mathematics - kopykitab

Strictly in accordance with the latest CBSE syllabus

By

Manisha MathurMSc, BEd

Bal Bharati Public SchoolRohini, Delhi

New Saraswati House (India) Pvt. Ltd.New Delhi–110002 (INDIA)

MATHEMATICS

VI

SALIENT FEATURES

• ChapterwisePointstoRemember• ChapterwisePulloutWorksheetsforSubjectAssessment• ChapterwisePulloutWorksheetsforEnrichmentActivity• FivePracticePapersbasedonthelatestexaminationpattern

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Revised edition 2018

ISBN: 978-93-5272-337-9

Published by: New Saraswati House (India) Pvt. Ltd.19 Ansari Road, Daryaganj, New Delhi-110002 (India)

The moral rights of the author has been asserted.

©Reserved with the Publishers

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– 3 –

We are glad to present the revised edition of Me ‘n’ Mine TM Mathematics for class VIII students in accordance with the latest CBSE syllabus.

This invaluable Me ‘n’ Mine TM series also provides practice material based on the latest CBSE guidelines for Social Science, Hindi, Sanskrit, Science and English for class VI students.

Salient features of this book are:

‘Points to Remember’ at the start of every chapter. Chapterwise and Topicwise Subject Assessment & Enrichment

Activity.Lots of chapterwise and topicwise pullout worksheets. These

worksheets have variety of questions such as MCQs, short answer and long answer questions.

Five practice papers with ample space for writing answers. These practice papers contain examination based questions.

Suggestions from readers are most welcome.

PUBLISHERS’ NOTE

– 5 –

NUMBER SYSTEM (60 hrs) (i) Knowing our Numbers Consolidatingthesenseofnumbernessupto5digits,size,estimationofnumbers,identifyingsmaller,larger,

etc.Placevalue(recapitulationandextension),connectives:useofsymbols=,<,>anduseofbrackets,wordproblemsonnumberoperationsinvolvinglargenumbersuptoamaximumof5digitsintheanswerafteralloperations.Thiswouldincludeconversionsofunitsoflength&mass(fromthelargertothesmallerunits),estimationofoutcomeofnumberoperations.Introductiontoasenseofthelargenessofandinitialfamiliaritywith,largenumberupto8digitsandapproximationoflargenumbers).

(ii) Playing with Numbers Simplification of brackets,multiples and factors, divisibility rule of 2, 3, 4, 5, 6, 8, 9, 10, 11. (All these

throughobservingpatterns.Childrenwouldbehelpedindeducingsomeandthenaskedtoderivesomethatareacombinationof thebasicpatternsofdivisibility).Even/oddandprime/compositenumbers,co-primenumbers,primefactorisation,everynumbercanbewrittenasproductsofprimefactors.HCFandLCM,primefactorisationanddivisionmethodforHCFandLCM,thepropertyLCM×HCF=productoftwonumbers.Allthisistobeembeddedincontextsthatbringoutthesignificanceandprovidemotivationtothechildforlearningtheseideas.

(iii) Whole Numbers Naturalnumbers,wholenumbers,propertiesofnumbers(commutative,associative,distributive,additive

identity,multiplicativeidentity),numberline.Seeingpatterns,identifyingandformulatingrulestobedonebychildren.(As familiarity with algebra grows, the child can express the generic pattern.)

(iv) Negative Numbers and Integers Hownegativenumbersarise,models ofnegativenumbers, connection to daily life, ordering ofnegative

numbers,representationofnegativenumbersonnumberline.Children to seepatterns,identifyandformulaterules.Whatareintegers,identificationofintegersonthenumberline,operationofadditionandsubtractionofintegers,showingtheoperationsonthenumberline(additionofnegativeintegerreducesthevalueofthenumber)comparisonofintegers,orderingofintegers.

(v) Fractions Revisionofwhata fraction is, fractionasapartofwhole, representationof fractions (pictoriallyandon

numberline),fractionasadivision,proper,improper&mixedfractions,equivalentfractions,comparisonoffractions,additionandsubtractionoffractions(Avoidlargeandcomplicatedunnecessarytasks).(Movingtowardsabstractioninfractions).

Reviewoftheideaofadecimalfraction,placevalueinthecontextofdecimalfraction,interconversionoffractionsanddecimalfractions(avoidrecurringdecimalsatthisstage),wordproblemsinvolvingadditionandsubtractionofdecimals(twooperationstogetheronmoney,mass,lengthandtemperature).

ALGEBRA (15 hrs)Introduction to Algebra Introductiontovariablethroughpatternsandthroughappropriatewordproblemsandgeneralisations (example5×1=5etc.). Generatesuchpatternswithmoreexamples. Introductiontounknownsthroughexampleswithsimplecontexts(singleoperations).

RATIO AND PROPORTION (15 hrs) Conceptofratio. Proportionasequalityoftworatios. Unitarymethod(withonlydirectvariationimplied). Wordproblems.

SYLLABUS

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GEOMETRY (65 hrs) (i) Basic Geometrical Ideas (2-D) Introductiontogeometry.Itslinkagewithandreflectionineverydayexperience. Line,linesegment,ray. Openandclosedfigures. Interiorandexteriorofclosedfigures. Curvilinearandlinearboundaries. Angle—vertex,arm,interiorandexterior. Triangle—vertices,sides,angles,interiorandexterior,altitudeandmedian. Quadrilateral—sides,vertices,angles,diagonals,adjacentsidesandoppositesides(onlyconvexquadrilateral

aretobediscussed),interiorandexteriorofaquadrilateral. Circle—centre,radius,diameter,arc,sector,chord,segment,semicircle,circumference,interiorandexterior. (ii) Understanding Elementary Shapes (2-D and 3-D) Measureoflinesegment. Measureofangles. Pairoflines –Intersectingandperpendicularlines –Parallellines Typesofangles—acute,obtuse,right,straight,reflex,completeandzeroangle. Classificationoftriangles(onthebasisofside,andofangles). Typesofquadrilaterals—trapezium,parallelogram,rectangle,square,rhombus. Simplepolygons(introduction)(Uptooctagonsregularsaswellasnon-regular). Identificationof3-Dshapes–cube,cuboid,cylinder,sphere,cone,prism(triangular),pyramid(triangular

andsquare).Identificationandlocatinginthesurroundings. Elementsof3-Dfigures(faces,edgesandvertices). Netsforcube,cuboid,cylinder,coneandtetrahedron. (iii) Symmetry : (reflection) Observationandidentificationof2-Dsymmetricalobjectsforreflectionsymmetry. Operationofreflection(takingmirrorimages)ofsimple2-Dobjects. Recognisingreflectionsymmetry(identifyingaxes). (iv) Constructions (using straight edge scale, protractor, compasses) Drawingofalinesegment. Constructionofcircle. Perpendicularbisector. Constructionofangles(usingprotractor). Angle60°and120°(usingcompasses). Anglebisector-makinganglesof30°,45°,90°etc.(usingcompasses). Angleequaltoagivenangle(usingcompasses). Drawingalineperpendiculartoagivenlinefromapoint(a)ontheline(b)outsidetheline.MENSURATION (15 hrs)Concept of Perimeter and Introduction to AreaIntroductionandgeneralunderstandingofperimeterusingmanyshapes.Shapesofdifferentkindswiththesameperimeter.Conceptofarea,areaofarectangleandasquare.Counter examples to different misconcepts related to perimeter and area. Perimeterofarectangleanditsspecialcase–asquare.Deducingtheformulaoftheperimeterforarectangleandthenasquarethroughpatternandgeneralisation.DATA HANDLING (10 hrs) (i)Whatisdata—choosingdatatoexamineahypothesis? (ii) Collectionandorganisationofdata—examplesoforganisingitintallybarsandatable. (iii) Pictograph—needforscalinginpictographsinterpretation&construction. (iv)Makingbargraphsforgivendatainterpretingbargraphs+.

1. KNOWING OUR NUMBERS

Subject Assessment .................................................................................................................................................. 11 • Points to Remember • Worksheets (1 to 8) Enrichment Activity ................................................................................................................................................. 27 • Lab Activity–1 • Lab Activity–2 • Project • Quiz

2. WHOLE NUMBERS

Subject Assessment .................................................................................................................................................. 29 • Points to Remember • Worksheets (9 to 15) Enrichment Activity ................................................................................................................................................. 43 • Lab Activity–1 • Lab Activity–2 • Project • Quiz

3. PLAYING WITH NUMBERS

Subject Assessment .................................................................................................................................................. 45 • Points to Remember • Worksheets (16 to 25) Enrichment Activity ................................................................................................................................................. 65 • Lab Activity–1 • Lab Activity–2

4. BASIC GEOMETRICAL IDEAS

Subject Assessment .................................................................................................................................................. 67 • Points to Remember • Worksheets (26 to 32) Enrichment Activity ................................................................................................................................................. 81 • Lab Activity–1 • Project • Quiz

5. UNDERSTANDING ELEMENTARY SHAPES

Subject Assessment .................................................................................................................................................. 83 • Points to Remember • Worksheets (33 to 40) Enrichment Activity ................................................................................................................................................. 99 • Lab Activity–1 • Lab Activity–2 • Project

6. INTEGERS

Subject Assessment ................................................................................................................................................ 101 • Points to Remember • Worksheets (41 to 46) Enrichment Activity ............................................................................................................................................... 113 • Lab Activity–1 • Project • Quiz

7. FRACTIONS

Subject Assessment ................................................................................................................................................ 115 • Points to Remember • Worksheets (47 to 55) Enrichment Activity ............................................................................................................................................... 133 • Lab Activity–1 • Lab Activity–2 • Project • Quiz

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CONTENTS

8. DECIMALS


9. DATA HANDLING


10. MENSURATION


11. ALGEBRA

Subject Assessment ................................................................................................................................................ 183 • Points to Remember • Worksheets (77 to 83) Enrichment Activity ............................................................................................................................................... 197 • Lab Activity–1 • Project • Quiz

12. RATIO AND PROPORTION


13. SYMMETRY AND PRACTICAL GEOMETRY


PRACTICE PAPERS • Practice Paper – 1 ........................................................................................................................................... 235 • Practice Paper – 2 ........................................................................................................................................... 240 • Practice Paper – 3 ........................................................................................................................................... 245 • Practice Paper – 4 ........................................................................................................................................... 250 • Practice Paper – 5 ........................................................................................................................................... 255

ANSWERS ........................................................................................................................................................... 263

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PULLOUTWORKSHEETS

KNOWING OUR NUMBERS 11

Choose the correct answer from the given four options in the following questions 1–18:

1. The numbers 2637, 3672, 7263, 7236 can be arranged in the descending order as

(A) 2637, 3672, 7236, 7263 (B) 7263, 7236, 3672, 2637 (C) 3672, 2637, 7263, 7236 (D) 7236, 2637, 3672, 7263 (1)

2. The difference between the greatest and the smallest 4-digit numbers that can be formed by the digits 5, 3, 0 and 8 such that 5 is always at the ones place and no digits are repeated is

(A) 5085 (B) 5220 (C) 4950 (D) 4945 (1)

3. The largest 3-digit number that can be formed by the digits 2, 5, 7 and 6 such that digits are not repeated is

(A) 726 (B) 752 (C) 762 (D) 765 (1)

4. A number equivalent to 9 × 10000000 + 9 × 1000000 + 2 × 100000 + 5 × 10000 + 3 × 100 + 1 × 1 is

(A) 99250301 (B) 10305299 (C) 29039051 (D) 92950301 (1)

5. The air distances of Dubai, Kabul, Colombo, and Dhaka from Delhi are 1045 km, 2412 km, 748 km, and 452 km, respectively. Among the given cities which is the farthest from Delhi?

(A) Kabul (B) Dhaka (C) Dubai (D) Colombo (1)

Name ....................................................... Class ................... Roll No. ...........

KNOWING OUR NUMBERSSUBJECT ASSESSMENT

WORKSHEET–11

MarksObtained

Max.Marks

18Time

40 Min.

Points to Remember

1 is the smallest natural number while 0 is the smallest whole number.

Greatest number of any number of digits, say ‘n’ added to 1 gives the smallest number of (n + 1) digits. Where, n = 1, 2, 3, .... . For example,

Greatest number Smallest number (one-digit) 9 + 1 = 10 (two-digit) (two-digit) 99 + 1 = 100 (three-digit) (three-digit) 999 + 1 = 1000 (four-digit) Ones period has three places: hundreds, tens and

ones. Thousands period has two places: ten thousands and

thousands. To compare numbers having different number of

digits, memorise that: (i) The number with more digits is greater. (ii) When two numbers have equal

number of digits, compare the digit at the extreme left. If they are equal, compare thenextdigit andsoon. If thenumber ishavingthegreaterdigit incorresponding place then it is a greater number.

To build the greatest number, rearrange the digits in decreasing order and to build the smallest number, these are arranged in increasing order.

In Roman numerals, numbers from 1 to 1000 areformedusingsymbolsI,V,X,L,C,D,M.

(i) The symbol I, X, C andM are repeated onlythreetimesbutV,CandDareneverrepeated.

(ii) Ifasmallersymbolisinsertedjustafterabiggersymbol,itisaddedbutifitisplacedjustbeforeabiggersymbol,thenitissubtracted.V,LandDareneverinsertedbeforeabiggersymbol.IissubtractedfromVandXonly.XissubtractedfromL,MandConly.

Multiple Choice Questions

12 MATHEMATICS–VI

6. The number, seven crore eight lakh fifty thousand

nine hundred six can be written in the numerical

form as

(A) 7850906 (B) 7805906

(C) 70850906 (D) 78050980 (1)

7. The number 950408 can be written in words as

(A) ninetyfivethousandfourhundredeight

(B) ninelakhfiftythousandfourhundredeight

(C) ninetyfivelakhfourhundredeight

(D) ninelakhfivethousandfourhundredeight (1)

8. The pair out of the following which has same weights is

(A) 40 kg and 400 g (B) 40 kg and 4000 g (C) 9 kg and 9000 g (D) 9 kg and 900 g (1)

9. The number, three million two hundred four thousand two can be written in numerical form as

(A) 30204002 (B) 3200402 (C) 3204002 (D) 3004202 (1)

10. The approximated sum of numbers 928276 and 71725 is ___________ .

(A) 1000000 (B) 1100000

(C) 2100000 (D) 2000000 (1)

11. The estimated product of 15289 and 587 is

(A) 8000000 (B) 8500000

(C) 9000000 (D) 9500000 (1)

12. 202 × 315 can be expanded as ___________ .

(A) 200 × 300 + 300 × 15 + 2 × 200 + 2 × 15 (B) 200 × 300 + 200 × 15 + 2 × 300 + 2 × 15 (C) 200 × 3 + 300 × 2 + 200 × 300 + 2 × 15 (D) 200 × 2 + 300 × 15 + 200 × 300 + 2 × 15 (1)

13. The sum of the Roman numerals LV and XCII can be written in Hindu-Arabic number as

(A) 138 (B) 147 (C) 153 (D) 163 (1)

14. The expression that can be obtained on multiplying 29 by the difference of 10 and 7 is

(A) 29 – (10 × 7) (B) (29 × 10) – 7 (C) 29 × (7 + 10) (D) 29 × (10 – 7) (1)

15. The difference between the greatest and the smallest numbers formed by the digits 1, 9, 7 and 5 without any repetition is

(A) 8172 (B) 8154 (C) 7678 (D) 6546 (1)

16. The number of millions in one crore is

(A) 10 (B) 20 (C) 50 (D) 100 (1)

17. The Roman numeral of 427 can be written as

(A) CDXXVII (B) CCCXXVII (C) CCXXVII (D) CXXVII (1)

18. The Roman numeral for 1000 is

(A) M (B) C

(C) D (D) L (1)

KNOWING OUR NUMBERS 13

1. Using any 5 different digits and make a number with condition that digit 8 is at the hundreds place. (1)

2. Write the number name for 11,25,000. (1)

3. Write 4,00,000 in the expanded form. (1)

4. What is the Roman numeral for 91? (1)

5. Write the number 1,08,374 in expanded form. (1)

6. Pick out the greatest and the smallest numbers from the following:

(i) 7245, 7545, 7524, 7425 (2)

Greatest number– .........................................

Smallest number– .........................................

(ii) 10001, 10010, 11000, 10100 (2)

Greatest number– .........................................

Smallest number– .........................................

7. Use the given digits without repetition and make the greatest and the smallest five-digit numbers.

7, 5, 2, 1, 3. (2)

8. Arrange the numbers 92181, 56342, 29165, 55634 in ascending order. (2)

Name ....................................................... Class ................... Roll No. ...........

KNOWING OUR NUMBERSSUBJECT ASSESSMENT

WORKSHEET–21

MarksObtained

Max.Marks

25Time

40 Min.

14 MATHEMATICS–VI

9. Give the correct solution for 9999 + 1. (2)

10. Write the largest and the smallest 7-digit numbers. (2)

11. How many crores make 100 lakhs? (2)

12. In a library, there are 23,180 books of English, 9,128 books of Hindi and 709 books of other languages. Find the total number of books in the library. (3)

13. A student multiplied 6,285 by 75 instead of multiplying by 57. How much was his answer greater than the correct answer? (3)

Me n Mine Pullout WorksheetsMathematics For Class - VI CBSE (New

Edition)

Publisher : New SaraswatiHouse

ISBN : 9789352723379 Author : Manisha Mathur

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