Download pdf - Curriculum Planning Guide: Literacy and Numeracy … Literacy and Numeracy Skills Strand – Strand and Unit Information 30 August 2017 Curriculum Planning Guide: Literacy and Numeracy

VCAL Literacy and Numeracy Skills Strand – Strand and Unit Information 30 August 2017

Curriculum Planning Guide:

Literacy and Numeracy Skills Strand

Strand and Unit Information


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Contents

Section 1: VCAL Literacy and Numeracy Skills Strand ...........................................................................................................4 Introduction ...............................................................................................................................................................................4 Aims ..........................................................................................................................................................................................4 Literacy Skills purpose statement ..............................................................................................................................................4 Numeracy Skills purpose statement ...........................................................................................................................................4 Selecting literacy and numeracy curriculum ..............................................................................................................................5 VCAL Literacy and Numeracy Skills units ...............................................................................................................................5 Literacy Skills Units Structure...................................................................................................................................................5 Numeracy Skills Units Structure ...............................................................................................................................................6

Section 2: VCAL Literacy units ...................................................................................................................................................7 Literacy Skills Foundation Reading and Writing ......................................................................................................................7 Unit purpose ..............................................................................................................................................................................7 Assessment ................................................................................................................................................................................7 Conditions of assessment...........................................................................................................................................................7 Learning outcomes 1-8 ..............................................................................................................................................................8

Literacy Skills Foundation Oral Communication .................................................................................................................... 11 Unit purpose ............................................................................................................................................................................ 11 Assessment .............................................................................................................................................................................. 11 Conditions of assessment......................................................................................................................................................... 11 Learning outcomes 1-4 ............................................................................................................................................................ 12

Literacy Skills Intermediate Reading and Writing................................................................................................................... 14 Unit purpose ............................................................................................................................................................................ 14 Assessment .............................................................................................................................................................................. 14 Conditions of assessment......................................................................................................................................................... 14 Learning outcomes 1-8 ............................................................................................................................................................ 15

Literacy Skills Intermediate Oral Communication .................................................................................................................. 18 Unit purpose ............................................................................................................................................................................ 18 Assessment .............................................................................................................................................................................. 18 Conditions of assessment......................................................................................................................................................... 18 Learning outcomes 1-4 ............................................................................................................................................................ 19

Literacy Skills Senior Reading and Writing ............................................................................................................................ 21 Unit purpose ............................................................................................................................................................................ 21 Assessment .............................................................................................................................................................................. 21 Conditions of assessment......................................................................................................................................................... 21 Learning outcomes 1-8 ............................................................................................................................................................ 22

Literacy Skills Senior Oral Communication ............................................................................................................................ 27 Unit purpose ............................................................................................................................................................................ 27 Assessment .............................................................................................................................................................................. 27 Conditions of assessment......................................................................................................................................................... 27 Learning outcomes 1-4 ............................................................................................................................................................ 28


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Section 3: VCAL Numeracy units ............................................................................................................................................. 30 Numeracy Skills Foundation ................................................................................................................................................... 30 Unit purpose ............................................................................................................................................................................ 30 Assessment .............................................................................................................................................................................. 30 Conditions of assessment......................................................................................................................................................... 30 Learning outcomes 1-5 ............................................................................................................................................................ 31

Numeracy Skills Intermediate – Unit 1 ................................................................................................................................... 36 Unit purpose ............................................................................................................................................................................ 36 Assessment .............................................................................................................................................................................. 36 Conditions of assessment......................................................................................................................................................... 36 Learning outcomes 1-4 ............................................................................................................................................................ 37

Numeracy Skills Intermediate – Unit 2 ................................................................................................................................... 41 Unit purpose ............................................................................................................................................................................ 41 Assessment .............................................................................................................................................................................. 41 Conditions of assessment......................................................................................................................................................... 41 Learning outcomes 1-4 ............................................................................................................................................................ 42

Numeracy Skills Senior – Unit 1 ............................................................................................................................................. 45 Unit purpose ............................................................................................................................................................................ 45 Assessment .............................................................................................................................................................................. 45 Conditions of assessment......................................................................................................................................................... 45 Learning outcomes 1-4 ............................................................................................................................................................ 46

Numeracy Skills Senior – Unit 2 ............................................................................................................................................. 51 Unit purpose ............................................................................................................................................................................ 51 Assessment .............................................................................................................................................................................. 51 Conditions of assessment......................................................................................................................................................... 51 Learning outcome 1-4 .............................................................................................................................................................. 52

Advanced Numeracy Skills Senior ............................................................................................................................................ 55 Unit purpose ............................................................................................................................................................................ 55 Assessment .............................................................................................................................................................................. 55 Conditions of assessment......................................................................................................................................................... 55 Learning outcoms 1-5 .............................................................................................................................................................. 56


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Section 1: VCAL Literacy and Numeracy Skills

Strand

Introduction

Curriculum selected for inclusion in the Literacy and Numeracy Skills Strand must be consistent

with the purpose statements of this strand. Through aligning curriculum with the purpose

statements of the curriculum strand, the learning program provides literacy and numeracy skills

development and experiences that are integral for the vocational, employability and personal

development outcomes of VCAL students.

Aims

Study in this strand is designed to:

develop knowledge, skills and attributes relevant to reading, writing and oral communication

and their practical application in the contexts of everyday life, family, employment, further

learning and community

develop knowledge, skills and attributes relevant to the practical application of numeracy in

the contexts of everyday life, further learning, work and community

provide pathways to further study and work.

Literacy Skills purpose statement

The purpose of literacy curriculum selected for this strand is to enable the development of skills,

knowledge and attributes relevant to reading, writing and oral communication and their practical

application in the contexts of everyday life, family, employment, further learning and community.

Literacy skills corresponding with these social contexts include literacy for self expression, practical

purposes, knowledge and public debate.

Literacy includes reading, writing and oral communication skills.

Numeracy Skills purpose statement

The purpose of numeracy curriculum selected for this strand is to enable the development of

knowledge, skills and attributes relevant to identifying, applying and communicating mathematical

information in the contexts of everyday life, family, employment, further learning and community.

Numeracy skills corresponding with these social contexts include mathematical knowledge and

techniques, financial literacy, planning and organising, measurement, data, representation, design,

problem solving, using software tools and devices and in further study in mathematics or related

fields.


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Selecting literacy and numeracy curriculum

Curriculum in the Literacy and Numeracy Skills Strand can include VCAL Literacy and Numeracy

Skills units or any VCE English units and any VCE Mathematics units and/or accredited

units/modules or certificates with a literacy/numeracy focus such as Certificates I, II and III in

General Education for Adults.

Note: Additional VCE units may be used to meet the eligibility requirements of this VCAL strand.

Please refer to the current VCE and VCAL Administrative Handbook for more information.

VCAL Literacy and Numeracy Skills units

The VCAL Literacy and Numeracy Skills units are:

- LIT011 Literacy Skills Foundation Reading and Writing

- LIT012 Literacy Skills Foundation Oral Communication

- LIT021 Literacy Skills Intermediate Reading and Writing

- LIT022 Literacy Skills Intermediate Oral Communication

- LIT031 Literacy Skills Senior Reading and Writing

- LIT032 Literacy Skills Senior Oral Communication

- NUM011 Numeracy Skills Foundation

- NUM021 Numeracy Skills Intermediate – Unit 1

- NUM022 Numeracy Skills Intermediate – Unit 2

- NUM031 Numeracy Skills Senior – Unit 1

- NUM032 Numeracy Skills Senior – Unit 2

- NUM041 Advanced Numeracy Skills Senior.

Literacy Skills Units Structure

The Literacy Skills units are designed at three levels – Foundation, Intermediate and Senior. Two

units exist at each level, as follows:

Foundation

- Literacy Skills Foundation Reading and Writing unit

- Literacy Skills Foundation Oral Communication unit.

Intermediate

- Literacy Skills Intermediate Reading and Writing unit

- Literacy Skills Intermediate Oral Communication unit.

Senior

- Literacy Skills Senior Reading and Writing unit

- Literacy Skills Senior Oral Communication unit.


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Numeracy Skills Units Structure

The Numeracy Skills units are designed at three levels – Foundation, Intermediate and Senior:

Foundation

- Numeracy Skills Foundation

Intermediate

- Numeracy Skills Intermediate unit 1

- Numeracy Skills Intermediate unit 2.

Senior

- Numeracy Skills Senior unit 1

- Numeracy Skills Senior unit 2

- Advanced Numeracy Skills Senior


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Section 2: VCAL Literacy units

Literacy Skills Foundation Reading and Writing Unit purpose

The purpose of this unit is to enable students to develop skills and knowledge to read and write

simple or short texts. Texts will deal with mainly personal and familiar topics but may include some

unfamiliar aspects.

At this level students, often with support, use the writing process with an awareness of the purpose

and audience of the text.

In reading students are able to identify the main point of the text, some key details and express an

opinion about the text as a whole as well as some of the details.

At the end of the Foundation Reading and Writing unit students will be able to read and

comprehend a range of simple short texts and write a range of short texts in a number of contexts

which may be interrelated.

Assessment

To be credited with this unit the student must demonstrate achievement in all eight learning

outcomes. All elements in a learning outcome must be met in the one task for students to

demonstrate achievement in that outcome.

Conditions of assessment

The conditions related to assessment of the learning outcome may differ according to the particular

learning environment, mode of delivery and field or topic of study.

Students should have access to:

a range of assessment tasks/activities

a learning environment appropriate to the task

appropriate ICT including software tools and devices

support and advice

communication supports as required, for example, dictionary and personal word lists.

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- Subject matter may be ‘everyday’ and may include some unfamiliar material.


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Learning outcome 1

Writing for Self Expression

Write a simple recount, narrative or expressive text on a familiar subject.

Elements

a. Use simple planning, drafting and editing processes to produce written texts

b. Use language and tone appropriate to text purpose and audience

c. Sequence and structure ideas, information and/or events coherently

d. Write at least one paragraph or equivalent

e. Spell, punctuate and use grammar sufficiently for the meaning of the text to be understood

Learning outcome 2

Writing for Practical Purposes

Write a simple instructional or transactional text on a familiar subject.

Elements



c. Sequence and structure information and/or ideas coherently

d. Write at least one paragraph or three to four pieces of information in point form

e. Spell, punctuate and use grammar sufficiently for the meaning to be understood

Learning outcome 3

Writing for Knowledge

Write a simple report or explanatory text on a familiar subject.

Elements



c. Sequence and structure information and ideas coherently


e. Spell, punctuate and use grammar sufficiently for the meaning to be understood


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Learning outcome 4

Writing for Public Debate

Write a simple persuasive and/or argumentative text expressing a point of view on a familiar

subject.

Elements

a. Use the processes of planning, drafting, editing and evaluation to produce written texts


c. Sequence and structure ideas and arguments coherently


e. Provide supporting evidence, which may be broad or general, for a point of view

f. Spell, punctuate and use grammar sufficiently for the meaning to be understood

Learning outcome 5

Reading for Self Expression

Demonstrate that meaning has been gained from reading a simple narrative, recount or expressive

text.

Elements

a. Identify the purpose of the text

b. Identify main ideas and key descriptive details in the text

c. Explain the meaning of key words and phrases

d. Identify similarities/differences between texts on similar subjects or with similar text types

e. Evaluate and express an opinion on the effectiveness of text

Learning outcome 6

Reading for Practical Purposes

Demonstrate that meaning has been gained from reading a simple instructional or transactional

text.

Elements


b. Identify the main ideas and/or key procedures



e. Express an opinion on the text or its subject matter


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Learning outcome 7

Reading for Knowledge

Demonstrate that meaning has been gained from reading a simple explanatory or informative text

on a familiar subject.

Elements


b. Identify the main ideas and key factual data in the text



e. Express an opinion on the text or on its subject matter

Learning outcome 8

Reading for Public Debate

Demonstrate that meaning has been gained from reading a simple persuasive or discursive text on

a familiar subject.

Elements

a. Identify the explicit and/or underlying purpose of a text

b. Identify the main ideas and key information and arguments in the text



e. Identify any persuasive devices used in the text

f. Express own view on the subject/text giving reasons


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Literacy Skills Foundation Oral Communication Unit purpose

At the end of this unit students will be able to use and respond to spoken language, around

everyday subject matter which may include some unfamiliar aspects, for a range of purposes in a

number of contexts which may be interrelated.

Assessment

The student must demonstrate achievement in all learning outcomes. Not all elements need to be met in the one assessment task/activity. Elements for one learning outcome can be met:

in an assessment task/activity individually

by being integrated with learning outcomes in other strands.


The student will have access to:

a flexible range of assessment tasks/activities/ICT options


support and assistance from aides, teachers, mentors and/or experts.

The subject matter will be ‘everyday’ and may include some unfamiliar aspects. Contexts may be

familiar and/or predictable.

Vocabulary may include some that is unknown or unfamiliar.

The student must have a reasonable opportunity to participate in any discussion/activity.


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Learning outcome 1

Oracy for Self Expression

Use and respond to spoken language to explore with others story and life experiences.

Elements

a. Participate in or share a short discussion, account or anecdote

b. Make some use of verbal and non-verbal features of spoken communication, which may

include: intonation, eye contact, gesture and pace

c. Begin to recognise the role verbal and non-verbal features play in conveying meaning in

other oral presentations

d. Reflect and evaluate the effectiveness of spoken language

Learning outcome 2

Oracy for Knowledge

Use and respond to spoken language that presents information about familiar topics.

Elements

a. Take part in a talk or discussion to provide or elicit information on a familiar topic.

b. Identify key points from a brief informative talk.

Learning outcome 3

Oracy for Practical Purposes

Use and respond to spoken language in short transactions in familiar contexts.

Elements

a. Give instructions taking into account the needs of the listener.

b. Exchange or obtain goods or services in real or simulated settings.

c. Identify key instructions in a short oral transaction.

d. Evaluate the effectiveness of language used.


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Learning outcome 4

Oracy for Exploring Issues and Problem Solving

Use and respond to spoken language to explore issues or solve problems on a familiar topic.

Elements

a. Express a point of view about an issue and elicit the point of view of another or others.

b. Participate in an oral exchange requiring some negotiation.

c. Demonstrate active listening.


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Literacy Skills Intermediate Reading and Writing Unit purpose

The purpose of this unit is to enable students to develop the skills and knowledge to read and write

a range of texts on everyday subject matters which include some unfamiliar aspects or material. At

this level students, once they have identified the audience and purpose of the text, use the writing

process to produce texts that link several ideas or pieces of information. In reading, students

identify how, and if, the writer has achieved his or her purpose and express an opinion on the text

taking into account its effectiveness.

At the end of the unit students will be able to read, comprehend and write a range of texts within a

variety of contexts.

Assessment

Examples of assessment tasks/activities which relate mainly to a specific learning outcome can be

found in learning outcome detail information.

To be credited with this unit the student must demonstrate achievement in all learning outcomes.

All elements in a learning outcome must be met in the one task for a student to demonstrate

achievement of that outcome.







support and advice

communication supports as required (for example, dictionary, personal word lists). Subject

matter will be everyday and will include some unfamiliar material.


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Learning outcome 1


Write a recount, narrative or expressive text.

Elements

a. Use the processes of planning, drafting and editing to produce written texts.

b. Use language and tone appropriate to text purpose and audience.

c. Sequence and structure information, ideas and events to suit purpose.

d. Link several pieces of information within a text rather than treating them as separate units.

e. Spell, punctuate and use grammar with reasonable accuracy.

Learning outcome 2


Write an instructional or transactional text.

Elements



c. Sequence and structure information and/or ideas logically to suit purpose.

d. Present several separate pieces of information within a text including detailed factual

descriptions or data.


Learning outcome 3


Write a report, explanatory or expository text.

Elements



c. Sequence and structure information and ideas logically to suit purpose.

d. Relate several separate pieces of factual information within a text rather than treating them

as separate units and reach a conclusion.



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Learning outcome 4


Write a persuasive, argumentative or discursive text.

Elements



c. Sequence and structure ideas and arguments to suit purpose.

d. Relate several ideas or pieces of information within a text rather than treating them as

separate units.

e. Provide evidence and argue persuasively for a point of view.

f. Spell, punctuate and use grammar with reasonable accuracy.

Learning outcome 5


Demonstrate that meaning has been gained from reading a narrative, recount or expressive text.

Elements

a. Identify the purpose of the text including any inferred purpose.

b. Identify main ideas and key words used to express them.

c. Identify the means used by the author to achieve the purpose of the text.

d. Compare or contrast with other texts.

e. Evaluate and express an opinion on the effectiveness of text.

Learning outcome 6


Demonstrate that meaning has been gained from reading an instructional or transactional text.

Elements


b. Identify the main ideas and key procedures.



e. Evaluate an express an opinion on the effectiveness of the text.


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Learning outcome 7


Demonstrate that meaning has been gained from reading an explanatory, expository or informative

text.

Elements


b. Identify the main ideas, supporting ideas and any examples.



e. Evaluate and express an opinion on the effectiveness of the text.

Learning outcome 8


Demonstrate that meaning has been gained from reading a persuasive, discursive or

argumentative text.

Elements


b. Identify the means used by the author to achieve the purpose of the text.

c. Identify the main arguments, ideas or suggestions used in the text.


e. Evaluate and express an opinion on the effectiveness of the text.

f. Express own opinion on the subject and give supporting reasons.


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Literacy Skills Intermediate Oral Communication Unit purpose

At the end of this unit students will be able to use and respond to spoken language including some

unfamiliar material within a variety of contexts.

Assessment

Not all elements have to be all met in the one task. Elements for one learning outcome can be met:

in one assessment task/activity

individually


Examples of assessment tasks can be found in the learning outcomes detail information.





support if required.

The subject matter will be every day and will include unfamiliar material. Contexts may be

unfamiliar.


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Learning outcome 1


Use and respond to spoken language to communicate story and life experience.

Elements

a. Share a narrative, recount or anecdote.

b. Make use of verbal and non-verbal features of spoken communication including: intonation,

eye contact, gesture, pace and pronunciation.

c. Demonstrate an understanding of the role of verbal and non-verbal features by commenting

on the effectiveness of others’ oral presentations.

Learning outcome 2

Oracy for Knowledge

Use and respond to spoken language in informative talks in a range of contexts.

Elements

a. Give an oral presentation answering questions if appropriate.

b. Identify key points and supporting information in an informative talk.

c. Comment on the content and effectiveness of an informative talk.

d. Make systematic notes from a spoken text in a chosen field of knowledge.

Learning outcome 3


Use and respond to spoken language in instructions and transactions.

Elements

a. Give instructions in several steps.

b. Identify the key points in an oral text that offer support, advice or service.

c. Comment on the content and effectiveness of oral instructions and transactions.


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Learning outcome 4


Use and respond to spoken language to explore issues or solve problems.

Elements

a. Participate in a group discussion on an issue, responding to and contributing alternative

ideas.

b. Use spoken language to identify and work towards solving problems with at least one other

person.

c. Comment on the range of ideas presented on an issue in a discussion.

d. Demonstrate active listening.


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Literacy Skills Senior Reading and Writing Unit purpose

The purpose of this unit is to enable students to develop the skills and knowledge to read and write

complex texts. The texts will deal with general situations and include some abstract concepts or

technical details. At this level, students produce texts that incorporate a range of ideas,

information, beliefs or processes and have control of the language devices appropriate to the type

of text. In reading, the student identifies the views shaping the text and the devices used to present

that view and express an opinion on the effectiveness and content of the text.

At the end of the unit students will be able to read, comprehend and write a range of complex texts

across a broad range of contexts.

Assessment

Examples of assessment tasks/activities which relate mainly to a specific learning outcome can be

found in the learning outcome details.

To be credited with this unit the student must demonstrate achievement in all the learning

outcomes. All elements for a learning outcome must be met in the one task for a student to

demonstrate achievement in that outcome.







support and advice

communication supports as required (for example, dictionary, personal word lists).

Subject matter will deal with general situations and some abstract or technical concepts and some

unfamiliar material.


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Learning outcome 1


Write a complex recount, narrative or expressive text.

Elements



c. Organise ideas and information to suit purpose.

d. Incorporate a range of topics, beliefs, issues or experiences.

e. Use literary devices to convey character, setting and/or emotions.

f. Spell, punctuate and use grammar with considerable accuracy.

Learning outcome 2


Write a complex instructional or transactional text.

Elements



c. Organise information and/or ideas logically to suit purpose.

d. Present specialist and/or technical knowledge, highlighting features of special note.

e. Present information accurately, clearly and concisely.


Learning outcome 3


Write a complex report, explanatory or expository text.

Elements



c. Sequence and structure information and ideas logically to suit purpose.

d. Present a range of abstract concepts and/or technical facts within a specialist field.

e. Present information accurately, clearly and concisely.



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Learning outcome 4


Write a complex persuasive, argumentative or discursive text.

Elements



c. Organise ideas and arguments to suit purpose.

d. Provide and integrate evidence to support own argument.

e. In an argumentative or discursive text acknowledge and rebut opposing point/s of view.


Learning outcome 5


Demonstrate that meaning has been gained from reading a complex, sustained narrative, recount

or expressive text.

Elements

a. Identify the purpose of the text including any inferred purpose and the means used to

achieve purpose.

b. Identify the fundamental point of view shaping the text and the devices used to present that

point of view (for example, characters).

c. Compare and contrast with other texts.

d. Present an opinion on the text taking into account the content and its effectiveness in

relation to the audience and purpose.


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Learning outcome 6


Demonstrate that meaning has been gained from reading a complex, sustained instructional or

transactional text.

Elements


achieve purpose.

b. Identify the key instructions and any interpretations.

c. Identify (if any) misleading information in the text.

d. Compare and contrast with other known texts.

e. Present an opinion on the text taking into account the content and its effectiveness in

relation to the audience and purpose.

Learning outcome 7


Demonstrate that meaning has been gained from reading a complex, sustained report,

explanatory, expository or informative text.

Elements


achieve purpose.

b. Differentiate between information and interpretation in the text.

c. Extract information relevant to given research task.

d. Compare and contrast with other texts.

e. Analyse the conclusions reached.

f. Present an opinion on the content and effectiveness of the text in relation to the audience

and purpose.


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Learning outcome 8


Demonstrate that meaning has been gained from reading a complex, sustained persuasive,

argumentative or discursive text.

Elements


achieve purpose.

b. Identify the underlying values system implicit in the text.

c. Compare and contrast with other texts.

d. Evaluate the arguments and evidence given.

e. Present an opinion on the text, taking into account the content and the effectiveness of the

text in relation to the audience and purpose.


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Literacy Skills Senior Oral Communication Unit purpose

At the end of this unit students will be able to use and respond to spoken language with complex

and abstract content across a broad range of contexts.

Assessment

Not all elements have to be all met in the one task. Elements for one learning outcome can be met:

in one assessment task/activity

individually


Examples of assessment tasks can be found in the learning outcomes detail information.





support if required.

The subject matter will deal with general situations and some abstract concepts. Contexts will be

unfamiliar, for example:

vocabulary used will be broad.

the structure of the oral text will be complex and will be characteristic of the text type. The

student must have a reasonable opportunity to participate in any discussion/activity.


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Learning outcome 1


Use and respond to spoken language to effectively communicate with others story and life

experience, in different contexts.

Elements

a. Present or participate in a sustained narrative, discussion, recount or anecdote

b. Make effective use of verbal and non-verbal features of spoken communication including:

intonation, eye contact, gesture, pace, pronunciation and projection

c. Demonstrate an understanding of the role of verbal and non-verbal features through critical

listening and analysis of other oral presentations

Learning outcome 2

Oracy for Knowledge

Use and respond to spoken language in sustained informative presentations in different contexts.

Elements

a. Plan and deliver a sustained presentation in a group setting using appropriate staging and

including open question time if appropriate.

b. Make notes systematically from information presented orally covering key points and

supporting information.

c. Evaluate the content and effectiveness of a complex oral text.

Learning outcome 3


Use and respond to spoken language in sustained and complex transactions in different contexts.

Elements

a. Give complex instructions, including difficulties to be avoided, when explaining a procedure

to others.

b. Respond to a complex inquiry or complaint, giving details of action or explanation of any

difficulties.

c. Evaluate the content and effectiveness of a complex spoken transaction.


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Learning outcome 4


Use and respond to spoken language in sustained discussions for the purpose of exploring issues

or problem solving in different contexts.

Elements

a. Use spoken language for the purpose of exploring ideas in an extended discussion,

comparing them with those of others and questioning others to clarify ideas.

b. Use spoken language to work in collaboration with others to meet an agreed objective.

c. Evaluate the content and effectiveness of a sustained discussion.

d. Demonstrate active listening.


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Section 3: VCAL Numeracy units

Numeracy Skills Foundation Unit purpose

The purpose of this unit is to enable students to develop the confidence and skills to perform

simple and familiar numeracy tasks and to develop the ability to make sense of mathematics in

their daily personal lives. The mathematics involved includes numbers and data, financial literacy,

time and location, measurement and design and the use of software tools and devices.

On completion of this unit students will be able to perform everyday mathematical tasks which

involve a single mathematical step or process. Mathematical ideas would be communicated using

highly familiar contexts and common everyday language and mathematical notation.

Assessment

Students must demonstrate achievement in all learning outcomes to be credited with this unit.


The conditions of assessment for the Numeracy Skills Foundation unit are that students use:

real life, relevant, familiar, personal or everyday contexts and materials where the mathematical

content is explicit

concrete objects (where possible) for spatial and diagrammatic representations

the context, their prior knowledge and personal experiences to derive meaning and check

reasonableness

support from mentors and/or teachers, advice/modelling and first/other language resources

personal ‘in the head’ or pen and paper methods, calculators and/or computers to solve

calculations and problems

oral descriptions using common, everyday, informal language and gestures for explanations,

answers and interpretations.


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Learning outcome 1

Numerical Skills and Processes

Use simple everyday numbers to perform one-step computations with and without software tools

and devices.

Elements

a. Mathematical knowledge and techniques

- Recognise whole numbers and simple, familiar fractions and decimals in numeral and word

form.

- Add, subtract, multiply and divide simple numbers, fractions and decimals including the use of

brackets.

- Order, use and interpret whole numbers and familiar, simple fractions and decimals in

everyday texts or simple tables.

- Express numbers as percentages.

b. Comparative mathematics

- Use ratio to describe relationships between two quantities.

- Demonstrate and apply the basic concept of average.

c. Estimation and approximation

- Estimate length, distance, quantity and weight in everyday situations.

d. Writing and interpreting numerical expressions

- Collect and organise familiar data.

- Construct simple tables, graphs or charts manually or using software tools.

- Perform simple calculations.

e. Applying mathematics

- Demonstrate the above mathematical skills and processes in a simple, practical project

including the use of software tools and devices.

- Demonstrate the above mathematical skills and processes in a hands-on, simple problem

solving activity.


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Learning outcome 2

Financial Literacy

Make simple decisions and perform basic monetary calculations involving money and demonstrate

an understanding of participation in a monetary society.

Elements


- Perform simple calculations with money; add simple costs.

- Use simple fractions as applied to money.

- Use money to give and receive correct change.


- Compare the different manual and electronic methods of buying and selling.

- Compare pricing of similar goods and/or services.

- Give examples of change in costs over time.


- Create a simple budget for a specific activity.

- Estimate change on large numbers (over $100).

- Estimate savings on discounted items.


- Use and interpret money notation and symbols, and associated language such as

more/less cheaper/expensive double/halve total.

- Read, understand and communicate information contained in a pay-slip and recognise

monetary terms.

- Calculate GST for sample items.


Compare the different manual and electronic methods of buying and selling

State the reasons for paying tax in a fair society

Describe in simple language why we have insurance and superannuation


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Learning outcome 3

Planning and Organising

Identify and use familiar numbers and units of measurement to make decisions about time,

location, data, resources and solve simple problems.

Elements


- Read and use time measuring devices such as clocks, watches, calendars.

- Give and follow simple oral directions for moving between locations.

- Read and use simple tables, diagrams, graphs and flow charts.

- Follow simple instructions/flow chart to complete a process or task.


- Compare simple tables and diagrams related to time on relevant documents or in familiar

situations.

- Compare data from similar tables or graphs using software tools and devices.

- Order and group numerical information so comparisons can be made.


- Estimate times and distances required to move between locations.

- Estimate amounts and quantities required in everyday or simple situations.


- Interpret and use simple concepts of relative position and location and identify key features

of simple maps.

- Interpret and use a calendar or planner to record information.

- Decide through reasoning the steps needed to solve simple numerical problems.


- Use software tools and devices to solve simple problems related to time and location.

- Apply simple problem solving techniques to solve one step numerical problems related to

planning and organisation.

- Communicate information about location and time using basic conventional terminology

such as hour, minute, day, week, month, before/after, longer/shorter, over/under, in

front/behind, left/right, up/down, through, opposite, on the corner and next to.


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Learning outcome 4

Measurement, Representation and Design Use simple, familiar units to measure, recognise and represent common two-dimensional shapes

and simple objects.

Elements


- Perform a range of simple operations relating to perimeter, area and volume.

- Describe and name common two and three-dimensional shapes and objects.

- Draw and interpret simple plans and diagrams representing familiar real-world objects.

- Use appropriate units of measurement and make simple conversions to common units.


- Choose and use appropriate measuring instruments from a given range of measuring

instruments (including technology).

- Recognise and compare familiar shapes and objects in relation to size and shape.


- Estimate lengths, areas and volumes in familiar contexts.

- Apply simple approximation techniques to reduce/enlarge simple diagrams and

representations of familiar real-life objects.


- Draw and interpret simple plans and diagrams and their familiar conventions, for

representing familiar real-life objects.

- Use the common units of measurement and their abbreviations such as millimetre,

centimetre, metre, kilogram, litre, to compare and measure materials or objects.


- Apply measurement in a basic, familiar context

- Demonstrate the use of technology in the application of measurement

- Assemble or model simple three-dimensional objects by following instructions, plans or

diagrams.


35

Learning outcome 5

Preparing for Work Use and communicate numerical skills in a practical context within the work environment.

Elements


- Obtain and have access to a tax file number and be able to use it on a form.

- Read, write, interpret and compare numbers related to time on relevant documents such as

work rosters (start, finish and break times) including 24-hour time.

- Understand break entitlements and break times.

- Demonstrate simple understanding of personal banking including opening and using a

personal bank account, providing numerical data for deposit of pay.


- Look at different award rates for a number of industries.

- Obtain the different wage scales for an apprenticeship or traineeship over the years of

training.


- Use and communicate processes of practical estimations and other assessment skills

appropriate to workplace contexts and tasks.

- Demonstrate the application of mixed numerical functions expected in a workplace with an

understanding of how they are used in a practical context.

- Understand and use a range of common written and oral workplace numerical language

(sentences, phrases and terms).


- Read and relate numerical information to peers and customers.

- Read, interpret and communicate numerical information in workplace forms, charts and

tables.


- Look at and interpret data from tables and graphs

- Use software tools and devices to describe data from a selected industry

- Read, interpret and complete simple workplace forms that include numerical content.


36

Numeracy Skills Intermediate – Unit 1 Unit purpose

The purpose of this unit is to enable students to develop everyday numeracy skills to make sense

of their daily personal and public lives. The mathematics involved includes numbers and data,

financial literacy, time and location, measurement and design and the use of software tools and

devices applied to tasks which are part of the students’ normal routine but also extending to

applications outside their immediate personal environment such as the workplace and the

community.

At the end of the unit students would be able to attempt a series of both single and multi-step

operations or tasks with some confidence, be able to select the appropriate method or approach

required, and would be able to communicate their ideas both verbally and in written form. They

would be at ease with straightforward calculations either manually and/or using software tools and

devices.

Assessment

Students must demonstrate achievement in all the learning outcomes to be credited with this unit.


The conditions of assessment for the Numeracy Skills Intermediate unit are that students:

use concrete, relevant, familiar contexts and materials where the mathematical content is

predictable and easily accessible

rely on context, prior knowledge and personal experience to derive meaning and check

reasonableness

perform where access to mentor/teacher and advice/modelling is available and recourse to

first/other language is acceptable

use a blend of personal ‘in the head’ methods, pen and paper methods and calculator

procedures

use a combination of oral and written general, and some mathematical, language, symbols and

abbreviations.


37

Learning outcome 1

Numerical Skills and Processes

Perform routine multi-step computations with and without software tools and devices.

Elements


- Identify and use whole numbers, including numbers up to millions, decimals to hundredths,

money and everyday fractions and percentages.

- Perform a range of calculations of whole numbers, fractions and decimals with the four

operations (+, –, x, ÷) incorporating an understanding of rounding and place value.

- Demonstrate an understanding of the order of the four arithmetical operations and use this

to solve multi-step calculations.

- Use and understand the phrases and symbols for mathematical operations add, and, total, difference, subtract, minus, take away, times multiply, share, divide, % of, double, quarter etc.


- Use and apply relevant ratio, rates and proportions, e.g. scales on maps and plans, in

familiar or routine situations, e.g. km/hr, $/kg, or mixing of ingredients.

- Demonstrate and apply the measures of central tendency (mean, mode and median).


- Make estimations and check reasonableness of processes and outcomes in relation to the

context.

- Estimate, approximate and measure length, mass, capacity/volume, time and temperature,

using simple instruments graduated in familiar units

- Identify and estimate common angles, e.g. as a rotation with a full turn = 360° and recognition of right angles as 90°.


- Convert between routine metric units demonstrating an understanding of common prefixe

- Collect and organise familiar and unfamiliar data and construct tables, graphs and charts,

manually or using software tools and devices.

- Find the mean, median and mode of collected data.

- Describe the variation and general trend of data from familiar contexts.

- Describe, compare and interpret the likelihood of everyday chance events (e.g. rolling a six

on a dice or the chance of rain) using qualitative terms such as certain, likely, impossible

and relate these to everyday or routine fractions, decimals or percentages.


- Demonstrate the above mathematical skills and processes in a multi-step project including

the use of software tools and devices.

- Demonstrate the above mathematical skills and processes in a hands-on, multi-step

problem solving activity using simple mathematical notation and symbols.


38

Learning outcome 2

Financial Literacy

Make decisions and perform routine monetary calculations involving money, manage personal finances and understand risk in familiar situations.

Elements


- Obtain accurate results for calculations involving money.

- Perform calculations involving bank statements and utility bills.

- Perform calculations involving percentages and fractions as they relate to money.


- Compare and contrast the different ways of buying and selling.

- Investigate ways to minimise risk with personal finances.

- Compare different costs of familiar goods and services over time.


- Create a budget recognising the difference between needs and wants.

- Estimate savings in a budget.

- Estimate, then calculate increases and decreases in percentages as they relate to money.


- Perform calculations involving credit cards and understand the different types of debt.

- Understand the language used on a sample payslip and check the accuracy of the

mathematics used.

- Investigate different income tax deductions.


- Solve problems involving tax - Apply monetary skills to a financial project - Describe saving and investment options, including superannuation options.


39

Learning outcome 3


Identify, use and interpret routine numbers and units of measurement to make decisions about

time, location, data, resources and solve routine multi-step problems.

Elements


- Use and calculate with time, for example converting between digital and analogue time and

calculating elapsed time.

- Use simple and unfamiliar timetables, charts, tables etc. to make calculations around

everyday situations.

- Use map indexes and keys to locate particular places of interest.

- Follow routine multi-step instructions/flow charts to complete a process or task.


- Compare 12 and 24 hour time systems and convert between them.

- Use familiar timetables to compare different ways of making the same journey.

- Compare data from familiar tables and graphs using software tools and devices.

- Demonstrate an understanding of the language of direction and travel and its mathematical

alternatives i.e. ½ turn = 1800, North East as 900


- Estimate distances and make judgments about time.

- Draw rough sketch maps or plans to describe route to or location of building or feature of

interest.

- Use number facts and rounding to give rough estimates of numerical calculations.


- Use distance, direction, coordinates, simple scales, labels, symbols and keys to read and

use everyday maps and plans.

- Interpret distances in terms of approximate travelling time such as 15 minutes walk, or 2

hours’ drive.

- Record information regarding time and location using tables and charts.

- Decide through reasoning the steps needed to solve multi-step numerical problems.


- Use software tools and devices to solve routine problems related to time and locations.

- Apply problem solving techniques to solve multi-step numerical problems related to

planning and organisation.


40

Learning outcome 4

Measurement, Representation and Design

Use units of measurement to measure, represent and interpret objects, plans and diagrams.

Elements


- Calculate and use routine operations related to perimeter, area, volume and capacity.

- Use appropriate units of measurement including vocational and in-home units of

measurement.

- Describe, name and represent common two and three-dimensional shapes and objects.

- Convert common units of measurement as they apply to length, area and volume.


- Recognise and classify simple transformations of familiar objects (including dilations,

reflections, rotations and translations).

- Represent a simple three-dimensional object as a two-dimensional drawing and apply exact

scaling techniques to reduce/enlarge the two-dimensional representation.

- Read and interpret calibrations on a range of familiar measuring instruments.

- Compare units of measurements as they apply to area and capacity (for example, acres to hectares, cubic centimetres to litres).


- Use approximation techniques to estimate common measurements.

- Apply rounding techniques to measurements.


- Create and interpret routine plans and diagrams and their familiar conventions, for

representing real-life objects.

- Apply scale techniques using ratios to enlarge/reduce plans representing real life objects.

- Use the names and symbols of the metric units of measurement.

- Interpret measurement in terms of the purpose of the practical situation.


- Create solids from nets for common three-dimensional shapes.

- Design and use simple two-dimensional plans to construct simple three-dimensional

objects.

- Apply measurement from familiar plans, charts or diagrams to make decisions regarding amounts and costs.


41

Numeracy Skills Intermediate – Unit 2 Unit purpose

The purpose of Unit 2 is to enable students to develop, refine, extend and apply numeracy

knowledge and skills through an investigation in a familiar industry area linked to the VET units in

your VCAL program or employment. The numeracy involved focuses on Number, Measurement,

Financial Numeracy, and Probability and Statistics.

This Unit seeks to extend students’ understanding of how numerical knowledge and skills can be

transferred to an industry area. The key processes involve identifying mathematics, applying it and

communicating the results.

Students develop an understanding of the practical components of planning and undertaking an in-

depth numeracy based project, linked to a familiar industry area. Students will also develop key

project management skills in a numeracy context, such as stating key aims, setting specific tasks,

establishing timelines and milestones, identifying and managing risk, and communicating results.

Students will be encouraged to develop and apply their skills of creative and critical thinking in the

planning and completion of the numeracy based project that will be negotiated with their

teacher/trainer.

At this level, students also share their knowledge and work independently and in teams.

On completion of this Unit students should be more confident in their ability to explore, develop and

apply numeracy related to employment in an industry area.

Assessment


Furthermore, students must be observed to demonstrate achievement on more than one occasion

and in different contexts to make sure that the assessment is consistent, reliable, fair and

equitable.


The conditions of assessment for the Numeracy Skills Intermediate Unit 2 are that students use:

concrete, relevant, familiar and personal contexts and materials where the mathematical

content is explicit

actual objects (where possible) for spatial and diagrammatic representations


reasonableness




oral descriptions using common, everyday, informal language and gestures for

explanations, answers and interpretations.


42

Learning outcome 1

Design a numeracy-based project plan in a familiar industry area

Elements

a. Select an industry area linked to the VET units in your VCAL program or employment

b. In consultation with your teacher, develop a numeracy based project plan using routine

calculations that is linked to the selected industry area, and focuses on Number,

Measurement, Financial Numeracy and Probability and Statistics. The project plan will

contain the following key features:

c. Select six enquiry based tasks from the table, ensuring that at least one task comes from

each of the four focus areas - Number, Measurement, Financial Numeracy and Probability

and Statistics and at least one task comes from each of the three Industry Stages – Inputs,

Processing, Outputs.

Alternatively, students may select and design their own tasks from each focus area and

Industry Stage from the table in consultation with their teacher. Any student selected task

or tasks must meet the elements stated in Learning Outcome 1.

Industry Stages Number Measurement Financial

Numeracy

Probability and

Statistics

Inputs

(resources such

as raw materials,

labour,

equipment,

capital and

source

information)

Identify the amounts of

inputs used in the

industry area

Investigate and

make calculations

using the ratios of

inputs used in the

industry area

Perform

calculations

involving cost of

the inputs used in

the industry area

Investigate data

trends over a set

period of time

relating to inputs

used in the

industry area

Processing

(the process of

transforming

inputs into

finished goods

and services)

Identify and compare

the numbers involved

in the

processing/production

stages in the industry

Describe the

importance of

Measurement in

your industry area

and use the

different types of

measurement and

their units

Research current

salary costs of the

industry

Compare data

trends over a set

period of time

relating to

processing used in

the industry area

Outputs

(transformed

inputs that are

returned to the

external

environment as

finished product

or service)

Research and interpret

the numerical data

linked to key sales

figures

Collect data and

perform

calculations

relating to outputs

units of

measurement in

the industry

Perform routine

calculations

involving

debit/credit in the

industry

Research key

statistical data

relating to the

outputs of the

industry area

d. Develop a numeracy-based project plan, including aims, numeracy skills, timelines and

measurable outcomes

e. Detail what time lines will be set to fully investigate the six tasks selected

f. Identify and justify the numerical skills and processes, including software tools and devices

and by hand skills that will be used in the investigations of the six tasks


43

g. Discuss the forms of software tools and devices that may be used to present the data from

the investigations of the six tasks

h. Discuss the forms of communication that may be used to present the learnings of the

investigations of the six tasks

i. Comment on any obstacles/barriers that may make undertaking any part/s of the selected

project plan difficult

j. Collaborate with others in the development of the numeracy-based project plan

Learning outcome 2

Apply numerical skills in an industry context

Elements

Consistent with the numeracy-based project plan students will:

a. Undertake research of the selected tasks identified in the project plan

b. Identify the numerical processes to be used to collect relevant data from the

investigations of the selected tasks

c. Use estimation, computation and technology techniques to collect relevant data from

the investigations of the selected tasks

d. Select and use appropriate numerical problem solving strategies

e. Perform a range of routine estimations and calculations, and draw inferences about the

numeracy in the selected industry area

f. Analyse the data collected for each of the six selected tasks, using one or two

methodologies.

Learning outcome 3

Use appropriate software tools and devices to represent data

Elements


a. Detail the various software tools and devices that could be used to properly represent the

data collected from the investigations of the selected numerical tasks

b. Describe the advantages and disadvantages of the various software tools and devices

available to properly represent the data collected from the investigations of the selected

numerical tasks

c. Justify the use of the software tools and devices selected to represent the data associated

with the investigations into the six tasks

d. Use the chosen software tools and devices to represent the numeracy aspects of your

investigations

e. Evaluate the use of the selected software tools and devices


44

Learning outcome 4

Communicate the results of your project

Elements


a. Use appropriate language of mathematics in communicating the results of the project

b. Use appropriate numeracy symbols and conventions in communicating results of your

project

c. Use appropriate software tools and devices in communicating results of your project

d. Communicate results to a relevant audience

e. Critically evaluate, following feedback.


45

Numeracy Skills Senior – Unit 1 Unit purpose

The purpose of this unit is to enable students to explore mathematics beyond its familiar and

everyday use to its application in wider, less personal contexts such as newspapers and other

media reports, workplace documents and procedures, and specific projects at home or in the

community.

At the end of the unit students will have the capacity to interpret and analyse how mathematics is

represented and used. They can recognise and use some of the conventions and symbolism of

formal mathematics. The mathematics involved would include numbers and data, financial

numeracy, time and location, measurement and design, the use of software tools and devices and

an introductory understanding of the use of formulae and problem-solving strategies.

Assessment

Students must demonstrate achievement in all the learning outcomes to be credited with this unit.


The conditions of assessment for the Numeracy Skills Senior unit are that students:

use concrete, relevant contexts and materials where the mathematical content is accessible

rely on prior knowledge, personal experience and mathematical knowledge to derive meaning,

make predictions and check reasonableness

perform where advice/modelling is available and recourse to first/other language is acceptable

use a blend of personal ‘in the head’ methods, pen and paper and calculator procedures (and

software programs where appropriate)

use a combination of oral and written mathematical and general language, symbols,

abbreviations and diagrams.


46

Learning outcome 1

Numerical Skills and Processes Fluently perform complex multi-step computations with and without software tools and devices.

Elements


- Use and apply order of arithmetical operations to solve equations with multi-step

calculations including the use of fractions, decimals up to thousandths and percentages.

- Use symbolic notation to perform arithmetic calculations including the use of relevant

positive and negative numbers and numbers expressed as roots and powers.

- Develop, interpret, solve and use substitution in routine formulae and algebraic expressions

as representations and conventions that describe relationships between variables in

relevant contexts, i.e. repair charges, cooking, Pythagoras’s theorem or in using workplace

formulae.


- Convert within the metric system and between metric units including the use of decimal

forms.

- Use and apply rates in familiar or routine situations, including using ratio notation, visual

keys and terminology such as km/hr, $/kg or $/m and apply these to related costs and

distance situations.


- Estimate, then accurately measure and calculate quantities, including for complex areas

and volumes using relevant measurement formulae with the ability to convert between a

range of metric units.

- Estimate and accurately measure angles relating to direction and use this to describe the

location of places.


- Collect, organise and represent data, including grouped data, e.g. in tables, spreadsheets,

graphs, plots.

- Interpret and draw conclusions about general trends of data, variations within data sets and

data reliability.

- Summarise a range of unfamiliar statistical data appropriately, including measures of

central tendency (mean, median, mode) and simple measures of spread, including

standard deviation and interquartile distance..

- Use knowledge about chance and probability to estimate and interpret the outcomes of

common chance events in both numerical and qualitative terms (for example, the odds of

tossing consecutive heads and tails).

- Interpret, analyse and draw inferences from unfamiliar data, in terms of validity and

accuracy.


47


- Use and apply knowledge about probability to a range of relevant contexts (e.g. sporting

events), calculate theoretical probabilities and use tree diagrams to investigate the

probability of outcomes in simple multiple event trials.

- Uses a combination of written mathematical and general language, including some

specialised mathematical symbolism, abbreviations, terminology and representation to

document, interpret and communicate the processes, results and implications of the

mathematical activities involved in the completion of a hands on complex project.

- Demonstrate the above mathematical skills in a range of processes to select an appropriate

method of solution to solve a complex real life problem. In doing this demonstrate how to

organise and represent the mathematical information in an alternative, useful form, use

developed estimating and assessment skills to check the outcomes and decide on the

appropriate degree of accuracy required and critically review the mathematics used and

the outcomes obtained to reflect on and question the outcomes and real-world implications.


48

Learning outcome 2

Financial Literacy Make decisions and perform monetary calculations involving money in unfamiliar contexts; manage

personal and business finances and understand risk in a range of situations.

Elements


- Perform multi-step calculations involving percentages as they relate to money.

- Convert between percentages, decimals, fractions and ratios as they relate to money.

- Use financial statements to perform calculations.


- Calculate and compare the difference in amount of interest paid by major banks.

- Demonstrate an understanding of minimising risk with personal finances.

- Calculate the interest cost of purchasing household items.


- Create and manage an accurate budget for a specific activity.

- Relate budgets to financial documents.

- Make financial decisions in a range of personal situations.


- Compare interest rates charged by different banks or financial institutions and make

decisions based on these observations.

- Interpret payslips and timesheets and perform calculations.

- Compare and communicate the role of personal tax and business taxes.


- Describe taxable deductions and apply to mathematical problems in a range of situations

- Describe and apply financial management skills to a specific enterprise

- Identify the advantages and disadvantages of short and long term investments.


49

Learning outcome 3


Identify, use and interpret routine numbers and units of measurement to make decisions about

time, location, data, resources and solve complex problems in unfamiliar situations.

Elements


- Solve problems involving duration, including using 12 and 24 hour time, within and across

time zones.

- Use and apply rates in familiar situations, e.g. km/hr and $/L.

- Use distance, direction, coordinates, simple scales, labels, symbols and keys to read and use complex maps, plans or diagrams.

- Follow complex multistep instructions/flow charts to complete tasks or processes.


- Analyse and compare schedules.

- Analyse and interpret relative positions of objects with regard to location.

- Make calculations and apply ratios involving scale on maps, plans or diagrams.

- Compare data from complex tables or graphs or schedules using software tools and

devices.


- Estimate and determine distances and make calculations involving time.

- Design and sequence numerical information into charts, plans or flow diagrams.

- Choose appropriate resources and use them to solve complex numerical problems.


- Interpret and use information and symbols on maps and plans including location, distance,

speed and rates, including ratio notation, visual keys, terminology such as N/S/W/E, km/h,

kph, litres/100 km, $/L.

- Record complex information regarding time and location using tables or charts.

- Decide through reasoning the steps needed to solve complex multistep numerical

problems.

-


- Use software tools and devices to solve complex problems related to time and location.

- Apply problem solving techniques to solve complex multistep numerical problems related to

planning and organisation in unfamiliar contexts.


50

Learning outcome 4

Measurement, Representation and Design Measure, draw, represent and interpret complex two and three-dimensional objects in

diagrammatic form and apply transformations to designs and demonstrate a fluent use of software

tools and devices.

Elements


- Interpret and use the concepts and units of temperature, length, mass, capacity, perimeter,

area and volume.

- Represent complex three-dimensional objects as two-dimensional nets.

- Draw and interpret complex two-dimensional plans and diagrams.

- Convert complex units of measurement.


- Identify transformations applied to familiar, real-life objects.

- Determine real-life measurements and produce a scaled diagram.

- Interpret a scaled diagram to determine the exact real-world measurements.

- Read and interpret detailed calibrations on a range of measuring instruments.


- Estimate, draw and measure in relation to size, cost or time.

- Make approximation of multiple amounts of units of measurement to obtain total estimates.


- Write and interpret plans and diagrams and their familiar conventions, for representing real-

life objects of a range of size and complexity.

- Apply scale techniques using ratio and proportion to enlarge/reduce complex plans.

- Use the names and symbols of the metric units of measurement and apply to conversions

- Judge whether complex models, plans and diagrams are representative of their original

model

- Use, calculate and interpret information based on maps and plans, including scales,

bearings, travel distances, speeds and times, and time zones.


- Read, set and interpret calibrations on a range of measuring instruments

- Select appropriate rules and formulae for measurement (perimeter, area, volume and

capacity) and apply to unfamiliar shapes and objects including polygons and spheres

- Assemble and model a functional three-dimensional object by following instructions, plans

or diagrams

- Adjust quantities of measurement using ratio and proportion.


51

Numeracy Skills Senior – Unit 2 Unit purpose

The purpose of Unit 2 is to enable students to develop, refine, extend and apply numeracy

knowledge and skills through an investigation in an unfamiliar industry area but in which you have

an interest and may seek future employment. The numeracy involved focuses on Number,

Measurement, Financial Numeracy, and Probability and Statistics.

This Unit seeks to extend students’ understanding of how numerical knowledge and skills can be

transferred to an industry area. The key processes involve identifying mathematics, applying it and

communicating the results.

Students develop an understanding of the practical components of planning and undertaking an in-

depth numeracy based project, linked to an unfamiliar industry area.

Students will also develop key project management skills in a numeracy context, such as stating

key aims, setting specific tasks, establishing timelines and milestones, identifying and managing

risk, and communicating results. Students will be encouraged to develop and apply their skills of

creative and critical thinking in the planning and completion of the numeracy based project that will

be negotiated with their teacher/trainer.

At this level, students also share their knowledge and work independently and in teams.

On completion of this Unit students should be more confident in their ability to explore, develop and

apply numeracy related to employment in an industry area.

Assessment


Furthermore, students must be observed to demonstrate achievement on more than one occasion

and in different contexts to make sure that the assessment is consistent, reliable, fair and

equitable.


The conditions of assessment for the Numeracy Skills Senior Unit 2 are that students use:

concrete, relevant, familiar and personal contexts and materials where the mathematical

content is explicit

actual objects (where possible) for spatial and diagrammatic representations


reasonableness




oral descriptions using common, every day, informal language and gestures for explanations,

answers and interpretations.


52

Learning outcome 1

Design a numeracy-based project plan in an unfamiliar industry area

Elements

a. Select an industry area with which you are unfamiliar but in which you have an interest and may seek future employment.

b. In consultation with your teacher, develop a numeracy based project plan using complex

calculations that is linked to the selected industry area, and focuses on Number,

Measurement, Financial Numeracy and Probability and Statistics. The project plan will

contain the following key features:

c. Select eight enquiry based tasks from the table, ensuring that at least one task comes from

each of the four focus areas - Number, Measurement, Financial Numeracy and Probability

and Statistics and at least one task comes from each of the three Industry Stages – Inputs,

Processing and Outputs.

Alternatively, students may select and design their own tasks from each focus area and

Industry Stage from the table in consultation with their teacher. Any student selected task

or tasks must meet the elements stated in Learning Outcome 1.

Industry Stages Number Measurement Financial

Numeracy

Probability and

Statistics

Inputs

(resources such as

raw materials,

labour, equipment,

capital and source

information)

Research and

record the

breakdown of the

inputs used in the

industry area

Undertake research

into travel times

taken by inputs to

reach the industry

area

Evaluate and

represent the cost

of the inputs in the

industry area

Analyse the trend

in the cost of the

inputs in the

industry area over

a set period and

estimate quantities

using probability

Processing

(the process of

transforming inputs

into finished goods

and services)

Compare and

contrast the

numbers involved

in the

processing/producti

on stages in the

industry

Conduct complex

measurements

appropriate to the

processing stages

of the industry area

Undertake research

into the monetary

value of the waste

produced in the

industry

Conduct a

mathematical

analysis of waste

products in the

processing stage

Outputs

(transformed inputs

that are returned to

the external

environment as

finished product or

service)

Discover and

present the key

sales figures in a

tabular and

graphical form

Investigate quality

control, scaling or

calibration in your

industry area

Perform complex

calculations

involving

debit/credit in the

industry

Conduct a detailed

analysis of the

sales figures over a

set period. Make

predictions about

future sales

d. Develop a numeracy-based project plan, including aims, numeracy skills, timelines and

measurable outcomes and how the results from this project will be communicated

e. Detail what time lines will be set to fully investigate the eight tasks selected

f. Identify and justify the numerical skills and processes that will be used in the investigations

of the eight tasks

g. Discuss the forms of software tools and devices that may be used to present the data from

the investigations of the eight tasks


53

h. Discuss the forms of communication that may be used to present the learnings of the

investigations of the eight tasks

i. Comment on any obstacles/barriers that may make undertaking any part/s of the selected

project plan difficult

j. Collaborate with others in the development of the numeracy-based project plan

Learning outcome 2

Apply numerical skills in an industry context

Elements


a. Undertake research of the eight selected tasks identified in the project plan

b. Identify the numerical processes to be used to collect relevant data from the investigations

of the eight selected tasks

c. Use estimation, computation and software tools and devices to collect relevant data from

the investigations of the eight selected tasks

d. Select and use appropriate numerical problem solving strategies

e. Perform a range of complex multistep estimations and calculations, and draw inferences

about the numeracy in your selected industry area

f. Comment upon the data collected from the investigations in terms of difficulties

encountered using the selected numerical processes

g. Analyse the learnings from the data collected for each of the eight selected tasks, using

multiple methodologies.

Learning outcome 3

Use appropriate software tools and devices to represent data

Elements


a. Detail the various software tools and devices that could be used to properly represent the

data from the investigations of the eight selected numerical tasks

b. Describe the advantages and disadvantages of the various software tools and devices

available to properly represent the data from the investigations of the eight selected

numerical tasks

c. Justify the use of the software tools and devices selected to represent the data associated

with the investigations of the eight selected numerical tasks

d. Use the chosen software tools and devices to represent the collected data from the

investigations of the eight selected numerical tasks

e. Evaluate the use of the selected software tools and devices

f. Use a minimum of two types of software tools and devices to demonstrate the numeracy

aspects of your project.


54

Learning outcome 4

Communicate the results of your project

Elements


a. Use appropriate language of mathematics in communicating the results of the project

b. Use appropriate numeracy symbols and conventions in communicating results of your

project

c. Use appropriate software tools and devices in communicating results of your project

d. Communicate results to a relevant audience in at least two different forms

e. Critically evaluate, following feedback


55

Advanced Numeracy Skills Senior

Unit purpose

The purpose of this unit is to provide students with an opportunity to further develop their

knowledge and skills of several fundamental areas of mathematics. The mathematics involved will

include: numerical calculations and formulae, analysis, algebraic techniques and problem-solving

strategies. At the end of the unit, students will be able to confidently apply mathematics with a

level of sophistication in a variety of STEM situations.

Assessment



The conditions of assessment for Advanced Numeracy Skills Senior are that students:

use relevant contexts and materials where the mathematical content may be hidden

use a range of mathematical experiences and knowledge to derive meaning, reflect and

critically review the mathematics involved

perform where some clarification and discussion of strategies is available if required and

recourse to first/other language is acceptable

use processes flexibly and interchangeably, selecting from pen and paper, mental and

electronically assisted strategies, including calculators (both statistical and graphing

calculators) and software programs where appropriate. The application of spreadsheets is

highly recommended as a learning tool

use a combination of oral and written mathematical and general language, symbols,

abbreviations and diagrams.


56

Learning outcome 1

Further Study in Maths – Data

Can use tables and graphs and measures of central tendency and spread to interpret, analyse and

describe information of relevance to self, work or community.

Elements


- Collect, group and represent statistical data in appropriate tabular and graphical form,

including using software programs or a graphing calculator.

- Use whole numbers, percentages, decimals or ratios used in a range of statistical

information.

- Find the three measures of central tendency – mean, median and modal class – for

grouped data.

- Calculate common measures of spread such as the range, common percentiles, and

standard deviation.

- Represent bi-variate data as a scatter plot.

- Find, use and interpret correlation coefficients.

b. Mathematical language

- Use the descriptive language of graphs, and measures of central tendency and spread, for

example maximum, minimum, increasing, decreasing, constant, slope, fluctuating, average,

above/below average, distorted, percentages

- Use appropriately words and symbols for graphs, and measures of central tendency and

spread such as the five-figure summary

- Scatter plot, correlation, correlation coefficient.

c. Interpretation

- Analyse the meaning of data, tables and graphs, any measures of central tendency and

spread, and the accompanying text in terms of personal implications, social consequences,

and their validity and accuracy

- Identify and discuss whether graphs or statistics have been used to distort or exaggerate

- Interpret data presented as a scatter plot in terms of the strength of relationship (strong or

weak) and the direction (positive or negative)

- Describe the appearance of a scatter plot if the correlation coefficient is –1, 1 or 0.


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Learning outcome 2

Further Study in Maths – Measurement

Can calculate complex measurement algorithms using the metric/SI system and apply practical

measurement using the concepts of errors, calibration, scale and rates.

Can apply advanced techniques of measurement, including aspects of design and calibration

Elements


- Identify and reduce errors with a range of measuring instruments

- Demonstrate an understanding of calibration to increase accuracy of measuring equipment

- Calculate complex measurements with a practical focus

- Use scale, ratio and proportion in complex practical situations

- Calculate complex rates as they apply in practical situations


- Use correct mathematical terminology and notation to describe error, calibration, scale,

rates and ratio.

c. Interpretation

- Design a system where accurate measurements of individual elements are necessary to

ensure the system can be successfully integrated. Critically evaluate the system identifying

errors.

Learning outcome 3

Further Study in Maths - Formulae and Graphs

Can develop and use formulae and their graphs to describe and represent relationships between

variables in a range of contexts.

Elements


- Use algebraic rules, formulae, graphs and their conventions.

- Identify general shapes and major characteristics of linear and simple non-linear graphs (for

example, parabolas and hyperbolas) and interpret their real world meanings.

- Create own equations, rules or sketch graphs from worded problems or observed

situations.

- Develop algebraic expressions, rules, formulae, or sketch graphs to generalise

straightforward number patterns or observable relationships between variables.

- Draw graphs using techniques such as plotting points; sketching from known main features

of an algebraic function; and using software tools and devices like a graphing calculator or

computer package.

- Use graphical techniques to solve equations.


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- Use symbolic notation and the representation of algebra such as simple indices, square

roots, brackets, alternative conventions for division, and signed numbers to express and

interpret formulae, rules and equations.

c. Interpretation

- Interpret and evaluate results obtained in the context of the original problem.

Learning outcome 4

Further Study in Maths – Algebraic Techniques

Can use algebraic techniques to investigate and solve mathematical problems.

Elements


- Demonstrate knowledge of the conventions and use of algebra.

- Create equations in problem-solving situations which involve one or two unknowns.

- Recognise the potential for algebraic techniques in problem-solving situations.

- Substitute appropriately in formulae or algebraic expressions to find particular values.

- Solve a range of equations using a variety of techniques such as: same operation on both

sides; backtracking; factorising; or guess, check and improve.


- Use symbolic notation and the representation of algebra such as indices, square roots,

brackets, alternative conventions for division, and signed numbers to express and interpret

formulae, rules and equations.

c. Interpretation

- Interpret and evaluate results obtained in the context of the original problem


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Learning outcome 5

Further Study in Maths – Problem Solving

Can apply formal mathematical skills and techniques to problem-solving to interpret, investigate

and solve mathematical problems using a range of mathematical skills across more than one topic.

Elements


- Identify a range of appropriate mathematical knowledge for the chosen area being studied

to interpret, investigate and solve mathematical problems.

- Apply and use appropriate mathematical skills and techniques from the chosen area to

demonstrate interpretation and investigation skills used to solve general mathematical

problems.

- Select, use and apply a range of algorithms.

- Where appropriate, the use of spreadsheets and specialized calculator or Computer

Algebra systems (CAS) functions, relevant to the chosen mathematical area is

recommended such as trigonometric, statistical and power functions.


- Use appropriately both oral and written language to explain procedures used to solve a

context based problem and to communicate the outcomes. It is expected that the use of

mathematical language related to problem solving and mathematical algorithms be

prevalent throughout the presentation of the work.

c. Interpretation

- Interpret and comment upon the results obtained in the context of the original problem.

- Use developed estimating and approximation skills to check the calculated outcomes and

decide on the appropriate degree of accuracy required for the situation.

- Interpret and critically review the mathematics used and the outcomes obtained to reflect

on and question the outcomes and real-world implications.