Numeracy

Personal futures

Courses aligned to the Years 9 to 12 Curriculum Framework belong to one of the five focus areas of Discipline-based study, Transdisciplinary projects, Professional studies, Work-based learning and Personal futures.

Numeracy Level 1 is a Personal futures course.

Personal futures courses prepare learners to be independent young adults, able to lead healthy, fulfilled and balanced lives. Learning is highly personalised. Learners develop strategies to optimise learning, make decisions, solve problems, set career and life goals and pursue areas of strong personal interest. Personal futures supports learners to develop the required knowledge, skills and understandings to make informed choices that enhance their own and others’ health and wellbeing. The inclusion of Personal futures as a focus area responds to a range of contemporary research findings highlighting the importance of learners having broad educational goals that include individual and collective wellbeing and opportunities for student agency as they navigate a complex and uncertain world.

Personal futures courses have three key features that guide teaching and learning:

• theory and dialogue
• informed action
• reflection and dialogue.

In this course learners will do this by:

• developing fundamental mathematics skills and numerate behaviours for life in meaningful contexts
• interacting and working with other people, engaging in mathematical discussions to explore ideas and compare solutions
• engaging with number to develop number sense and basic number skills to identify challenges and solve problems
• using mathematical reasoning and reflection to trial strategies, check solutions, generate knowledge and take informed action.

The Numeracy Level 1 course is designed to develop learners’ fundamental mathematics skills and numerate behaviours and their ability to apply mathematical thinking and reasoning in real world contexts. In doing so, the course enables learners to understand how mathematics can support them to understand and take informed action in familiar and personally relevant contexts.

This course enables learners to:

• use basic number skills independently in situations involving money, routine fractions, decimals and percentages
• recognise and interpret patterns, shapes, maps and plans
• estimate, calculate, measure and solve problems involving time, temperature, length, perimeter, mass, volume and capacity
• understand the likelihood of chance events and engage with information found in tables, graphs and charts.

This course is specifically designed for learners who require flexible and individualised learning programs. Successful completion of the course will provide learners with a level of numeracy that will enable them to move toward greater autonomy and independence in everyday living and the workforce. This course does not enable learners to achieve the everyday adult standard – mathematics.

The purpose of Years 9 to 12 Education is to enable all learners to achieve their potential through Years 9 to 12 and beyond in further study, training or employment.

Years 9 to 12 Education enables personal empowerment, cultural transmission, preparation for citizenship and preparation for work.

This course is built on the principles of access, agency, excellence, balance, support and achievement as part of a range of programs that enables learners to access a diverse and flexible range of learning opportunities suited to their level of readiness, interests and aspirations

On successful completion of this course, learners will be able to:

1. communicate thinking, strategies and solutions using appropriate mathematical or statistical language
2. plan, organise and manage learning to complete tasks and assess progress
3. demonstrate an understanding of, and use number properties and basic operations to represent familiar and personally relevant situations and solve problems
4. apply mathematical reasoning to make predictions, represent relationships and explain thinking in familiar and personally relevant situations
5. act as creative, critical and reflective thinkers to assess ideas and take informed action in familiar and personally relevant situations
6. identify and use routine fractions, decimals, percentages, money amounts and interpret patterns in familiar and personally relevant situations
7. gather, organise and interpret data and describe likelihood of chance events in familiar and personally relevant situations
8. interpret, measure and estimate quantities and interpret shapes, maps and plans in familiar and personally relevant situations

The Numeracy Level 1 course enables continuity for learners who have successfully completed Preliminary Mathematics Stage 4. Learners may also have previously had an agreed Individual Education Plan in place or otherwise engaged with the Australian Curriculum: Mathematics F-10.

Numeracy Level 1 will provide the foundational number skills and numerate behaviour for learners wanting to consolidate and expand their knowledge and skills in Mathematics Level 1. This course also supports the basic numeracy needed for real world contexts and other senior secondary courses such as Science Level 1 and Food and Cooking Essentials Level 1.

Numeracy Level 1 may also be a potential pathway to Essential Skills Numeracy Level 2.

The general capabilities addressed specifically in this course are:

• Critical and creative thinking
• Literacy
• Numeracy
• Personal and social capability

The cross-curriculum priorities enabled through this course are:

• Aboriginal and Torres Strait Islander histories and cultures
• Sustainability

This course has a complexity level of 1. 

For a full description of courses at a complexity level of 1, please refer to the Levels of Complexity - Tasmanian Senior Secondary Education document.

This course has a size value of 15. Upon successful completion of this course (i.e., a Preliminary Achievement (PA) award or higher), a learner will gain 15 credit points at Level 1 towards the Participation Standard of the Tasmanian Certificate of Education (TCE).

This course consists of three 50-hour modules.

Module 1: Numbers and patterns

Module 2: Everyday chance and data

Module 3: Everyday measurement and shape

Access

This course requires learners to collaborate with others. Learners who have previously successfully completed a Levels 1 to 4 Mathematics courses cannot access this course.

Resource requirements

The learning outcomes in this course require learners to have access to measurement instruments including thermometers, stopwatches, tape measures and concrete materials including play money, Australian denominations, counters, dice, spinners, blocks and three-dimensional models.

Learners will require occasional access to general calculators in this course. On occasions, computers and the internet will be required to enable learners’ access to interactive models, information and simple data sources such as newspaper articles or store catalogues.

Module 1: Numbers and patterns

This module contains four topics:

• understanding number properties
• decimals, percentages and money
• fractions
• patterns

In this module, learners will review the basic properties of number, simple mathematical operations and the concept of place value. They will carry out simple money calculations, describe patterns in their surrounding environment and explore different representations of numbers. The knowledge, understanding and skills gained in this module are fundamental for engagement throughout the course.

Module 1 learning outcomes

The following learning outcomes are a focus of this module:

1. communicate thinking, strategies and solutions using appropriate mathematical or statistical language
2. plan, organise and manage learning to complete tasks and assess progress
3. demonstrate an understanding of,  and use number properties and basic operations to represent familiar and personally relevant situations and solve problems
4. apply mathematical reasoning to make predictions, represent relationships and explain thinking in familiar and personally relevant situations
5. act as creative, critical and reflective thinkers to assess ideas and take informed action in familiar and personally relevant situations
6. identify and use routine fractions, decimals, percentages, money amounts and interpret patterns in familiar and personally relevant situations.

Module 1 content

Key knowledge and skills

Topic 1 – understanding number properties

This topic has two sub-topics:

• basic number skills and operations
• place value.

Basic number skills and operations

• recognise language related to number; for example:
  • few, less, more, none, all, double, triple, halve, third, first
• count in different contexts; for example:
  
  • count forward by tens
  • count backwards from 100
  • count with coins
  • count time on an analogue clock in five-minute intervals
• use ordinal terms and post determiners in everyday contexts; for example:
  
  • ‘it was Frederick’s first (1st) birthday’
  • ‘Next you need to add the cherries’
• recognise factors and multiples in numbers up to 50 
• recognise fractions in everyday contexts; for example:
  
  • add `1/4`  cup sugar to the cake mix
• recognise the concepts of percentage increase and percentage decrease
• recognise decimals and percentages in everyday contexts; for example:
  
  • a 30% off sale
  • purchasing 1.5 kg of pumpkin
• use addition, subtraction, multiplication and division in everyday contexts; for example:
  
  • if I have $10 and want to buy two loaves of bread that each cost $4.50, do I have enough money?
• complete number sentences involving one or more operations by calculating missing values; for example:
  
  • `8× ? = 24,? - ? = 5,? + 7 - 3 = 8` and relate to everyday contexts
• use a calculator to solve number problems; for example:
  
  • how many cans of soft drink will I have if there are 6 cans in a carton and I buy 3 cartons? If I am having a party with 20 people, will there be enough soft drink for everyone to drink 1 can?
• solve number problems and explain the strategies used.

Place value

• identify which digit is in a given place value for a number; for example:
  
  • identify how many hundreds there are in 523
• match place value to the digits of an integer
• recognise, read and record numbers and interpret numerical information in various contexts; for example:
  
  • numbers in sports scores and statistics
  • residential and commercial building addresses
• compare and order numbers in various contexts; for example:
  
  • least to most expensive property sale
  • events occurring over time.

Topic 2 – decimals, percentages and money

• read, write, order and compare decimal numbers
• recognise, match, sort, order and use Australian currency to purchase items
• read and write money amounts in numerals and words
• estimate costs and change on single item purchases; for example:
  
  • select appropriate coins and notes to tender after estimating costs
  • use rounding to estimate the amount of change due, such as rounding to the whole dollar or 50c
  • recognise whether they have been given the correct change during a purchase
• recognise, read and write the % symbol as ‘per cent’
• recognise and explain the meaning of a percentage as a part of 100
• interpret the use of percentages in everyday life; for example:
  
  • what is meant by '25% off' in a sale, or an '80% goal-kicking success rate'
• recognise that there are alternate methods of using a calculator to calculate percentages of amounts; for example:
  
  • using a % key or using 'percentage ÷ 100 x amount' or using the decimal equivalent of the percentage.

Topic 3 – fractions

• recognise language related to fractions; for example:
  
  • equal parts, share, divide, whole, half, quarter
• identify routine fractions in written and numeric form; for example:
  
  • halves, quarters, thirds, tenths, `1/2,1/3,2/3,1/4,3/4,4/10`  etc.
• identify fractions in everyday contexts; for example:
  
  • walking a third of the way up the street
  • going to a half-price sale
  • buying half a dozen eggs
• recognise that a fraction represents a whole divided into a number of equal parts
• recognise the numerator as the number of equal fractional parts and the denominator as the number of equal parts the whole has been divided into; for example:
  
  • `3/(4` means three out of four equal parts
• recognise how many parts are needed to make a whole or 100%; for example:
  
  • four quarters = one whole
• represent fractions using a variety of strategies, including concrete materials, diagrams and numerals as appropriate
• represent fractions for given situations; for example:
  
  • write the fraction `1/4` when they eat 2 out of 8 slices of pizza
  • express 50c as `1/2` of a dollar
  • describe each region of a netball court as a one-third
• compare fractions, using language relating to size; for example:
  
  • recognise that half of something is more than a quarter of it
  • recognise that two-thirds of something is twice as much as one-third of something
• divide diagrams, objects, groups of objects or numbers into fractional parts; for example:
  
  • divide a group of objects into quarters
  • cut a sandwich in half
  • divide a flag into thirds
• represent equivalent fractional parts in different ways; for example:
  
  • how many different ways can you represent one half of this rectangle?
• solve simple problems involving addition and subtraction of routine fractions using concrete materials, diagrams, formal recording methods or calculators
• represent decimals as fractions of 10, 100, etc; for example:
  
  • 0.3 = `3/10`
• represent percentages as fractions of 100; for example:
  
  • 40% = `40/100`.

Topic 4 - patterns

• recognise patterns in the environment; for example:
  
  • in nature
  • in artwork
  • in company logos
  • in the home
  • in the classroom
  • in pictures
  • online
• recognise, copy and continue shape and whole number patterns
• create shape and whole number patterns
• describe shape and whole number patterns informally; for example:
  
  • 'The house numbers on this side of the street are all odd and go up by twos’
• develop a rule for a given whole number pattern and express it mathematically; for example:
  
  • add five to the previous number
  • double the number and take away 1
  • for each bullseye, add 10 to the competitor’s total.

Module 1 work requirements summary

This module includes the following work requirement:

• one folio containing ten short responses to pattern and algebraic reasoning questions.

See Appendix 3 for the full specifications of the work requirements of this course.

Module 1 assessment

This module has a focus on criteria 1, 2, 3, 4, 5 and 6.

Module 2: Everyday chance and data

This module contains four topics:

• gathering data
• organising and displaying data
• modelling and interpreting situations
• probability of events.

In this module, learners will learn about and apply different data collection techniques. They will practise organising and displaying data, describe chance events, explore simple mathematical models and draw simple conclusions based on given information.

Module 2 learning outcomes

The following learning outcomes are a focus of this module:

1. communicate thinking, strategies and solutions using appropriate mathematical or statistical language
2. plan, organise and manage learning to complete tasks and assess progress
3. understand and use number properties and basic operations to represent familiar and personally relevant situations and solve problems
4. apply mathematical reasoning to make predictions, represent relationships and explain thinking in familiar and personally relevant situations
5. act as creative, critical and reflective thinkers to assess ideas and take informed action in familiar and personally relevant situations
7. gather, organise and interpret data and describe likelihood of chance events in familiar and personally relevant situations.

Module 2 content

Key knowledge and skills

Topic 1 – gathering data

• recognise information in a variety of tables and graphs
• recognise features of tables and graphs
• recognise examples of data observable in everyday life
• identify the purpose of collecting a set of data; for example:
  • identify why the owner of the local shop may want to know the most popular flavour of drink purchased
• pose a question that may be answered by a set of data
• identify a range of ways that data can be collected to answer a given question; for example:
  
  • a verbal or written survey
  • observations
  • research on the internet
• use digital technology to conduct surveys; for example:
  
  • online survey tools
• select the best method to collect desired data
• design an appropriate data-collection tool for a given purpose
• explain the need to avoid bias when collecting data and suggest ways to do so
• read a range of graphs and tables to gather information
• investigate datasets related to a range of cross-curricular focus areas; for example:
  
  • data on the environment
  • data related to Australia’s neighbouring regions and cultures
  • local, state and national census data from the Australian Bureau of Statistics.

Topic 2 – organising and displaying data

• record collected data using a variety of means; for example:
  
  • tally marks
  • concrete materials
  • symbols
  • digital technologies
• order and sort numbers using terms; for example:
  
  • ascending, descending
  • increasing, decreasing
  • ‘from 1 to 10 inclusive’
• order and sort data into groups, categories or ranges
• complete pre-constructed data tables either on paper or digitally; for example:
  
  • a spreadsheet.

Topic 3 – modelling and interpreting situations

• read, interpret and draw conclusions from graphs that model real situations; for example:
  
  • use a graph of blood alcohol content levels over time to estimate when a person could safely drive a car after drinking alcohol
• display information from real-life situations in simple graphs; for example:
  
  • plot the cost of watering the vegetable garden against the number of litres of water required on a line graph
• complete a table of values from a graph; for example:
  
  • tabulate the number of various food items sold at the canteen by day for the past month.

Topic 4 – probability of events

• recognise language related to chance and probability; for example:
  
  • certain, highly likely, likely, probably, unlikely, impossible, 50:50
• recognise the elements of chance in everyday events
• recognise that some events are entirely related to chance; for example:
  
  • purchasing the winning raffle ticket
• recognise that the range of probabilities is from 0 to 1, or from 0 to 100% in percentage terms
• represent probabilities using a range of notations; for example:
  
  • words, fractions, percentages
• recognise equally likely events; for example:
  
  • getting heads or tails on a coin
• recognise non-equally likely events; for example:
  
  • randomly selecting a green marble from a bag containing unequal numbers of each colour marble
• order events based on their probability
• understand the term ‘random’ as applied to probability; for example:
  
  • ‘a participant will be selected at random’
• describe the likelihood of familiar events.

Module 2 work requirements summary

This module includes the following work requirement:

• one multimodal project: collecting data to answer a question.

See Appendix 3 for the full specifications of the work requirements of this course.

Module 2 assessment

This module has a focus on criteria 1, 2, 3, 4, 5 and 7.

Module 3: Everyday measurement and shape

This module contains four topics:

• length and perimeter
• shapes, maps and plans
• time and temperature
• mass, capacity and volume.

A major focus of this module is developing learners’ skills in measuring time, length, mass, temperature and capacity using appropriate measuring devices and metric units. Where appropriate, the skills developed should be applied to relevant real-life situations. Additionally, learners will explore the properties of two-dimensional shapes and three-dimensional objects, measure perimeters, recognise the connection between mass, capacity and volume and interpret familiar maps and plans.

Module 3 learning outcomes

The following learning outcomes are a focus of this module:

1. communicate thinking, strategies and solutions using appropriate mathematical or statistical language
2. plan, organise and manage learning to complete tasks and assess progress
3. demonstrate an understanding of, and use number properties and basic operations to represent familiar and personally relevant situations and solve problems
4. apply mathematical reasoning to make predictions, represent relationships and explain thinking in familiar and personally relevant situations
5. act as creative, critical and reflective thinkers to assess ideas and take informed action in familiar and personally relevant situations
8. interpret, measure and estimate quantities and interpret shapes, maps and plans in familiar and personally relevant situations.

Module 3 content

Key knowledge and skills

Topic 1 – length and perimeter

• recognise language and comparative language that relates to length; for example:
  
  • tall, short, height, length, longer, shorter, ruler, tape measure, odometer, distance
• recognise metric units of length, their abbreviations and conversions between them
• recognise appropriate units and devices to measure lengths
• estimate and compare lengths and distances; for example:
  
  • the length of a deck compared to the length of an outdoor dining table that would go on the deck
• estimate and measure lengths using a range of devices in everyday situations
• use and compare the accuracy of using different devices; for example:
  
  • measure the length of a modular lounge with a tape measure and a 30-centimetre ruler
• investigate ways to measure distances that are not straight or accessible; for example:
  
  • using a piece of string on a map, using a smartphone app, using a trundle wheel or taking readings on the car odometer
• convert between metric units of length
• solve problems involving length; for example:
  
  • buying a garden hose that is long enough for a yard that is 20 m long
  • buying bird netting to cover a garden bed
• recognise language and comparative language that relates to perimeter; for example:
  • longer than
  • shorter than
  • distance
  • ruler
  • tape measure
• recognise the perimeter of two-dimensional shapes
• recognise metric units of perimeter, their abbreviations and conversions between them
• recognise appropriate units and devices to measure perimeter
• identify or describe the perimeter of two-dimensional shapes using everyday language
• estimate and compare perimeter; for example:
  
  • how much fencing is required to surround the paddock?
• estimate and measure perimeter using a variety of strategies; for example:
  
  • using a tape measure
  • using string and measuring the string
  • using a smartphone app
• calculate perimeters by measuring sides and adding them together
• calculate perimeters by adding given side lengths from diagrammatic representations of shapes
• solve problems involving perimeter; for example:
  
  • calculate how much barricade tape is required to cordon off the cricket pitch area of the school oval.

Topic 2 – shapes, maps and plans

This topic has two sub-topics:

• two-dimensional and three-dimensional shapes
• maps and plans.

Two-dimensional and three-dimensional shapes

• recognise, identify, match and sort shapes in the environment; for example:
  
  • in nature
  • in artwork
  • in company logos
  • in the home
  • in the classroom
  • in pictures
  • online 
• recognise attributes, similarities and differences of shapes in the environment and in a range of contexts; for example:
  • putting a round tablecloth on a square table
• identify or describe attributes, similarities and differences of shapes in the environment and in a range of contexts using everyday language; for example:
  
  • stacked rolls of toilet paper in the cupboard
  • the shapes made by line markings on a netball court
• make representations of two-dimensional shapes using technology as appropriate; for example:
  
  • a house plan
  • a courtyard
• recognise tessellations, identifying the shapes involved
• continue or create tessellations using different methods; for example:
  
  • grids or graph paper, technology or concrete materials
• explore the number of faces, edges and corners, whether the faces are flat or not, whether the shape can be stacked, packed or rolled
• make representations of three-dimensional shapes using technology as appropriate; for example:
  
  • using nets to construct a model of a biscuit tin or letterbox.

Maps and plans

• recognise and respond to the language of maps; for example:
  
  • scale
  • direction
  • north
• recognise the purpose and functions of maps
• recognise that maps represent and describe real things; for example:
  
  • regions
  • road types
• use maps to locate positions or gather information; for example:
  
  • the nearest petrol station
• identify typical features of a map; for example:
  
  • key, scale, grid, compass rose
• identify directions on a map in a variety of ways; for example:
  
  • using compass directions and their abbreviations
  • using directional language; such as left and right
• develop skills in using maps; for example:
  
  • locate something or describe the location of something on a map using simple grid references
  • read and use a map key or legend
• recognise and respond to the language of position; for example:
  
  • inside, outside, above, below, beside, behind, in-front, left, right, across, opposite
• recognise the purpose and functions of plans
• recognise that plans represent real things; for example:
  
  • buildings
  • traffic flow
• identify typical features that are represented on a plan; for example:
  
  • doors and windows on a building plan
  • direction of traffic on a roadmap
• use plans to locate positions or gather information; for example:
  
  • interpret a plan of their school
  • use a plan of a theatre to locate their allocated seat
  • use the floorplan of a shopping centre to find a toilet
• recognise different elevation views of a building and match elevation drawings to aspects of a building
• construct simple plans; for example:
  
  • complete a floor plan of their bedroom or home using models or drawings
• interpret the key, legend on a plan.

Topic 3 – time and temperature

• recognise language that relates to time; for example:
  
  • first, before, next, during, after
• identify names and sequence of days of the week, months of the year and seasons
• associate activities with times of day or periods of time; for example:
  
  • eat breakfast in the morning
  • go to the bathroom at lunchtime
  • catch the bus after packing my bag at the end of the lesson
  • doctor’s appointment at 4 pm, call friends in the afternoon
  • shower in the evening
  • complete homework for tomorrow 
  • go on an overnight school trip
  • go shopping on the weekend
• associate events with days of the week, months and seasons; for example:
  
  • sport training on Friday
  • favourite TV show airing every evening from Monday to Friday
  • no school on the weekend
  • Mum’s birthday is in March
  • swim at the beach in summer
  • wear warm clothes in winter
• follow sequences of events; for example:
  
  • eat breakfast, wash dishes, brush teeth, travel to school
  • put mobile phone in locker after lunch, go to the toilet, wash hands
• read digital time using am and pm notation
• identify analogue time initially to the hour, half hour and quarter hours
• recognise the passage of time; for example:
  
  • the lunch bell will ring in 5 minutes
  • the bus is running half an hour late
  • my birthday is next Thursday
  • the school dance was a fortnight ago.
• order units of time; for example:
  
  • seconds, hours, months, centuries
• describe and compare events using appropriate units and language to represent time; for example:
  
  • weekly exercise
  • an annual celebration
  • arrive at work 10 minutes earlier than usual
  • the journey takes longer on the train than in the car
  • it is faster to dry my hair with the hairdryer than it is to let it drip-dry
• relate times on digital and analogue clocks and watches to activities; for example:
  
  • watching a favourite TV show that airs at 7.00 pm
  • catching the bus that leaves at 3.30 pm
• use calendars and planners to identify and relate times, dates, months and special occasions; for example:
  
  • I will go to lunch after this class
  • I have production rehearsals on Thursday
  • Anzac Day is 18 days away
• measure the time taken for various events
• plan personal events or schedules, taking into account the best time to do them and how long they will take; for example:
  
  • planning a party, sending invitations, buying a present, ordering a cake, buying party supplies
  • meeting a friend for lunch before going to the movies
  • taking the dog for a walk before preparing dinner
  • submitting a job application or paying bills on time
• estimate time of the day; for example:
  
  • it is nearly time to go home
  • it is close to midday
  • it will be dark outside soon
• estimate and measure passage of time; for example:
  
  • how long it takes to get to the city
  • the parking meter must be close to expiring
  • my nephew must be due for a nap
• estimate and measure passage of time using a range of devices including stopwatches and personal devices; for example:
  
  • how long it takes to cook a meal, play a game, complete a task at work
• use units of time and their abbreviations; for example:
  
  • hr, min
• calculate elapsed time; for example:
  
  • the flight leaves at 11:30 am and we touchdown at 3.15 pm
  • the number of hours between start and finish work times
  • the number of holiday days between Christmas and New Year
• convert units of time; for example:
  
  • 60 minutes = 1 hour
  • 90 minutes = 11/2 hours
  • 1 day = 24 hours
  • 7 days = 1 week
• recognise language and comparative language that relates to temperature; for example:
  
  • hot
  • boiling
  • lukewarm
  • colder than
  • thermometer
  • degree
  • Celsius
• recognise the unit °C and its abbreviation
• recognise familiar temperatures; for example:
  
  • human body
  • freezing water
  • boiling water
• recognise alternative units and measuring devices
• estimate and measure temperatures using a range of devices
• apply knowledge of temperature to make judgements or decisions; for example:
  
  • if a baby has a body temperature above 38°C you should call a doctor
  • a weather prediction of 32C will mean you should wear cool clothes and pack sun protection and a drink of water
  • do not put your hand in boiling water or get into a steaming hot bath
• solve problems involving temperature; for example:
  
  • if the fridge is set for 4.2C and I turn it down another half a degree, what temperature will it be set to?

Topic 4 - mass, capacity and volume

• recognise language and comparative language that relates to mass; for example:
  
  • light
  • heavy
  • lighter
  • heavier
  • weight
  • scales
  • gram
• recognise metric units of mass, their abbreviations and conversions between them 
• recognise appropriate units and devices to measure mass
• estimate and measure masses using a range of devices in everyday situations; for example:
  
  • a packed suitcase
  • a cat when establishing how much medicine to administer
  • ingredients when following a recipe
• estimate and compare masses; for example:
  
  • the mass of different brands of hand luggage
• measure masses with a requested degree of accuracy; for example:
  
  • cooking ingredients to the nearest gram when following a recipe
• convert between metric units of mass
• solve problems involving mass; for example:
  
  • how many oranges to use in a recipe that needs 1.2 kg of oranges
  • what can be stored on a shelf if the maximum mass the shelf can hold is 10 kg
• recognise language and comparative language that relates to volume; for example:
  
  • size
  • space
  • cubic units
• recognise language and comparative language that relates to capacity; for example:
  
  • half full
  • empty
• recognise the concept of capacity and how it relates to volume
• solve problems involving capacity; for example:
  
  • how many 600mL bottles of water can be filled from the 4.8L drum before it is empty?

Module 3 work requirements summary

This module includes the following work requirement:

• one folio containing ten short responses to everyday measurement and shape questions.

See Appendix 3 for the full specifications of the work requirements of this course.

Module 3 assessment

This module has a focus on criteria 1, 2, 3, 4, 5 and 8.

Criterion-based assessment is a form of outcomes assessment that identifies the extent of learner achievement at an appropriate endpoint of study. Although assessment as part of the learning program is continuous, much of it is formative and is done to help learners identify what they need to do to attain the maximum benefit from their study of the course. Therefore, assessment for summative reporting to TASC will focus on what both teacher and learner understand to reflect endpoint achievement.

The standard of achievement each learner attains on each criterion is recorded as a rating ‘A’, ‘B’, or ‘C’, according to the outcomes specified in the standards section of the course.

A ‘t’ notation must be used where a learner demonstrates any achievement against a criterion less than the standard specified for the ‘C’ rating.

A ‘z’ notation is to be used where a learner provides no evidence of achievement at all.

Internal assessment of all criteria will be made by the provider. Providers will report the learner’s rating for each criterion to TASC.

The following processes will be facilitated by TASC to ensure there is:

• a match between the standards of achievement specified in the course and the skills and knowledge demonstrated by individual learners
• community confidence in the integrity and meaning of the qualification.

Process

TASC will verify that the provider’s course delivery and assessment meet the course requirements and community expectations for fairness, integrity and validity of qualifications TASC issues. This will involve checking:

• Provider standard 1: scope and sequence documentation:
  
  • course delivery plan
  • course assessment plan, assessment matrix
• Provider standard 2: student attendance records
• Provider standard 3: examples of assessments tools and instruments and associated rubrics and marking guides
• Provider standard 1 and 3: examples of student work including that related to any work requirements articulated in the course document
• Provider standard 4: class records of assessment.

This process will be scheduled by TASC using a risk-based approach.

The assessment for Numeracy Level 1 will be based on the degree to which the learner can:

1. identify and communicate mathematical information and ideas and apply mathematical conventions
2. manage and take responsibility for learning and assess mathematical development
3. identify and use number properties and basic operations to represent situations and solve problems
4. apply mathematical reasoning to make inferences, generalise relationships and explain thinking
5. develop, apply and reflect on mathematical strategies to solve problems, refine personal decisions and take informed action
6. apply knowledge and techniques to solve problems and make informed choices in situations involving number and pattern
7. apply knowledge and techniques to solve problems and make informed choices in situations involving chance and data
8. apply knowledge and techniques to solve problems and make informed choices in situations involving measurement and shape.

Numeracy Level 1 (with the award of):

EXCEPTIONAL ACHIEVEMENT

HIGH ACHIEVEMENT

COMMENDABLE ACHIEVEMENT

SATISFACTORY ACHIEVEMENT

PRELIMINARY ACHIEVEMENT

The final award will be determined by the Office of Tasmanian Assessment, Standards and Certification from 8 ratings.

The minimum requirements for an award in this course are as follows:

EXCEPTIONAL ACHIEVEMENT (EA)
6 ‘A’ ratings, 2 ‘B’ ratings

HIGH ACHIEVEMENT (HA)
3 ‘A’ ratings, 4 ‘B’ ratings, 1 ‘C’ rating

COMMENDABLE ACHIEVEMENT (CA)
4 ‘B’ ratings, 3 ‘C’ ratings

SATISFACTORY ACHIEVEMENT (SA)
6 ‘C’ ratings

PRELIMINARY ACHIEVEMENT (PA)
4 ‘C’ ratings

A learner who otherwise achieves the rating for a CA (Commendable Achievement) or SA (Satisfactory Achievement) award but who fails to show any evidence of achievement in one or more criteria (‘z’ notation) will be issued with a PA (Preliminary Achievement) award.

Version 1

Accredited on 7 April 2022 for use from 1 January 2023 to 31 December 2027.

Version 1a

Approved on 26 May 2022. The names for modules 2 and 3 under the title Course structure and delivery on page 7 were swapped to maintain consistency throughout the course document.

Line of sight

Alignment to curriculum frameworks

Numeracy Level 1 aligns with course content and illustrations of performance contained in:

• Numeracy Level 1 and 2 of the Australian Core Skills Framework (ACSF)
• Australian Curriculum: Mathematics F-4. This course enables learners to consolidate gaps in learning for concepts first introduced in the Foundation year of the Australian Curriculum, through to concepts that are introduced for the first time in Year 4.

Work requirements

The work requirements of a course are processes, products or performances that provide a significant demonstration of achievement that is measurable against the course’s standards. Work requirements need not be the sole form of assessment for a module.

Module 1 work requirements specifications

Work requirement 1 of 1

Title of work requirement: Pattern and algebraic reasoning

Mode or format: folio of short responses: written question and answer, oral interview or both and mathematical calculations or manipulation of materials

Description: Learners will complete a series of short responses where they will choose to employ a range of mathematical techniques and procedures, problem-solving strategies and mathematical reasoning to make informed choices relating to familiar and personally relevant contexts involving numbers and patterns. Learners set goals, manage resources and in collaborative tasks identify their own contribution to the work.

Evidence of mathematical thinking and calculations can be captured through observation or recording of use of manipulatives. Learner responses and discussion can be captured through written, oral or augmented alternative communication (AAC) methods as appropriate for the learner. Additionally, where possible, learners will be provided with opportunities to collaborate in pairs, or small groups and be enabled to engage in mathematical discussion to share ideas, solutions and thinking.

Size: ten responses equivalent to 2-3 written sentences each and associated mathematical calculations

Timing: ongoing throughout module

External agencies: at teacher discretion

Relevant criteria:

• Criterion 1: E1, 2, 3, 4, 5 
• Criterion 2: E1, 2, 3, 4, 5 
• Criterion 3: E1, 2, 3 4,
• Criterion 4: E1, 2, 3 
• Criterion 5: E1, 2, 3, 4, 5 
• Criterion 6: E1, 2, 3, 4 

Module 2 work requirements specifications

Work requirement 1 of 1

Title of work requirement: Using data to answer a question

Mode or format: project – multimodal presentation

Description: Learners will complete a data collection and representation project where they will employ a range of mathematical techniques and procedures, problem-solving strategies and mathematical reasoning to make informed choices relating to a familiar and personally relevant context of their choice. Learners set goals, manage resources and in collaborative tasks, identify their own contribution to the work.

Evidence of data collection, organisation and representation can be captured through observation or recording of use of manipulatives, learner responses and discussion can be captured through written, oral or AAC methods as appropriate for the learner. Additionally, where possible, learners will be provided with opportunities to collaborate in pairs or small groups, and will be enabled to engage in mathematical discussion to discuss their findings.

Size: Multimodal presentation must include the representation of data in tables and charts, a discussion of findings, and an answer to the statistical question in any format appropriate to the learner.

Timing: ongoing throughout module

External agencies: at teacher discretion

Relevant criteria:

• Criterion 1: E1, 2, 3, 4, 5
• Criterion 2: E1, 2, 3, 4, 5
• Criterion 3: E1, 2, 3 4
• Criterion 4: E1, 2, 3
• Criterion 5: E1, 2, 3, 4
• Criterion 7: E1, 2, 3 4

Module 3 work requirements specifications

Work requirement 1 of 1

Title of work requirement: Everyday measurement and shape

Mode or format: folio of short responses, written question and answer, or oral interview or both and mathematical calculations or manipulation of materials

Description: Learners will complete a series of short responses where they will choose to employ a range of mathematical techniques and procedures, problem-solving strategies and mathematical reasoning to make informed choices relating to familiar and personally relevant contexts involving measurement and shapes. Learners set goals, manage resources and in collaborative tasks, identify their own contribution to the work.

Evidence of mathematical thinking and calculations can be captured through observation or recording of use of manipulatives and learner responses and discussion can be captured through written, oral or AAC methods as appropriate for the learner. Additionally, where possible, learners will be provided with opportunities to collaborate in pairs, or small groups, and will be enabled to engage in mathematical discussion to share ideas, solutions and thinking.

Size: ten responses equivalent to 2-3 written sentences each and associated mathematical calculations

Timing: ongoing throughout module

External agencies: at teacher discretion

Relevant criteria:

• Criterion 1: E1, 2, 3, 4, 5
• Criterion 2: E1, 2, 3, 4, 5
• Criterion 3: E1, 2, 3, 4
• Criterion 4: E1, 2, 3
• Criterion 5: E1, 2, 3 4
• Criterion 8: E1, 2, 3, 4, 5

General capabilities and cross-curriculum priorities

Learning across the curriculum content, including the cross-curriculum priorities and general Capabilities, assists students to achieve the broad learning outcomes defined in the Alice Springs (Mparntwe) Education Declaration (December 2019).

General capabilities:

The general capabilities play a significant role in the Australian Curriculum in equipping young Australians to live and work successfully in the twenty-first century.

In the Australian Curriculum, capability encompasses knowledge, skills, behaviours and dispositions. Students develop capability when they apply knowledge and skills confidently, effectively and appropriately in complex and changing circumstances, in their learning at school and in their lives outside school.

The general capabilities include:

• Critical and creative thinking
• Ethical understanding
• Information and communication technology capability
• Intercultural understanding
• Literacy
• Numeracy
• Personal and social capability

Cross-curriculum priorities:

Cross-curriculum priorities enable students to develop understanding about and address the contemporary issues they face, for their own benefit and for the benefit of Australia as a whole. The priorities provide national, regional and global dimensions which will enrich the curriculum through development of considered and focused content that fits naturally within learning areas. Incorporation of the priorities will encourage conversations between students, teachers and the wider community.

The cross-curriculum priorities include:

• Aboriginal and Torres Strait Islander histories and cultures
• Asia and Australia’s engagement with Asia
• Sustainability

Glossary

array

An array is an ordered collection of objects or numbers. Rectangular arrays are commonly used in primary mathematics; for example, two arrays of dots, 2 by 12 and 4 by 6, produce two different representations of the number 24.

calculates

Determine or find; for example a number or answer by using mathematical processes; obtain a numerical answer showing the relevant stages in the working; ascertain or determine from given facts, figures or information.

capacity

The amount that a container will hold; for example, the amount of water (mL) required to fill a fish tank is its capacity. Volume is the space (cm3) occupied.

estimation

A skill requiring being able to conceptualise and mentally manipulate numbers or quantities to find an approximate answer. The capacity to make reasonable adjustments to numbers is essential in estimating.

equivalence

Two expressions are said to be equivalent if they are equal in value.

equivalent fractions

Equivalent fractions are alternative ways of writing the same fraction; for example: `1/2=  2/4=  5/10`

expected results

The results expected from calculating the probability.

Face, shape

Any of the individual flat surfaces of a solid object.

factors

Numbers are factors, or divisors, of another number if they multiply to give that number; for example, 3 and 4 are factors of 12 as 3 × 4 = 12.

for each

The ‘for each’ idea of multiplication is sometimes used as a way of describing the product of different combinations. For example, if for each sandwich there are two choices of bread and for each choice of bread there are three choices of filling, there will be six different sandwich options (2 x 3).

fractions as part-whole relationships

Dividing quantities using fractions as part-whole relationships requires maintaining the multiplicative relationship between each part and the whole; for example, sharing in the ratio 2 parts to 1 part means `2/3`and `1/3` of the whole.

grid reference

A grid reference identifies a region on a map. Coordinates and gridlines are used to refer to specific features or locations; for example, “In the map below, the school is located at the grid reference C4”.

number sentence

A number sentence is typically a statement of equality or inequality using numbers and common symbols; for example: 8 + 5 = 13 and 16 - ☐ = 10 are both number sentences.

order of operations

The order of performing mathematical operations:

1. evaluate brackets or grouping symbols first
2. evaluate any powers and roots
3. working left to right, evaluate any multiplication and division
4. working left to right, evaluate any addition or subtraction

May also be known as BODMAS, BIDMAS, BEDMAS, etc.

partitioning

Partitioning means dividing a quantity into parts. In the early years, it commonly refers to the ability to think about numbers as made up of two or more parts, such as, 10 is 8 and 2 or 126 is 100 and 20 and 6. In later years it refers to dividing both continuous and discrete quantities into equal parts.

picture graph

A picture graph is a statistical graph for organising and displaying categorical data.

place value system

The place value system of our numbers is based on 10. The value of a digit in a numeral is determined by multiplying its face value by the power of ten assigned to its position (283 = 2 x 100 + 8 x 10 + 3 x 1). The quantity represented by a numeral is then the sum of the values represented by its individual digits (283 = 200 + 80 + 3). The base-ten place value system used to write numerals has both multiplicative and additive properties.

probability

The likelihood or chance of something; the relative frequency of the occurrence of an event as measured by the ratio of the number of cases or alternatives favourable to the event to the total number of cases or alternatives.

product

A product is the result of multiplying together two or more numbers; for example, 36 is the product of 9 and 4.

recognise numerals

Selects a named numeral from a randomly displayed group of displayed numerals.

renames

Expresses a number in equivalent ways by interpreting the relationship between the place value powers of ten; for example, 243 can be renamed 2 hundreds and 43 ones or 24 tens and 3 ones.

repeated addition

Adding the same number again and again. A strategy sometimes used for multiplication.

rounding

The decimal expansion of a real number is rounded when it is approximated by a terminating decimal that has a given number of decimal digits to the right of the decimal point.
Rounding to n decimal places is achieved by removing all decimal digits beyond (to the right of) the nth digit to the right of the decimal place and adjusting the remaining digits where necessary.

If the first digit removed (the(n+1)th digit) is less than 5 the preceding digit is not changed; for example, 4.02749 becomes 4.027 when rounded to 3 decimal places.

If the first digit removed is greater than or equal to 5, then the preceding digit is increased by 1; for example, 6.1234586 becomes 6.12346 when rounded to 5 decimal places.

routine fractions

Routine fractions are those fractions commonly used in estimating and for making comparisons to other numbers; for example, `1/2,1/3,1/4,3/4`

sharing model of division

In the sharing model of division, the divisor indicates a whole number of equal groups and the quotient, the result of division, is the size of each part. In 12 ÷ 3 = 4, twelve is shared into 3 equal groups and there are 4 in each group.

skip counting

Skip counting is counting in multiples; for example, three, six, nine, twelve, …