Skip to main content Skip to navigation

Mathematics

Filter
Filter
  1. 4
  2. 5
  3. 6
  4. 7
  5. 8
  6. 9
  7. 10

Level 4

Level 4 Description

In Level 4, students extend the number system to simple decimal fractions, and broaden their use of measures and scales.

Students model, represent and order numbers to tens of thousands, and extend place value to tenths and hundredths. They investigate odd and even numbers and explore number patterns based on multiples of 3, 4, 6, 7, 8 and 9. Students develop facility with multiplication facts...

Show more

Level 4 Content Descriptions

Measurement and Geometry

Using units of measurement Elaborations
  1. Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (VCMMG165)
    1. reading and interpreting, to the nearest graduation, the graduated scales on a range of measuring instruments
  2. Compare objects using familiar metric units of area and volume (VCMMG166)
    1. comparing areas using grid paper
    2. comparing volume using centicubes
    3. recognising that metric units are not the only units used throughout the world, for example measuring the area of floor space using tatami mats (Japan), using squares for room and house area (Australia)
  3. Convert between units of time (VCMMG167)
    1. identifying and using the correct operation for converting units of time
  4. Use am and pm notation and solve simple time problems (VCMMG168)
    1. calculating the time spent at school during a normal school day
    2. calculating the time required to travel between two locations
    3. determining arrival time given departure time
Shape Elaborations
  1. Compare the areas of regular and irregular shapes by informal means (VCMMG169)
    1. comparing areas using metric units, such as counting the number of square centimetres required to cover two areas by overlaying the areas with a grid of centimetre squares
  2. Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (VCMMG170)
    1. identifying common two-dimensional shapes that are part of a composite shape by re-creating it from these shapes
    2. creating two-dimensional shapes from verbal or written instructions
  3. Explain and compare the geometric properties of two-dimensional shapes and three-dimensional objects (VCMMG171)
    1. describing the similarities and differences between two-dimensional shapes and three-dimensional objects
    2. recognising two-dimensional shapes that are the faces for three-dimensional objects such as prisms, pyramids and platonic solids (including tetrahedrons, cubes and dodecahedrons)
Location and transformation Elaborations
  1. Use simple scales, legends and directions to interpret information contained in basic maps (VCMMG172)
    1. identifying the scale used on maps of cities and rural areas in Australia and a city in Indonesia and describing the difference
    2. using directions to find features on a map
  2. Create symmetrical patterns, pictures and shapes with and without digital technologies (VCMMG173)
    1. using stimulus materials such as the motifs in Central Asian textiles, Tibetan artefacts, Indian lotus designs and symmetry in Yolngu or Central and Western Desert art
Geometric reasoning Elaborations
  1. Compare angles and classify them as equal to, greater than or less than a right angle (VCMMG174)
    1. creating angles and comparing them to a right angle using digital technologies

Level 4 Achievement Standard

Number and Algebra

Students recall multiplication facts to 10 x 10 and related division facts. They choose appropriate strategies for calculations involving multiplication and division, with and without the use of digital technology, and estimate answers accurately enough for the context. Students solve simple purchasing problems with and without the use of digital technology. They locate familiar fractions on a number line, recognise common equivalent fractions in familiar contexts and make connections between fractions and decimal notations up to two decimal places. Students identify unknown quantities in number sentences. They use the properties of odd and even numbers and describe number patterns resulting from multiplication. Students continue number sequences involving multiples of single-digit numbers and unit fractions, and locate them on a number line.

Measurement and Geometry

Students compare areas of regular and irregular shapes, using informal units. They solve problems involving time duration. Students use scaled instruments to measure length, angle, area, mass, capacity and temperature of shapes and objects. They convert between units of time. Students create symmetrical simple and composite shapes and patterns, with and without the use of digital technology. They classify angles in relation to a right angle. Students interpret information contained in maps.

Statistics and Probability

Students describe different methods for data collection and representation, and evaluate their effectiveness. They construct data displays from given or collected data, with and without the use of digital technology. Students list the probabilities of everyday events. They identify dependent and independent events.

Level 5

Level 5 Description

In Level 5, students extend decimal fractions to thousandths, and explore the ideas of factors, multiples and divisibility.

Students use estimation and rounding for all four operations, with and without the use of technology for calculation. They solve multiple digit problems involving addition, subtraction, multiplication and division by single digit divisors with remainders. Students represent...

Show more

Level 5 Content Descriptions

Measurement and Geometry

Using units of measurement Elaborations
  1. Choose appropriate units of measurement for length, area, volume, capacity and mass (VCMMG195)
    1. investigating alternative measures of scale to demonstrate that these vary between countries and change over time. For example, temperature measurement in Australia, Indonesia, Japan and USA
    2. recognising that some units of measurement are better suited for some tasks than others, for example kilometres rather than metres to measure the distance between two towns
  2. Calculate the perimeter and area of rectangles and the volume and capacity of prisms using familiar metric units (VCMMG196)
    1. exploring efficient ways of calculating the perimeters of rectangles such as adding the length and width together and doubling the result
    2. exploring efficient ways of finding the areas of rectangles
    3. measuring volume and capacity by counting the number of cubes (cubic centimetres)
    4. exploring efficient ways of finding the volume and capacity of rectangular prisms and cubes
  3. Compare 12- and 24-hour time systems and convert between them (VCMMG197)
    1. investigating the ways time was and is measured in different Aboriginal Country, such as using tidal change
    2. using units hours, minutes and seconds
Shape Elaborations
  1. Connect three-dimensional objects with their nets and other two-dimensional representations (VCMMG198)
    1. identifying the shape and relative position of each face of a solid to determine the net of the solid, including that of prisms and pyramids
    2. representing two-dimensional shapes such as photographs, sketches and images created by digital technologies
Location and transformation Elaborations
  1. Use a grid reference system to describe locations. Describe routes using landmarks and directional language (VCMMG199)
    1. comparing aerial views of Country, desert paintings and maps with grid references
    2. creating a grid reference system for the classroom and using it to locate objects and describe routes from one object to another
  2. Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries (VCMMG200)
    1. identifying and describing the line and rotational symmetry of a range of two-dimensional shapes, by manually cutting, folding and turning shapes and by using digital technologies
    2. identifying the effects of transformations by manually flipping, sliding and turning two-dimensional shapes and by using digital technologies
  3. Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original (VCMMG201)
    1. using digital technologies to enlarge shapes
    2. using a grid system to enlarge a favourite image or cartoon
Geometric reasoning Elaborations
  1. Estimate, measure and compare angles using degrees. Construct angles using a protractor (VCMMG202)
    1. measuring and constructing angles using both 180° and 360° protractors
    2. recognising that angles have arms and a vertex, and that size is the amount of turn required for one arm to coincide with the other

Level 5 Achievement Standard

Number and Algebra

Students solve simple problems involving the four operations using a range of strategies including digital technology. They estimate to check the reasonableness of answers and approximate answers by rounding. Students identify and describe factors and multiples. They explain plans for simple budgets. Students order decimals and unit fractions and locate them on a number line. Students add and subtract fractions with the same denominator. They find unknown quantities in number sentences and continue patterns by adding or subtracting fractions and decimals.

Measurement and Geometry

Students use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles and volume, and capacity of rectangular prisms. They convert between 12 and 24-hour time. Students use a grid reference system to locate landmarks. They estimate angles, and use protractors and digital technology to construct and measure angles. Students connect three-dimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry.

Statistics and Probability

Students pose questions to gather data and construct various displays appropriate for the data, with and without the use of digital technology. They compare and interpret different data sets. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities as a number from 0 to 1.

Level 6

Level 6 Description

In Level 6, students work with prime, composite, square and triangular numbers and carry out mental, written and technology based computation to solve whole number problems involving all four operations. They explore everyday situations involving integers, and use a number line to represent them. They scale decimals by powers of ten, and add and subtract decimals with and without technology,...

Show more

Level 6 Content Descriptions

Measurement and Geometry

Using units of measurement Elaborations
  1. Connect decimal representations to the metric system (VCMMG222)
    1. recognising the equivalence of measurements such as 1.25 metres and 125 centimetres
  2. Convert between common metric units of length, mass and capacity (VCMMG223)
    1. identifying and using the correct operations when converting units including millimetres, centimetres, metres, kilometres, milligrams, grams, kilograms, tonnes, millilitres, litres, kilolitres and megalitres
    2. recognising the significance of the prefixes in units of measurement
  3. Solve problems involving the comparison of lengths and areas using appropriate units (VCMMG224)
    1. recognising and investigating familiar objects using concrete materials and digital technologies
  4. Connect volume and capacity and their units of measurement (VCMMG225)
    1. recognising that 1ml is equivalent to 1cm3
  5. Interpret and use timetables (VCMMG226)
    1. planning a trip involving one or more modes of public transport
    2. developing a timetable of daily activities
  6. Measure, calculate and compare elapsed time (VCMMG227)
    1. recognising that some units of time are better suited for some tasks than others, for example, seconds rather than minutes to measure the duration of a short event
    2. using a stopwatch to measure and compare the duration of a series of events, for example, how long does it take to jump a skipping rope 100 times
    3. using the starting and finishing times to calculate and compare elapsed time, for example, the time taken to walk to school compared to the time taken to ride to school
Shape Elaborations
  1. Construct simple prisms and pyramids (VCMMG228)
    1. considering the history and significance of pyramids from a range of cultural perspectives including those structures found in China, Korea and Indonesia
    2. constructing prisms and pyramids from nets, and skeletal models
Location and transformation Elaborations
  1. Investigate the effect of combinations of transformations on simple and composite shapes, including creating tessellations, with and without the use of digital technologies (VCMMG229)
    1. understanding which attributes of a shape remain the same or change under the effects of transformations such as size, shape or orientation
    2. creating tessellations with simple shapes or simple composite shapes
  2. Introduce the Cartesian coordinate system using all four quadrants (VCMMG230)
    1. understanding that the Cartesian plane provides a graphical or visual way of describing location
Geometric reasoning Elaborations
  1. Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles (VCMMG231)
    1. identifying the size of a right angle as 90° and defining acute, obtuse, straight and reflex angles
    2. measuring, estimating and comparing angles in degrees and classifying angles according to their sizes
    3. investigating the use of rotation and symmetry in the diagrammatic representations of kinship relationships of Central and Western Desert people
    4. recognising and using the two alternate conventions for naming angles

Level 6 Achievement Standard

Number and Algebra

Students recognise the properties of prime, composite, square and triangular numbers and determine sets of these numbers. They solve problems that involve all four operations with whole numbers and describe the use of integers in everyday contexts. Students locate fractions and integers on a number line and connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students calculate a simple fraction of a quantity and calculate common percentage discounts on sale items, with and without the use of digital technology. They make connections between the powers of 10 and the multiplication and division of decimals. Students add, subtract and multiply decimals and divide decimals where the result is rational. Students write number sentences using brackets and order of operations, and specify rules used to generate sequences involving whole numbers, fractions and decimals. They use ordered pairs of integers to represent coordinates of points and locate a point in any one of the four quadrants on the Cartesian plane.

Measurement and Geometry

Students relate decimals to the metric system and choose appropriate units of measurement to perform a calculation. They solve problems involving time, length and area, and make connections between capacity and volume. Students interpret a variety of everyday timetables. They solve problems using the properties of angles and investigate simple combinations of transformations in the plane, with and without the use of digital technology. Students construct simple prisms and pyramids.

Statistics and Probability

Students interpret and compare a variety of data displays, including displays for two categorical variables. They analyse and evaluate data from secondary sources. Students compare observed and expected frequencies of events, including those where outcomes of trials are generated with the use of digital technology. They specify, list and communicate probabilities of events using simple ratios, fractions, decimals and percentages.

Level 7

Level 7 Description

In Level 7, students work with powers of whole numbers, use index notation, represent numbers as products of powers of prime numbers, and investigate square roots of perfect squares. They use number properties to assist with calculation and order, and to add and subtract integers. Students find equivalent fractions, represent positive and negative fractions and mixed numbers on a number line...

Show more

Level 7 Content Descriptions

Measurement and Geometry

Using units of measurement Elaborations
  1. Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving (VCMMG258)
    1. building on the understanding of the area of rectangles to develop formulas for the area of triangles
    2. establishing that the area of a triangle is half the area of an appropriate rectangle
    3. using area formulas for rectangles and triangles to solve problems involving areas of surfaces
  2. Calculate volumes of rectangular prisms (VCMMG259)
    1. investigating volumes of cubes and rectangular prisms and establishing and using the formula V = l × b × h
    2. understanding and using cubic units when interpreting and finding volumes of cubes and rectangular prisms
Shape Elaborations
  1. Draw different views of prisms and solids formed from combinations of prisms (VCMMG260)
    1. using aerial views of buildings and other 3-D structures to visualise the structure of the building or prism
Location and transformation Elaborations
  1. Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries (VCMMG261)
    1. describing patterns and investigating different ways to produce the same transformation such as using two successive reflections to provide the same result as a translation
    2. creating and re-creating patterns using combinations of reflections and rotations, using digital technologies
Geometric reasoning Elaborations
  1. Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal (VCMMG264)
    1. defining and classifying pairs of angles as complementary, supplementary, adjacent and vertically opposite
  2. Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning (VCMMG265)
    1. constructing parallel and perpendicular lines using their properties, a pair of compasses and a ruler, and dynamic geometry software
    2. defining and identifying the relationships between alternate, corresponding and co-interior angles for a pair of parallel lines cut by a transversal
  3. Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral (VCMMG263)
    1. using concrete materials and digital technologies to investigate the angle sum of a triangle and quadrilateral
  4. Classify triangles according to their side and angle properties and describe quadrilaterals (VCMMG262)
    1. identifying side and angle properties of scalene, isosceles, right-angled and obtuse-angled triangles
    2. describing squares, rectangles, rhombuses, parallelograms, kites and trapeziums

Level 7 Achievement Standard

Number and Algebra

Students solve problems involving the order, addition and subtraction of integers. They make the connections between whole numbers and index notation and the relationship between perfect squares and square roots. They solve problems involving all four operations with fractions, decimals, percentages and their equivalences, and express fractions in their simplest form. Students compare the cost of items to make financial decisions, with and without the use of digital technology. They make simple estimates to judge the reasonableness of results. Students use variables to represent arbitrary numbers and connect the laws and properties of number to algebra and substitute numbers into algebraic expressions. They assign ordered pairs to given points on the Cartesian plane and interpret and analyse graphs of relations from real data. Students develop simple linear models for situations, make predictions based on these models, solve related equations and check their solutions.

Measurement and Geometry

Students use formulas for the area and perimeter of rectangles. They classify triangles and quadrilaterals and represent transformations of these shapes on the Cartesian plane, with and without the use of digital technology. Students name the types of angles formed by transversals crossing parallel lines and solve simple numerical problems involving these lines and angles. They describe different views of three-dimensional objects, and use models, sketches and digital technology to represent these views. Students calculate volumes of rectangular prisms.

Statistics and Probability

Students identify issues involving the collection of discrete and continuous data from primary and secondary sources. They construct stem-and-leaf plots and dot-plots. Students identify or calculate mean, mode, median and range for data sets, using digital technology for larger data sets. They describe the relationship between the median and mean in data displays. Students determine the sample space for simple experiments with equally likely outcomes, and assign probabilities outcomes.

Level 8

Level 8 Description

In Level 8, students consolidate their proficiency with the four arithmetic operations, and combinations of these, for general computation involving natural numbers, integers and rational numbers, with and without the use of technology. They represent these numbers on the real number line. They extend the use of indices and develop the index laws using number examples. Students investigate the...

Show more

Level 8 Content Descriptions

Measurement and Geometry

Using units of measurement Elaborations
  1. Choose appropriate units of measurement for area and volume and convert from one unit to another (VCMMG286)
    1. choosing units for area including mm2, cm2, m2, hectares, km2, and units for volume including mm3, cm3, m3
    2. recognising that the conversion factors for area units are the squares of those for the corresponding linear units
    3. recognising that the conversion factors for volume units are the cubes of those for the corresponding linear units
  2. Find perimeters and areas of parallelograms, trapeziums, rhombuses and kites (VCMMG287)
    1. establishing and using formulas for areas such as trapeziums, rhombuses and kites
  3. Investigate the relationship between features of circles such as circumference, area, radius and diameter. Use formulas to solve problems involving determining radius, diameter, circumference and area from each other (VCMMG288)
    1. investigating the circumference and area of circles with materials or by measuring, to establish an understanding of formulas
    2. investigating the area of circles using a square grid or by rearranging a circle divided into sectors
    3. solving problems given one of radius, diameter, circumference or area of a circle, then the other quantities are determined from this
  4. Develop the formulas for volumes of rectangular and triangular prisms and prisms in general. Use formulas to solve problems involving volume (VCMMG289)
    1. investigating the relationship between volumes of rectangular and triangular prisms
  5. Solve problems involving duration, including using 12- and 24-hour time within a single time zone (VCMMG290)
    1. identifying regions in Australia and countries in Asia that are in the same time zone
Geometric reasoning Elaborations
  1. Define congruence of plane shapes using transformations and use transformations of congruent shapes to produce regular patterns in the plane including tessellations with and without the use of digital technology (VCMMG291)
    1. understanding the properties that determine congruence of triangles and recognising which transformations create congruent figures
    2. establishing that two figures are congruent if one shape lies exactly on top of the other after one or more transformations (translation, reflection, rotation), and recognising that the matching sides and the matching angles are equal
    3. exploring tiling patterns in art and design
  2. Develop the conditions for congruence of triangles (VCMMG292)
    1. investigating the minimal conditions needed for the unique construction of triangles, leading to the establishment of the conditions for congruence (SSS, SAS, ASA and RHS)
    2. solving problems using the properties of congruent figures
    3. constructing triangles using the conditions for congruence
  3. Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning (VCMMG293)
    1. establishing the properties of squares, rectangles, parallelograms, rhombuses, trapeziums and kites
    2. identifying properties related to side lengths, parallel sides, angles, diagonals and symmetry

Level 8 Achievement Standard

Number and Algebra

Students use efficient mental and written strategies to make estimates and carry out the four operations with integers, and apply the index laws to whole numbers. They identify and describe rational and irrational numbers in context. Students estimate answers and solve everyday problems involving profit and loss rates, ratios and percentages, with and without the use of digital technology. They simplify a variety of algebraic expressions and connect expansion and factorisation of linear expressions. Students solve linear equations and graph linear relationships on the Cartesian plane.

Measurement and Geometry

Students convert between units of measurement for area and for volume. They find the perimeter and area of parallelograms, rhombuses and kites. Students name the features of circles, calculate circumference and area, and solve problems relating to the volume of prisms. They make sense of time duration in real applications, including the use of 24-hour time. Students identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. They use tools, including digital technology, to construct congruent shapes.

Statistics and Probability

Students explain issues related to the collection of sample data and discuss the effect of outliers on means and medians of the data. They use various approaches, including the use of digital technology, to generate simple random samples from a population. Students model situations with Venn diagrams and two-way tables and explain the use of 'not', 'and' and 'or'. Students choose appropriate language to describe events and experiments. They determine complementary events and calculate the sum of probabilities.

Level 9

Level 9 Description

In Level 9, students develop familiarity with a broader range of non-linear and linear functions and relations, and related algebra and graphs.

Students apply index laws with integer indices to a range of numerical expressions and extend this to algebraic expressions involving numbers and pro-numerals. They use indices to express very large and very small numbers in scientific notation, and apply...

Show more

Level 9 Content Descriptions

Measurement and Geometry

Using units of measurement Elaborations
  1. Calculate the areas of composite shapes (VCMMG312)
    1. understanding that partitioning composite shapes into rectangles and triangles is a strategy for solving problems involving area
  2. Calculate the surface area and volume of cylinders and solve related problems (VCMMG313)
    1. analysing nets of cylinders to establish formulas for surface area
    2. connecting the volume and capacity of a cylinder to solve authentic problems
  3. Solve problems involving the surface area and volume of right prisms (VCMMG314)
    1. solving practical problems involving surface area and volume of right prisms
  4. Investigate very small and very large time scales and intervals (VCMMG315)
    1. investigating the usefulness of scientific notation in representing very large and very small numbers
Geometric reasoning Elaborations
  1. Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar (VCMMG316)
    1. establishing the conditions for similarity of two triangles and comparing this to the conditions for congruence
    2. using the properties of similarity and ratio, and correct mathematical notation and language, to solve problems involving enlargement. For example, scale diagrams
    3. using the enlargement transformation to establish similarityunderstanding that similarity and congruence help describe relationships between geometrical shapes and are important elements of reasoning and proof
  2. Solve problems using ratio and scale factors in similar figures (VCMMG317)
    1. establishing the relationship between areas of similar figures and the ratio of corresponding sides (scale factor)
Pythagoras and trigonometry Elaborations
  1. Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles (VCMMG318)
    1. understanding that Pythagoras' Theorem is a useful tool in determining unknown lengths in right-angled triangles and has widespread applications
    2. recognising that right-angled triangle calculations may generate results that can be integers, fractions or irrational numbers
  2. Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles (VCMMG319)
    1. developing understanding of the relationship between the corresponding sides of similar right-angled triangles
  3. Apply trigonometry to solve right-angled triangle problems (VCMMG320)
    1. understanding the terms 'adjacent' and 'opposite' sides in a right-angled triangle
    2. selecting and accurately using the correct trigonometric ratio to find unknown sides (adjacent, opposite and hypotenuse) and angles in right-angled triangles

Level 9 Achievement Standard

Number and Algebra

Students apply the index laws using integer indices to variables and numbers, express numbers in scientific notation, solve problems involving very small and very large numbers, and check the order of magnitude of calculations. They solve problems involving simple interest. Students use the distributive law to expand algebraic expressions, including binomial expressions, and simplify a range of algebraic expressions. They find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment using a range of strategies including the use of digital technology. Students sketch and draw linear and non-linear relations, solve simple related equations and explain the relationship between the graphical and symbolic forms, with and without the use of digital technology.

Measurement and Geometry

Students solve measurement problems involving perimeter and area of composite shapes, surface area and volume of rectangular prisms and cylinders, with and without the use of digital technology. They relate three-dimensional objects to two-dimensional representations. Students explain similarity of triangles, interpret ratios and scale factors in similar figures, and apply Pythagoras's theorem and trigonometry to solve problems involving angles and lengths in right-angled triangles.

Statistics and Probability

Students compare techniques for collecting data from primary and secondary sources, and identify questions and issues involving different data types. They construct histograms and back-to-back stem-and-leaf plots with and without the use of digital technology. Students identify mean and median in skewed, symmetric and bi-modal displays and use these to describe and interpret the distribution of the data. They calculate relative frequencies to estimate probabilities. Students list outcomes for two-step experiments and assign probabilities for those outcomes and related events.

Level 10

Level 10 Description

In Level 10, students extend their use of mathematical models to a wide range of familiar and unfamiliar contexts, involving the use of all types of real numbers. They recognise the role of logical argument and proof in establishing mathematical propositions. Students apply mental, written or technology-assisted forms of computation as appropriate, and routinely use estimation to validate or...

Show more

Level 10 Content Descriptions

Measurement and Geometry

Using units of measurement Elaborations
  1. Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids (VCMMG343)
    1. investigating and determining the volumes and surface areas of composite solids by considering the individual solids from which they are constructed
Geometric reasoning Elaborations
  1. Formulate proofs involving congruent triangles and angle properties (VCMMG344)
    1. applying an understanding of relationships to deduce properties of geometric figures (for example the base angles of an isosceles triangle are equal)
  2. Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes (VCMMG345)
    1. distinguishing between a practical demonstration and a proof (for example demonstrating triangles are congruent by placing them on top of each other, as compared to using congruence tests to establish that triangles are congruent)
    2. performing a sequence of steps to determine an unknown angle giving a justification in moving from one step to the next.
    3. communicating a proof using a sequence of logically connected statements
Pythagoras and trigonometry Elaborations
  1. Solve right-angled triangle problems including those involving direction and angles of elevation and depression (VCMMG346)
    1. applying Pythagoras's Theorem and trigonometry to problems in surveying and design

Level 10 Achievement Standard

Number and Algebra

Students recognise the connection between simple and compound interest. They solve problems involving linear equations and inequalities, quadratic equations and pairs of simultaneous linear equations and related graphs, with and without the use of digital technology. Students substitute into formulas, find unknown values, manipulate linear algebraic expressions, expand binomial expressions and factorise monic and simple non-monic quadratic expressions, with and without the use of digital technology. They represent linear, quadratic and exponential functions numerically, graphically and algebraically, and use them to model situations and solve practical problems.

Measurement and Geometry

Students solve and explain surface area and volume problems relating to composite solids. They use parallel and perpendicular lines, angle and triangle properties, similarity, trigonometry and congruence to solve practical problems and develop proofs involving lengths, angles and areas in plane shapes. They use digital technology to construct and manipulate geometric shapes and objects, and explore symmetry and pattern in two dimensions.

Statistics and Probability

Students compare univariate data sets by referring to summary statistics and the shape of their displays. They describe bivariate data where the independent variable is time and use scatter-plots generated by digital technology to investigate relationships between two continuous variables. Students evaluate the use of statistics in the media. They list outcomes for multi-step chance experiments involving independent and dependent events, and assign probabilities for these experiments.

Scroll to the top of the page