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Five Certificate levels

Students who achieve the ACER Certificate in Mathematics Level 5 demonstrate the ability to apply knowledge and skills in problem solving situations, which sometimes may be unfamiliar. Understanding a range of different content areas may be required to answer a question. The content areas included are:

Number and algebra

  • The use and application of real numbers
  • Calculation of simple and compound interest, and financial applications
  • Graph, solve and use linear and quadratic equations and inequalities
  • Use algebraic fractions in problems
  • Use algebraic and graphical representations of a variety of relations including linear, exponential, quadratic and other simple conics

Measurement and geometry

  • Calculate and use surface area and volume of various 3D shapes to solve problems
  • Solve problems involving scale factors, similarity or congruence
  • Use and apply Pythagoras theorem
  • Use and apply trigonometric ratios
  • Solve problems involving logic and the use of geometrical reasoning and proof

Statistics and probability

  • Calculate and interpret probabilities for a range of different situations
  • Calculate and interpret statistical data including measures of centre (such as mean and median) and measures of spread (such as interquartile range)
  • Construct, interpret and analyse a range of plots and graphs, including univariate and bivariate data sets

Students who achieve the ACER Certificate in Mathematics Level 4 demonstrate the ability to apply knowledge and skills in problem solving situations, which sometimes may be unfamiliar. Understanding a range of different content areas may be required to answer a question. The content areas included are:

Number and algebra

  • The use and application of real numbers, including index laws and scientific notation
  • Calculation of simple and compound interest, and financial applications
  • Graph, solve and use linear and quadratic equations and inequalities
  • Use algebraic fractions in problems

Measurement and geometry

  • Calculate and use surface area and volume of various 3D shapes to solve problems
  • Solve problems involving scale factors, similarity or congruence
  • Use and apply Pythagoras theorem
  • Use and apply trigonometric ratios

Statistics and probability

  • Calculate and interpret probabilities for a range of different situations
  • Calculate and interpret statistical data including measures of centre (such as mean and median) and measures of spread (such as range and interquartile range)
  • Construct and interpret a range of plots and graphs

Students who achieve the ACER Certificate in Mathematics Level 3 demonstrate mathematical and numeracy skills. Number and Algebra, Measurement and Geometry, Statistics and Probability are assessed. The assessment tasks provide information about students' mathematical knowledge, as well as their ability to apply their knowledge and reasoning skills to solve everyday problems.

Number and algebra

  • Use negative numbers in calculations
  • Solve one and two-step problems
  • Convert between fractions, decimals and percentages
  • Use fractions, decimals and percentages in calculations
  • Interpret distance-time (line) graphs
  • Identify a number pattern that is extended
  • Use proportions and ratios when solving problems

Measurement and geometry

  • Read and interpret timetables
  • Find the area of compound shapes
  • Convert between units of measurement
  • Identify key features of 3D objects such as faces, edges and vertices
  • Match 3D shapes and their nets
  • Identify and give coordinates of a point

Statistics and probability

  • Read and understand tables and graphs including two-way tables
  • Calculate the mean, median, mode and range
  • Use and find probability for a range of different activities

Students who achieve the ACER Certificate in Mathematics Level 2 demonstrate mathematical and numeracy skills. Number and Algebra, Measurement and Geometry, Statistics and Probability are assessed. The assessment tasks provide information about students' mathematical knowledge, as well as their ability to apply their knowledge and reasoning skills to solve everyday problems.

Number and algebra

  • Use multiplication and division in multi-step problems
  • Use fractions in calculations or on number lines
  • Add and subtract decimals
  • Continue number patterns including those with decimals, fractions and shapes

Measurement and geometry

  • Tell time and convert between 12 and 24-hour time
  • Read and use timetables
  • Find perimeter and area of shapes
  • Find volume of objects
  • Identify cross-sections
  • Read maps and find the distance between two locations on a map
  • Find and identify angles
  • Reflect or rotate shapes

Statistics and probability

  • Read and understand different tables and graphs including column graphs and pie charts
  • Use and find probability for objects such as dice and spinners

Students who achieve the ACER Certificate in Mathematics Level 1 demonstrate mathematical and numeracy skills. Number and Algebra, Measurement and Geometry, Statistics and Probability are assessed. The assessment tasks provide information about students' mathematical knowledge, as well as their ability to apply their knowledge and reasoning skills to solve everyday problems.

Number and algebra

  • Use addition, subtraction, multiplication and division in questions and problems
  • Recognise and use fractions e.g. on a number line
  • Continue number patterns and find missing numbers in number patterns

Measurement and geometry

  • Tell time and solve problems with time
  • Measure distance and length
  • Recognise and name shapes
  • Find area and perimeter
  • Identify symmetry

Statistics and probability

  • Reading and understand different tables and graphs
  • Use and understand simple probability

Students who achieve the ACER Certificate in Reading Level 5 are expert readers. They demonstrate this through linking pieces of related deeply embedded information when there is strongly competing information. They interpret complex technical ideas, dense language and complex, abstract ideas. They are able to compare subtle differences between ideas and identify nuanced relationships. They confidently make sophisticated, critical evaluations and are able to identify logical flaws in complex texts. They extrapolate key ideas from the text and construct complex hypotheses.

Retrieving

  • Locate multiple pieces of information that are not explicitly referenced and are deeply embedded and dispersed throughout complex texts where there is much strongly competing information
  • Deal with large amounts of competing information and retrieve technical information from complex or unusual maps, diagrams and tables.

Interpreting

  • Link pieces of related information that are deeply embedded in highly competing information, to interpret complex technical ideas, dense language and complex, abstract ideas
  • Compare subtle differences between ideas
  • Identify nuanced relationships such as how disparate images echo each other, or how an image provides insight into an aspect of a character
  • Make inferences to explain implicit arguments and sophisticated, symbolic references
  • Select evidence to infer subtle differences in perspective and to justify interpretations of ambiguity.

Reflecting

  • Make sophisticated, critical evaluations of texts including those that deal with information that undermines commonly held expectations
  • Identify logical flaws in complex texts
  • Reflect on underlying abstract themes such as the nature of freedom
  • Analyse subtle, emotive elements of texts
  • Extrapolate from the text to construct complex hypotheses.

Students who achieve the ACER Certificate in Reading Level 4 locate and link pieces of related information, some of which are deeply embedded in unrelated contexts, across extended complex texts. They interpret highly technical or abstract ideas. They can identify diverse relationships, inherent contradictions and plausible alternative conclusions. Students infer how subtle text features undermine or emphasise certain meanings. Increasingly they make critical evaluations and analyse a variety of subtle authorial techniques including irony and voice.

Retrieving

  • Retrieve multiple pieces of information where information is embedded in a context that differs from the idea or topic being sought or there are multiple references to the same topic
  • Deal with large amounts of competing information and retrieve technical information from complex or unusual maps, diagrams and tables.

Interpreting

  • Interpret the meaning of complex words and phrases from the context
  • Make multiple links across a lengthy text to interpret a complex idea
  • Make connections between unusual diagrams or tables and the text
  • Recognise diverse relationships between ideas, such as identifying when an idea supports or contradicts an overarching concept in a text
  • Synthesise information to interpret the subtle actions or behaviour of a character
  • Recognise an underlying motive from understated clues
  • Relate ideas across a text to make sense of an argument where the main idea is not explicitly stated

Reflecting

  • Identify the advantages and disadvantages of communicating information in different ways
  • Recognise some subtle use of authorial devices in creating tones and suggesting attitudes
  • Infer the purpose, in context, of punctuation used in some less conventional ways, such as to undermine or emphasise meaning

Students who achieve the ACER Certificate in Reading Level 3 demonstrate a wide variety of comprehension skills including reading closely to make careful distinctions and identifying subtle, scattered clues to support an inference in texts with complex aspects such as unusual diagrams, extended metaphors, difficult vocabulary or long, dense sentences.

Students who achieve the ACER Certificate in Reading Level 3 demonstrate skills to:

Find Information

  • Scan for numbers and capitalisation to locate key information
  • Identify embedded keywords to help with scanning
  • Find synonyms of key words to locate embedded information

Interpret Meaning

  • Interpret information across charts and tables
  • Link written ideas with information expressed in a chart
  • Understand three dimensions represented in a chart
  • Locate information in a chart according to given criteria
  • Identify implied attitudes with supporting evidence

Critique and Review

  • Locate typical text features to identify persuasive techniques
  • Identify main ideas
  • Identify evidence to support ideas

Vocabulary

  • Identify a synonym in context
  • Select a word with a specific meaning from a group of related words
  • Identify a word that does not belong to a given group of words
  • Classify similar sounding words to their specific meaning
  • Classify words according to the activity they refer to
  • Sort words that denote different degrees of an attribute

Students who achieve the ACER Certificate in Reading Level 2 demonstrate a variety of simple comprehension skills. They manage some competing information in many common text types that are largely familiar, but include an element of complexity such as an unusual voice, a subtle implication or a non-linear timeline.

Students who achieve the ACER Certificate in Reading Level 2 demonstrate skills to:

Find Information

  • Scan lengthy information texts to locate key points
  • Retrieve multiple pieces of information across a text
  • Discard competing information to locate the relevant information
  • Scan for key words to locate an opinion
  • Locate arguments to support an idea

Interpret Meaning

  • Identify relevant clues when interpreting implied meaning
  • Discard possible interpretations when there is not enough evidence to support the interpretation
  • Generalise about a character's behaviour to identify a character trait
  • Identify reasons for a character's statement in a narrative text
  • Recognise the purpose of an example in a persuasive text
  • Identify an expert's reaction to an explanation as presented in a persuasive text

Critique and Review

  • Draw on everyday knowledge of stereotypes to identify persuasive techniques
  • Recognise the use of narrative techniques like plot twist
  • Explain how narrative techniques meet the purpose of the text

Vocabulary

  • Identify a synonym in context
  • Classify words according to the position they refer to
  • Identify a word that does not belong to a given group of words
  • Distinguish the meaning of easily confused words
  • Select a word with a specific meaning from a group of related words
  • Identify a range of meanings of a single word
  • Identify a common meaning for a group of words

Students who achieve the ACER Certificate in Reading Level 1 demonstrate a variety of simple comprehension skills including managing low-level competing information in a range of familiar common text types that may include some implied or unfamiliar ideas. Students who achieve the ACER Certificate in Reading Level 1 demonstrate skills to:

Find Information

  • Locate key information in a familiar and unfamiliar context
  • Locate relevant data and symbols in and across tables, graphs and text
  • Locate key information to confirm understanding

Interpret Meaning

  • Use tone as evidence for inferences
  • Select evidence to support a hypothesis
  • Link information across several paragraphs

Critique and Review

  • Identify the effects of the form
  • Identify how ideas are presented in a text
  • Identify the intended purpose of a narrative technique
  • Identify the intended purpose of a persuasive technique

Vocabulary

  • Identify a range of meanings of a single word
  • Identify a word that does not belong to a given group of words
  • Select a word with a specific meaning from a group of related words
  • Identify a synonym in context