Year 7 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 7, students represent natural numbers in expanded form and as products of prime factors, using exponent notation. They solve problems involving squares of numbers and square roots of perfect square numbers. Students solve problems involving addition and subtraction of integers. They use all 4 operations in calculations involving positive fractions and decimals, choosing efficient calculation strategies. Students choose between equivalent representations of rational numbers and percentages to assist in calculations. They use mathematical modelling to solve practical problems involving rational numbers, percentages and ratios in financial and other applied contexts, justifying choices of representation. Students use algebraic expressions to represent situations, describe the relationships between variables from authentic data and substitute values into formulas to determine unknown values. They solve linear equations with natural number solutions. Students create tables of values related to algebraic expressions and formulas, and describe the effect of variation.
They apply knowledge of angle relationships and the sum of angles in a triangle to solve problems, giving reasons. Students use formulas for the areas of triangles and parallelograms and the volumes of rectangular and triangular prisms to solve problems. They describe the relationships between the radius, diameter and circumference of a circle. Students classify polygons according to their features and create an algorithm designed to sort and classify shapes. They represent objects two-dimensionally in different ways, describing the usefulness of these representations. Students use coordinates to describe transformations of points in the plane.
They plan and conduct statistical investigations involving discrete and continuous numerical data, using appropriate displays. Students interpret data in terms of the shape of distribution and summary statistics, identifying possible outliers. They decide which measure of central tendency is most suitable and explain their reasoning. Students list sample spaces for single step experiments, assign probabilities to outcomes and predict relative frequencies for related events. They conduct repeated single-step chance experiments and run simulations using digital tools, giving reasons for differences between predicted and observed results.
The 20 achievement standard statements
Open a statement to see the content descriptors ACARA links to it, then open a descriptor's elaborations.
By the end of Year 7, students represent natural numbers in expanded form and as products of prime factors, using exponent notation.
Content descriptorAC9M7N02 Number
represent natural numbers as products of powers of prime numbers using exponent notation
Elaborations (3)
- Elaboration applying knowledge of factors to strategies for expressing natural numbers as products of powers of prime factors, such as repeated division by prime factors or creating factor trees; for example, 48=6\times8=2\times3\times2\times2\times2=3^1\times2^4=3\times2^4
- Elaboration developing familiarity with the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 and powers of 2; the sequence 1, 3, 9, 27, 81, 243, 729 and powers of 3; and the sequence 1, 5, 25, 125, 625 and powers of 5
- Elaboration solving problems involving lowest common multiples and greatest common divisors (highest common factors) for pairs of natural numbers by comparing their prime factorisation
Content descriptorAC9M7N03 Number
represent natural numbers in expanded notation using place value and powers of 10
Elaborations (3)
- Elaboration investigating exponent notation for powers of 10 such as “one hundred thousand” is 100 000=10×10×10×10×10=10^5
- Elaboration relating the sequences 10, 100, 1000, 10 000 … and 10^1, 10^2, 10^3, 10^4 ...
- Elaboration applying and explaining the connections between place value and expanded notations; for example, 7000=7×10^3 and 3750=3×10^3+7×10^2+5×10^1
They solve problems involving squares of numbers and square roots of perfect square numbers.
Content descriptorAC9M7N01 Number
describe the relationship between perfect square numbers and square roots, and use squares of numbers and square roots of perfect square numbers to solve problems
Elaborations (5)
- Elaboration investigating squares of natural numbers from one to 20, and connecting them to visual representations such as dots arranged in a square pattern
- Elaboration using the square and square root notation, and the distributive property and area diagrams to calculate the squares of two-digit numbers; for example, 43^2=(40+3)^2=40^2+2\times40\times3+3^2=1600+240+9=1849
- Elaboration determining between which 2 consecutive natural numbers the square root of a given number lies; for example, 43 is between the square numbers 36 and 49 so \sqrt{43} is between \sqrt{36} and \sqrt{49} and therefore between 6 and 7
- Elaboration generating a list of perfect square numbers and describing any emerging patterns; for example, the last digit of perfect square numbers, or the difference between consecutive square numbers, and recognising the constant second difference
- Elaboration using the relationship between perfect square numbers and their square roots to determine the perimeter of a square tiled floor using square tiles; for example, an area of floor with 144 square tiles has a perimeter of 48 tile lengths
Students solve problems involving addition and subtraction of integers.
Content descriptorAC9M7N07 Number
compare, order and solve problems involving addition and subtraction of integers
Elaborations (3)
- Elaboration using less-than and greater-than notation in expressions when comparing and ordering integers; for example, negative 5 is less than positive 2 and can be represented as (-5)\leq(+2);\;(-3)\geq(-6)
- Elaboration discussing language such as “addition”, “subtraction”, “magnitude”, “difference”, “sign” and synonyms of these terms
- Elaboration ordering, adding and subtracting integers using a number line
They use all 4 operations in calculations involving positive fractions and decimals, choosing efficient calculation strategies.
Content descriptorAC9M7N05 Number
round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of solutions
Elaborations (3)
- Elaboration identifying the interval between a pair of consecutive integers that includes a given rational number
- Elaboration choosing and applying conventions for rounding correct to a specified number of decimal places based upon the context
- Elaboration checking that the accuracy of rounding is suitable for context and purpose, such as the amount of paint required and cost estimate for renovating a house; for example, purchasing 2 litres of paint to paint the bedroom even though 1.89 litres is the exact answer or estimating a renovation budget to the nearest \$100
Content descriptorAC9M7N06 Number
use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies
Elaborations (6)
- Elaboration solving addition and subtraction problems involving fractions and decimals; for example, using rectangular arrays with dimensions equal to the denominators, algebra tiles, digital tools or informal jottings
- Elaboration choosing an appropriate numerical representation for a problem so that efficient computations can be made, such as 12.5%, 1/8, 0.125 or 125/1000
- Elaboration developing efficient strategies with appropriate use of the commutative and associative properties, place value, patterning, and multiplication facts to solve multiplication and division problems involving fractions and decimals; for example, using the commutative property to calculate 2/3 of 1/2 giving 1/2 of 2/3=1/3
- Elaboration solving multiplicative problems involving fractions and decimals using fraction walls, rectangular arrays, algebra tiles, calculators or informal jottings
- Elaboration developing efficient strategies with appropriate use of the commutative and associative properties, regrouping or partitioning to solve additive problems involving fractions and decimals
- Elaboration carry out calculations to solve problems using the representation that makes computations efficient such as 12.5% of 96 is more efficiently calculated as 1/8 of 96, including contexts such as comparing land-use by calculating the total local municipal area set aside for parkland or manufacturing and retail, the amount of protein in daily food intake across several days, or increases/decreases in energy accounts each account cycle
Students choose between equivalent representations of rational numbers and percentages to assist in calculations.
Content descriptorAC9M7N04 Number
find equivalent representations of rational numbers and represent rational numbers on a number line
Elaborations (4)
- Elaboration investigating equivalence of fractions using common multiples and a fraction wall, diagrams or a number line to show that a fraction such as 2/3 is equivalent to 4/6 and 6/9 and therefore 2/3<5/6
- Elaboration expressing a fraction in simplest form using common divisors
- Elaboration applying and explaining the equivalence between fraction, decimal and percentage representations of rational numbers; for example, 16\%, 0.16, 16/100 and 4/25, using manipulatives, number lines or diagrams
- Elaboration representing positive and negative fractions and mixed numerals on various intervals of the real number line, including intervals that are not symmetrical about zero
Content descriptorAC9M7N06 Number
use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies
Elaborations (6)
- Elaboration solving addition and subtraction problems involving fractions and decimals; for example, using rectangular arrays with dimensions equal to the denominators, algebra tiles, digital tools or informal jottings
- Elaboration choosing an appropriate numerical representation for a problem so that efficient computations can be made, such as 12.5%, 1/8, 0.125 or 125/1000
- Elaboration developing efficient strategies with appropriate use of the commutative and associative properties, place value, patterning, and multiplication facts to solve multiplication and division problems involving fractions and decimals; for example, using the commutative property to calculate 2/3 of 1/2 giving 1/2 of 2/3=1/3
- Elaboration solving multiplicative problems involving fractions and decimals using fraction walls, rectangular arrays, algebra tiles, calculators or informal jottings
- Elaboration developing efficient strategies with appropriate use of the commutative and associative properties, regrouping or partitioning to solve additive problems involving fractions and decimals
- Elaboration carry out calculations to solve problems using the representation that makes computations efficient such as 12.5% of 96 is more efficiently calculated as 1/8 of 96, including contexts such as comparing land-use by calculating the total local municipal area set aside for parkland or manufacturing and retail, the amount of protein in daily food intake across several days, or increases/decreases in energy accounts each account cycle
They use mathematical modelling to solve practical problems involving rational numbers, percentages and ratios in financial and other applied contexts, justifying choices of representation.
Content descriptorAC9M7M06 Measurement
use mathematical modelling to solve practical problems involving ratios; formulate problems, interpret and communicate solutions in terms of the situation, justifying choices made about the representation
Elaborations (4)
- Elaboration using fractions to model and solve ratio problems involving comparison of quantities, and considering part-part and part-whole relations
- Elaboration modelling and solving practical problems involving ratios of length, capacity or mass, such as in construction, design, food or textile production; for example, mixing concrete, the golden ratio in design, mixing a salad dressing
- Elaboration modelling the situation using manipulatives, diagrams and/or mathematical discussion; for example, mixing primary colours in a variety of ratios to investigate how new colours are created and the strength of those colours
- Elaboration investigating commercialised substances founded on First Nations Australians’ knowledges of substances including pharmaceuticals and toxins, understanding how ratios are used in their development
Content descriptorAC9M7N04 Number
find equivalent representations of rational numbers and represent rational numbers on a number line
Elaborations (4)
- Elaboration investigating equivalence of fractions using common multiples and a fraction wall, diagrams or a number line to show that a fraction such as 2/3 is equivalent to 4/6 and 6/9 and therefore 2/3<5/6
- Elaboration expressing a fraction in simplest form using common divisors
- Elaboration applying and explaining the equivalence between fraction, decimal and percentage representations of rational numbers; for example, 16\%, 0.16, 16/100 and 4/25, using manipulatives, number lines or diagrams
- Elaboration representing positive and negative fractions and mixed numerals on various intervals of the real number line, including intervals that are not symmetrical about zero
Content descriptorAC9M7N06 Number
use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies
Elaborations (6)
- Elaboration solving addition and subtraction problems involving fractions and decimals; for example, using rectangular arrays with dimensions equal to the denominators, algebra tiles, digital tools or informal jottings
- Elaboration choosing an appropriate numerical representation for a problem so that efficient computations can be made, such as 12.5%, 1/8, 0.125 or 125/1000
- Elaboration developing efficient strategies with appropriate use of the commutative and associative properties, place value, patterning, and multiplication facts to solve multiplication and division problems involving fractions and decimals; for example, using the commutative property to calculate 2/3 of 1/2 giving 1/2 of 2/3=1/3
- Elaboration solving multiplicative problems involving fractions and decimals using fraction walls, rectangular arrays, algebra tiles, calculators or informal jottings
- Elaboration developing efficient strategies with appropriate use of the commutative and associative properties, regrouping or partitioning to solve additive problems involving fractions and decimals
- Elaboration carry out calculations to solve problems using the representation that makes computations efficient such as 12.5% of 96 is more efficiently calculated as 1/8 of 96, including contexts such as comparing land-use by calculating the total local municipal area set aside for parkland or manufacturing and retail, the amount of protein in daily food intake across several days, or increases/decreases in energy accounts each account cycle
Content descriptorAC9M7N08 Number
recognise, represent and solve problems involving ratios
Elaborations (4)
- Elaboration using diagrams, physical or virtual materials to represent ratios, recognising that ratios express the quantitative relationship between 2 or more groups; for example, using counters or coloured beads to show the ratios 1:4 and 1:1:2
- Elaboration using fractions to solve ratio problems involving comparison of quantities and considering part-part and part-whole relations; for example, dividing a set into the ratio 1:2 by determining the number of parts as 3
- Elaboration sharing quantities in a given ratio; for example, sharing an amount of money in a given ratio, such as sharing \$20 in the ratio 2:3
- Elaboration applying ratios to realistic and meaningful contexts; for example, mixing 500 millilitres of a liquid with a concentration of 1:4 means 1/5 concentrate and 4/5 water so, 0.2 of 500 millilitres is concentrate and 0.8 of 500 millilitres is water; interpreting results in context
Content descriptorAC9M7N09 Number
use mathematical modelling to solve practical problems, involving rational numbers and percentages, including financial contexts; formulate problems, choosing representations and efficient calculation strategies, using digital tools as appropriate; interpret and communicate solutions in terms of the situation, justifying choices made about the representation
Elaborations (4)
- Elaboration modelling additive situations involving positive and negative quantities; for example, a lift travelling up and down floors in a high-rise apartment where the ground floor is interpreted as zero; in geography when determining altitude above and below sea level
- Elaboration modelling contexts involving proportion, such as the proportion of students attending the school disco, proportion of bottle cost to recycling refund, proportion of school site that is green space, 55% of Year 7 students attended the end of term function or 23% of the school population voted yes to a change of school uniform; interpreting and communicating answers in terms of the context of the situation
- Elaboration modelling financial problems involving profit and loss, credits and debits, gains and losses; for example, holding a fundraising sausage sizzle and determining whether the event made a percentage profit or loss
- Elaboration using mathematical modelling to investigate the proportion of land mass/area of Australian First Nations Peoples’ traditional grain belt compared with Australia’s current grain belt
Students use algebraic expressions to represent situations, describe the relationships between variables from authentic data and substitute values into formulas to determine unknown values.
Content descriptorAC9M7A01 Algebra
recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown
Elaborations (4)
- Elaboration linking variables to attributes and measures being modelled when using formulas, such as the area of a rectangle is equal to the length x width as A\;=\;l\;\times\;w or using p\;=\;6g\;+\;b to describe a total of points expressed as goals (worth 6 points) and behinds (worth one point)
- Elaboration interpreting and using formulas obtained from other sources; for example, maximum heart rates and target heart rates for moderate exercise
- Elaboration substituting numerical values for variables when using formulas and calculating the value of an unknown in practical situations; for example, calculating weekly wage W given base wage b and overtime hours h at 1.5 times rate r, W\;=\;b+1.5\times h\times r, using values for mass m and volume v to determine density d of a substance where d\;=\;\frac mv
- Elaboration using everyday formulas and their application to contexts on Country/Place, investigating the relationships between variables
Content descriptorAC9M7A02 Algebra
formulate algebraic expressions using constants, variables, operations and brackets
Elaborations (3)
- Elaboration generalising arithmetic expressions to algebraic expressions involving constants, variables, operations and brackets; for example, 7+7+7=3\times7,\;x+x+x=3\times x noting that 3x includes implied multiplication and recognising the difference between 3x+4 and 3(x+4)
- Elaboration formulating algebraic expressions that represent mathematical relationships; for example, translating from words to symbols, “think of a number” type of activities
- Elaboration recognising and applying the concept of variable as something that can change in value, investigating the relationships between variables, and the application to processes on Country/Place, including how cultural expressions of First Nations Australians, such as storytelling, communicate mathematical relationships that can be represented as mathematical expressions
Content descriptorAC9M7A04 Algebra
describe relationships between variables represented in graphs of functions from authentic data
Elaborations (5)
- Elaboration using graphs to analyse a building’s electricity or gas usage over a period of time, the value of shares on a stock market, or the temperature during a day, interpreting and discussing the relationships they represent
- Elaboration using travel graphs to compare the distance travelled to and from school, interpreting and discussing features of travel graphs such as the slope of lines and the meaning of horizontal line segments
- Elaboration telling the story behind what is being represented in graphs of functions; for example, graphs representing pouring rates or distance versus time
- Elaboration exploring how functions are used in machine learning to model relationships; for example, in linear regression models, a linear function is used to map input features to predictions
- Elaboration using graphs of evaporation rates to explore and discuss First Nations Australians’ methods of water resource management
Content descriptorAC9M7A06 Algebra
manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables
Elaborations (5)
- Elaboration experimenting with different sets of tables of values from formulas; for example, using volume of a rectangular prism = length × width × height, and specifying a fixed width and equal length and varying the height
- Elaboration using spreadsheets and the formula function to recognise the effect of changing parameters on the entries in cells
- Elaboration analysing distance travelled for different combinations of average speed and time of travel using a table of values and the distance formula
- Elaboration exploring how deep learning models used for training artificial intelligence agents can involve the manipulation of mathematical functions with multiple variables; for example, conducting a sensitivity analysis to understand the artificial intelligence model's behaviour
- Elaboration understanding that the relationship between variables in an artificial intelligence model assists with explainability and interpretability; for example, manipulating and analysing formulas allows researchers to gain insights into how and why a model makes certain predictions
They solve linear equations with natural number solutions.
Content descriptorAC9M7A03 Algebra
solve one-variable linear equations with natural number solutions; verify the solution by substitution
Elaborations (3)
- Elaboration recognising that solving an equation is a process of determining a value that makes the equation true; using substitution to determine whether a given number is a solution to an equation or not
- Elaboration solving equations using concrete materials, the balance model, and backtracking, explaining the process
- Elaboration solving linear equations such as 3x+7=19 algebraically, and verifying the solution by substitution
Students create tables of values related to algebraic expressions and formulas, and describe the effect of variation.
Content descriptorAC9M7A05 Algebra
generate tables of values from visually growing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane
Elaborations (5)
- Elaboration plotting points from a table of values generated using simple linear functions and recognising patterns, such as the points lie on a straight line
- Elaboration discussing and using variables to create a general rule and use the rule to determine the value of the dependent variable for any given value of the independent variable; for example, plotting the value of the circumference of a circle for varying values of radius
- Elaboration using function machines to generate a table of ordered pairs using input and output values, plotting the relationships on a Cartesian plane and describing the graph in terms of shape
- Elaboration using diagrams and manipulatives to form linear growth patterns, representing these patterns in tables and describing the relationship in terms of the way the pattern is growing and in the context of the situation
- Elaboration using a simple general-purpose programming language to create and use algorithms that generate growing patterns and graphing the relationships on a Cartesian plane
Content descriptorAC9M7A06 Algebra
manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables
Elaborations (5)
- Elaboration experimenting with different sets of tables of values from formulas; for example, using volume of a rectangular prism = length × width × height, and specifying a fixed width and equal length and varying the height
- Elaboration using spreadsheets and the formula function to recognise the effect of changing parameters on the entries in cells
- Elaboration analysing distance travelled for different combinations of average speed and time of travel using a table of values and the distance formula
- Elaboration exploring how deep learning models used for training artificial intelligence agents can involve the manipulation of mathematical functions with multiple variables; for example, conducting a sensitivity analysis to understand the artificial intelligence model's behaviour
- Elaboration understanding that the relationship between variables in an artificial intelligence model assists with explainability and interpretability; for example, manipulating and analysing formulas allows researchers to gain insights into how and why a model makes certain predictions
They apply knowledge of angle relationships and the sum of angles in a triangle to solve problems, giving reasons.
Content descriptorAC9M7M04 Measurement
identify corresponding, alternate and co-interior relationships between angles formed when parallel lines are crossed by a transversal; use them to solve problems and explain reasons
Elaborations (4)
- Elaboration constructing a pair of parallel lines and a pair of perpendicular lines using their properties, a pair of compasses and a ruler, set squares or using dynamic geometry software
- Elaboration using dynamic geometry software to identify relationships between alternate, corresponding and co-interior angles for a pair of parallel lines cut by a transversal
- Elaboration using dynamic geometry software to demonstrate how angles and their properties are involved in the design and construction of scissor lifts, folding umbrellas, toolboxes and cherry pickers
- Elaboration using geometric reasoning of angle properties to generalise the angle relationships of parallel lines and transversals, and related properties such as the size of an exterior angle of a triangle is equal to the sum of the sizes of opposite and non-adjacent interior angles, and the sum of the sizes of interior angles in a triangle in the plane is equal to the size of 2 right angles or 180°
Content descriptorAC9M7M05 Measurement
demonstrate that the interior angle sum of a triangle in the plane is 180° and apply this to determine the interior angle sum of other shapes and the size of unknown angles
Elaborations (2)
- Elaboration using concrete materials to demonstrate that the sum of the interior angles of a triangle is 180°; for example, using paper triangles and tearing to demonstrate that the interior angles when combined form 180°
- Elaboration using decomposition and the angle sum of a triangle to generalise the interior angle sum of an n-sided polygon, as 180(n-2)\;=\;180n-360
Students use formulas for the areas of triangles and parallelograms and the volumes of rectangular and triangular prisms to solve problems.
Content descriptorAC9M7A01 Algebra
recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown
Elaborations (4)
- Elaboration linking variables to attributes and measures being modelled when using formulas, such as the area of a rectangle is equal to the length x width as A\;=\;l\;\times\;w or using p\;=\;6g\;+\;b to describe a total of points expressed as goals (worth 6 points) and behinds (worth one point)
- Elaboration interpreting and using formulas obtained from other sources; for example, maximum heart rates and target heart rates for moderate exercise
- Elaboration substituting numerical values for variables when using formulas and calculating the value of an unknown in practical situations; for example, calculating weekly wage W given base wage b and overtime hours h at 1.5 times rate r, W\;=\;b+1.5\times h\times r, using values for mass m and volume v to determine density d of a substance where d\;=\;\frac mv
- Elaboration using everyday formulas and their application to contexts on Country/Place, investigating the relationships between variables
Content descriptorAC9M7M01 Measurement
solve problems involving the area of triangles and parallelograms using established formulas and appropriate units
Elaborations (3)
- Elaboration using the formula for the area of a rectangle and the array structure to derive the formula for the area of a triangle and the area of a parallelogram , given their perpendicular heights; for example, establish that the area of a triangle is half the area of an appropriate rectangle by using the spatial relationship between rectangles and different types of triangles
- Elaboration using dynamic geometry software to demonstrate how the sliding of the vertex of a triangle at a fixed altitude opposite a side leaves the area of the triangle unchanged
- Elaboration using established formulas to solve practical problems involving the area of triangles, parallelograms and rectangles; for example, estimating the cost of materials needed to make shade sails based on a price per metre or determining different combinations of dimensions that lead to a given area
Content descriptorAC9M7M02 Measurement
solve problems involving the volume of right prisms including rectangular and triangular prisms, using established formulas and appropriate units
Elaborations (4)
- Elaboration building a rectangular prism out of unit cubes and showing that the measure of volume is the same as would be found by multiplying the 3 edge lengths or by multiplying the area of the base by the height/length
- Elaboration developing the connection between the area of the parallel cross-section (base), the height and volume of a rectangular or triangular prism to other prisms
- Elaboration connecting the area of the floor space and the number of floors of a high-rise building to calculate the volume of a building
- Elaboration using dynamic geometry software, spatial reasoning and prediction to derive the formula for the volume of prisms
They describe the relationships between the radius, diameter and circumference of a circle.
Content descriptorAC9M7M03 Measurement
describe the relationship between π and the features of circles including the circumference, radius and diameter
Elaborations (4)
- Elaboration recognising the features of circles and their relationships to one another; for example, labelling the parts of a circle including centre, radius, diameter, circumference and using one of radius, diameter or circumference to determine the measure of the other 2; understanding that the diameter of a circle is twice the radius, or that the radius is the circumference divided by 2π
- Elaboration comparing the circumference of circles in relation to their radius and diameter with materials and measuring, to establish measurement formulas; for example, using a compass to draw several circles, then using string to approximate the circumference, comparing the length of string to the diameter of the circle
- Elaboration investigating π as the constant in the proportional relationship between the circumference of a circle and its diameter, and historical approximations from different civilisations, including Egypt, Babylon, Greece, India and China
- Elaboration investigating the applications and significance of circles in everyday life of First Nations Australians such as in basketry, symbols and architecture, recognising the relationships between the centre, radius, diameter and circumference
Students classify polygons according to their features and create an algorithm designed to sort and classify shapes.
Content descriptorAC9M7SP02 Space
classify triangles, quadrilaterals and other polygons according to their side and angle properties; identify and reason about relationships
Elaborations (4)
- Elaboration using strips of paper with parallel sides to make triangles and quadrilaterals, and contrasting the rigidity of triangles with the flexibility of quadrilaterals
- Elaboration constructing triangles with 3 given side lengths and discussing the question, “Can any 3 lengths be used to form the sides of a triangle?”
- Elaboration identifying and communicating about side and angle properties of scalene, isosceles, equilateral, right-angled, acute and obtuse triangles using geometric conventions
- Elaboration describing, comparing and contrasting squares, rectangles, rhombuses, parallelograms, kites and trapeziums, explaining the relationships between these shapes
Content descriptorAC9M7SP04 Space
design and create algorithms involving a sequence of steps and decisions that will sort and classify sets of shapes according to their attributes, and describe how the algorithms work
Elaborations (3)
- Elaboration creating a classification scheme for triangles based on sides and angles, using a flow chart using sequences and decisions
- Elaboration creating a flow chart or hierarchy for quadrilaterals that shows the relationships between trapeziums, parallelograms, rhombuses, rectangles, squares and kites
- Elaboration creating a classification scheme for regular, irregular, concave or convex polygons that are sorted according to the number of sides
They represent objects two-dimensionally in different ways, describing the usefulness of these representations.
Content descriptorAC9M7SP01 Space
represent objects in 2 dimensions; discuss and reason about the advantages and disadvantages of different representations
Elaborations (6)
- Elaboration deconstructing packaging to identify shapes and nets
- Elaboration using different nets to construct prisms and determining which nets will make a cube, rectangular prism, triangular prism or pyramid
- Elaboration using aerial views of buildings and other three-dimensional structures to visualise the footprint made by the building or structure, identifying prisms that could approximate the structure
- Elaboration building objects by interpreting isometric and perspective drawings
- Elaboration using isometric and square grid paper to draw views of front, back, side, top and bottom of objects
- Elaboration exploring different two-dimensional representations of objects in First Nations Australians’ artworks or cultural maps of Country/Place
Students use coordinates to describe transformations of points in the plane.
Content descriptorAC9M7SP03 Space
describe transformations of a set of points using coordinates in the Cartesian plane, translations and reflections on an axis, and rotations about a given point
Elaborations (3)
- Elaboration using digital tools to transform shapes in the Cartesian plane, describing and recording the transformations
- Elaboration describing patterns and investigating different ways to produce the same transformation, such as using 2 successive reflections to provide the same result as a translation
- Elaboration experimenting with, creating and re-creating patterns using combinations of translations, reflections and rotations, using digital tools
They plan and conduct statistical investigations involving discrete and continuous numerical data, using appropriate displays.
Content descriptorAC9M7ST01 Statistics
acquire data sets for discrete and continuous numerical variables and calculate the range, median, mean and mode; make and justify decisions about which measures of central tendency provide useful insights into the nature of the distribution of data
Elaborations (5)
- Elaboration understanding that summarising data by calculating measures of centre can help make sense of the data, commenting on skewness or symmetry of data and the use of mean and median as representative measures
- Elaboration comparing the mean, median, mode and range of displays of data from a given context, and explaining how outliers may affect summary statistics
- Elaboration recognising how different data sets can have the same measures of central tendency and experimenting with how varying data affects these measures
- Elaboration acquire continuous numerical data by taking measurement samples during a science experiment, observation or field study, comparing measures of central tendency and identifying any anomalies in the distribution of data
- Elaboration exploring how descriptive statistics are used by artificial intelligence developers to summarise and analyse data, assist the artificial intelligence in making informed decisions, and gain insights from the processed data; for example, descriptive statistics in recommendation systems can help analyse user behaviour and preferences
Content descriptorAC9M7ST02 Statistics
create different types of numerical data displays including stem-and-leaf plots using software where appropriate; describe and compare the distribution of data, commenting on the shape, centre and spread including outliers and determining the range, median, mean and mode
Elaborations (6)
- Elaboration using ordered stem-and-leaf plots to record and display numerical data collected in a class investigation, such as constructing a class plot of height in centimetres on a shared stem-and-leaf plot for which the stems 12, 13, 14, 15, 16 and 17 have been produced
- Elaboration comparing variation in attributes by category using split stem-and-leaf plots or dot plots; interpreting the shape of the distribution using qualitative terms to describe symmetry or skewness, “average” in terms of the mean, median and mode, and the amount of variation based on qualitative descriptions of the spread of the data
- Elaboration connecting features of the data display; for example, highest frequency, clusters, gaps, symmetry or skewness, to the mode, range and median, and the question in context; describing the shape of distributions using terms such as "positive skew", "negative skew", "symmetric" and "bi-modal" and discussing the location of the median and mean on these distributions
- Elaboration using mean and median to compare data sets, identifying possible outliers and explaining how these may affect the comparison; recognising how different displays make specific information about data more evident, including proportions, and measures of mean, mode or median, spread and extreme values; understanding that the median and the mean will be the same or similar for symmetric distributions but different for distributions that are skewed
- Elaboration comparing the mean and median of data with and without extremes; for example, estimation of standard measures for length or mass, informally considering for a given set of data what might constitute an unexpected, unusual or extreme data value
- Elaboration exploring how artificial intelligence systems can also use descriptive statistics to identify outliers or anomalies in data; for example, fraud detection and quality control
Content descriptorAC9M7ST03 Statistics
plan and conduct statistical investigations involving data for discrete and continuous numerical variables; analyse and interpret distributions of data and report findings in terms of shape and summary statistics
Elaborations (3)
- Elaboration conducting an investigation to draw conclusions about whether teenagers have faster reaction times than adults
- Elaboration conducting an investigation to support claims that a modification of a Science, Technology, Engineering and Mathematics (STEM) related design has improved performance
- Elaboration using secondary data from the Reconciliation Barometer to conduct and report on statistical investigations relating to First Nations Australians
Students interpret data in terms of the shape of distribution and summary statistics, identifying possible outliers.
Content descriptorAC9M7ST01 Statistics
acquire data sets for discrete and continuous numerical variables and calculate the range, median, mean and mode; make and justify decisions about which measures of central tendency provide useful insights into the nature of the distribution of data
Elaborations (5)
- Elaboration understanding that summarising data by calculating measures of centre can help make sense of the data, commenting on skewness or symmetry of data and the use of mean and median as representative measures
- Elaboration comparing the mean, median, mode and range of displays of data from a given context, and explaining how outliers may affect summary statistics
- Elaboration recognising how different data sets can have the same measures of central tendency and experimenting with how varying data affects these measures
- Elaboration acquire continuous numerical data by taking measurement samples during a science experiment, observation or field study, comparing measures of central tendency and identifying any anomalies in the distribution of data
- Elaboration exploring how descriptive statistics are used by artificial intelligence developers to summarise and analyse data, assist the artificial intelligence in making informed decisions, and gain insights from the processed data; for example, descriptive statistics in recommendation systems can help analyse user behaviour and preferences
Content descriptorAC9M7ST02 Statistics
create different types of numerical data displays including stem-and-leaf plots using software where appropriate; describe and compare the distribution of data, commenting on the shape, centre and spread including outliers and determining the range, median, mean and mode
Elaborations (6)
- Elaboration using ordered stem-and-leaf plots to record and display numerical data collected in a class investigation, such as constructing a class plot of height in centimetres on a shared stem-and-leaf plot for which the stems 12, 13, 14, 15, 16 and 17 have been produced
- Elaboration comparing variation in attributes by category using split stem-and-leaf plots or dot plots; interpreting the shape of the distribution using qualitative terms to describe symmetry or skewness, “average” in terms of the mean, median and mode, and the amount of variation based on qualitative descriptions of the spread of the data
- Elaboration connecting features of the data display; for example, highest frequency, clusters, gaps, symmetry or skewness, to the mode, range and median, and the question in context; describing the shape of distributions using terms such as "positive skew", "negative skew", "symmetric" and "bi-modal" and discussing the location of the median and mean on these distributions
- Elaboration using mean and median to compare data sets, identifying possible outliers and explaining how these may affect the comparison; recognising how different displays make specific information about data more evident, including proportions, and measures of mean, mode or median, spread and extreme values; understanding that the median and the mean will be the same or similar for symmetric distributions but different for distributions that are skewed
- Elaboration comparing the mean and median of data with and without extremes; for example, estimation of standard measures for length or mass, informally considering for a given set of data what might constitute an unexpected, unusual or extreme data value
- Elaboration exploring how artificial intelligence systems can also use descriptive statistics to identify outliers or anomalies in data; for example, fraud detection and quality control
They decide which measure of central tendency is most suitable and explain their reasoning.
Content descriptorAC9M7ST01 Statistics
acquire data sets for discrete and continuous numerical variables and calculate the range, median, mean and mode; make and justify decisions about which measures of central tendency provide useful insights into the nature of the distribution of data
Elaborations (5)
- Elaboration understanding that summarising data by calculating measures of centre can help make sense of the data, commenting on skewness or symmetry of data and the use of mean and median as representative measures
- Elaboration comparing the mean, median, mode and range of displays of data from a given context, and explaining how outliers may affect summary statistics
- Elaboration recognising how different data sets can have the same measures of central tendency and experimenting with how varying data affects these measures
- Elaboration acquire continuous numerical data by taking measurement samples during a science experiment, observation or field study, comparing measures of central tendency and identifying any anomalies in the distribution of data
- Elaboration exploring how descriptive statistics are used by artificial intelligence developers to summarise and analyse data, assist the artificial intelligence in making informed decisions, and gain insights from the processed data; for example, descriptive statistics in recommendation systems can help analyse user behaviour and preferences
Content descriptorAC9M7ST02 Statistics
create different types of numerical data displays including stem-and-leaf plots using software where appropriate; describe and compare the distribution of data, commenting on the shape, centre and spread including outliers and determining the range, median, mean and mode
Elaborations (6)
- Elaboration using ordered stem-and-leaf plots to record and display numerical data collected in a class investigation, such as constructing a class plot of height in centimetres on a shared stem-and-leaf plot for which the stems 12, 13, 14, 15, 16 and 17 have been produced
- Elaboration comparing variation in attributes by category using split stem-and-leaf plots or dot plots; interpreting the shape of the distribution using qualitative terms to describe symmetry or skewness, “average” in terms of the mean, median and mode, and the amount of variation based on qualitative descriptions of the spread of the data
- Elaboration connecting features of the data display; for example, highest frequency, clusters, gaps, symmetry or skewness, to the mode, range and median, and the question in context; describing the shape of distributions using terms such as "positive skew", "negative skew", "symmetric" and "bi-modal" and discussing the location of the median and mean on these distributions
- Elaboration using mean and median to compare data sets, identifying possible outliers and explaining how these may affect the comparison; recognising how different displays make specific information about data more evident, including proportions, and measures of mean, mode or median, spread and extreme values; understanding that the median and the mean will be the same or similar for symmetric distributions but different for distributions that are skewed
- Elaboration comparing the mean and median of data with and without extremes; for example, estimation of standard measures for length or mass, informally considering for a given set of data what might constitute an unexpected, unusual or extreme data value
- Elaboration exploring how artificial intelligence systems can also use descriptive statistics to identify outliers or anomalies in data; for example, fraud detection and quality control
Students list sample spaces for single step experiments, assign probabilities to outcomes and predict relative frequencies for related events.
Content descriptorAC9M7P01 Probability
identify the sample space for single-stage events; assign probabilities to the outcomes of these events and predict relative frequencies for related events
Elaborations (4)
- Elaboration discussing the meaning of probability terminology; for example, “probability”, “sample space”, “favourable outcome”, “trial”, “experiment” and “event”
- Elaboration listing sample spaces for games involving throwing a coin or a dice, spinners, or lucky dip
- Elaboration exploring how relative frequencies can be used to make predictions by estimating the probability of an event; for example, in natural language processing (NLP), predictive text algorithms use the relative frequency of words in a set of texts to predict the next word in a sentence
- Elaboration assigning the probability for throwing a 6 on a dice and using this to predict the number of times a 6 will occur when a dice is thrown multiple times
They conduct repeated single-step chance experiments and run simulations using digital tools, giving reasons for differences between predicted and observed results.
Content descriptorAC9M7P01 Probability
identify the sample space for single-stage events; assign probabilities to the outcomes of these events and predict relative frequencies for related events
Elaborations (4)
- Elaboration discussing the meaning of probability terminology; for example, “probability”, “sample space”, “favourable outcome”, “trial”, “experiment” and “event”
- Elaboration listing sample spaces for games involving throwing a coin or a dice, spinners, or lucky dip
- Elaboration exploring how relative frequencies can be used to make predictions by estimating the probability of an event; for example, in natural language processing (NLP), predictive text algorithms use the relative frequency of words in a set of texts to predict the next word in a sentence
- Elaboration assigning the probability for throwing a 6 on a dice and using this to predict the number of times a 6 will occur when a dice is thrown multiple times
Content descriptorAC9M7P02 Probability
conduct repeated chance experiments and run simulations with a large number of trials using digital tools; compare predictions about outcomes with observed results, explaining the differences
Elaborations (3)
- Elaboration developing an understanding of the law of large numbers through using experiments and simulations to conduct large numbers of trials for seemingly random events and discussing findings
- Elaboration conducting simulations using online simulation tools and comparing the combined results of a large number of trials to predicted results
- Elaboration exploring and observing First Nations Australian children’s instructive games; for example, Koara from the Jawi and Bardi Peoples of Sunday Island in Western Australia, to investigate probability, predicting outcomes for an event and comparing with increasingly larger numbers of trials, and between observed and expected results
This achievement standard describes the expected learning for Year 7 Mathematics. Use it to plan teaching and assessment with the Australian Curriculum v9.
At a Glance
| Strand | Substrand | CDs | Elaborations |
|---|---|---|---|
| Algebra | — | 6 | 25 |
| Measurement | — | 6 | 21 |
| Number | — | 9 | 35 |
| Probability | — | 2 | 7 |
| Space | — | 4 | 16 |
| Statistics | — | 3 | 14 |
| Total | 30 | 118 | |