Mathematics Subject Outline — Stage 1 (for Teaching in 2016)

7/25/2019 Mathematics Subject Outline Stage 1 (for Teaching in 2016)

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Su&to%ic 15412 T e Num&er Line

+ey 0ue)tion) and +ey Conce%t) Con)ideration) for De'e!o%in" Teac in"and Learnin" Strate"ie)

The number line represents all real numbers.

(hat are some properties of special subsets ofthe realsG 'ational and irrational numbers

#onsider surds and their operations7 $


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Su&to%ic 15452 Introduction to Mat ematica! Induction


Fow can a statement concerning all positiveintegers be provedG

This topic can be introduced through well-=nownanalogies such as climbing a ladder or =noc=ingdown dominoes. $


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Su&to%ic 15462 Com%!e: Num&er)


(h! were comple< numbers HinventedAG

8efine the imaginar! number i as a solution to

the :uadratic e:uation2 1 0. x + =

"nalog! can be drawn with the e


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Su&to%ic 15472 T e Com%!e: #Ar"and$ P!ane


Fow can comple< numbers be representedgeometricall!G #artesian form on the "rgand 8iagram

The #artesian plane as e


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Su&to%ic 15482 Root) of E=uation)


(hat has been the advantage of introducingcomple< numbersG

The introduction of i enables the solution of allreal :uadratic e:uations and the factorisationof all :uadratic pol!nomials into linear factors

#onsider the formula for solution of :uadratice:uations% with emphasis on arithmeticinvolving i.

(hen the solutions of a real :uadratic e:uationare comple


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The assessment design criteria are based on the learning re:uirements and are used b!teachers to7 clarif! for the student what he or she needs to learn

design opportunities for the student to provide evidence of his or her learning at thehighest level of achievement.

The assessment design criteria consist of specific features that7 students need to demonstrate in their evidence of learning teachers loo= for as evidence that students have met the learning re:uirements.

or this subject% the assessment design criteria are7 concepts and techni:ues reasoning and communication.

Stage 1 Mathematics 2016 63


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The specific features of these criteria are described below.

The set of assessments% as a whole% gives students opportunities to demonstrate each ofthe specific features b! the completion of stud! of the subject.

Conce%t) and Tec ni=ue)The specific features are as follows7#T1 9nowledge and understanding of concepts and relationships.#T2 Selection and application of mathematical techni:ues and algorithms to find

solutions to problems in a variet! of conte


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concepts and techni:ues reasoning and communication.

A))e))ment Ty%e 52 Mat ematica! In'e)ti"ationor a 10-credit subject% students complete at least one mathematical investigation.

or a 20-credit subject% students complete at least two mathematical investigations.

Students investigate mathematical relationships% concepts% or problems% which ma! beset in an applied conte


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$ach investigation report% e


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Performance Standard) for Sta"e 1 Mat ematic)

- Concepts and Techniques Reasoning and Communication

A #omprehensive =nowledge and understanding ofconcepts and relationships.

Fighl! effective selection and application ofmathematical techni:ues and algorithms to findefficient and accurate solutions to routine and comple

Mathematics Subject Outline — Stage 1 (for Teaching in 2016)

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