Maths Syllabus Section 2

1

Mathematics

Mathematics

Upper primary

Syllabus 2003

Section 2

Learning outcomes

and indicators

2

Upper primary syllabus

Issued free to schools by the Department of Education

Published in 2003 by the Department of Education, Papua New Guinea

© Copyright 2003, Department of Education, Papua New Guinea

All rights reserved. No part of this publication may be reproduced, storedin a retrieval system, or transmitted in any form or by any meanselectronic, mechanical, photocopying, recording or otherwise without theprior written permission of the publisher.

ISBN 9980–930–19–5

Acknowledgements

The Upper Primary Mathematics Syllabus was prepared by theCurriculum Development Division of the Department of Educationand was coordinated by Steven Tandale.

The Mathematics Subject Advisory Committee as well ascommunity members, teachers, inspectors, educators andrepresentatives from government and non-governmentorganisations have developed this syllabus through meetings,workshops and trialing.

This document was developed with the support of the AustralianGovernment through the Curriculum Reform ImplementationProject.

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Mathematics

Secretary’s Message

The current reforms in education have been in progress since1992. The Education Reform has emphasised community-basedschooling, the use of vernacular languages in schools, theintroduction of Elementary Schools and the expansion of Primaryschooling to grade 8 and increased access to Grades 9 and 10.

This syllabus is to be used by Upper Primary (Grades 6, 7 and 8)students in Primary schools throughout Papua New Guinea. Thissyllabus develops, extends, links and builds upon concepts, skillsand attitudes flowing from Lower Primary (Grades 3, 4 and 5). Thissyllabus provides a sound foundation for further learning in thereformed school system.

Students’ language abilities, already gained in their homeenvironments and during the previous years of schooling, must berespected, built on and extended. Vernacular languages have alarge part to play in our students’ formative years and their firstlanguage should be used to promote a deeper understanding ofdifficult concepts when this is appropriate.

The Upper Primary Mathematics Syllabus contributes significantlytowards achieving Integral Human Development. Without a soundworking knowledge of mathematics, a person’s ability to functioneffectively is severely restricted. This course is designed topromote both a firm understanding of practical everydaymathematics and the theoretical basis to support higher learning.

By studying Mathematics, students will take an active role inbuilding their societies and appreciating others by using theacquired numeracy skills.

Building on the Lower Primary course, students focus ondeveloping numerical, analytical and investigative skills to solvereal life problems likely to be encountered in their societies as wellas in the outside world. This knowledge and skills will enablestudents to perform mathematical tasks in everyday life and to beuseful members of society as well as preparing for furthermathematical studies.

This course is designed to allow and indeed to encourage activeintegration primarily between the different units of mathematics andalso between mathematics and all other subjects. Such integrationwill result in providing the practice and skills that will set the groundfor lifelong learning.

I commend and approve this syllabus as the official curriculum forMathematics to be used in all Upper Primary schools throughoutPapua New Guinea.

Peter M. BakiSecretary for Education

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Learning Outcomes

Strand Grade 6 Grade 7 Grade 8

Number andApplication

6.1.1 Add, subtract,multiply and dividefractions

7.1.1 Solve problemsrequiring any of the fouroperations includingmixed numbers

8.1.1 Apply fractions inproblem solving

6.1.2 Add, subtract,multiply and dividedecimals

7.1.2 Use decimals tosolve problems set infamiliar contexts

8.1.2 Use decimals tosolve real life problems

6.1.3 Convert betweensimple fractions anddecimals

7.1.3 Convert betweenfractions, decimals andpercentages

8.1.3 Convert freelybetween fractions,decimals, percentagesand ratios

6.1.4 Link fractions anddecimals topercentages and solvesimple percentageproblems

7.1.4 Use percentages ina variety of real lifesituations

8.1.4 Solve problems inany situation thatinvolves percentages

6.1.5 Recognise ratios 7.1.5 Convert betweenratio and fractions

8.1.5 Apply ratios insolving problems fromreal life

7.1.6 Recognise andrelate rates to graphs

8.1.6 Apply rates to solvesimple problems fromreal life

6.1.7 Recognise andexplain the use ofdirected numbers

7.1.7 Use directednumbers in concreteproblems

8.1.7 Apply directednumbers in problemsolving

6.1.8 Use indices to thepower of 2 and 3

7.1.8 Use positiveindices greater thanthe power of 1

8.1.8 Use integer indicesand fractional indiceswhere the answers arerational

Numbering of Learning OutcomesEach Learning Outcome is numbered with three digits, such as 6.2.3.The first number refers to the Grade level. The second number refers to the Strand. The third number refers to the Outcome in the Strand.Thus, 6.2.3 refers to an Outcome at Grade 6, Strand 2 and Outcome number 3.

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Mathematics


Space andShape

6.2.1 Estimate, measureand compare usingmetric units

7.2.1 Estimate andmeasure using metricunits and lengths frommaps and othersources

6.2.2 Convert betweenmetric units of lengthand round off

7.2.2 Use appropriatemetric units incalculations

6.2.3 Calculate theperimeter of shapes

7.2.3 Investigate andmeasure thecircumference ofcircles

6.2.4 Find the area ofcomposite shapes

7.2.4 Compare areas byestimation

6.2.5 Investigate and usearea rules for trianglesand rectangles

7.2.5 Investigate arearules for quadrilaterals

8.2.5 Investigate the areaof circles

6.2.6 Investigate volumesof simple solids todetermine rules

7.2.6 Investigate volumesof compound prismaticsolids and use rules todetermine volumes

8.2.6 Investigate volumesof cylinders, cones andpyramids and applysome volume rules

6.2.7 Investigate capacity 7.2.7 Investigate therelationships betweencapacity and volume

8.2.7 Apply capacity andvolume measurementsin problem solving

6.2.8 Convert betweenmetric units

7.2.8 Use appropriateunits for capacity andsolve capacityproblems

8.2.8 Convert between avariety of units:capacityand volume, and metricand imperial

6



Space andShape

6.2.9 Draw andinvestigate properties ofpolygons

7.2.9 Draw, investigateand make physicalmodels of quadrilaterals

8.2.9 Make physicalmodels of circles andinvestigate theirproperties

6.2.10 Make tessellationsusing regular shapes

7.2.10 Create irregularshapes that tessellate

8.2.10 Investigaterotational tessellations

6.2.11 Identify differentangles

7.2.11 Determine theinterior and exteriorangles of triangles andquadrilaterals

8.2.11 Investigateproperties of interiorand exterior angles ofpolygons

7.2.12 Construct anddetermine properties ofangles

8.2.12 Use appropriatewords to identify anddescribe angles andshapes accurately

6.2.13 Construct nets ofregular solids

7.2.13 Design nets forvarious solids

8.2.13 Associate netswith the solids theyform

6.2.14 Identify and usecompass directions

7.2.14 Give the directionof a location relative toothers as a bearing

8.2.14 Use and readmaps accurately

6.2.15 Use and makekeys and scales onmaps

7.2.15 Make mapshaving scales andkeys, from suitabledata

6.2.16 Use map gridsand coordinates tolocate points

7.2.16 Use a four-quadrant number plane

8.2.16 Use longitude andlatitude to locate placeson a map

7

Mathematics


Measurement 6.3.1 Use appropriateunits for weights inmeasurements andcalculations

7.3.1 Use charts andgraphs to read andrecord weights andsolve problems relatedto weight

8.3.1 Solve real lifeweight problems

7.3.2 Recognise weightas a force

8.3.2 Differentiatebetween weight andmass

6.3.3 Investigatetemperature and thethermometer as ameasuring instrument

7.3.3 Read athermometer scale andcomparemeasurements

8.3.3 Displaytemperatures includingthose from specialistthermometers

6.3.4 Use a variety oftime records

7.3.4 Manipulate time tosolve problems

8.3.4 Recogniserelationships betweenlocation and time

8.3.5 Use time-ratecalculations

Chance andData

6.4.1 Collect andinterpret locally relevantstatistical data

7.4.1 Compare sets ofdata

8.4.1 Interpretinformation presentedstatistically

6.4.2 Explore empty sets,intersections andunions

7.4.2 Use a variety ofclassification methods

8.4.2 Use sets to solveproblems from real life

6.4.3 Explore the resultsof independent events

7.4.3 Calculateprobabilities fromindividual eventprobabilities

8.4.3 Explore the socialimplications ofprobability

6.4.4 Discuss sources oferror meaningfully

7.4.4 Apply strategies toreduce error

8.4.4 Combine error-reducing strategies toget the best result

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Chance andData

6.4.5 Discuss the valueof accuracy

7.4.5 Choose appropriatelevels of accuracy

8.4.5 Represent levels ofaccuracy

6.4.6 Estimate quantitiesand numbers

7.4.6 Use a variety ofestimation strategies

8.4.6 Identify and selectappropriate estimationstrategies

6.4.7 Round off amounts 7.4.7 Estimate sums ofmoney

8.4.7 Estimate results ofcalculations

Patterns andAlgebra

6.5.1 Identify differentmethods used forpacking

7.5.1 Use differentpacking patterns topack objects

8.5.1 Apply packingpatterns in solvingproblems in real life

6.5.2 Explore numberpatterns

7.5.2 Relate numberpatterns and algebraicstatements

8.5.2 Recognise and usepatterns in processes

6.5.3 Use pronumerals 7.5.3 Substitutenumbers forpronumerals

8.5.3 Manipulate simplealgebraic expressionsand solve real lifeproblems

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Mathematics

Learning Outcomes and Indicators

STRAND : NUMBER AND APPLICATION

Sub-strand Grade 6 Grade 7 Grade 8

Fractions 6.1.1 Add, subtractmultiply and dividefractions

7.1.1 Solve problemsrequiring any of thefour operationsinvolving mixednumbers

8.1.1 Apply fractions inproblem solving

Indicators Students will beachieving this when they,for example

Students will beachieving this when they,for example


• add and subtractfractions, includingthose with differentdenominators, andmixed numbers

• freely convert betweenmixed numbers andimproper fractions

• use the reciprocal of afraction to solve adivision problem bymultiplication

• multiply and dividefractions, includingthose with differentdenominators, andmixed numbers

• correctly place fractionsand mixed numbers ona number line to showcomparative size

• solve simple problemsthat require theaddition, subtraction,multiplication or divisionof fractions

• solve problems bymethods of dividedrectangles

• solve problems by firstconverting to improperfractions

• solve problems thatrequire addition and orsubtraction of mixednumbers with anysimple denominators

• solve simple problems,which require morethan one operation

• solve division problems

• solve problems such as12 1/

4 x 1/

2

• solve problems like

121/2 x 0.25 by using

fractions

• solve problems such as‘In a class of 45, thereare 27 boys. One thirdof the boys and half ofthe girls play soccer.How many soccerplayers are there in theclass?’

All Indicators are listedas bullet points aftereach Outcome. The listof Indicators alwaysbegins with the followingstatement: ‘Students willbe achieving thisoutcome when they, forexample’.

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Decimals 6.1.2 Add, subtractmultiply and dividedecimals

7.1.2 Use decimals insolving problems set infamiliar contexts

8.1.2 Use decimals tosolve real lifeproblems

Indicators Students will beachieving this whenthey, for example



• solve problems such as0.320 + 1.162, 2.711 -1.304

• solve problems such as3.162 x 4, 2.255 ÷ 3

• solve problems such asone metre of materialcosts K5.25, how muchdo 5 metres cost?

• solve problems such as0.115 - 2.015, 12.101 -6.0009

• solve problems such as2.1115 x 5, 3.002 x 2.11and 12.20121 dividedby 32

• solve problems such asthe sum of 1.455 kmplus 450.5 m + 0.100km

• use decimals to threeplaces in solvingproblems set in afamiliar context

• solve money-basedproblems using any ofthe four operations

• round decimals to anygiven number of places

• solve problems fromreal life situations

• present data in decimalformat accurately

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Mathematics


Fractions andDecimals

6.1.3 Convert betweensimple fractions anddecimals

7.1.3 Convert betweenfractions, decimalsand percentages

8.1.3 Convert freelybetween fractions,decimals, percentagesand ratios




• change 1/2 to 0.5,

1/4 to 0.25, 3/

4 to 0.75,

3/10

to 0.3, and 4/10

to 0.4

• change for example 0.5to 1/

2, 0.32 = 32/

100 = 8/

25

• change 3/8 to 0.375 to371/

2% or 37.5% (avoid

fractions which lead torepeating decimals)

• change 2.015 to 2015/1000

= 403/200

to 201.5% or2011/

2%

• change 60% to 60/100

=6/

10 = to 0.60

• change 75% to 3:4 to 3/4

to 0.75

• change 50% to 1/2 to 0.5

to 1:1

• use percentage,decimal notationfraction or ratiointerchangeably to suitthe application

• solve problems such asK15.00 + 10%,as K15 + (.01 x K15) =K15 + K1.50 = K16.50

Sub-strandGrade 6

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Grade 7 Grade 8

Decimals andPercentages

6.1.4 Link fractions anddecimals topercentages and solvesimple percentageproblems

7.1.4 Use percentage ina variety of real lifesituations

8.1.4 Solve problems inany situation thatinvolves percentages


Students will beachieving this whenthey, for example


• show percentage as ashaded fraction of a 100squares

• convert 10, 15, 20, 25,50 75, 80 and 100% todecimals and fractions

• convert 1/10

,1/5, 1/

4, 1/

2, 3/

4

and 1 whole to decimalsand %

• mark percentages,decimals, fractions andmixed numberscorrectly on a numberline to show theirrelative size.

• solve calculations suchas 5% of 50, 10% of 73,3% of 24, 120% ofK5.00.

• answer questions suchas ‘What is the price ofa K25.00 meri blouse ifthe store is offering 20%off?’

• evaluate simple interestproblems such as K1000.00 @ 10% per yearfor 2 years

• determine the price ofarticles with 10%discount

• determine the price ofarticles plus 10% VAT

• solve problems such as‘A car is sold forK16,500 including 10%VAT. What is the pricewithout VAT?’

• solve problemsinvolving percentagesthat would beencountered in atrading situation

13

Mathematics


Ratios andRates

6.1.5 Recognise ratios 7.1.5 Convert betweenratios and fractions

8.1.5 Apply ratios insolving problems fromreal life

IndicatorsStudents will beachieving this when they,for example



• identify problems suchas ‘add 1 part powderedmilk to 4 parts water’ asratio problems.

• identify scales on mapsas ratios

• name situations inwhich ratios are used,such as gears on a caror bicycle, levers,mixtures and state therelevant ratio from eachexample

• change 3:7 to 3/10

:7/10

where 10 = 3+7

• simplify 8:12 by dividingcommon factor, such as8:12 = 2:3 or changingratios to fractions 8:12 =8/

12 = 2/

3 and 8/

20 =2/

5 and

2/5 = 2:5

• solve VAT problemswhere VAT is applied inthe ratio 1:10

• solve mixing problems,such as ‘Concrete maybe mixed in the ratio2:5.5, cement, sandand gravel? How manybuckets of cementshould be mixed with 30buckets of gravel?’

14



Ratios andRates

7.1.6 Recognise andrelate rates to graphs

8.1.6 Apply rates to solvesimple problems fromreal life

IndicatorsStudents will beachieving this when they,for example


• determine the rate of agraph as its slope or riseover run

• recognise a rate as afraction of two differentitems, such as 3 metresfor every 5 seconds, is arate of 3/

5 m/s or 0.6 m/s

• solve problems such as‘How much for fivemetres at a rate of K6per metre?’ ‘How longwill it take to travel 20km at a rate of 5 km/hour?’

• solve problems such as‘Water is dripping froma tap at a rate of 42drops every 6 minutes,how long will it take todrip 400 drops?’

15

Mathematics


DirectedNumbers

6.1.7 Recognise andexplain the use ofdirected numbers

7.1.7 Use directednumbers in concreteproblems

8.1.7 Apply directednumbers in problemsolving




• name a variety ofmeasurements that canbe negative, such astemperature, elevationor balance of anaccount

• explain the meaning ofa negativemeasurement in eachsituation above

• determine solutions toproblems by use ofnumber lines, countersor other aids, positiveor negative

• solve problems such as3-5, -2 x 10

• solve problems such asfinding an accountbalance at the end of atrading period duringwhich the account fallsbelow zero

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Indices 6.1.8 Use indices to thepower of 2 and 3

7.1.8 Use positive indicesgreater than the powerof 1

8.1.8 Use integer indicesand fractional indiceswhere the answers arerational




• calculate solutions tonumbers such as 32, 43

• express products like 4x4 as 42, 9 x 9 as 92, 3x 3 x 3 as 33

• recognise 1, 4, 9, 16,25, 49, 64, 81, 100 assquare numbers

• recognise 1, 8, 27 and64 as cubic numbers

• calculate numberssuch as 25, 34

• express products like3 x 3 x 3 x 3 x 3 as 35

• use whole numberindices positive,negative and zero

• can show the patternsformed by use ofindices

• recognise that 31 = 3,40 = 1 and 6—3 = 1/

63

• recognise squarenumbers between 1and 200 and henceknow their squareroots

• recognise cubicnumbers to 100 andhence know their cubicroots

• find solutions toproblems such as‘What numbermultiplied by itself isequal to 36?’

• recognise that 2 is thesame as the squareroot of 4

17

Mathematics

Strand: SPACE AND SHAPES


Length 6.2.1 Estimate, measureand compare usingmetric units

7.2.1 Estimate andmeasure using metricunits and lengths frommaps and othersources



• offer reasonableestimates for heights ofobjects in a picturebased on heights offamiliar objects

• offer reasonableestimates for lengths ofobjects they candirectly observe: ± 10%

• measure a variety ofobjects to the nearestmm, cm, or mdepending on the initialsize

• measure longerdistances in kilometresor metres asappropriate

• choose an appropriateunit for any givenmeasurement

• estimate lengths inmetres and kilometresto within ±10%

• measure the distancearound the schoolboundary in metres andcompare it with theirprior estimate

• measure the distancefrom home or town inkilometres using a mapand its scale

• use appropriate metricunits to measure longdistances

• measure accuratelyusing appropriate toolsand units

18



Length 6.2.2 Convert betweenmetric units of lengthand round off

7.2.2 Use appropriatemetric units incalculations



• convert metres tomillimetres or viceversa

• convert metres tokilometres or vice versa

• sum groupmeasurements ofmixed units to get ananswer in a single unit

• determine a length of abuilding given sufficientmeasurements of partsin different unitsincluding also somefractionalmeasurements

• round off amounts tothe nearest place asappropriate

• convert a mixture ofmeasurements to asingle measurementand round off to thelowest accuracy beforeaddition and subtraction

• convert to the samemeasurement andmultiply or divide thenround to the sameaccuracy as themeasurements

• convert mixed units tothose that result in theeasiest calculations

• freely convert units in aproblem to make thesolution simpler

19

Mathematics


Length 6.2.3 Calculate theperimeter of shapes

7.2.3 Investigate andmeasure thecircumference of circles



• measure the threesides of a triangle anddetermine its perimeter

• measure just two sidesof a rectangle todetermine its perimeterusing rules they havedetermined themselves

• measure the distancearound circles andother irregular objectsby suitable strategies

• use rolling andwrapping of string orpaper around cylindersto measurecircumference

• divide circumference bydiameter to determine afixed ratio

• obtain reasonableestimate of the value ofC/D, that is π to ± 10%from measured values

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Area 6.2.4 Find the area ofcomposite shapes

7.2.4 Compare areas byestimation



• divide compound areasinto square metres orsquare centimetres asappropriate and countthese to determine thetotal area

• find the area of aclassroom floor notincluding the spacesoccupied by cupboardsor the teacher’s desks

• find the area of theclassroom end wallincluding the triangle atthe top

• find the area of theclassroom sidewallexcluding the windowsand the door

• distinguish areasdiffering by as little as10% through visualinspection andestimation only

• regularly makeestimates of areasaccurate to ±10%before calculation andcompare these to thecalculated value toverify the calculation

21

Mathematics


Area 6.2.5 Investigate and usearea rules for trianglesand rectangles

7.2.5 Investigate arearules for quadrilaterals




• solve the area of arectangle by multiplyingthe number of squaresalong adjacent sides

• solve for the area of atriangle by halving theproduct of its heightand base

• find the area ofcompound shapes byapplying the rules tocomponent parts andadding or subtractingas required

• solve the area oftrapeziums, kites,parallelograms andrhombuses by suitablerules

• solve areas of irregularquadrilaterals bytreating them ascompound shapes

• compare the area ofcircles to the area ofinscribed squares andthe square of thediameter

• determine the area ofcircles by countingsquares

• relate the measuredarea of circles to thesquare of the diameter

• circumference:C = πD

8.2.5 Investigate thearea of circles

22



Volume 6.2.6 Investigate volumesof simple solids todetermine rules

7.2.6 Investigate volumesof compound prismaticsolids and use rules todetermine volumes




• determine volumes ofsimple solids: cubesand cuboids, bycounting unit cubes

• determine volumes ofsimple solids: prisms,by counting unit layersand multiplying by thearea of each layer

• determine volumes ofsimple solids: prisms,from suitable lengthmeasurements

• determine volumes ofcompound prismaticsolids as the sum ofvolume of its parts

• regularly find volumesof simple solids byapplying rules forvolume

• determine the capacityof hollow cylinders,pyramids and conesand convert that tovolumes and use theresults relate to thelength measurementsof the shapes

• build approximations tothe shapes fromcenticubes to determineapproximate volumesand again relate theseto the length measures

• recognise that thevolume of a cylindercan be found bymultiplying the area ofthe end by its height orlength

• recognise that both thevolume of a cone and apyramid depend on thearea of the base andheight in the same wayas each other

• solve problemsinvolving calculation ofvolumes by choosingappropriate rules andusing them

8.2.6 Investigate volumesof cylinders, cones andpyramids and applysome volume rules

23

Mathematics


Capacity 6.2.7 Investigate capacity 7.2.7 Investigate therelationship betweencapacity and volume

8.2.7 Apply capacity andvolume measurementsin problem solving




• Compare the capacityof different shapedcontainers bymeasuring thecapacity in mL or L asappropriate, usingmeasuring cups orcylinders

• Submerge objects ofknown volume tomeasure theirdisplacement

• Determine the volumeof a given quantity ofliquid by placing it in acontainer of regularshape so that thevolume can becalculated

• Convert freely betweencapacity and volumemeasures during theproblem-solvingprocess as convenient

24



Capacity 6.2.8 Convert betweenmetric units

7.2.8 Use appropriateunits for capacity andsolve capacityproblems

8.2.8 Convert between avariety of units:capacity and volume,and metric and imperial




• change freely betweenthe different units ofcapacity, such as 345mL = 0.345 L

• change betweendifferent units of area:square centimetres,square metres,hectares

• change between thedifferent units ofvolume: cubiccentimetres and cubicmetres

• determine the capacityof a container given itsmeasurements inlength units

• choose capacitymeasurementsappropriate to the sizeof the vessel, such asfor a cuboidal vessel 5m x 0.2 m x 0.01 m, V =0.010 m cubed, whichis most sensiblyexpressed as 10 L as acapacity

• convert betweengallons and litres, feetand metres, inchesand millimetres using1 gallon = 4.5 L, 1 foot= 0.3 m and 1 inch =25 mm as sufficientlyaccurate conversions

• convert betweencapacity measuresand volume measures

25

Mathematics


Shapes 6.2.9 Draw andinvestigate properties ofpolygons

7.2.9 Draw, investigateand make physicalmodels of quadrilaterals

8.2.9 Make physicalmodels of circles andinvestigate theirproperties




• describe models ofrectangles andtriangles, such as ‘Arectangle has two equallonger opposite sidesand two equal shorteropposite sides, one pairat right angles to theother pair’

• draw regular polygonssuch as triangles,rectangles, squares upto dodecagons

• identify some propertiesof polygons, such asthe number of edges,vertices, angles, axis ofsymmetry, number ofpairs of parallel sides

• make models ofquadrilaterals:parallelogram, rhombus,kite and trapeziumusing paper, card,sticks, wire

• make models ofquadrilaterals andname them, such as‘parallelogram’

• draw quadrilateralssuch as parallelogram,rhombus, kite andtrapezium

• identify the propertiesof quadrilaterals drawnby students, such asnumber of parallelsides, number andposition of equal lengthsides, equal angles,complementary angles,axis of symmetry

• draw circles on cardand cut them out

• mark diameter, radius,centre, circumferencearc, segment on circlesthey have drawn andcut out

• show relationshipbetween parts of acircle, such ascircumference anddiameter, diameter andradius, sector and arc

• investigate value of pi:π , by measuring thecircumference and thediameter of cylindricalitems

26



Tessellations 6.2.10 Make tessellationsusing regular shapes

7.2.10 Create irregularshapes that tessellate

8.2.10 Investigaterotational tessellations




• make tessellationsusing regular shapescut from paper or card

• draw tessellations usingregular shapes

• distinguish betweentessellating and non-tessellating regularshapes

• use a rectangular pieceof paper and make anirregular cut through themiddle and then gluethe two outer edgestogether to make anirregular tessellatingshape

• repeat the process bycutting the shape in theperpendicular directionand rejoining to make atessellating shape withall edges irregula

• create interestingshapes that tessellate

• Create tessellationsthat have rotationalsymmetry

• Identify traditional andmodern patterns inhandcrafts withrotational symmetry

27

Mathematics


Angles andShape

6.2.11 Identify differentangles

7.2.11 Determine theinterior and exteriorangles of triangles andquadrilaterals

8.2.11 Investigateproperties of interiorand exterior angles ofpolygons




• use two paper armsfastened together at apoint to make acute,right, obtuse, straightand reflex angles

• identify the differenttypes of angle formedby the hands on a clockface, such as threeo’clock is a right angle

• label different anglesaccording to type

• are able to add andsubtract angles

• use words such as rightangle, obtuse angle,reflex angle to describeangles in shapes

• use words such assupplementary,complementary,adjacent, interior,exterior to describeangles in differentpositions andrelationship to eachother

• determine the totalinterior and exteriorangles of triangles bymeasuring the separateangles and addingthem together

• determine the totalinterior angles ofquadrilaterals by cuttingoff the corners andplacing them togetherto find the total angle

• determine the totalinterior angles oftriangles by cutting offthe corners and placingthem together to findthe total angles

• find the interior anglesum for simplepolygons

• make a rule for theinterior angle sum ofpolygons based onnumbers of internaltriangles

• explain the relationshipof exterior and interiorangles

28



Angles 7.2.12 Construct anddetermine properties ofangles

8.2.12 Use appropriateterms to describeangles and shapesaccurately



• construct angles: fullturn, straight, right, 60°,45°, 30°, usingcompasses and rulers

• estimate the size ofangles and thenmeasure them withprotractors

• bisect angles (straight,right, 60°, 30°) usingcompasses and rulersand show therelationship betweenthe different parts andthe whole

• use properties ofcongruent, adjacent,complementary andsupplementary anglesto identify unknownangles

• identify congruent,adjacent,supplementary andcomplementary angles

• use words such ascomplementary,supplementary,corresponding, co-interior, exterior,alternate, transversaland alternate angles todescribe angles andshapes

• use the above types ofangles to determineunknown or missingangles

29

Mathematics


Nets 6.2.13 Construct nets ofregular solids

7.2.13 Design nets forvarious solids

8.2.13 Associate netswith the solids theyform




• make nets of simplesolids such as cubes,cuboids and prisms

• construct solids fromtheir nets

• design and constructnets for cuboids, andsimple prisms

• make a net for a coneor pyramid

• identify and make 3-dimensional shapesusing various nets

• construct the nets ofvarious solid figures onsquared papers, suchas triangular prism,cylinder, rectangularprism

• turn nets of solids suchas cube, cuboid, prismand cylinder to their 3-dimensional shapes

• differentiate betweenreal nets and other‘non-net’ patterns of flatshapes

30



Direction 6.2.14 Identify and usecompass directions

7.2.14 Give the directionof a location relative toothers as a bearing

8.2.14 Use and readmaps accurately

Indicators Students will beachieving this when, theyfor example

Students will beachieving this when, theyfor example


• identify and indicate thefour main compassdirections, North,South, West and East,and the intermediatepoints: NE, NW, SE andSW

• follow directions givenin terms of compassdirection and distancetravelled

• locate a place on a mapor in real life

• state directionaccurately as a bearing

• use appropriatecompass directions tostate a bearingaccurately

• determine a directionfrom a given bearing

• construct a scale mapof the local communityor school, usingsuitable measurementsof distances anddirections

• find places on a mapquickly and be able tospecify position on amap to others

• use the key and scaleto interpret maps

• construct sketch mapsto communicatelocation informationclearly and efficiently

31

Mathematics


Maps andCoordinates

6.2.15 Use and makekeys and scales onmaps

7.2.15 Make maps havingscales and keys fromsuitable data



• demonstrate an abilityto read and use a key

• give the correct realdistance from a map byapplying the map scale

• choose a scale suitablefor making a map oftheir class room

• make a map of theirclassroom using asuitable scale

• create a suitable key torepresent items in theirclassroom, on a map

32



Maps andCoordinates

6.2.16 Use map gridsand coordinates tolocate points

7.2.16 Use a four-quadrant number plane

8.2.16 Use longitude andlatitude to locate placeson a map




• identify locations on amap given gridreferences orcoordinates

• use number pairs ascoordinate references

• plot points on anumber plane by useof ordered pairs withpositive and negativevalues

• record the orderedpair coordinates ofpoints shown on afour-quadrant numberplane

• locate a town or mapfeature by its latitudeand longitude only indegrees and minutes

• give latitude andlongitude for a givenlocality to the nearestminute by reading froma suitable map

33

Mathematics

Strand : MEASUREMENT


Weight 6.3.1 Use appropriateunits for weights inmeasurements andcalculations

7.3.1 Use charts andgraphs to read andrecord weights andsolve problems relatedto weight

8.3.1 Solve real lifeweight problems withconfidence andcompetence




• use grams, kilograms ortonnes as appropriatefor the quantity beingmeasured

• use addition,subtraction,multiplication anddivision to solve weight-related problems

• plot data on a weight forage graph andcomment meaningfullyon the result

• take a series of weightmeasurements to findan average weight

• take tabulated price percash crop unit weight tovalue a given weight ofcash crop

• use a weight for agebaby weight chart toread and record babyweights and commentas to health statusbased on that

• use children’s weightfor age or height chartto determine their ownideal weight and tocomment on theiractual weight

• use appropriateoperations to solveproblems involvingweight

• determine the yield fora cash crop given theaverage weight perhectare

34



Weight 7.3.2 Recognise weightas a force

8.3.2 Differentiatebetween weight andmass



• compare weight as adownward pull to otherforces in otherdirections

• measure the pull ofweight as a force byuse of springs, rubberbands or force meters

• recognise that an objectkeeps its mass but canalter its weightdepending on itslocation

35

Mathematics


Temperature 6.3.3 Investigatetemperature and thethermometer as ameasuring instrument

7.3.3 Read athermometer scale andcomparemeasurements

8.3.3 Displaytemperatures includingthose from specialistthermometers




• appropriately use thewords hot, cold andwarm to describetemperatures

• offer reasonableestimates of air, water,and body temperaturein degrees Celsius byfeel: ± 5 degrees

• use a thermometer tomeasure varioustemperatures in theirenvironment

• read the measurementoff the thermometerscale accurately

• recognise thatthermometers can havenegative numbers on itsscale, givingtemperatures colderthen zero degreesCelsius: 0oC

• read the temperaturefrom a picture of athermometer scale

• measure airtemperature and statehow this compares tothe daily average asgiven on an annualtemperature graph fortheir area

• measure watertemperature andcompare to tabulatedtemperatures

• record temperaturesfrom wet and dry bulbthermometers and usethese to determinehumidity from a chart

• record bodytemperature to thenearest tenth of adegree using a clinicalthermometer andcompare this to normalbody temperature

• record daily maximumand minimumtemperatures using amaximum and minimumthermometer and usethese to establish longterm temperaturerecords

36



Time 6.3.4 Use a variety oftime records

7.3.4 Manipulate time tosolve problems

8.3.4 Recogniserelationships betweenlocation and time




• use time lines,timetables, timeschedules, diaries andcalendars accurately

• solve ‘time remaining’ or‘time since’ problemsinvolving hours andminutes

• solve simple time-related problems

• determine the time inother cities of the worldbased on the timedifference with the timein Papua New Guinea

37

Mathematics


Time 8.3.5 Use time-ratecalculations


• use speed to determinedistance travelled

• use pay rates todetermine pay earned

38


Strand: CHANCE AND DATA


Statistics 6.4.1 Collect andinterpret locally relevantstatistical data

7.4.1 Compare sets ofdata

8.4.1 Interpretinformation presentedstatistically




• use surveys,questionnaires andinterviews to collectinteresting data fromtheir community, schooland class

• collate data in tallytables

• present data in bargraphs, pictograms orhistograms

• use an appropriate formof average, (mean,median, mode) to makesuitable collectivestatements about theirdata

• use the words range,mean, median, modeand sample-size withunderstanding

• identify inappropriateinterpretations of setsof data presented in themedia

• explain the distinctionbetween the threeaverages: mean, mode,median, as a measureof central tendency

• interpret, construct andlabel graphs

• draw and usefrequency distributiontables

• correctly interpretinformation presentedin a variety of statisticalgraphs

• apply relevant bargraphs, pictograms,histograms and piecharts to statisticalinformation

• present collated data intables and graphs:pictograms, columngraphs, bar graphs, linegraphs, time graphs,pie charts

• interpret percentageincreases over a periodof time, such aspopulation, mineralproduction, export andimport statistics

• calculate the threeaverages: mean,median and modeusing given data

• use results from arandom sample tomake prediction forfuture results

39

Mathematics


Sets 6.4.2 Explore empty sets,intersections andunions

7.4.2 Use a variety ofclassification methods

8.4.2 Use sets to solveproblems from real life




• define and recognisean empty set as agroup with nomembers with aparticular attribute

• define and recogniseintersection sets, whenmembers belong totwo or more sets

• define and recogniseunion sets when allmembers aremembers of twogroups

• using Venn diagramsto solve problems

• classify objects up tothree levels of attributes

• identify examples ofsets that have commonattributes

• use Venn diagrams toillustrate classifications

40



Probability 6.4.3 Explore the resultsof independent events

7.4.3 Calculateprobabilities fromindividual eventprobabilities

8.4.3 Explore the socialimplications ofprobability




• identify possibleoutcomes from aparticular event and thelikelihood of thesedifferent eventsoccurring in terms ofpossible, impossible,certain

• describe and sequenceevents on a continuumof impossible, unlikely,equal chance, mostlikely, likely and certain

• consider and describeprobability in everydayevents

• investigate the effectsof non random choice

• calculate and describeprobabilities ofeveryday events

• discuss situations thatdepend on chance

• explore and discuss thechances of losing andwinning in games

• discuss the socialconsequences ofgambling

• discuss the reasonspeople gamble and theconsequences ofpromotional gambling

• investigate the spreadof gambling throughoutmost everyday activities

• comment on theimportance of chance insituations, such as jobapplications, courseselections, examinationresults, health, cropproduction

41

Mathematics


Error andAccuracy

6.4.4 Discuss sources oferror meaningfully

7.4.4 Apply strategies toreduce error

8.4.4 Combine error-reducing strategies toget the best results




• consider errors causedby rounding to thenearest scale unit

• consider errors causedby the accuracy of toolsused

• consider errors causedby the competence of aperson using tools

• consider errors causedby changes to thematerial beingmeasured

• consider errors causedby errors introduced bycalculation

• use appropriatemeasuring tools reliably

• reduce parallax erro

• make repeatedmeasurements andaverage results

• apply a variety of error-reducing strategies

• recognise errors andtake steps to reducethe effects of theseerrors

42



Accuracy andError

6.4.5 Discuss the valueof accuracy

7.4.5 Choose appropriatelevels of accuracy

8.4.5 Represent levels ofaccuracy




• consider the need toorder more materialsthan required and thecost implications

• talk about theconsequences ofinaccuratemeasurements

• measure to suitablelevels of accuracy asrequired for the task

• use conventions suchas ± amount or ±percentage to bracketerrors

• use error bars ongraphicalrepresentations

43

Mathematics


Estimation 6.4.6 Estimate quantitiesand numbers

7.4.6 Use a variety ofestimation strategies

8.4.6 Identify and selectappropriate estimationstrategies




• make estimates ofquantities beforemeasurement to within± 20%

• use estimates ofquantities to check thevalidity ofmeasurements theymake

• estimate expectedresults of calculationsand use these to checkthe validity of theircalculations

• estimate by comparisonto other familiarquantities and items

• estimate by dividinginto manageable parts

• use estimationstrategies that giveconsistently closeresults whencompared tomeasurements

• estimate consistentlyto better than ±10%

44



Estimation 6.4.7 Round off amounts 7.4.7 Estimate sums ofmoney

8.4.7 Estimate results ofcalculations




• round fractions of atoea to the nearestwhole toea

• round money to thenearest whole Kina

• round lengths to thenearest 1 cm, 10 cm,1 m, 10 m, 100 m,1 km as appropriate

• round othermeasurements tosuitable place value

• give a close value aftera quick inspection of anumber of coins andnotes spread on a table

• use mentalapproximations toestimate a price perkilogram given a pricefor 750 g

• use rounding and otherappropriate methods toobtain an approximateanswer to a calculation

• use estimated resultswhere the exact answeris not necessary

• compare estimatedresults with exactresults to check validityof results

45

Mathematics

Strand : PATTERNS AND ALGEBRA


Packing 6.5.1 Identify differentmethods used forpacking

7.5.1 Use differentpacking patterns topack objects

8.5.1 Apply packingpatterns in solvingproblems from real life




• discuss and usepacking concepts

• identify packingpatterns, tree plantingsand spacing of othercash crops, such astriangular spacing andsquare spacing of cashcrop trees

• pack cylinders (cans orjars) to achieve highestnumber on a givenshelf space

• arrange spheres in athree dimensionalpattern that is stable

• use a square andtriangular array to plantseedlings in a field ortray

• solve real life problemsby identifying the bestpacking strategies andusing them to packvarious goods

46



Algebra 6.5.2 Explore numberpatterns

7.5.2 Relate numberpatterns and algebraicstatements

8.5.2 Recognise anduse patterns inprocesses




• identify numberpatterns such astriangle numbers,square numbers,Fibonacci series,various arithmetic andgeometric series

• find the next term in aseries–with justification

• create a numberpattern from their ownstated rule

• describe numberpatterns by using analgebraic expression

• make number patternsgiven a simplealgebraic expression

• apply similar patterns tonew situations to solveproblems

• apply process patternsin problem solving

47

Mathematics


Algebra 6.5.3 Introducepronumerals

7.5.3 Substitute numbersfor pronumerals

8.5.3 Manipulate simplealgebraic expressionsand solve real lifeproblems




• evaluate a pro-numeralin a number sentence

• make up a rule todescribe a numberpattern and usepronumerals in the rule

• substitute pronumeralswith numerals in simpleequations

• simplify simplealgebraic expressions

• use distributive laws toexpand algebraicexpressions

• identify factors

• identify common factors

• solve simple algebraicexpressions bysubstitution,

• apply problem solvingequations to solveproblems

48


References

NDOE (1995) Secondary School Mathematics 7A. Longman,South Melbourne

NDOE (1995) Secondary School Mathematics 7B. Longman,South Melbourne

NDOE (1995) Secondary School Mathematics 8A. Longman,South Melbourne

NDOE (1995) Secondary School Mathematics 8B. Longman,South Melbourne

NDOE (2001) Grade 5 Mathematics Student Book 5A. Oxford,South Melbourne

NDOE (2001) Grade 5 Mathematics Student Book 5B. Oxford,South Melbourne

NDOE (2001) Grade 5 Mathematics Teachers Guide. Oxford,South Melbourne

NDOE (n.d.) Grade 6 Mathematics Student Book 6A. Oxford,South Melbourne

NDOE (n.d.) Grade 6 Mathematics Student Book 6B. Oxford,South Melbourne

NDOE (n.d.) Grade 6 Mathematics Teachers Guide. Oxford, SouthMelbourne

NDOE (1999) Upper Primary Mathematics Syllabus. (draft)

NDOE (1998) Lower Primary Mathematics Syllabus. (draft)

NDOE (1992) Community School Mathematics Pupils Book6A.NDOE, Waigani

NDOE (1992) Community School Mathematics Pupils Book6B.NDOE, Waigani

NDOE (1992) Community School Mathematics Teachers Guide6A.NDOE, Waigani

NDOE (1992) Community School Mathematics Teachers Guide6B.NDOE, Waigani

Documents

Maths Syllabus Section 2