**Module 1: Measurement**

Within measurement, learners will use estimation and calculation to make comparisons between measurements including perimeter, area, volume and capacity. They will estimate, calculate and convert between different units of mass, quantities of time, distance and speed. They will read and interpret schedules, maps, scale and timetables when solving problems involving travel.

Learners will:

- use an accurate interpretation of measuring instruments in practical investigations of measurement including:
- simple and familiar measuring tools, such as a measuring tape, electronic bathroom scales, compass (analog/digital), trundle wheel and stopwatch
- where possible, workplace specific measuring tools, such as a radar, electronic scales, temperature gauge, pressure gauge

- use metric units of length, their abbreviations, conversions between them, and demonstrate appropriate levels of accuracy and choice of units
- estimate lengths
- convert between metric units of length and other length units as appropriate

- calculate perimeters of familiar shapes, including: triangles, squares, rectangles, circles and composites of these
- review Pythagoras’ Theorem and apply to solve practical problems in two dimensions

- use metric units of area, their abbreviations, conversions between them and appropriate choices of units
- estimate areas of different shapes
- convert between hectares and acres
- use formulas to calculate areas of rectangles, triangles and circles
- use metric units of mass, their abbreviations, conversions between them and demonstrate appropriate choices of units
- estimate mass of different objects
- use metric units of volume, their abbreviations, conversions between them and appropriate choices of units
- understand the relationship between volume and capacity, recognising that 1 cm3 = 1 mL, and 1 m3 = 1 kL
- estimate volume and capacity of various objects
- use formulas to find the volume and capacity of regular objects; cubes, rectangular and triangular prisms, cylinders and spheres
- use units of time, conversions between units, fractional, digital and decimal representations
- represent time using 12 hour and 24 hour clocks
- calculate time intervals, such as: time between, time ahead, time behind
- interpret rosters, schedules, timetables and charts, such as: work rosters and schedules, tide charts, sunrise charts and moon phases
- read and interpret maps, including understanding compass directions, using keys/legends and using scales to find distances on maps and plans, such as: road maps, street maps, bushwalking maps,model plans and site plans
- optimise distances through trial and error and systematic methods, such as: shortest path, routes to visit all towns and routes to use all roads
- solve practical problems using bearings
- identify the appropriate units for different activities, such as: walking, running, swimming and flying
- calculate speed, distance or time using the formula speed = distance/time
- calculate the time for a journey from distances estimated from maps
- interpret distance versus time graphs
- calculate and interpret the average speed (e.g. a 4 hour trip covering 250 km).

*Examples in context:*

*determining the dimensions/measurements of food packaging*

*determining the length of the lines on a sporting field to find the cost of marking it*

*in a practical situation, verify the square of a corner using Pythagoras’ Theorem*

*investigate the relationship between a person’s footprint size and their height in the context of crime scene investigations*

*determining the area of the walls of a room for the purpose of painting*

*comparing the area of different house blocks of the same perimeter*

*comparing and discussing the components of different food types for the components of packaged food expressed as grams*

*finding the volume of water collected from a roof under different conditions*

* finding the volume of various packaging*

*calculating and interpreting dosages for children and adults from dosage panels on medicines given age or weight*

*calculating reaction times through experiments*

*using several timetables and electronic technologies to plan the most time efficient routes*

*comparing time travelled by car with other modes of transport*

*calculating distances travelled to school and the time taken to get from home to school considering different average speeds*

*using a car GPS navigation system*

*orienteering exercises*

*using scales to find distances on maps, such as road maps, street maps, bushwalking maps, online maps and Cadastral (land survey) Maps*
*using scales to identify measurements on plans, such as model plans, building plans, and site plans*
*calculating stopping distances for different speeds through use of formula for different conditions, such as road type, tyre conditions, types of vehicle.*

**Module 2: Finance**

Within finance, learners will use estimation and calculation to create and compare budgets and transactional records. They will calculate prices after applying percentage discounts or mark-ups. They will calculate unit prices (e.g. price per kilogram) and use unit prices in real-life situations such as menu costing or creating a shopping budget. They will investigate simple interest and tax rates and apply to real-life situations.

Learners will:

- express a calculated amount to the nearest cent (e.g. 13.5489 = $13.55)
- apply rounding of a total to the nearest 5 cents
- increase or decrease an amount by a given percentage e.g. discounts, GST, etc.
- perform calculations involving the management of money in real-life situations, including keeping financial records and budgeting
- using money in relation to measurement (e.g. price per kilogram)
- calculate simple interest
- calculate tax payment (e.g. using an online calculator)
- calculate costs involved with credit (e.g. interest free purchases) or contract (e.g. mobile phone plan) situations.

*Examples in context:*

*practical experience in cash handling including mental reconciliation skills and counting back change after a transaction*

*determining best value when the same item is offered in two sizes at different prices*

*using tables to record transactions showing income and expenditure*

*using tables to complete a basic single entry profit and loss statement*

*using, where possible, technology associated with handling transactions such as a cash register, EFTPOS machine, and computer*

*investigating different ways of transacting business such as cash, electronic funds transfer, debit cards, credit cards, order form and charge accounts*

*using a hardware store price list to prepare a budget for a project like adding a timber deck to a home*

*investigating different modes of financial record keeping e.g. pay slips, invoices, bank statements, credit card statements, cash books*

*investigating and compiling a glossary to define terms and jargon associated with handling money in work-based environments*

*calculating simple interest for repayment of items over time*

* investigating methods of getting paid: salary, wage, piece rate, commission*

* investigating exchange rates between currencies*

*calculating tax payment and terms for workers according to their circumstances*

*completing a tax form for a given scenario*

*discussing advantages/disadvantages of ‘Do-It-Yourself’ projects*

*preparing a poster or presentation detailing tips for purchasing a car*

*researching the costs involved in running a car*

* investigating budgets using ‘Essi Money’ (a web-based scenario that puts learners in a real-life budget management situation)*

* preparing a weekly or monthly budget for the living away from home situation*

*investigating costs involved in paying for goods using an ‘interest free period’ contract*

* investigating costs involved in paying for a house using a mortgage loan and the effect upon total cost and duration of the loan of paying extra repayments.*

**Module 3: Statistics**

Within statistics, learners will create, read and interpret tables, graphs and diagrams. They will classify, present, interpret and summarise data collected through investigations and/or researched from secondary sources. They will perform calculations to determine the mean, median and mode of numerical data sources.

Learners will:

- use and interpret information presented in graphs, such as: conversion graphs, line graphs, step graphs, column graphs, pie graphs and picture graphs
- discuss and interpret graphs found in the media and in factual texts
- interpret and use two-way tables in real-life situations, such as rosters, schedules and more complex workplace situations
- recognise and describe trend patterns in tables and graphs
- sketch plan and elevation views of a 3D solid
- determine and use the most appropriate type of graph to best display a data set
- draw graphs from given data to represent practical situations
- use spreadsheets to tabulate and graph data
- use simple (linear) graphs to model real-life situations
- identify examples of categorical data
- identify examples of numerical data
- display categorical data in tables and column graphs
- display numerical data as frequency distributions, scatterplots and histograms
- compare the suitability of different methods of data presentation in real-world contexts
- identify the mode and range
- calculate measures of central tendency; the arithmetic mean and the median
- investigate real-world examples from the media illustrating inappropriate uses, or misuses, of measures of central tendency and spread.

*Examples in context:*

*analysing and interpreting a range of graphical information of global weather patterns that affect food growth*

*analysing and interpreting a range of graphical information given on gas and electricity bills*

*interpreting graphs showing growth ranges for children (height or weight or head circumference versus age)*

*interpreting hourly hospital charts showing temperature and pulse*

* interpreting graphs showing life expectancy with different variables*

*interpreting a step graph showing rates of taxation*

*expressing ingredients of particular food types as percentages of the total quantity, or per serving size, or per 100 grams, presenting the information in different formats e.g. column graphs and pie graph*

*drawing a line graph to represent any data that demonstrates a continuous change e.g. hourly temperature*

*creating graphs to show the deductions from gross wages such as income tax, medicare levy, superannuation*

*analysing and interpreting a range of statistical information related to car theft, car accidents and driver behaviour*

*using statistics and graphs to find the number of people in each blood type given the population percentages of blood types in different countries*

*using blood usage statistics to predict the amount of blood needed at different times of the year*

* investigate the relationship between a person’s footprint size and their height in the context of crime scene investigations*

*investigate the relationship between the length of a candle and the time that it has been burning.*

Mathematical Skills : Numeric Calculations

Within *Workplace Maths*, learners will engage in numeric calculations to solve real world problems involving measurement, time and motion, statistics and finance. As such, learners will explore concepts and carry out calculations relating to the use of algebra and proportional reasoning (including percentages, rates and ratios). These concepts will support learners to engage with calculations and explore the concepts of measurement (linear measure, area measure, mass, volume and capacity, distance, time, speed and navigation). Similarly, these concepts will support learners to engage with calculations and explore the concepts of statistics (tables, graphs, diagrams, data) and finance (percentage increases/decreases, financial records and budgeting, price per unit rates, transactions, tax and interest rates).

Within the course content relating to numeric calculations learners will:

- calculate with whole numbers, decimals, fractions and percentages and use these appropriate to context
- use the four basic operations algorithmically (division with single digit divisor)
- recall and use of basic multiplication table facts
- use mental multiplication and division by 10, 100 and 1000
- apply arithmetic operations according to their correct order
- calculate and interpret averages
- solve practical problems requiring basic number operations
- ascertain the reasonableness of answers to arithmetic calculations
- use leading digit approximation to obtain estimates of calculations
- check results of calculations for accuracy
- use a calculator for multi-step calculations, accurately and appropriately including the use of its memory as applicable
- recognise the significance of place value after the decimal point
- recognise and use equivalent fractions, decimals and percentages and the ability to convert from one form to another
- understand the relationship between division and fractions and the use of fractions to represent sharing situations (e.g. 5 metre length of timber divided equally into 8 parts. 5÷8 = 5/8 metre or 0.625 metres each)
- multiply a whole number by a fraction, decimal or percentage in a problem context
- round up or round down numbers to the nearest 10, 100 or 1000 or the required number of decimal places
- use mathematical knowledge to solve problems in a range of contexts.

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Examples in context:*

*creating a budget for living at home and for living independently*

*calculating various costs per day, week, month using tables, spreadsheets, and estimation e.g. food, clothing, transport, utility costs*

*creating and evaluating daily menus to meet the minimum daily nutritional and energy needs*

*creating a travel log for a journey involving different modes of travel at varied speeds.*

*calculating the average time taken to travel to school according to distance and transport type.*

*recording aspects of maths encountered in VET programs, part-time jobs or over the course of a day.*

**Mathematical Skills: Algebra and Proportional Reasoning**

Within the course content relating to the use of algebra and proportional reasoning (percentages, rates and ratios) learners will:

- understand the notion of directed numbers
- substitute numerical values into algebraic expressions, to find the value of an unknown
- calculate a percentage of a given amount
- determine one amount expressed as a percentage of another
- demonstrate an understanding of the elementary ideas and notation of ratio
- understand the relationship between fractions and ratio
- express a ratio in simplest form
- find the ratio of two quantities
- divide a quantity in a given ratio
- use ratio to describe simple scales
- use rates to make comparisons
- convert between different units e.g. units of measure, exchange rates etc.
- identify common usage such as: litres/second as a rate of flow,, km/h as a rate to describe speed or beats/minute as a rate describing pulse rate

*Examples in context:*

*the use of substitution in formulas related to Measurement and Finance*

* rearranging formulas to solve for the unknown in formulas related to Measurement, Statistics and Finance*

*calculating and comparing monthly and weekly amounts available for accommodation with varying income levels using percentages*

* using percentages to compare the different components of personal expenditure*

*expressing ingredients of packaged food as percentages of the total quantity, or per serving size, or per 100 grams*

*comparing body ratios such as hip height versus stride length, foot length versus height, body mass index*

*comparing ratios such as those found in recipes*

*using rates to compare and evaluate nutritional information e.g. quantity per serve and quantity per 100g*

*using unit prices (price per kilogram, per litre, etc.) to determine ‘best’ buys*

*using rates to find fuel consumption for different vehicles in different driving conditions*

*completing calculations with rates, including solving problems involving direct proportion in terms of rate e.g. if a person works for 3 weeks at a rate of $300 per week, how much do they earn?*

*using percentages of maximum heart rate, compare the speed or distance travelled in a fitness test e.g. on a rowing machine or treadmill*

*discuss various ratios used in machines. For example: gear ratios, power to weight ratios*

*calculating the ratio of ingredients from a recipe or ratio of macronutrients from a meal plan / food diary*

*analysing rates from data sources e.g. increase in parts per million (ppm) of CO2 over time*

*using rates to find fuel consumption for different vehicles in different driving conditions*

*calculating heart rates as beats per minute given the number of beats and different time periods*

*applying rates to calculate the energy used in various activities over different time periods*

*completing calculations with rates, including solving problems involving direct proportion in terms of rate e.g. if a car travels for 3 hours at a constant speed of 80km/hr, how far does it travel? *

*completing calculations with rates involving inverse proportion. For example calculating the time taken to travel a set distance at a constant speed.*