A\;and\;B)+Pr(A\;and\;not\;B)+Pr(not\;A\;and\;B)+Pr(not\;A\;and\;not\;B)=\;1 to calculate probabilities, including the special case of mutually exclusive events where Pr(A\;and\;B)\;=\;0
- Elaboration using Venn diagrams or two-way tables to demonstrate the difference between events that are mutually exclusive, such as whether a coin toss will land on a head or a tail, or those that are not mutually exclusive, such as people who have blonde hair and people who have blue eyes
- Elaboration exploring First Nations Australian children’s instructive games; for example, Battendi from the Ngarrindjeri Peoples of Lake Murray and Lake Albert in southern Australia, applying possible combinations and relationships and calculating probabilities using two-way tables and Venn diagrams
They conduct experiments and simulations using digital tools to determine related probabilities of compound events.
Content descriptorAC9M8P01 Probability
recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts
Elaborations (4)
- Elaboration understanding that knowing the probability of an event allows the probability of its complement to be found, including for those events that are not equally likely, such as getting a specific novelty toy in a supermarket promotion
- Elaboration using the relationship that for a single event A, Pr(A)+Pr(\;not\;A)\;=\;1; for example, if the probability that it rains on a particular day is 80\%, the probability that it does not rain on that day is 20\%, or the probability of not getting a 6 on a single roll of a fair dice is 1-1/6=5/6
- Elaboration using the sum of probabilities to solve problems, such as the probability of starting a game by throwing a 5 or 6 on a dice is 1/3 and probability of not throwing a 5 or 6 is 2/3
- Elaboration investigating how various applications of artificial intelligence use the probability of complementary events when assessing the likelihood of favourable and unfavourable outcomes and making informed decisions based on these probabilities; for example, in binary classification problems where data is classified into one of two categories, such as spam or not spam, fraud or not fraud
Content descriptorAC9M8P02 Probability
determine all possible combinations for 2 events, using two-way tables, tree diagrams and Venn diagrams, and use these to determine probabilities of specific outcomes in practical situations
Elaborations (4)
- Elaboration describing events using language of “at least”, exclusive “or” (A or B but not both), inclusive “or” (A or B or both) and “and”
- Elaboration using the relation Pr(A\;and\;B)+Pr(A\;and\;not\;B)+Pr(not\;A\;and\;B)+Pr(not\;A\;and\;not\;B)=\;1 to calculate probabilities, including the special case of mutually exclusive events where Pr(A\;and\;B)\;=\;0
- Elaboration using Venn diagrams or two-way tables to demonstrate the difference between events that are mutually exclusive, such as whether a coin toss will land on a head or a tail, or those that are not mutually exclusive, such as people who have blonde hair and people who have blue eyes
- Elaboration exploring First Nations Australian children’s instructive games; for example, Battendi from the Ngarrindjeri Peoples of Lake Murray and Lake Albert in southern Australia, applying possible combinations and relationships and calculating probabilities using two-way tables and Venn diagrams
Content descriptorAC9M8P03 Probability
conduct repeated chance experiments and simulations, using digital tools to determine probabilities for compound events, and describe results
Elaborations (3)
- Elaboration using digital tools, including generative artificial intelligence, to conduct probability simulations involving compound events
- Elaboration using a random number generator and digital tools, including generative artificial intelligence, to simulate rolling 2 dice and calculating the difference between them, investigating what difference is likely to occur more often
- Elaboration using online simulation software to conduct probability simulations to determine in the long run if events are complementary
This achievement standard describes the expected learning for Year 8 Mathematics. Use it to plan teaching and assessment with the Australian Curriculum v9.
At a Glance
| Strand | Substrand | CDs | Elaborations |
|---|---|---|---|
| Algebra | — | 4 | 17 |
| Measurement | — | 7 | 29 |
| Number | — | 5 | 17 |
| Probability | — | 3 | 11 |
| Space | — | 4 | 18 |
| Statistics | — | 4 | 18 |
| Total | 27 | 110 | |