skip to main content
NSW Syllabuses

Stage 5 stage statements

English Stage 5 Stage Statement

By the end of Stage 5 students respond to and compose a comprehensive range of imaginative, factual and critical texts using different modes and technologies. They enjoy, reflect on, critically assess and articulate processes of response and composition. They respond to and compose a wide range of simple and complex texts for pleasure, critical analysis and information-gathering, varying their approach according to a text's purpose, audience and context. They focus on details of texts to analyse meaning, perspective, cultural assumptions, ideologies and language.

Students use varying technologies to compose texts. They apply their knowledge of the elements that shape meaning in texts. They use a range of strategies to shape their texts to address purpose and audience in different contexts. They conform to or challenge an audience's preconceptions and expectations about content and form, and they evaluate the effectiveness of each approach. Students display a developing personal style in their personal, imaginative, critical and analytical compositions. They work through the composing process, including planning, researching, drafting, conferencing, editing and publishing. Students reflect on their composing process and how it has affected the final version of their text.

Students respond to texts from different cultures that offer a range of perspectives. In considering possible meanings, they develop sustained interpretations supported by evidence and think creatively beyond the text. They infer and interpret, and investigate the similarities and differences between and among texts. Through close and wide engagement with texts students extend their imaginations and engage with images of their real and imagined worlds. They respond imaginatively and critically to verbal and visual imagery and iconography, considering how these and other features reflect the cultural context of the text. By critically evaluating texts, students identify strengths and weaknesses and are able to articulate coherent responses. From their responses to individual texts they generalise about views of the world and strategies that are used to communicate and sustain such views.

Students reflect on their own and others' learning, assessing learning strategies and purposes to adapt their knowledge, understanding and skills to new contexts.

Mathematics Stage 5 Stage Statement

Mathematics Stage 5.1

By the end of Stage 5.1, students explain and verify mathematical relationships, select and use appropriate strategies to solve problems, and link mathematical ideas to existing knowledge and understanding. They use mathematical language and notation to explain mathematical ideas, and interpret tables, diagrams and text in mathematical situations.

Students apply their knowledge of percentages, fractions and decimals to financial problems related to earning and spending money, taxation, and simple and compound interest. They simplify and evaluate numerical expressions using index laws for positive and zero indices, round numbers to a specified number of significant figures, and express numbers in scientific notation. Students apply the index laws to simplify algebraic expressions. They determine the midpoint, gradient and length of intervals on the Cartesian plane and draw graphs of linear and simple non-linear relationships.

Skills in measurement are further developed to include finding the areas of composite shapes and the surface areas of rectangular and triangular prisms. Students describe the limit of accuracy of measurements. They apply right-angled triangle trigonometry to practical situations, including those involving angles of elevation and depression. They apply the properties of similar figures to find side lengths in problems related to similar figures.

Students' statistical skills are extended to include considering shape and skewness of distributions, comparing data and data displays, and evaluating the reliability of statistical claims. They also determine the relative frequencies of events in chance experiments and calculate probabilities from information displayed in Venn diagrams and two-way tables.

Mathematics Stage 5.2

By the end of Stage 5.2, students use mathematical arguments to reach and justify conclusions. When communicating mathematical ideas, they use appropriate mathematical language and algebraic, statistical and other notations and conventions in written, oral or graphical form. Students use suitable problem-solving strategies, which include selecting and organising key information, and they extend their inquiries by identifying and working on related problems.

Students apply their knowledge of percentages, fractions and decimals to problems involving conversion of rates, direct proportion, and financial contexts related to compound interest and depreciation.

Students apply the index laws with integer indices to simplify expressions. They operate with algebraic fractions, expand binomial products and factorise monic quadratic trinomial expressions. They solve linear equations and use them to solve word problems. They solve linear inequalities and linear simultaneous equations. Students solve simple quadratic equations and solve monic quadratic equations by factorisation. On the Cartesian plane they draw and interpret graphs of straight lines, and simple parabolas, circles and exponential graphs. Students determine the equations of straight lines and use the properties of parallel and perpendicular lines on the Cartesian plane.

Students extend their skills in measurement to solve problems involving the surface areas and volumes of right prisms, cylinders and related composite solids. They use trigonometric ratios to solve problems in which angles may be measured to the nearest second, and problems involving bearings and angles of elevation and depression. In geometry, they use deductive reasoning in numerical and non-numerical problems, drawing on their knowledge of the properties of congruent triangles, the angle properties of polygons, and the properties of quadrilaterals.

Statistical skills are extended to include the construction of box-and-whisker plots and the calculation of interquartile range to analyse and compare data sets in appropriate data displays. Students investigate bivariate data sets and use scatter plots to describe relationships between variables. They evaluate the sources of data in statistical reports. In their study of probability, students record and determine probabilities of events in multi-step chance experiments and examine conditional language.

Mathematics Stage 5.3

By the end of Stage 5.3, students use deductive reasoning in problem solving and in presenting arguments and formal proofs. They interpret and apply formal definitions and generalisations and connect and apply mathematical ideas within and across substrands. They demonstrate fluency in selecting, combining and applying relevant knowledge, skills and understanding in the solution of familiar and unfamiliar problems.

Students operate with irrational numbers and extend their knowledge of the number system to include all real numbers. They analyse and describe physical phenomena and rates of change. Algebraic skills are extended to expanding the special binomial products and factorising non-monic quadratic expressions, using a variety of techniques. Students solve complex linear equations, non-monic quadratic equations, simple cubic equations, and simultaneous equations involving one linear and one non-linear equation. They solve practical problems using linear, quadratic and simultaneous equations. They change the subject of literal equations. Students generate, describe and graph straight lines, parabolas, cubics, hyperbolas and circles. They use formulas to calculate midpoint, gradient and distance on the Cartesian plane, and to determine the equations of straight lines.

Students solve problems involving the surface areas and volumes of pyramids, cones and spheres, and related composite solids. They explore similarity relationships for area and volume. They determine exact trigonometric ratios for 30°, 45° and 60°, extend trigonometric ratios to obtuse angles, and sketch sine and cosine curves for angular values from 0° to 360°. Students apply the sine and cosine rules for finding unknown angles and/or sides in non-right-angled triangles. They use Pythagoras' theorem and trigonometry to solve problems in three dimensions.

Their knowledge of a wide range of geometrical facts and relationships is used to prove general properties in geometry, extending the concepts of similarity and congruence to more generalised applications. Students prove known properties of triangles, quadrilaterals and circles.

Students use standard deviation to analyse data, and interpolate and extrapolate from bivariate data using lines of best fit. They investigate statistical reports and explore how data is used to inform decision-making processes.

Science Stage 5 Stage Statement

By the end of Stage 5 students use scientific inquiry by actively engaging in using and applying the processes of Working Scientifically to increase their understanding of and about the world around them. By engaging in scientific inquiry, students develop their understanding of science ideas and concepts, how scientific knowledge is refined over time and the significance of scientific evidence in evaluating claims, explanations and predictions.

Students formulate questions or hypotheses to be investigated scientifically. They apply scientific understanding and critical thinking skills to suggest possible solutions to identified problems. Individually and collaboratively they plan and undertake a range of types of first-hand investigations to accurately collect data using appropriate units, assessing risk and considering ethical issues associated with the method. They design and conduct controlled experiments to collect valid and reliable first-hand data.

In Stage 5 students process, analyse and evaluate data and information from first-hand investigations to draw conclusions consistent with the evidence, identifying sources of uncertainty and possible alternative explanations for findings. They assess the validity and reliability of claims made in secondary sources. They evaluate the methods and strategies they and others use and ways in which the quality of data could be improved, including the appropriate use of digital technologies. They communicate science ideas for specific purposes and construct evidence-based arguments using appropriate scientific language, conventions and representations.

Students apply models, theories and laws to explain phenomena and situations involving energy, force and motion. They explain the concept of energy conservation, by describing energy transfers and transformations within systems.

Students describe changing ideas about the structure of the Earth, origins of the universe and the diversity of life on the Earth to illustrate how models, theories and laws are refined over time by the scientific community as new evidence becomes available. They describe situations where advances in scientific understanding may depend on developments in technology, and that technological advances are frequently linked to scientific discoveries.

Students explain how scientific understanding has contributed to knowledge about global patterns of geological activity and interactions between global systems. They analyse interactions between components and processes within biological systems and their responses to external changes. They use scientific evidence to assess whether claims, explanations and predictions are supported and can be used to evaluate predictions and inform decisions related to contemporary issues.

Students explain the organisation of the periodic table, chemical reactions and natural radioactivity in terms of atoms. They describe how different factors influence the rate of chemical reactions and the importance of a range of types of chemical reactions in the production of substances.

By the end of Stage 5 students describe how the values and needs of contemporary society can influence the focus of scientific research and technological development in a variety of areas, including efficiency of use of electricity and non-renewable energy sources, the development of new materials, biotechnology, and plant, animal and human health. They outline examples of where the applications of the advances of science, emerging sciences and technologies significantly affect people's lives, including generating new career opportunities.

History Stage 5 Stage Statement

By the end of Stage 5, students describe, explain and assess the historical forces and factors that shaped the modern world and Australia. They sequence and explain the significant patterns of continuity and change in the development of the modern world and Australia. They explain and analyse the motives and actions of past individuals and groups in the historical contexts that shaped the modern world and Australia. Students explain and analyse the causes and effects of events and developments in the modern world and Australia. Students explain the context for people's actions in the past. They explain the significance of events and developments from a range of perspectives. They explain different interpretations of the past and recognise the evidence used to support these interpretations.

Students sequence events and developments within a chronological framework, and identify relationships between events across different periods of time and places. When researching, students develop, evaluate and modify questions to frame an historical inquiry. They process, analyse and synthesise information from a range of primary and secondary sources and use it as evidence to answer inquiry questions. Students analyse sources to identify motivations, values and attitudes. When evaluating these sources, they analyse and draw conclusions about their usefulness, taking into account their origin, purpose and context. They develop and justify their own interpretations about the past. Students develop texts, particularly explanations and discussions, incorporating historical arguments. In developing these texts and organising and presenting their arguments, students use historical terms and concepts, evidence identified in sources and they reference these sources. Students will have undertaken a relevant site study either by visiting an actual site or through a virtual source.

Geography Stage 5 Stage Statement

By the end of Stage 5, students explain geographical processes that change features and characteristics of places and environments over time and across scales and explain the likely consequences of these changes. They analyse interconnections between people, places and environments and propose explanations for distributions, patterns and spatial variations over time and across scales. Students compare changing environments, analyse global differences in human wellbeing, explore alternative views to geographical challenges and assess strategies to address challenges using environmental, social and economic criteria.

Students undertake geographical inquiry to extend knowledge and understanding, and make generalisations and inferences about people, places and environments through the collection, analysis and evaluation of primary data and secondary information. They propose explanations for significant patterns, trends, relationships and anomalies in geographical phenomena. Students propose solutions, and may take action to address contemporary geographical challenges, taking into account alternative points of view and predicted outcomes. Students participate in relevant fieldwork to collect primary data and enhance their personal capabilities and workplace skills.