Level 8 - Victorian Curriculum

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Mathematics Version 2.0

Mathematics Version 2.0 Level Description

In Level 8, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of mathematics that...

In Level 8, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of mathematics that develop their understanding of and fluency with concepts, procedures and processes by making connections, reasoning, problem-solving and practice. Proficiency in mathematics enables students to respond to familiar and unfamiliar situations by employing mathematical strategies to make informed decisions and solve problems efficiently.

Students further develop proficiency and positive dispositions towards mathematics and its use as they:

extend computation with combinations of the 4 operations with integers and positive rational numbers; recognise the relationship between fractions and their terminating or recurring decimal representations; convert between fraction and decimal forms of rational numbers and locate them on the real number line
extend the exponent laws to numerical calculations involving positive and zero exponents, and solve a broad range of practical problems, using mental methods, written algorithms and digital tools
use mathematical modelling to solve problems in a broad range of contexts that involve ratios with 2 or more terms, percentage increase and decrease, proportions with decimal values, and rates in measurement contexts, and apply proportional reasoning
manipulate linear and other algebraic expressions, recognise and model situations using linear relations and solve related equations using tables, graphs and algebra
interpret and explain demonstrations and proofs of Pythagoras’ theorem and investigate irrational numbers, their infinite non-recurring decimal representation and their approximate location on the real number line
select metric measurement units fit for purpose and convert between units, recognising the effects of different levels of measurement accuracy on the results of computations, and relate these to interval estimates for measurements in various contexts
apply knowledge of the relationships between π and the features of circles to solve problems involving circumference and area, establish sets of congruency and similarity conditions for common shapes in the plane and create algorithms to test for these conditions, and discuss examples and counterexamples
construct and locate objects with reference to three-dimensional coordinates using digital tools
consider a variety of situations involving complementary and mutually exclusive events, and combinations of 2 events; and represent these using tables and diagrams, conducting simulations and calculating corresponding probabilities
examine experimental and observational data and identify populations and samples with respect to context; investigate variation in summary statistics across samples of varying size; and discuss their findings.

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Mathematics Version 2.0 Content Descriptions

Number

recognise irrational numbers in applied contexts, including π and numbers that develop from the square root of positive real numbers that are not perfect squares, and recognise that irrational numbers cannot develop from the division of integer values by natural numbers (VC2M8N01)
establish and apply the exponent laws with positive integer exponents and the zero exponent, using exponent notation with numbers (VC2M8N02)
convert between fractions and terminating or recurring decimals, using digital tools as appropriate (VC2M8N03)
use the 4 operations with integers and with rational numbers, choosing and using efficient mental and written strategies, and digital tools where appropriate, and making estimates for these computations (VC2M8N04)
solve problems involving the use of percentages, including percentage increases and decreases and percentage error, with and without digital tools (VC2M8N05)
use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts involving profit and loss; formulate problems, choosing efficient mental and written calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the context, reviewing the appropriateness of the model (VC2M8N06)

Algebra

create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties (VC2M8A01)
graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution (VC2M8A02)
use mathematical modelling to solve applied problems involving linear relations, including financial contexts involving profit and loss; formulate problems with linear functions, and choose a representation; interpret and communicate solutions in terms of the context, and review the appropriateness of the model (VC2M8A03)
use algorithms and related testing procedures to identify and correct errors (VC2M8A04)
experiment with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patterns (VC2M8A05)

Measurement

solve problems involving the area and perimeter of irregular and composite shapes using appropriate units (VC2M8M01)
solve problems involving the volume and capacity of right prisms using appropriate units (VC2M8M02)
solve problems involving the circumference and area of a circle using formulas and appropriate units (VC2M8M03)
solve problems involving time and duration, including using 12- and 24-hour time across multiple time zones (VC2M8M04)
recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure (VC2M8M05)
use Pythagoras’ theorem to solve problems involving the side lengths of right-angled triangles (VC2M8M06)
use mathematical modelling to solve practical problems involving ratios and rates, including distance-time problems for travel at a constant speed and financial contexts; formulate problems; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model (VC2M8M07)

Space

identify the conditions for congruence and similarity of triangles and explain the conditions for other sets of common shapes to be congruent or similar, including those formed by transformations (VC2M8SP01)
establish properties of quadrilaterals using congruent triangles and angle properties, and solve related problems explaining reasoning (VC2M8SP02)
describe in different ways the position and location of three-dimensional objects in 3 dimensions, including using a three-dimensional Cartesian coordinate system with the use of dynamic geometry software or other digital tools (VC2M8SP03)
design and test algorithms involving a sequence of steps and decisions that identify congruency or similarity of shapes, and describe how the algorithm works (VC2M8SP04)

Statistics

distinguish between a population and a sample, and investigate techniques for data collection including census, sampling, experiment and observation, and explain the practicalities and implications of obtaining data through these techniques (VC2M8ST01)
analyse and report on the distribution of data from primary and secondary sources using random and non-random sampling techniques (VC2M8ST02)
compare variations in distributions and proportions obtained from random samples of the same size drawn from a population and recognise the effect of sample size on this variation (VC2M8ST03)
plan and conduct statistical investigations involving samples of a population; use ethical and fair methods to make inferences about the population and report findings, acknowledging uncertainty (VC2M8ST04)

Probability

recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts (VC2M8P01)
determine all possible outcome combinations for 2 events, using two-way tables, tree diagrams and Venn diagrams, and use these to determine probabilities of specific events in practical situations (VC2M8P02)
conduct repeated chance experiments and simulations, using digital tools to determine probabilities for compound events, and describe results (VC2M8P03 )

Mathematics Version 2.0 Achievement Standard

By the end of Level 8, students recognise irrational numbers as numbers that cannot develop from the division of integer values by natural numbers and terminating or recurring decimals. They apply the exponent laws to calculations with numbers involving positive integer exponents. Students solve problems involving the 4 operations with integers and positive rational numbers. They use mathematical modelling to solve practical problems involving ratios, percentages and rates in measurement and financial contexts.

Students apply algebraic properties to simplify, rearrange, expand and factorise linear expressions. They graph linear relations and solve linear equations with rational solutions and one-variable inequalities, graphically and algebraically. Students plot linear and non-linear relations on the Cartesian plane, with and without the use of digital tools. Students use mathematical modelling to solve problems using linear relations, interpreting and reviewing the model in context. They make and test conjectures involving linear relations by developing algorithms and using digital tools.

Students use appropriate metric units when solving measurement problems involving the perimeter and area of composite shapes, and volume of right prisms. They use Pythagoras’ theorem to solve measurement problems involving unknown lengths of right-angled triangles. Students use formulas to solve problems involving the area and circumference of circles. They solve problems of duration involving 12- and 24-hour cycles across multiple time zones.

Students use 3 dimensions to locate and describe position. They identify conditions for congruency and similarity in triangles and other common shapes, and design and test algorithms to test for congruency and similarity. Students apply the properties of quadrilaterals to solve problems.

Students conduct statistical investigations and explain the implications of obtaining data through sampling. Students analyse and describe the distribution of data. They compare the variation in distributions of random samples of the same and different size from a given population with respect to shape, measures of central tendency and range.

Students represent the possible combinations of 2 events with tables and diagrams, and determine related probabilities to solve practical problems. They conduct experiments or simulations using digital tools to determine related probabilities of compound events.

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