1. Content descriptors
The descriptors span Number, Algebra, Measurement, Space, Statistics and Probability and identify the mathematics students need opportunities to learn.
Australian Curriculum v9
Year 10 Mathematics Curriculum: Achievement Standard and Content Descriptors
Bring the Year 10 Mathematics achievement standard and its 21 linked content descriptors into one planning view. The strand groups make it easier to balance mathematical knowledge, fluency, reasoning and problem solving across a teaching program.
Available combined curriculum hubs
Browse published Mathematics curriculum maps.
All Mathematics achievement standards | All Mathematics content descriptors
How the curriculum elements fit together
2. Learning and assessment
A coherent program revisits important concepts through connected problems rather than treating each descriptor as a separate lesson.
3. Achievement standard
Use a varied body of evidence that shows students selecting, applying and communicating mathematics in familiar and unfamiliar situations.
ASMATY10
Open the standalone ASMATY10 page →
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 10, students recognise the effect of approximations of real numbers in repeated calculations. They use mathematical modelling to solve problems involving growth and decay in financial and other applied situations, applying linear, quadratic and exponential functions as appropriate, and solve related equations, numerically and graphically. Students make and test conjectures involving functions and relations using digital tools. They solve problems involving simultaneous linear equations and linear inequalities in 2 variables graphically and justify solutions.
Students interpret and use logarithmic scales representing small or large quantities or change in applied contexts. They solve measurement problems involving surface area and volume of composite objects. Students apply Pythagoras’ theorem and trigonometry to solve practical problems involving right-angled triangles. They identify the impact of measurement errors on the accuracy of results. Students use mathematical modelling to solve practical problems involving proportion and scaling, evaluating and modifying models, and reporting assumptions, methods and findings. They use deductive reasoning, theorems and algorithms to solve spatial problems. Students interpret networks used to represent practical situations and describe connectedness.
They plan and conduct statistical investigations involving bivariate data. Students represent the distribution of data involving 2 variables, using tables and scatter plots, and comment on possible association. They analyse inferences and conclusions in the media, noting potential sources of bias. Students compare the distribution of continuous numerical data, using various displays, and discuss distributions in terms of centre, spread, shape and outliers. They apply conditional probability to solve problems involving compound events. Students design and conduct simulations involving conditional probability, using digital tools.
The 17 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 10, students recognise the effect of approximations of real numbers in repeated calculations.
Content descriptorAC9M10M03 Measurement
solve practical problems applying Pythagoras’ theorem and trigonometry of right-angled triangles, including problems involving direction and angles of elevation and depression
Elaborations (6)
- Elaboration applying right-angled trigonometry to solve navigation problems involving bearings; for example, determining the bearing and estimating the distance of the final leg of an orienteering course
- Elaboration applying Pythagoras’ theorem and trigonometry to problems in surveying and design, where three-dimensional problems are decomposed into two-dimensional problems; for example, investigating the dimensions of the smallest box needed to package an object of a particular length
- Elaboration using a clinometer to measure angles of inclination, and applying trigonometry, and proportional reasoning to determine the height of buildings in practical contexts
- Elaboration applying Pythagoras’ theorem and trigonometry, and using dynamic geometric software, to design three-dimensional models of practical situations involving angles of elevation and depression; for example, modelling a crime scene
- Elaboration investigating how autonomous vehicles use algorithms that use Pythagoras' theorem and trigonometry to calculate distance and navigate spaces; for example, if an autonomous vehicle knows its current position (x, y) and the coordinates of a target location (x', y'), it can determine the straight-line distance between them using the formula distance =\sqrt{(x'-x)^2 + (y'-y)^2}
- Elaboration exploring navigation, design of technologies or surveying by First Nations Australians, investigating geometric and spatial reasoning, and how these connect to trigonometry
Content descriptorAC9M10N01 Number
recognise the effect of using approximations of real numbers in repeated calculations and compare the results when using exact representations
Elaborations (2)
- Elaboration comparing and contrasting the effect of truncation or rounding on the final result of calculations when using approximations of real numbers rather than exact representations
- Elaboration investigating the impact of approximation on multiple calculations in contexts that involve the area of compound shapes involving circles, the surface area and volume of compound objects, and repeated calculations of simple interest where the solutions are not exact cents
They use mathematical modelling to solve problems involving growth and decay in financial and other applied situations, applying linear, quadratic and exponential functions as appropriate, and solve related equations, numerically and graphically.
Content descriptorAC9M10A01 Algebra
expand, factorise and simplify expressions and solve equations algebraically, applying exponent laws involving products, quotients and powers of variables, and the distributive property
Elaborations (2)
- Elaboration explaining the relationship between factorisation and expansion, including the completed square form for quadratic expressions
- Elaboration applying knowledge of exponent laws to algebraic terms and using both positive and negative integral exponents to simplifying algebraic expressions and solve equations algebraically
Content descriptorAC9M10A03 Algebra
recognise the connection between algebraic and graphical representations of exponential relations and solve related exponential equations, using digital tools where appropriate
Elaborations (4)
- Elaboration recognising that in a table of values, if the ratio between consecutive values of the dependent variable is constant, then it is an exponential relation
- Elaboration investigating the links between algebraic and graphical representations of exponential functions using graphing software
- Elaboration using digital tools with symbolic manipulation functionality to systematically explore exponential relations
- Elaboration investigating First Nations Australian Ranger groups’ and other groups’ programs that attempt to eradicate feral animals for survival of native animals on Country/Place, exploring the competition between feral and native animals and their impact on natural resources by formulating exponential equations for population growth for each animal species
Content descriptorAC9M10A04 Algebra
use mathematical modelling to solve applied problems involving growth and decay, including financial contexts; formulate problems, choosing to apply linear, quadratic or exponential models; interpret solutions in terms of the situation; evaluate and modify models as necessary and report assumptions, methods and findings
Elaborations (5)
- Elaboration modelling situations and choosing between linear, quadratic and exponential models by representing relationships in a table of values and recognising that linear functions have constant first differences, quadratic functions have constant second differences and exponential functions have a constant ratio between consecutive values of the dependent variable
- Elaboration modelling situations involving exponential growth and decay, and contrasting this with linear growth or decay; for example, situations involving constant percentage change and constant ratio; determining doubling time and half-life and approximate intervals for which the values of the model lie within a given range
- Elaboration modelling situations that involve working with authentic information, data and interest rates to calculate compound interest and solve related problems
- Elaboration modelling and investigating how exponential equations are used in carbon dating to estimate the age of First Nations Australians’ artefacts or material culture
- Elaboration modelling and formulating situations involving population growths of native animals on Country/Place with varying reproductive behaviour, using exponential equations and critiquing their applicability to real-world situations
Students make and test conjectures involving functions and relations using digital tools.
Content descriptorAC9M10A05 Algebra
experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns
Elaborations (7)
- Elaboration applying the graphing zoom functionality of digital tools and systematically refining intervals to identify approximate location of points of intersection of the graphs of 2 functions, such as x^2=2^x
- Elaboration applying a bisection algorithm to determine the approximate location of the horizontal axis intercepts of the graph of a quadratic function such as f(x)=2x^2-3x-7
- Elaboration applying transformations to the graph of x^2+y^2=1
- Elaboration identifying the coordinates of any points of intersection of the graph of a linear function with the graph of a quadratic function or a circle
- Elaboration identifying intervals on the real number line over which a given quadratic function is positive or negative
- Elaboration using a table of values to determine when an exponential growth or decay function exceeds or falls below a given value, such as monitoring the trend in value of a share price in a context of exponential growth or decay
- Elaboration investigating how functions and relations serve as the mathematical underpinnings of machine learning, allowing data to be transformed, models to be defined and optimisation to occur
They solve problems involving simultaneous linear equations and linear inequalities in 2 variables graphically and justify solutions.
Content descriptorAC9M10A02 Algebra
solve linear inequalities and simultaneous linear equations in 2 variables; interpret solutions graphically and communicate solutions in terms of the situation
Elaborations (6)
- Elaboration investigating situations involving linear equations in context, such as multiple quotes for a job, or profit and loss; solving the equations graphically, giving solutions in everyday language, such as “break-even point” or “point to change providers” for the job
- Elaboration describing the solution of simultaneous equations within the context of the situation
- Elaboration graphing regions corresponding to inequalities in the Cartesian plane; for example, graphing 2x+3y<24 and verifying using a test point such as (0, 0)
- Elaboration identifying all the combinations of trips to the movies, each costing \$12, and ice-skating sessions, each costing \$21, as the integer solutions for an entertainment budget of up to \$150 for the school holidays; expressing algebraically as 12m+21s\leq150
- Elaboration testing when a circle of a specified radius has a corresponding area greater than a given value, or whether a point satisfies an inequality; for example, whether the point (3, 5) satisfies 2y<x^2
- Elaboration investigating the strategies inherent in First Nations Australian children’s instructive games; for example, Weme from the Warlpiri Peoples of central Australia, and their connection to strategies to solve simultaneous linear equations in 2 variables
Students interpret and use logarithmic scales representing small or large quantities or change in applied contexts.
Content descriptorAC9M10M02 Measurement
interpret and use logarithmic scales in applied contexts involving small and large quantities and change
Elaborations (5)
- Elaboration understanding that the logarithmic scale is calibrated in terms of order of magnitude; for example, doubling or powers of 10
- Elaboration identifying and interpreting data representations (charts and graphs) that use logarithmic scales and discussing when it is appropriate to use this type of scale and when it is not appropriate; for example, graphs representing percentage change, a wide range of values or exponential growth
- Elaboration investigating and interpreting logarithmic scales used in real-world contexts; for example, Richter, decibel and sensitivity scales or growth in investments, timescales and the spread of micro-organisms and disease and describing reasons for choosing to use a logarithmic scale rather than a linear scale
- Elaboration investigating how logarithmic scaling can be used in machine learning algorithms to compress large values while preserving small ones, allowing the algorithms to efficiently work on problems with a wide range of values
- Elaboration investigating dating methods of geological sites to provide evidence of First Peoples of Australia’s human presence in Australia, including the Madjedbebe dig in the Northern Territory, that use logarithmic scales (scientific notation) and measurement accuracy in the dating
They solve measurement problems involving surface area and volume of composite objects.
Content descriptorAC9M10M01 Measurement
solve problems involving the surface area and volume of composite objects using appropriate units
Elaborations (3)
- Elaboration determining the volumes and surface areas of composite solids, formed from a range of right prisms and cylinders, by considering the individual solids from which they are constructed
- Elaboration estimating the surface area and volume of composite objects in practical contexts
- Elaboration using mathematical modelling to provide solutions to problems involving surface area and volume; for example, ascertaining the rainfall that can be saved from a roof top and the optimal shape and dimensions for rainwater storage based on where it will be located on a property; determining whether to hire extra freezer space for the amount of ice cream required at a fundraising event for the school or community
Students apply Pythagoras’ theorem and trigonometry to solve practical problems involving right-angled triangles.
Content descriptorAC9M10M03 Measurement
solve practical problems applying Pythagoras’ theorem and trigonometry of right-angled triangles, including problems involving direction and angles of elevation and depression
Elaborations (6)
- Elaboration applying right-angled trigonometry to solve navigation problems involving bearings; for example, determining the bearing and estimating the distance of the final leg of an orienteering course
- Elaboration applying Pythagoras’ theorem and trigonometry to problems in surveying and design, where three-dimensional problems are decomposed into two-dimensional problems; for example, investigating the dimensions of the smallest box needed to package an object of a particular length
- Elaboration using a clinometer to measure angles of inclination, and applying trigonometry, and proportional reasoning to determine the height of buildings in practical contexts
- Elaboration applying Pythagoras’ theorem and trigonometry, and using dynamic geometric software, to design three-dimensional models of practical situations involving angles of elevation and depression; for example, modelling a crime scene
- Elaboration investigating how autonomous vehicles use algorithms that use Pythagoras' theorem and trigonometry to calculate distance and navigate spaces; for example, if an autonomous vehicle knows its current position (x, y) and the coordinates of a target location (x', y'), it can determine the straight-line distance between them using the formula distance =\sqrt{(x'-x)^2 + (y'-y)^2}
- Elaboration exploring navigation, design of technologies or surveying by First Nations Australians, investigating geometric and spatial reasoning, and how these connect to trigonometry
They identify the impact of measurement errors on the accuracy of results.
Content descriptorAC9M10M04 Measurement
identify the impact of measurement errors on the accuracy of results in practical contexts
Elaborations (5)
- Elaboration describing settings where measurement errors may impact research results and how measurement data impacted by error can result in biased findings
- Elaboration analysing instruments and methods for measuring in investigations and modelling activities
- Elaboration determining the impact that compounding errors have on financial calculations; for example, considering the effect of truncation on money amounts for large scale customer populations
- Elaboration investigating the impact of measurement errors in the perception and control systems of autonomous vehicles, such as measurement errors due to sensor limitations
- Elaboration investigating scientific measuring techniques, including dating methods and genetic sequencing, applied to First Peoples of Australia and their artefacts, and the social impact of measurement errors
Students use mathematical modelling to solve practical problems involving proportion and scaling, evaluating and modifying models, and reporting assumptions, methods and findings.
Content descriptorAC9M10M05 Measurement
use mathematical modelling to solve practical problems involving proportion and scaling of objects; formulate problems and interpret solutions in terms of the situation; evaluate and modify models as necessary, and report assumptions, methods and findings
Elaborations (5)
- Elaboration using plans and elevation drawings to investigate making changes to building designs, employing appropriate scales and converting to actual measurements within the context to make decisions about changes
- Elaboration analysing and applying scale and ratios in situations such as production prototypes and 3D printing; for example, using a 3D printer to produce scaled versions of actual objects
- Elaboration estimating the scale of an object, such as a toy car, by measuring a linear dimension and using a typical car dimension to work out the scale factor
- Elaboration investigating compliance with building codes and standards in design and construction, such as for escalators in shopping centres
- Elaboration investigating how artificial intelligence image generators use proportion and scaling techniques, such as aspect ratio preservation, to ensure that the generated content adheres to realistic visual principles and maintains appropriate relationships between objects and elements within the scene
They use deductive reasoning, theorems and algorithms to solve spatial problems.
Content descriptorAC9M10SP01 Space
apply deductive reasoning to proofs involving shapes in the plane and use theorems to solve spatial problems
Elaborations (6)
- Elaboration distinguishing between a practical demonstration and a proof; for example, demonstrating that triangles are congruent by placing them on top of each other, as compared to using congruence tests to establish that triangles are congruent
- Elaboration developing proofs involving congruent triangles and angle properties, communicating the proof using a sequence of logically connected statements
- Elaboration applying an understanding of relationships to deduce properties of geometric figures; for example, the base angles of an isosceles triangle are equal
- Elaboration investigating proofs of geometric theorems and using them to solve spatial problems; for example, applying logical reasoning and similarity to proofs and numerical exercises involving plane shapes; using visual proofs to justify solutions
- Elaboration using dynamic geometric software to investigate the shortest path that touches 3 sides of a rectangle, starting and finishing at the same point and proving that the path forms a parallelogram
- Elaboration investigating how automated theorem provers (ATP) and interactive proof assistants (IPA) allow mathematicians and artificial intelligence systems to work collaboratively to construct or test formal proofs
Content descriptorAC9M10SP03 Space
design, test and refine solutions to spatial problems using algorithms and digital tools; communicate and justify solutions
Elaborations (5)
- Elaboration designing and making scale models of three-dimensional objects using digital tools; for example, making components of a puzzle using a three-dimensional printer, planning and designing the puzzle using principles of tessellations
- Elaboration applying a computational thinking approach to solving problems involving networks; for example, connectedness, coverage and weighted measures; taking different routes and choosing the most efficient route to take when travelling by car using virtual map software
- Elaboration defining and decomposing spatial problems, creating and applying algorithms to generate solutions, evaluating and communicating solutions in terms of the problem; for example, designing a floor plan for a department store that limits congestion at key areas such as checkouts, changing rooms and popular sale items
- Elaboration designing, creating and testing algorithms using pseudocode or flow charts for producing self-similar patterns; validating algorithms using a range of test cases to compare their output
- Elaboration exploring geospatial technologies used by First Nations Australians’ communities to consider spatial problems including position and transformation
Students interpret networks used to represent practical situations and describe connectedness.
Content descriptorAC9M10SP02 Space
interpret networks and network diagrams used to represent relationships in practical situations and describe connectedness
Elaborations (6)
- Elaboration investigating how networks and network diagrams can be used to model authentic situations, recognising what real world quantity is represented by the nodes (vertices), and what real world quantity is represented by the links between them (edges)
- Elaboration investigating the use of graphs to represent a network, analysing connectedness; for example, investigating the “The Seven Bridges of Königsberg” problem
- Elaboration investigating how polyhedra can be represented as a network using edges, vertices, interior and exterior faces; representing the number of edges, vertices and faces in a table and demonstrating how Euler’s formula F + V = E + 2 applies
- Elaboration investigating how a social network, intranet, local area network (LAN), electrical wiring or wireless network of a home can be represented as a network diagram to specify relationships; for example, using network diagrams to investigate practical problems involving connections, power overload or the need for routers
- Elaboration investigating the use of networks to represent authentic situations; for example, rail or air travel between or within London, Paris, Hong Kong; a food web representing a simple eco-system; metabolic networks and other chemical or biological structures
- Elaboration representing First Nations Australians’ kinship systems using network diagrams and exploring the significance of relationships to Country/Place
They plan and conduct statistical investigations involving bivariate data.
Content descriptorAC9M10ST03 Statistics
construct scatterplots and comment on the association between the 2 numerical variables in terms of strength, direction and linearity
Elaborations (6)
- Elaboration discussing the difference between association and cause and effect, and relating this to situations such as health, diversity of species and climate control
- Elaboration using statistical evidence to make, justify and critique claims about association between variables, such as in contexts of climate change, migration, online shopping and social media
- Elaboration informally using a line of good fit by eye to discuss reliability of any predictions
- Elaboration exploring how scatter plots and association help data scientists gain insights into the data, identify relationships, and can be applied to machine learning to make informed decisions about feature engineering and assess model performance
- Elaboration investigating artificial intelligence systems that analyse bivariate data to forecast or make predictions based on association using correlation analysis and discussing limitations; for example, the artificial intelligence may not capture the causality between variables or account for the contextual or ethical implications
- Elaboration investigating the relationship between 2 variables of spear throwers used by First Peoples of Australia by using data to construct scatterplots, make comparisons and draw conclusions
Content descriptorAC9M10ST04 Statistics
construct two-way tables and discuss possible relationship between categorical variables
Elaborations (3)
- Elaboration using two-way tables to investigate and comparing the survey responses to questions involving five-point Likert scale against 2 different categories of respondents; for example, junior compared to senior students’ responses to a survey question
- Elaboration recording data in two-way tables and using percentages and proportions to identify patterns and associations in the data
- Elaboration conducting a litter survey around the school, considering the relationship between different categorical variables such as the day of the week as canteen specials might lead to different types of litter or the weather due to hot days leading to more ice blocks and cold drinks being sold
Content descriptorAC9M10ST05 Statistics
plan and conduct statistical investigations of situations that involve bivariate data; evaluate and report findings with consideration of limitations of any inferences
Elaborations (4)
- Elaboration designing statistical investigations that collect bivariate data over time through observation, experiment or measurement; graphing, interpreting and analysing data; and reporting within the context of the statistical investigation question
- Elaboration investigating anecdotal claims including those concerning climate, housing affordability and natural resources, with consideration of data validity and limitations of interpolation or extrapolation
- Elaboration using a statistical investigation to address the question, “Is there a relationship between vaccines and immunity from a virus”
- Elaboration investigating biodiversity changes in Australia before and after colonisation by comparing related bivariate numerical data, discussing and reporting on associations
Students represent the distribution of data involving 2 variables, using tables and scatter plots, and comment on possible association.
Content descriptorAC9M10ST03 Statistics
construct scatterplots and comment on the association between the 2 numerical variables in terms of strength, direction and linearity
Elaborations (6)
- Elaboration discussing the difference between association and cause and effect, and relating this to situations such as health, diversity of species and climate control
- Elaboration using statistical evidence to make, justify and critique claims about association between variables, such as in contexts of climate change, migration, online shopping and social media
- Elaboration informally using a line of good fit by eye to discuss reliability of any predictions
- Elaboration exploring how scatter plots and association help data scientists gain insights into the data, identify relationships, and can be applied to machine learning to make informed decisions about feature engineering and assess model performance
- Elaboration investigating artificial intelligence systems that analyse bivariate data to forecast or make predictions based on association using correlation analysis and discussing limitations; for example, the artificial intelligence may not capture the causality between variables or account for the contextual or ethical implications
- Elaboration investigating the relationship between 2 variables of spear throwers used by First Peoples of Australia by using data to construct scatterplots, make comparisons and draw conclusions
Content descriptorAC9M10ST04 Statistics
construct two-way tables and discuss possible relationship between categorical variables
Elaborations (3)
- Elaboration using two-way tables to investigate and comparing the survey responses to questions involving five-point Likert scale against 2 different categories of respondents; for example, junior compared to senior students’ responses to a survey question
- Elaboration recording data in two-way tables and using percentages and proportions to identify patterns and associations in the data
- Elaboration conducting a litter survey around the school, considering the relationship between different categorical variables such as the day of the week as canteen specials might lead to different types of litter or the weather due to hot days leading to more ice blocks and cold drinks being sold
They analyse inferences and conclusions in the media, noting potential sources of bias.
Content descriptorAC9M10ST01 Statistics
analyse claims, inferences and conclusions of statistical reports in the media, including ethical considerations and identification of potential sources of bias
Elaborations (6)
- Elaboration identifying potentially misleading data representations in the media such as graphs with broken axes and scales that do not start at zero or are nonlinear; recognising when data is not related to the claim, not representative of the population or is deliberately being used to mislead, or support a claim or biased point of view
- Elaboration investigating the source and size of the sample from which the data was collected and deciding whether the sample is appropriately representative of the population
- Elaboration investigating population rates and discussing potential ethical considerations when presenting statistical data involving infection rates, and the number of cases per head of population
- Elaboration using secondary data to predict the number of people likely to be infected with a strain of flu or experience side effects with a certain medication, discussing the ethical considerations of reporting of such data to the wider public, considering validity claims and samples sizes
- Elaboration recognising how the identification of bias is a critical aspect of machine learning and deep learning because biases can significantly impact the fairness, accuracy and ethical implications of artificial intelligence systems
- Elaboration using the concept of Indigenous data sovereignty to critique and evaluate the Australian Government’s “Closing the Gap” report
Students compare the distribution of continuous numerical data, using various displays, and discuss distributions in terms of centre, spread, shape and outliers.
Content descriptorAC9M10ST02 Statistics
compare data distributions for continuous numerical variables using appropriate data displays including boxplots; discuss the shapes of these distributions in terms of centre, spread, shape and outliers in the context of the data
Elaborations (6)
- Elaboration constructing and interpreting box plots and using them to compare data sets, understanding that box plots are an efficient and common way of representing and summarising data and can facilitate comparisons between data sets
- Elaboration comparing shapes of distributions using box plots, histograms, cumulative frequency graphs and dot plots, discussing symmetry, skew and modality
- Elaboration using digital tools to compare boxplots and histograms as displays of the same data in the light of the statistical questions being addressed and the effectiveness of the display in helping to answer the question
- Elaboration finding the five-number summary (minimum and maximum values, median, and upper and lower quartiles) and using its graphical representation, the box plot, as tools for both numerically and visually comparing the centre and spread of data sets
- Elaboration comparing the information that can be extracted and the stories that can be told about continuous and discrete numerical data sets that have been displayed in different ways, including histograms, dot plots, box plots and cumulative frequency graphs
- Elaboration exploring how the identification and appropriate handling of outliers is an important step in machine learning to ensure that they don't unduly influence the model
Content descriptorAC9M10ST03 Statistics
construct scatterplots and comment on the association between the 2 numerical variables in terms of strength, direction and linearity
Elaborations (6)
- Elaboration discussing the difference between association and cause and effect, and relating this to situations such as health, diversity of species and climate control
- Elaboration using statistical evidence to make, justify and critique claims about association between variables, such as in contexts of climate change, migration, online shopping and social media
- Elaboration informally using a line of good fit by eye to discuss reliability of any predictions
- Elaboration exploring how scatter plots and association help data scientists gain insights into the data, identify relationships, and can be applied to machine learning to make informed decisions about feature engineering and assess model performance
- Elaboration investigating artificial intelligence systems that analyse bivariate data to forecast or make predictions based on association using correlation analysis and discussing limitations; for example, the artificial intelligence may not capture the causality between variables or account for the contextual or ethical implications
- Elaboration investigating the relationship between 2 variables of spear throwers used by First Peoples of Australia by using data to construct scatterplots, make comparisons and draw conclusions
They apply conditional probability to solve problems involving compound events.
Content descriptorAC9M10P01 Probability
use the language of “if .... then”, “given”, “of”, “knowing that” to describe and interpret situations involving conditional probability
Elaborations (3)
- Elaboration using two-way tables and Venn diagrams to understand conditional statements using the language of “if ... then ...”, “given”, “of”, “knowing that” and identifying common mistakes in interpreting such language
- Elaboration using arrays and tree diagrams to represent, interpret and compare probabilities of dependent and independent events
- Elaboration investigating how conditional probability is used in natural language processing tasks like text or image generation, language translation, data augmentation and recommendation systems
Content descriptorAC9M10P02 Probability
design and conduct repeated chance experiments and simulations using digital tools to model conditional probability and interpret results
Elaborations (5)
- Elaboration using samples of different sizes with and without replacement from a population to identify when the difference in methods becomes negligible
- Elaboration recognising that an event can be dependent on another event and that this will affect the way its probability is calculated
- Elaboration using simulations to gather data on frequencies for situations involving chance that appear to be counter-intuitive, such as the three-door problem or the birthday problem
- Elaboration identifying situations in real-life where probability simulations are used for decision-making, such as supply and demand of product, insurance risk and queueing
- Elaboration using simulation to predict the number of people likely to be infected with a strain of flu or virus
Students design and conduct simulations involving conditional probability, using digital tools.
Content descriptorAC9M10P01 Probability
use the language of “if .... then”, “given”, “of”, “knowing that” to describe and interpret situations involving conditional probability
Elaborations (3)
- Elaboration using two-way tables and Venn diagrams to understand conditional statements using the language of “if ... then ...”, “given”, “of”, “knowing that” and identifying common mistakes in interpreting such language
- Elaboration using arrays and tree diagrams to represent, interpret and compare probabilities of dependent and independent events
- Elaboration investigating how conditional probability is used in natural language processing tasks like text or image generation, language translation, data augmentation and recommendation systems
Content descriptorAC9M10P02 Probability
design and conduct repeated chance experiments and simulations using digital tools to model conditional probability and interpret results
Elaborations (5)
- Elaboration using samples of different sizes with and without replacement from a population to identify when the difference in methods becomes negligible
- Elaboration recognising that an event can be dependent on another event and that this will affect the way its probability is calculated
- Elaboration using simulations to gather data on frequencies for situations involving chance that appear to be counter-intuitive, such as the three-door problem or the birthday problem
- Elaboration identifying situations in real-life where probability simulations are used for decision-making, such as supply and demand of product, insurance risk and queueing
- Elaboration using simulation to predict the number of people likely to be infected with a strain of flu or virus
About the strands
The 21 content descriptors linked to ASMATY10 sit under these strands.
Number
Number concepts, representations, operations and applications students develop and connect.
Algebra
Patterns, relationships, expressions, equations and algebraic reasoning students learn to use.
Measurement
Attributes, units, measurement relationships and applications students investigate and apply.
Space
Geometric properties, spatial reasoning, representations and transformations students explore.
Statistics
How students collect, represent, analyse and interpret data to answer questions.
Probability
Chance, uncertainty and the ways students describe and analyse possible outcomes.
A practical planning sequence
- Choose the curriculum focus. Choose the mathematical concepts and connections that anchor the sequence.
- Select a meaningful context. Use purposeful problems, representations and digital tools where they strengthen understanding.
- Plan connected learning. Use the linked descriptors together where that creates a coherent sequence.
- Map the evidence. Collect evidence of fluency, reasoning, problem solving and mathematical communication.
Turn this curriculum map into a teaching sequence
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