MathematicsNumeracy2017 Subject Outline

Year 10

NORTHERN TERRITORY BOARD OF STUDIES

Northern Territory Board of Studies

EndorsementThis subject outline was endorsed by the Northern Territory Board of Studies (NTBOS) in August 2016.AcknowledgementThank you to the teachers participating in the working group who consulted over an extended period of time to create this curriculum document.

CONTENTSINTRODUCTION......................................................................................................................................... 4

LEARNING AREA COURSES AND SENIOR SECONDARY PATHWAYS.........................................................4YEAR 10 TO NTCET PROGRESSION........................................................................................................4LEARNING AREA.................................................................................................................................... 5SUBJECTS.............................................................................................................................................. 5LENGTH................................................................................................................................................. 5BACKGROUND....................................................................................................................................... 5PURPOSE............................................................................................................................................... 5CAPABILITIES......................................................................................................................................... 6

LEARNING SCOPE AND REQUIREMENTS....................................................................................................9OVERVIEW............................................................................................................................................. 9YEAR 10A CONSIDERATIONS.................................................................................................................9YEAR 10 PROFICIENCIES AND CONTENT DESCRIPTIONS........................................................................9YEAR 10 ACHIEVEMENT STANDARD.....................................................................................................11

ASSESSMENT SCOPE AND REQUIREMENTS.............................................................................................12EVIDENCE OF LEARNING......................................................................................................................12ASSESSMENT DESIGN CRITERIA..........................................................................................................12SCHOOL ASSESSMENT.........................................................................................................................15PERFORMANCE STANDARDS................................................................................................................16

SUPPORT MATERIALS..............................................................................................................................19ADVICE ON ETHICAL STUDY AND RESEARCH.......................................................................................21ASSESSMENT INTEGRITY.....................................................................................................................21GLOSSARY, STUDENT WORK SAMPLES AND EXPLANATORY VIDEOS...................................................21

REFERENCES..........................................................................................................................................21

INTRODUCTION

Year 10 Mathematics aims to instil in students an appreciation of the elegance and power of mathematical reasoning. Mathematical ideas have evolved across all cultures over thousands of years, and are constantly developing. Digital technologies are facilitating this expansion of ideas and providing access to new tools for continuing mathematical exploration and invention. The curriculum focuses on developing increasingly sophisticated and refined mathematical understanding, fluency, reasoning, and problem-solving skills. These proficiencies enable students to respond to familiar and unfamiliar situations by employing mathematical strategies to make informed decisions and solve problems efficiently.

Year 10 Numeracy aims to allow students the opportunity to extend their mathematical skills in ways that apply to practical problem-solving in everyday and workplace contexts. Year 10 Numeracy places a strong emphasis on developing students’ computational skills and expanding their ability to apply their mathematical skills in flexible and resourceful ways.

LEARNING AREA COURSES AND SENIOR SECONDARY PATHWAYSStudents will undertake a course which caters for their level of learning area development from the Year 10 Australian Curriculum: Mathematics .

The Year 10 course will provide the foundation knowledge, skills and understandings to enable students to successfully proceed to appropriate Stage 1 NTCET Mathematics learning area.

The Year 10A course provides extension opportunities for students intending further study in Stage 1 and Stage 2 Mathematics.

Note: The essential aspects of 10A are included in the curriculum for Specialist Mathematics and Mathematical Methods.

YEAR 10 TO NTCET PROGRESSION

NTBOSYear 10

NTCETYear 11 – Stage 1

NTCETYear 12 – Stage 2

MathematicsYear 10/10A

MathematicsGeneral MathematicsEssential Mathematics

Specialist MathematicsMathematical MethodsGeneral MathematicsEssential Mathematics

NumeracyGeneral Mathematics*Essential Mathematics

General MathematicsEssential Mathematics

*It is advised that Numeracy students attempting Stage 1 and Stage 2 General Mathematics have achieved numeracy levels commensurate to Year 10 AC Achievement Standards.

LEARNING AREAMathematics

SUBJECTSMathematicsNumeracy

LENGTH120 hours per year

BACKGROUNDThe Australian Curriculum states that:

“Teachers use the Australian Curriculum content and achievement standards first to identify current levels of learning and achievement and then to select the most appropriate content (possibly from across several year levels) to teach individual students and/or groups of students. This takes into account that in each class there may be students with a range of prior achievement (below, at, and above the year level expectations) and that teachers plan to build on current learning” (Australian Curriculum and Assessment Authority, 2016).

These principles underpin the design and structure of the Northern Territory Year 10 Mathematics and Numeracy subjects which, in particular, cater for students who are “below, at and above the year level expectations”. Students will also be provided with skills and pathways for the successful completion of the Northern Territory Certificate of Education and Training (NTCET) Numeracy requirements.

PURPOSEThis document provides a strategy for aligning the learning requirements of the Australian Curriculum and the assessment requirements of the NTCET. The Australian Curriculum provides the content descriptors and achievement standards for Year 10 Mathematics and for Year 10 Numeracy.

The NTCET through assessment design criteria and performance standards provides a common standard for student achievement at Stage 1 and Stage 2 and this will inform and shape the language and standards for achievement in Year 10 mathematics subjects. To cater for a diversity of student needs at Year 10, two subjects have been developed; Mathematics and Numeracy.

The Mathematics subject is designed for students with a numeracy level “at and above” a standard required for success at Year 10 Australian Curriculum.

The Numeracy subject has been designed for students with a numeracy level “below” the standard required for success at Year 10 Australian Curriculum.

CAPABILITIES The capabilities connect student learning within and across subjects in a range of contexts. They include essential knowledge and skills that enable people to act in effective and successful ways.The SACE identifies seven capabilities. They are: Literacy Numeracy Information and communication technology (ICT) capability Critical and creative thinking Personal and social capability Ethical understanding Intercultural understanding.

LiteracyIn this subject students develop their literacy capability by, for example: communicating mathematical reasoning and ideas for different purposes, using

appropriate language and representations, such as symbols, equations, tables, and graphs interpreting and responding to appropriate mathematical language and representations analysing information and explaining mathematical results.

Mathematics provides a specialised language to describe and analyse phenomena. It provides a rich context for students to extend their ability to read, write, visualise, and talk about situations that involve investigating and solving problems.

Students apply and extend their literacy skills and strategies by using verbal, graphical, numerical, and symbolic forms of representing problems and displaying statistical information. Students learn to communicate their findings in different ways, using different systems of representation.

NumeracyBeing numerate is essential for participating in contemporary society. Students need to reason, calculate, and communicate to solve problems. Through the study of mathematics, they understand and use skills, concepts, and technologies in a range of contexts that can be applied to: using measurement in the physical world gathering, representing, interpreting, and analysing data using spatial sense and geometric reasoning investigating chance processes using number, number patterns, and relationships between numbers working with graphical, statistical and algebraic representations, and other mathematical

models.

Information and Communication Technology (ICT) CapabilityIn this subject students develop their information and communication technology capability by, for example: understanding the role of electronic technology in the study of mathematics making informed decisions about the use of electronic technology understanding the mathematics involved in computations carried out using technologies,

so that reasonable interpretations can be made of the results.Students extend their skills in using technology effectively and processing large amounts of quantitative information. Students use ICT to extend their theoretical mathematical understanding and apply mathematical knowledge to a range of problems. They use software relevant for study and/or workplace contexts. This may include tools for statistical analysis, algorithm generation, data representation and manipulation, and complex calculation. They use digital tools to make

connections between mathematical theory, practice, and application; for example, to use data, address problems, and operate systems in particular situations.

Critical and Creative ThinkingIn this subject students develop critical and creative thinking by, for example: building confidence in applying knowledge and problem-solving skills in a range of

mathematical contexts developing mathematical reasoning skills to think logically and make sense of the world understanding how to make and test projections from mathematical models interpreting results and drawing appropriate conclusions reflecting on the effectiveness of mathematical models, including the recognition of

assumptions, strengths, and limitations using mathematics to solve practical problems and as a tool for learning making connections between concrete, pictorial, symbolic, verbal, written, and mental

representations of mathematical ideas thinking abstractly, making and testing conjectures, and explaining processes.

Problem-solving in mathematics builds students’ depth of conceptual understanding and supports development of critical and creative thinking. Learning through problem-solving helps students when they encounter new situations. They develop their creative and critical thinking capability by listening, discussing, conjecturing, and testing different strategies. They learn the importance of self-correction in building their conceptual understanding and mathematical skills.

Personal and Social CapabilityIn this subject students develop their personal and social capability by, for example: arriving at a sense of self as a capable and confident user of mathematics through

expressing and presenting ideas in a variety of ways appreciating the usefulness of mathematical skills for life and career opportunities and

achievements understanding the contribution of mathematics and mathematicians to society.

The elements of personal and social competence relevant to mathematics include the application of mathematical skills for informed decision-making, active citizenship, and effective self-management. Students build their personal and social competence in mathematics through setting and monitoring personal and academic goals, taking initiative, and building adaptability, communication, and teamwork.Students use mathematics as a tool to solve problems they encounter in their personal and working lives. They acquire a repertoire of strategies and build the confidence needed to: meet the challenges and innovations of a rapidly changing world be the designers and innovators of the future, and leaders in their fields.

Ethical UnderstandingIn this subject students develop their ethical understanding by, for example: gaining knowledge and understanding of ways in which mathematics can be used to

support an argument or point of view examining critically ways in which the media present particular perspectives sharing their learning and valuing the skills of others considering the social consequences of making decisions based on mathematical results acknowledging and learning from errors rather than denying findings and/or evidence.

Areas of ethical understanding relevant to mathematics include issues associated with ethical decision-making and working collaboratively as part of students’ mathematically related explorations. They develop ethical understanding in mathematics through considering social responsibility in ethical dilemmas that may arise when solving problems in personal, social, community, and/or workplace contexts.

Intercultural UnderstandingIn this subject students develop their intercultural understanding by, for example: understanding mathematics as a body of knowledge that uses universal symbols which

have their origins in many cultures understanding how mathematics assists individuals, groups, and societies to operate

successfully across cultures in the global, knowledge-based economy.

Mathematics is a shared language that crosses borders and cultures, and is understood and used globally.

Students read about, represent, view, listen to, and discuss mathematical ideas. They become aware of the historical threads from different cultures that have led to the current bodies of mathematical knowledge. These opportunities allow students to create links between their own language and ideas and the formal language and symbols of mathematics.

LEARNING SCOPE AND REQUIREMENTS

OVERVIEWTeachers are to use the content descriptions of the Australian Curriculum to develop a program for their students. There are 41 content descriptions for mathematics that are organised into three strands: number and algebra, measurement and geometry and statistics and probability. The content descriptions are organised according to strand, however for teachers of students working at a Year 10A standard, these descriptions are indicated with the 10A code.

YEAR 10A CONSIDERATIONS

10 10A:

Number and Algebra content description

numberMeasurement and

Geometry Statistics and Probability

1 2 3 4 5 1 2 3 4 5 1 2 3 4 56 7 8 9 10 6 7 8 9 10 6 7 8 9 1011 12 13 14 15 1116 17 18 19 20

YEAR 10 PROFICIENCIES AND CONTENT DESCRIPTIONSThe proficiency strands understanding, fluency, problem-solving and reasoning are an integral part of mathematics content across the three content strands: number and algebra, measurement and geometry, and statistics and probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. The achievement standards reflect the content and encompass the proficiencies.

At this year level: understanding includes applying the four operations to algebraic fractions, finding

unknowns in formulas after substitution, making the connection between equations of relations and their graphs, comparing simple and compound interest in financial contexts and determining probabilities of two- and three-step experiments

fluency includes factorising and expanding algebraic expressions, using a range of strategies to solve equations and using calculations to investigate the shape of data sets

problem-solving includes calculating the surface area and volume of a diverse range of prisms to solve practical problems, finding unknown lengths and angles using applications of trigonometry, using algebraic and graphical techniques to find solutions to simultaneous equations and inequalities and investigating independence of events

reasoning includes formulating geometric proofs involving congruence and similarity, interpreting and evaluating media statements and interpreting and comparing data sets.

Strand: Number and Algebra

Money and financial mathematics1. Connect the compound interest formula to repeated applications of simple interest using

appropriate digital technologies (ACMNA229)

Real numbers2. 10A - Define rational and irrational numbers and perform operations with surds and

fractional indices (ACMNA264) 3. 10A - Use the definition of a logarithm to establish and apply the laws of logarithms

(ACMNA265)

Patterns and algebra4. Factorise algebraic expressions by taking out a common algebraic factor (ACMNA230) 5. Simplify algebraic products and quotients using index laws (ACMNA231) 6. Apply the four operations to simple algebraic fractions with numerical denominators

(ACMNA232) 7. Expand binomial products and factorise monic quadratic expressions using a variety of

strategies (ACMNA233) 8. Substitute values into formulas to determine an unknown (ACMNA234) 9. 10A - Investigate the concept of a polynomial and apply the factor and remainder

theorems to solve problems (ACMNA266)

Linear and non-linear relationships10.Solve problems involving linear equations, including those derived from formulas

(ACMNA235) 11.Solve linear inequalities and graph their solutions on a number line (ACMNA236) 12.Solve linear simultaneous equations, using algebraic and graphical techniques, including

using digital technology (ACMNA237) 13.Solve problems involving parallel and perpendicular lines (ACMNA238) 14.Explore the connection between algebraic and graphical representations of relations such

as simple quadratics, circles and exponentials using digital technology as appropriate (ACMNA239)

15.Solve linear equations involving simple algebraic fractions (ACMNA240) 16.Solve simple quadratic equations using a range of strategies (ACMNA241)17.10A - Describe, interpret and sketch parabolas, hyperbolas, circles and exponential

functions and their transformations (ACMNA267) 18.10A - Solve simple exponential equations (ACMNA270) 19.10A - Apply understanding of polynomials to sketch a range of curves and describe the

features of these curves from their equation (ACMNA268) 20.10A - Factorise monic and non-monic quadratic expressions and solve a wide range of

quadratic equations derived from a variety of contexts (ACMNA269)

Strand: Measurement and Geometry

Using units of measurement1. Solve problems involving surface area and volume for a range of prisms, cylinders and

composite solids (ACMMG242) 2. 10A - Solve problems involving surface area and volume of right pyramids, right cones,

spheres and related composite solids (ACMMG271)

Geometric reasoning3. Formulate proofs involving congruent triangles and angle properties (ACMMG243) 4. Apply logical reasoning, including the use of congruence and similarity, to proofs and

numerical exercises involving plane shapes (ACMMG244) 5. 10A - Prove and apply angle and chord properties of circles (ACMMG272)

Pythagoras and trigonometry6. Solve right-angled triangle problems including those involving direction and angles of

elevation and depression (ACMMG245)7. 10A - Establish the sine, cosine and area rules for any triangle and solve related problems

(ACMMG273) 8. 10A - Use the unit circle to define trigonometric functions, and graph them with and

without the use of digital technologies (ACMMG274) 9. 10A - Solve simple trigonometric equations (ACMMG275) 10.10A - Apply Pythagoras’ Theorem and trigonometry to solving three-dimensional problems

in right-angled triangles (ACMMG276)

Strand: Statistics and Probability

Chance1. Describe the results of two- and three-step chance experiments, both with and without

replacements, assign probabilities to outcomes and determine probabilities of events. Investigate the concept of independence (ACMSP246)

2. Use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language (ACMSP247)

3. 10A - Investigate reports of studies in digital media and elsewhere for information on their planning and implementation (ACMSP277)

Data representation and interpretation4. Determine quartiles and interquartile range (ACMSP248) 5. Construct and interpret box plots and use them to compare data sets (ACMSP249) 6. Compare shapes of box plots to corresponding histograms and dot plots (ACMSP250) 7. Use scatter plots to investigate and comment on relationships between two numerical

variables (ACMSP251) 8. Investigate and describe bivariate numerical data where the independent variable is time

(ACMSP252) 9. Evaluate statistical reports in the media and other places by linking claims to displays,

statistics and representative data (ACMSP253)10.10A - Calculate and interpret the mean and standard deviation of data and use these to

compare data sets (ACMSP278) 11.10A - Use information technologies to investigate bivariate numerical data sets. Where

appropriate use a straight line to describe the relationship allowing for variation (ACMSP279)

YEAR 10 ACHIEVEMENT STANDARDThe Achievement Standard is aligned with the performance standards for Year 10 Mathematics. The Performance Standards are to be used for the assessment of student learning.

By the end of Year 10, students recognise the connection between simple and compound interest. They solve problems involving linear equations and inequalities. They make the connections between algebraic and graphical representations of relations. Students solve surface area and volume problems relating to composite solids. They recognise the relationships between parallel and perpendicular lines. Students apply deductive reasoning to proofs and numerical exercises involving plane shapes. They compare data sets by referring to the shapes of the various data displays. They describe bivariate data where the independent variable is time. Students describe statistical relationships between two continuous variables. They evaluate statistical reports.

Students expand binomial expressions and factorise monic quadratic expressions. They find unknown values after substitution into formulas. They perform the four

operations with simple algebraic fractions. Students solve simple quadratic equations and pairs of simultaneous equations.

They use triangle and angle properties to prove congruence and similarity. Students use trigonometry to calculate unknown angles in right-angled triangles. Students list outcomes for multi-step chance experiments and assign probabilities for these experiments. They calculate quartiles and inter-quartile ranges. Australian Curriculum

ASSESSMENT SCOPE AND REQUIREMENTSAssessment at Year 10 is school based

EVIDENCE OF LEARNINGMathematicsThe following assessment types enable students to demonstrate their learning in Year 10 Mathematics:

Assessment type 1: Skills and application tasks -at least two tasksAssessment type 2: Investigation – at least one task

For Year 10 Mathematics subject, students should provide evidence of their learning through four assessments:

At least two from Assessment Type 1 At least one from Assessment Type 2 One other from either Assessment Type

Each assessment type should have a weighting of at least 20%.

Numeracy The following assessment types enable students to demonstrate their learning in Year 10 Numeracy:

Assessment type 1: Skills and application tasks – at least two tasksAssessment type 2: Folio – at least one task

For Year 10 Numeracy subject, students should provide evidence of their learning through four assessments:

At least two from Assessment Type 1 At least one from Assessment Type 2 One other from either Assessment Type

Each assessment type should have a weighting of at least 20%.

ASSESSMENT DESIGN CRITERIAThe Assessment design criteria are based on the learning requirements and are used by teachers to: clarify for the students what he or she needs to learn design opportunities for the student to provide evidence of his or her learning at the

highest level of achievement.

The assessment design criteria consist of specific features that: students need to demonstrate in their evidence of learning

teachers look for as evidence that students have met the learning requirements.

For this subject, the assessment design criteria are:• Concepts and Techniques• Reasoning and Communication

The specific features of these criteria are described below.The set of assessments, as a whole, give students opportunities to demonstrate each of the specific features by the completion of study.

Assessment Design Criteria Continued

MathematicsThe specific features of the criteria are described below:

Concepts and Techniques Reasoning and Communication

CT1 Knowledge and understanding of concepts and relationships

CT2 Selection and application of mathematical techniques and algorithms to find solutions to problems in a variety of contexts

CT3 Development and/or application of mathematical models

CT4 Use of electronic technology to find solutions to mathematical problems

RC1 Interpretation of mathematical results

RC2 Drawing conclusions from mathematical results, with an understanding of their reasonableness and limitations

RC3 Use of appropriate mathematical notation, representations, and terminology

RC4 Communication of mathematical ideas and reasoning to develop logical arguments

RC5 Development and testing of valid predictions

NumeracyThe specific features of the criteria are described below:

Concepts and Techniques Reasoning and Communication

CT1 Knowledge and understanding of mathematical information and concepts

CT2 Application of mathematical skills and techniques to find solutions to practical problems in contexts

CT3 Gathering, representation, and interpretation of information or data in context

CT4 Use of electronic technology to find solutions to practical problems

RC1 Interpretation of mathematical results

RC2 Use of mathematical reasoning to draw conclusions and consider the appropriateness of solutions

RC3 Use of appropriate mathematical notation, representations, and terminology

RC4 Communication of mathematical ideas and information

Year 10 Mathematics and Numeracy assessment overview

NTBOS Year 10 Subject

Australian Curriculum Content Strands and Descriptions

Assessment Types, Tasks and Weighting

Performance Standards for Assessments

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1. Skills and Applications Tasks - at least two skills and applications tasks per semester

2. INVESTIGATION - at least one per semester

each assessment type should have a weighting of at least 20%

For a semester length Mathematics subject, students provide evidence of their learning through four assessment tasks

No task should be more than six A4 pages if written or the equivalent in multimodal form.

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Reasoning and Communication

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Number and Algebra

1, 4-8, 10-16- or from appropriate AC

year level

Measurement and Geometry1, 3-4, 6- or from appropriate AC

year level

Statistics and Probability

1-2, 4-9- or from appropriate AC

year level

1. Skills and Applications Tasks - at least two skills and applications tasks per semester

2. FOLIO - at least one investigation for the folio per semester

each assessment type should have a weighting of at least 20%

for a semester length Numeracy subject, students provide evidence of their learning through four assessment tasks

no task should be more than four A4 pages if written, or the equivalent in multimodal form

Concepts and Techniques

1 - 4

Reasoning and Communication

1 - 4

SCHOOL ASSESSMENTAssessment Type 1: At least two Skills and Applications TasksSkills and applications tasks are completed under the direct supervision of the teacher. Students find solutions to mathematical problems that may:• be routine, complex, analytical, and/or interpretative• be posed in a variety of familiar and new contexts• require discerning use of electronic technology.

Please note – in Stage 2 subjects there are specific requirements relating to the use of calculators and notes. Consideration could be given to students who require support when undertaking Numeracy. Students solve practical mathematical problems in everyday contexts where:• tasks can be presented in different formats• assessment conditions may vary and should be guided by the cohort requirements• flexibility is given in style of task and time allocation.

Assessment Type 2: At least one Mathematical Investigation (Mathematics course) OR Folio Task (Numeracy course)

MATHEMATICS COURSEStudents investigate mathematical relationships, concepts, or problems, which may be set in an applied context. The subject of a mathematical investigation may be derived from one or more content strands. Teachers will need to provide support and clear directions for the first mathematical

investigation subsequent investigations could be less directed and set within more open-ended contexts each student must submit an individual report.

When students complete a report on the mathematical investigation it may take a variety of forms, but would usually include the following: an outline/introduction of the problem and context the method investigated or applied to find a solution, in terms of the mathematical model

or strategy used the application of the mathematical model or strategy, including:

- relevant data and/or information - mathematical calculations, results and graphs and other appropriate

representations- the analysis and interpretation of results, including consideration of the

reasonableness and limitations of the Investigations or results a conclusion stating the outcome of the investigation in the context of the problem a bibliography and appendices, as appropriate, may be used.

The format of an investigation report may be written or multimodal. No task should be more than six A4 pages in minimum 10 font if written or the equivalent in multimodal form.

NUMERACY COURSE

Either individually or in a group, students undertake planning, apply their skills to gather, represent, and interpret data, and individually propose or develop a solution to a practical mathematical problem based in an everyday or workplace context. The subject of the problem may be derived from one or more content strands. Each student must submit an individual model or solution. Teachers will need to: give students advice and directions on setting and solving mathematical problems support students’ progress in arriving at a mathematical solution

The folio tasks may take a variety of forms and be submitted in either a written or multimodal format. The length of each folio task can vary however, no task should be more than four A4 pages in minimum 10 font if written, or the equivalent in multimodal form.

PERFORMANCE STANDARDSThe performance standards describe five levels of achievement, A to E.

Each level of achievement describes the knowledge, skills, and understanding that teachers refer to in deciding how well a student has demonstrated his or her learning on the basis of the evidence provided.

During the teaching and learning program the teacher gives students feedback on their learning, with reference to the performance standards.

Students can also refer to the performance standards to identify the knowledge skills and understanding that they have demonstrated and those specific features that they still need to demonstrate to reach their highest possible level of achievement.

At the student’s completion of study of a subject, the teacher makes a decision about the quality of the student’s learning by:

• referring to the performance standards• taking into account the weighting of each assessment type• assigning a subject grade between A and E.

PERFORMANCE STANDARDS FOR YEAR 10 MATHEMATICS

Concepts and Techniques Reasoning and CommunicationA Comprehensive knowledge and

understanding of concepts and relationships.

Highly effective selection and application of mathematical techniques and algorithms to find efficient and accurate solutions to routine and complex problems in a variety of contexts.

Successful development and application of mathematical models to find concise and accurate solutions.

Appropriate and effective use of electronic technology to find accurate solutions to routine and complex problems.

Comprehensive interpretation of mathematical results in the context of the problem.

Drawing logical conclusions from mathematical results, with a comprehensive understanding of their reasonableness and limitations.

Proficient and accurate use of appropriate mathematical notation, representations, and terminology.

Highly effective communication of mathematical ideas and reasoning to develop logical and concise arguments.

Formation and testing of appropriate predictions, using sound mathematical evidence.

B Some depth of knowledge and understanding of concepts and relationships.

Mostly effective selection and application of mathematical techniques and algorithms to find mostly accurate solutions to routine and some complex problems in a variety of contexts.

Attempted development and successful application of mathematical models to find mostly accurate solutions.

Mostly appropriate and effective use of electronic technology to find mostly accurate solutions to routine and some complex problems.

Mostly appropriate interpretation of mathematical results in the context of the problem.

Drawing mostly logical conclusions from mathematical results, with some depth of understanding of their reasonableness and limitations.

Mostly accurate use of appropriate mathematical notation, representations, and terminology.

Mostly effective communication of mathematical ideas and reasoning to develop mostly logical arguments.

Formation and testing of mostly appropriate predictions, using some mathematical evidence.

C Generally competent knowledge and understanding of concepts and relationships.

Generally effective selection and application of mathematical techniques and algorithms to find mostly accurate solutions to routine problems in different contexts.

Application of mathematical models to find generally accurate solutions.

Generally appropriate and effective use

Generally appropriate interpretation of mathematical results in the context of the problem.

Drawing some logical conclusions from mathematical results, with some understanding of their reasonableness and limitations.

Generally appropriate use of mathematical notation, representations, and terminology, with reasonable accuracy.

Generally effective communication of

Concepts and Techniques Reasoning and Communicationof electronic technology to find mostly accurate solutions to routine problems.

mathematical ideas and reasoning to develop some logical arguments.

Formation of an appropriate prediction and some attempt to test it using mathematical evidence.

D Basic knowledge and some understanding of concepts and relationships.

Some selection and application of mathematical techniques and algorithms to find some accurate solutions to routine problems in context.

Some application of mathematical models to find some accurate or partially accurate solutions.

Some appropriate use of electronic technology to find some accurate solutions to routine problems.

Some interpretation of mathematical results.Drawing some conclusions from mathematical results, with some awareness of their reasonableness.

Some appropriate use of mathematical notation, representations, and terminology, with some accuracy.

Some communication of mathematical ideas, with attempted reasoning and/or arguments.

Attempted formation of a prediction with limited attempt to test it using mathematical evidence.

E Limited knowledge or understanding of concepts and relationships.

Attempted selection and limited application of mathematical techniques or algorithms, with limited accuracy in solving routine problems.

Attempted application of mathematical models, with limited accuracy.

Attempted use of electronic technology, with limited accuracy in solving routine problems.

Limited interpretation of mathematical results.Limited understanding of the meaning of mathematical results, their reasonableness or limitations.

Limited use of appropriate mathematical notation, representations, or terminology, with limited accuracy.

Attempted communication of mathematical ideas, with limited reasoning.

Limited attempt to form or test a prediction.

PERFORMANCE STANDARDS FOR YEAR 10 NUMERACY

Concepts and Techniques Reasoning and CommunicationA Knowledge and understanding of

mathematical information and concepts in familiar and unfamiliar contexts.

Highly effective application of mathematical skills and techniques to find efficient and accurate solutions to routine and complex problems in a variety of contexts.

Gathering, representation, and interpretation of a range of information or data in familiar and unfamiliar contexts.

Appropriate and effective use of electronic technology to find accurate solutions to routine and complex problems.

Accurate interpretation of mathematical results in familiar and unfamiliar contexts.

Highly effective use of mathematical reasoning to draw conclusions and consider the appropriateness of solutions to routine and complex problems.

Proficient and accurate use of appropriate mathematical notation, representations, and terminology.

Clear and effective communication of mathematical ideas and information to develop logical and concise arguments.

B Knowledge and understanding of mathematical information and concepts in familiar and some unfamiliar contexts.

Effective application of mathematical skills and techniques to find mostly accurate solutions to routine and some complex problems in a variety of contexts.

Gathering, representation, and interpretation of information or data in familiar and some unfamiliar contexts.

Mostly appropriate and effective use of electronic technology to find mostly accurate solutions to routine and some complex problems.

Mostly accurate interpretation of mathematical results in familiar and some unfamiliar contexts.

Effective use of mathematical reasoning to draw conclusions and consider the appropriateness of solutions to routine and some complex problems.

Mostly accurate use of appropriate mathematical notation, representations, and terminology.

Clear and appropriate communication of mathematical ideas and information to develop some logical arguments.

C Knowledge and understanding of simple mathematical information and concepts in familiar contexts.

Application of some mathematical skills and techniques to find solutions to routine problems in familiar contexts.

Gathering, representation, and interpretation of information or data in familiar contexts.

Generally appropriate and some effective use of electronic technology to find solutions to routine problems.

Generally accurate interpretation of mathematical results in familiar contexts.

Appropriate use of mathematical reasoning to draw conclusions and consider the appropriateness of solutions to routine problems.

Generally appropriate use of familiar mathematical notation, representations, and terminology.

Appropriate communication of mathematical ideas and information.

Concepts and Techniques Reasoning and CommunicationD Basic knowledge and some understanding

of simple mathematical information and concepts in some familiar contexts.

Application of basic mathematical skills and techniques to find partial solutions to routine problems in some contexts.

Some gathering, representation, and basic interpretation of simple information or data in familiar contexts.

Some appropriate use of electronic technology to find solutions to routine problems.

Some interpretation of mathematical results in some familiar contexts.

Attempted use of mathematical reasoning to consider the appropriateness of solutions to routine problems.

Some use of familiar mathematical notation, representations, and terminology.

Attempted communication of simple mathematical ideas and information.

E Limited knowledge or understanding of mathematical information or concepts.

Attempted application of basic mathematical skills or techniques, with limited accuracy in solving routine problems.

Some gathering and attempted representation of simple information or data in a familiar context.

Attempted use of electronic technology to find a solution to a routine problem.

Limited interpretation of mathematical results.

Limited awareness of the use of mathematical reasoning in solving a problem.

Limited use of mathematical notation, representations, or terminology.

Attempted communication of an aspect of mathematical information.

SUPPORT MATERIALS

ADVICE ON ETHICAL STUDY AND RESEARCHPolicy advice for students and teachers on ethical study and research practices is available in the guidelines on the ethical conduct of research in the SACE on the SACE website (www.sace.sa.edu.au).

ASSESSMENT INTEGRITY The SACE Assuring Assessment Integrity Policy outlines the principles and processes that teachers and assessors follow to assure the integrity of student assessments. This policy is available on the SACE website (www.sace.sa.edu.au) as part of the SACE Policy Framework.The SACE Board uses a range of quality assurance processes so that the grades awarded for student achievement in the school assessment are applied consistently and fairly against the performance standards for a subject, and are comparable across all schools.Information and guidelines on quality assurance in assessment are available on the SACE website.

GLOSSARY, STUDENT WORK SAMPLES AND EXPLANATORY VIDEOS Australian Curriculum: Mathematics

Glossary [Note: once in the glossary site, click on the relevant letter for mathematics terminology you are looking for.]

Australian Curriculum: Mathematics Year 10 Work Sample Portfolios

Year 10 Mathematics portfolio – Satisfactory Year 10 Mathematics portfolio – Above Satisfactory Year 10 Mathematics portfolio – Below Satisfactory

Australian Curriculum: Mathematics – Resources for Year 10 teachers from the Leading Learning Series and ACARA– Understanding and Making the Australian Curriculum Work for Us.

Mathematics: What is it for? Sound bites mathematics Bringing maths to life The intent of the Australian Curriculum: Mathematics The Guiding Principles of Mathematics Professor Peter Sullivan

REFERENCES

Australian Curriculum and Assessment Authority. (2017, Jan 3). Implications for teaching, assessing and reporting. Retrieved from Australian Curriculum: http://www.australiancurriculum.edu.au

Australian Curriculum and Reporting Authority. (2017, Jan 3). Australian Curriculum. Retrieved from www.australiancurriculum.edu.au

NTCET. (2017, Jan 3). Department of Education. Retrieved from www.nt.gov.au