# Essential Mathematics 2019 v1.1

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## Introduction

### Rationale

Assumed knowledge refers to the topic that teachers can expect students to know before starting this subject. When students have a solid understanding of an important concept or procedure, they are more easily able to make connections with related new topics and apply what they already know to new problems.

Learning area structure

### Course structure

Students should be given the opportunity in Units 1 and 2 to experience and respond to the types of tests they will encounter in Units 3 and 4. For reporting purposes, schools should develop at least one test per unit, with a maximum of four tests in Units 1 and 2.

## Teaching and learning

• Syllabus objectives
• Underpinning factors
• Aboriginal perspectives and Torres Strait Islander perspectives
• Pedagogical and conceptual frameworks
• Subject matter

21st century skills - the attributes and skills students need to prepare them for higher education, work and engagement in a complex and rapidly changing world. To be successful in mathematics assessment, students must understand the subject matter (organized into areas of mathematics), use a range of cognitive skills, and apply these to problems of varying degrees of difficulty, from simple and routine, in unknown, complex situations. contexts and multi-step solutions (Grønmo et al. 2015). The relationship between the areas of mathematics in core mathematics, the level of cognitive skills required (the objective of the curriculum) and the degree of difficulty is shown in three dimensions for the mathematics problems in the following diagram.

## Assessment — general information

### Formative assessments — Units 1 and 2

Students who demonstrate that they only master simple subject matter can achieve a maximum of a C grade in total.

### Summative assessments — Units 3 and 4

The instrument-specific standards describe the characteristics that are evident in student responses and are consistent with the identified assessment objectives. The instrument-specific standards identify the evidence at each level (A–E) for each of the criteria.

## Exiting a course of study

### Exit folios

This syllabus provides instrument-specific standards for the three summative internal assessments in units 3 and 4. The assessment objectives are taken from the unit objectives and are contextualised to the assessment instrument's requirements.

Determining an exit result

## Reporting standards

The student demonstrates a thorough knowledge of and understanding of the simple and complex material; recognizes, recalls and uses facts, rules, definitions and procedures; and understand and apply mathematical concepts and techniques to solve problems drawn from numbers, data, place and time, measurement and economics. The student demonstrates knowledge and understanding of the simple subject; recognizes, recalls and uses facts, rules, definitions and procedures; and understand and apply mathematical concepts and techniques to solve problems drawn from numbers, data, place and time, measurement and economics.

## Unit objectives

The subject matter of the topics in this unit should be used in contexts that are meaningful and of interest to the students. Subject matter describes the concepts, ideas, knowledge, understanding and skills that students will learn in Unit 1.

Fundamental topic: Calculations

Topic 1: Number

Topic 2: Representing data

Topic 3: Graphs

## Assessment guidance

Subject material describes the concepts, ideas, knowledge, understanding and skills that students must learn in Unit 2.

Unit objectives

Fundamental topic: Calculations

Topic 1: Managing money

Topic 2: Time and motion

Topic 3: Data collection

Assessment guidance

Unit description

Unit objectives

Fundamental topic: Calculations

Topic 1: Measurement

Topic 2: Scales, plans and models

Topic 3: Summarising and comparing data

## Assessment

### Summative internal assessment 1: Problem-solving and modelling

A problem-solving and modeling task is an assessment instrument developed in response to a mathematical inquiry scenario or context. Students must provide an answer to a specific task or problem that must be set in a context that highlights a real application of mathematics. The task requires students to use relevant stimulus material involving the chosen subject and must be of sufficient scope to allow students to address all stages of the problem-solving and modeling approach (see Section 1.2.4).

The following table summarizes the criteria and assessment objectives for the problem-solving and modeling task.

### Summative internal assessment 2: Common internal assessment

Length: the number of short-answer items should allow students to complete the answers in the time allotted. After the CIA has been administered, student responses are scored by the teacher(s) using this guide. The subject matter in this unit should be applied in a context that is meaningful and of interest to students.

Two possible contexts that can be used in this unit are 'Healthcare Mathematics' and 'Mortgage Mathematics'. Subject matter describes the concepts, ideas, knowledge, understanding and skills that students will learn in Unit 4.

Unit objectives

Fundamental topic: Calculations

Topic 1: Bivariate graphs

Topic 2: Probability and relative frequencies

Topic 3: Loans and compound interest

## Assessment

Summative internal assessment 3: Problem-solving and modelling

### Summative internal assessment 4: Examination

Problems of this difficulty require students to demonstrate. knowledge of and insight into the subject matter and application of skills in a situation where:. knowledge of [complex] matter is required to solve the problem; And. all information to solve the problem is not directly identifiable. the required procedure is not apparent from the way the problem is stated; And. in a context where students have had limited prior experience. Problems of this difficulty require students to demonstrate. knowledge of and insight into the subject matter and application of skills in a situation where:. knowledge of [complex] matter is required to solve the problem; And. all the information to solve the problem is identifiable, that is. the required procedure is apparent from the way the problem is stated, or. in a context that has been a focus of previous learning. Problems of this difficulty level require students to demonstrate. knowledge of and insight into the subject matter and application of skills in a situation where:. knowledge of simple subjects is required to solve the problem; And. all the information to solve the problem is identifiable, that is. the required procedure is apparent from the way the problem is stated, or. is in a context that has been a focus of prior learning.

Short response format, consisting of a number of items that ask students to respond to the following activities:. draw, label or interpret charts, tables or diagrams. justifying solutions using appropriate mathematical language, if applicable. respond to seen or unseen stimulus material. given stimulus - teachers must ensure that the purpose of the technique is not compromised. unseen stimulus — materials or questions should not be copied from information or texts that students have previously seen or used directly in class. when stimulus materials are used, they will be concise enough to allow students sufficient time to engage with them; for stimulus material that is long, complex or large in number, this will be shared with students prior to taking the test instrument. only the QCAA formula sheet must be provided. use of technology is required; schools should specify the technology used, e.g. scientific calculator, graphing calculator, spreadsheet program and/or other mathematical software. Equal to > 50% for part A simple questions only. accomplished highly trained or proficient in a particular activity; perfected in knowledge or training; expert. the condition or quality of being true, correct, or exact; be free from errors or defects; precision or exactness; correctness;. in science, the extent to which a measurement result represents the quantity it purports to measure; an accurate measurement result includes an estimate of the true value and an estimate of the uncertainty. precise precise and exact; to the point; in accordance with or exactly in accordance with a truth, standard, rule, model, convention or known fact; free from errors or defects; careful; correct in all details. proficient very/very proficient or proficient at something; expert. sufficiently satisfactory or acceptable in quality or quantity equal to the requirement or occasion. algorithm has a precisely defined procedure that can be applied and followed systematically to a conclusion. dissect to identify and investigate component parts and/or their relationships; break down or examine to identify the essential elements, features, components or structure; determine the logic and reasonableness of information; examine or consider something in order to explain and interpret it, with the aim of finding meaning or connections and identifying patterns, similarities and differences. when an observer looks at an object that is lower than 'the eye of the observer', the angle between the line of sight and the horizontal is called the angle of inclination. when an observer looks at an object that is higher than "the observer's eye," the angle between the line of sight and the horizontal is called the angle of elevation. applied learning the acquisition and application of knowledge, understanding and skills in real or real-life contexts that may include workplace, industry and community situations; it emphasizes learning by doing and includes both theory and the application of theory, linking subject knowledge and understanding with the development of practical skills. Applied subject a subject with work and vocational education as primary learning path; it emphasizes applied learning and community connections;. a subject for which a syllabus has been developed by the QCAA with the following characteristics: results of courses developed on the basis of applied syllabuses contribute to the KCE; results can contribute to ATAR calculations apply knowledge and insight in response to a given situation or. circumstance; perform or use a procedure in a particular or particular situation; to judge the value, significance, or status of something; evaluate or consider a text. appreciate the worth or value of something recognize or pass judgment on it; fully understand; understand its full implications. suitably acceptable; suitable or appropriate for a particular purpose, circumstance, context, etc. suitable for the purpose or occasion; appropriate, appropriate field of study a department of or a section within a unit. argue giving reasons for or against something; challenge or discuss a problem or idea; to convince, prove, or attempt to prove by means of an ordered collection of objects or numbers. aspect a particular part of a feature of something; assessing a facet, phase, or part of a whole measuring, determining, evaluating, estimating, or passing judgment on its value. quality, outcomes, results, magnitude, significance, nature or extent of something assessment purposeful and systematic collection of information about students. instrument a tool or device used to collect information about student performance. drawn from the objectives of the unit and contextualized for the requirements of the assessment tool. see also 'syllabus objectives', 'unit objectives') assessment.

𝑄𝑄1 is the median of the bottom half of the data (excluding the median, 𝑄𝑄2, of the data set). 𝑄𝑄3 is the median of the top half of the data (excluding the median, 𝑄𝑄2, of the data set). hence 𝐼𝐼𝑄𝑄𝐼𝐼 is the width of an interval containing the middle 50%. approximately) of the data values; to be exactly 50%, the sample size must be a multiple of four. Goos, M, Geiger, V & Dole, S 2012, 'Auditing the numeracy requirements of the middle years curriculum', Mathematics Education: Expanding horizons - Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia, Mathematics Education Research Group of Australasia, Singapore, pp.

Figure

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