The statements in this section, taken from documents endorsed by Education Ministers as the agreed and common base for course development, are to be used to define expectations for the meaning (nature, scope and level of demand) of relevant aspects of the sections in this document setting out course requirements, learning outcomes, the course content and standards in the assessment.
Australian Senior Secondary Curriculum: Essential Mathematics
Unit 1 - Topic 1: Calculations, percentages and rates
Calculations:
- solve practical problems requiring basic number operations (ACMEM001)
- apply arithmetic operations according to their correct order (ACMEM002)
- ascertain the reasonableness of answers to arithmetic calculations (ACMEM003)
- use leading-digit approximation to obtain estimates of calculations (ACMEM004)
- use a calculator for multi-step calculations (ACMEM005)
- check results of calculations for accuracy (ACMEM006)
- recognise the significance of place value after the decimal point (ACMEM007)
- evaluate decimal fractions to the required number of decimal places (ACMEM008)
- round up or round down numbers to the required number of decimal places (ACMEM009)
- apply approximation strategies for calculations (ACMEM010).
Percentages:
- calculate a percentage of a given amount (ACMEM011)
- determine one amount expressed as a percentage of another (ACMEM012).
Rates:
- identify common usage of rates; for example, km/h as a rate to describe speed, beats/minute as a rate to describe pulse (ACMEM014)
- convert units of rates occurring in practical situations to solve problems (ACMEM015)
- use rates to make comparisons; for example, using unit prices to compare best buys, comparing heart rates after exercise (ACMEM016).
Unit 1 - Topic 2: Measurement
Linear measure:
- use metric units of length, their abbreviations, conversions between them, and appropriate levels of accuracy and choice of units (ACMEM017)
- estimate lengths (ACMEM018)
- convert between metric units of length and other length units (ACMEM019)
- calculate perimeters of familiar shapes, including triangles, squares, rectangles, and composites of these (ACMEM020).
Area measure:
- use metric units of area, their abbreviations, conversions between them, and appropriate choices of units (ACMEM021)
- estimate the areas of different shapes (ACMEM022)
- convert between metric units of area and other area units (ACMEM023)
- calculate areas of rectangles and triangles (ACMEM024).
Mass:
- use metric units of mass, their abbreviations, conversions between them, and appropriate choices of units (ACMEM025)
- estimate the mass of different objects (ACMEM026).
Volume and capacity:
- use metric units of volume, their abbreviations, conversions between them, and appropriate choices of units (ACMEM027)
- understand the relationship between volume and capacity (ACMEM028)
- estimate volume and capacity of various objects (ACMEM029)
- calculate the volume of objects, such as cubes and rectangular and triangular prisms (ACMEM030).
Unit 1 - Topic 3: Algebra
General substitution:
- substitute given values for the other pronumerals in a mathematical formula to find the value of the subject of the formula (ACMEM036).
Unit 1 - Topic 4: Graphs
Reading and interpreting graphs:
- interpret information presented in graphs, such as conversion graphs, line graphs, step graphs, column graphs and picture graphs (ACMEM037)
- interpret information presented in two-way tables (ACMEM038)
- discuss and interpret graphs found in the media and in factual texts (ACMEM039).
Drawing graphs:
- determine which type of graph is best used to display a dataset (ACMEM040)
- use spreadsheets to tabulate and graph data (ACMEM041)
- draw a line graph to represent any data that demonstrate a continuous change, such as hourly temperature (ACMEM042).
Unit 2 - Topic 1: Representing and comparing data
Classifying data:
- identify examples of categorical data (ACMEM043)
- identify examples of numerical data (ACMEM044).
Data presentation and interpretation:
- display categorical data in tables and column graphs (ACMEM045)
- display numerical data as frequency distributions, dot plots, stem and leaf plots, and histograms (ACMEM046)
- compare the suitability of different methods of data presentation in real-world contexts (ACMEM048).
Summarising and interpreting data:
- identify the mode (ACMEM049)
- calculate measures of central tendency, the arithmetic mean and the median (ACMEM050)
- investigate the suitability of measures of central tendency in various real-world contexts (ACMEM051)
- calculate and interpret statistical measures of spread, such as the range (part of ACMEM055)
- investigate real-world examples from the media illustrating inappropriate uses, or misuses, of measures of central tendency and spread (ACMEM056).
Unit 2 - Topic 3: Rates and ratios
Ratios:
- demonstrate an understanding of the elementary ideas and notation of ratio (ACMEM065)
- understand the relationship between fractions and ratio (ACMEM066)
- express a ratio in simplest form (ACMEM067)
- find the ratio of two quantities (ACMEM068)
- divide a quantity in a given ratio (ACMEM069)
- use ratio to describe simple scales (ACMEM070).
Unit 2 - Topic 4: Time and motion
Time:
- use units of time, conversions between units, fractional, digital and decimal representations (ACMEM076)
- represent time using 12-hour and 24-hour clocks (ACMEM077)
- calculate time intervals, such as time between, time ahead, time behind (ACMEM078)
- interpret timetables, such as bus, train and ferry timetables (ACMEM079)
- use several timetables and electronic technologies to plan the most time-efficient routes (ACMEM080).
Distance:
- use scales to find distances, such as on maps; for example, road maps, street maps, bushwalking maps, online maps and Cadastral Maps (ACMEM083)
- optimise distances through trial-and-error and systematic methods; for example, shortest path, routes to visit all towns, and routes to use all roads (ACMEM084).
Speed:
- identify the appropriate units for different activities, such as walking, running, swimming and flying (ACMEM085)
- calculate speed, distance or time using the formula speed = distance/time (ACMEM086)
- calculate the time or costs for a journey from distances estimated from maps (ACMEM087)
- interpret distance-versus-time graphs (ACMEM088)
- calculate and interpret average speed; for example, a 4-hour trip covering 250 km (ACMEM089).
Unit 3 - Topic 2: Scales, plans and models
Right-angled triangles:
- apply Pythagoras’ theorem to solve problems (ACMEM116)
- solve problems involving bearings (ACMEM120).