Ambani Vidyalaya, Surat MATHEMATICS! Clean Upmagicmaths.org/pdf/cleanUp 051014.pdf · CLEAN UP THE...

Prof. M A ThiruthuvadossCell: 9445204774

for Excellence in Mathematics

http://www.magicmaths.org

The MessClean Up

Savethe Children

&MATHEMATICS!

the Nation

Redeemthe Maths

Ambani Vidyalaya, Surat

Christ Church, Byculla -Mumbai

Open to All (See Full Balcony)-Madurai

MCC, Chetput - Chennai

VES Inst. of Tech., Chembur

Holy Cross, Tadong - Sikkim

CLEAN UP THE MESS - REDEEM THE MATHS 2

IN A NUT-SHELL

Mathematics is naturalEven non-school goers use maths skills. They NEVER say it is this much difficult..

THE SCHOOL-MATHS IS MESSED-UPIt is made difficult intentionally by ` chasers.

TEXT BOOK is their AK 47 or HOWITZER.Textbooks are manipulated in every possible & even impossible way..

(Even the Times Tabes is ULTA!)

NCERT GUDIELINESI have not seen one textbook that follows NCERTguidelines for textbooks.NCERT textbook is the Worst example.No textbook is worth the paper it is printed on!

BLOATED TEXTBOOKSTextbooks grow in size, weight and intentionallycreated CONFUSION!.

Bloated to About 4 Times

SAM

E

NCERT Guidelinesfor Text-Books saysDo not listFormulae, Results &Definitions

TN Std. 8 textbook gives

23 formulae.

Originally only 2Text-book orFormula Factory?

TN Std. 9 book240 pages in 2007

300 pages in 2011;

HOW? WHY??

• Maths Contents• Teaching-time• Learning-time

But Books Grow!How?

CLEANING UP1. GENUINE TEXTBOOKS

Get REAL Maths books

They will be slim (a fourth in size & weight);

Need not cut the foot to fit the shoe

2. NUMBER FLUENCYBharat gave numbers and number-skills to theworld.

Today our children are scared of numbers!

We do not teach numbers;

because We DO NOT KNOWor we follow FOREIGN EXPERTS and NOT OUR BHARATH ANCESTORS.

Concentrate on numberskills alone in Primary.You may teach ‘any thing else’, if you need to,according to social, political demands

Allow our children to enjoy numbers.They will automatically enjoy mathematics

and soar to greater heights.

NCERT Guidelines!

1. Child friendly language2. Teacher not to teach3. Facilitate a Discussion By children In their own words4. Children observe ideas5. They generalise ideas In their own words6. Textbooks not to list ideas Results, Formulae, ...7. Learning Concepts; Not complicated calculation8. Learning to think to solve, Not learning old methods To very old problems

Shri Bhascaracharya

Taught (in 1150 A.D.)8 Multiplication Methods8 Operations for Fractions

Srinivasa Ramanujanhad said,

“Numbers are myfriends”.

Today, Our Children• Fear Numbers• Count Fingers• Guess Answers


JUST A QUICK LOOK

IS

SCHOOL MATHSDIFFICULT?

YES!VERY DIFFICULT!

Children find mathematics, not just

difficult, but almost impossible.Most give up on it VERY EARLY.

These days children fear, shed tears and even commit suicides.

They keep doing ‘something’ in the nameof mathematics out of compulsion.while the society talks periodically ofcentums, passes and fails meaninglessly

The National Curriculum Framework (2005):Some problems in School Mathematics Education

A majority of children have a sense offear and failure regarding Mathemat-ics. Hence, they give up early on, anddrop out of serious mathematicallearning. .....

The NATIONAL

CurriculumFramework (2005)

Some Problems in

School MathematicsEducation

1. A majority of childrenhave a sense of fear and fail-ure regarding Mathematics.Hence, they give up early on,and drop out of seriousmathematical learning.

2. The curriculum isdisappointing not only tothis non-participatingmajority, but also to thetalented minority byoffering them nochallenges.

3. Problem, exercises andmethods of evaluation aremechanical and repetitive,with too much emphasis oncomputation. Areas ofMathematics such as spatialthinking are not developedenough in the curriculum.

4. Teachers lack confi-dence, preparation and sup-port.


IS

NATURAL MATHSDIFFICULT?

NO!Outside the school,Children & Adults use MANYNATURAL (mathematical)skills.

They ‘pick up’ these skillsEFFORTLESSLY, as they grow,

by Observing,Imitating &

Repeating.

They never fearnor complain

about these skills.This is theNATURAL LEARNING PROCESS!

NATURAL LEARNING

Joy of Imitating

LEARNINGBY

IMITATION

The UNIQUELEARNING

METHODin Nature

Imitation isFUN and Play

Children LOVEthis IMITATION

BECAUSE THEY LEARNNATURAL MATHS

by Natural Learning Process

by Choice &without Compulsion

Examples of NATURAL SKILLS:1) The young girl draws kolams that needs lotsof mathematical (Geometric) skills.

But in school, she may fail a geometry test!

2) The youngster speeding on the bicycle, bendsthe exact amount balancing his cycle and himselfwhen he negotiates a curve.

But he has not even heardof Dynamics!

3) Then there was this 2nd Standardgirl-child near Madurai who came late toschool. When questioned, she said she hadto cook the meal (as her mother was away)and feed her younger brother and then cometo school.

Now cooking involves estimation,ratio and proportion, judgement,decision-making etc.

KOLAM

Drawing kolam involves:1. Free-hand drawing2. Estimation, judgement3. Straight line orientation4. Curves, Triangles,

Circles, Squares,Rhombuses, etc.

5. Symmetery, proportion

Riding Bicycles

Banking!Dynamics!!What’s it?


TEX

T-B

OO

KS

AR

E H

IGH

LY M

AN

IPU

LATE

D T

O A

CH

IEV

E TH

IS

THEN WHY ISSCHOOL MATHS

DIFFICULT?

BECAUSE

MATHEMATICSIS

MADEDIFFICULT

INTENTIONALLY

JAI!TO THEMIGHTY

`

HOWMATHS IS

MADE DIFFICULT?

1. NO FOUNDATION

2. Teach NO TABLES or teach ‘MODERN(!)

CONFUSING TABLES’

3. TEXT-BOOKS TEACH(Not Teachers) in Class

or Teachers BLINDLY followtextbooks

4. TEXT BOOKS are nowTERROR-BOOKS

Through the text-booksChildren,Mathematics and the

Nationare held to ransom.

The

single cause

forMathematics

being Difficult

is

the

TERROR-BOOKin the guise ofTEXT-BOOK

TodayAny Textbook

is

BLOATEDto

4 timesthe size

fullof

NON-MATHS


HOWIS MATHS MADE DIFFICULT?

1. NO FOUNDATIONA child must be able to add, subtract, multiply & divide(+, –, x & ÷) numbers mentally and instantly. This isthe basis or foundation of Mathemtics.

Drive A Car Without WheelsToday, most children can not do any of these. Howdo you drive a car without wheels?

Walking Skill Not Necessary‘Neo and pseudo’ ‘educationists’ ‘believe’ walking skillis unnecessary; cycle is there! When there arecalculators, why ... ... ...?

Tables Deprecated; Alternative?The proven method, to lay the foundation, is to teachtables. Now teaching tables is depricated withoutoffering any valid alternative.

Our Children, Guinea Pigs?New untried ‘methods’ are tried out on our children asguinea pigs, from time to time. They remain highlysuccessful (on government reports) on paper or on TVshows. Children score 200/200. But still they countfingers to add two numbers!

The Nation pretendsto build

Mathematicson this

non-existing foundation!?

An Australian Experience

The Australian State ofNew South Walesexperimented with the‘modern’ methods of

Not teaching tables,Not teaching spelling etc.

for over a decade towardsthe end of the lastmillennium.

Do Not teach tablesSchools did not teach tables.Even parents who taughttables at home were takento task.

Maths Became a MessChildren became confusedand maths skills sufferedeven further.

Drop ‘Modern Methods’The ‘modern’ methodswere dropped like a hotpotato.Because they were alert,honest sensible andsensitive.

Teach The TablesThe State reverted to thetraditional method of the‘Three R’s:

Reading,Riting and

Rithmetic


2. TABLES & ‘MODERN(!) TABLES’Consider Multiplication: 4th Table4th Table means, we count 4’s or by 4’s

Traditional:1 x 4 = 4 (One 4 is 4)2 x 4 = 8 (Two 4’s are 8)3 x 4 = 12 (Three 4’s are 12)4 x 4 = 16 (Four 4’s are 16)

... ... ... ... ... ...

8 x 4 = 32 (Eight 4’s are 32)9 x 4 = 36 (Nine 4’s are 36)

and so on. we clearly count 4’s.

‘ Modern’:4 x 1 = 4 (Four 1’s is 4)4 x 2 = 8 (Four 2’s are 8)4 x 3 = 12 (Four 3’s are 12)4 x 4 = 16 (Four 4’s are 16)

... ... ... ... ... ...

4 x 8 = 32 (Four 8’s are 32)4 x 9 = 36 (Four 9’s are 36)

and so on. We do not count 4’s or by 4’s. We count 4 of something else.

Question: How many 4’s in 32?Traditional table Answer

Eight 4’s are 32. So, eight 4’s.“Modern” table Answet

Four 8’s are 32. So, eight 4’s.YOU JUDGE FOR YOURSELF

COUNTING & TABLES

Counting is too slow.Addition:Count by lumpsMultiplication:Count by same-sized lumpsSubtraction:Count by lumps downwardsDivision:

How many equal lumps

Addition, Subtraction &

Multiplication TablesHelp us to get

Combination of numbersInstantly.

‘Book of Tables’(tha;g;ghL)

from Sivakasi

an EXTRA set oftables!

Addition Tables

Subtraction Tables

Multiplication Tables

Multiplication Tables

(Modern - GJKiw)

Find out why



1. FOUNDATION2. ‘MODERN(!) TABLES’3. TEXT-BOOKS TEACH IN CLASS4. TEXT BOOKS are TERROR BOOKS

There isNo Maths

No LogicNo Conventions

Nothing that is of Value EXCEPT NON-SENSE!

What better way than a sample?

Compare following few pages of solutions:Textbk Solutions on LEFT PAGENormal Solutions on RIGHT PAGE

Compare following aspects:• Length of Solutions• Using Wrong, DEVIOUS methods• Difficulty of Numbers & Solutions• Working upto huge numbers and• Answers appear suddenly; HOW?• Large Numbers & Unnecessary Fractions• Non-simplification of calculations in time• Using Non-Existing formulae• Encourage children to mug-up formulae• Purposely bringing in fractional numbers• Basic number facts explained with fractions!• Problems not graded• Exercises do not have any aim or goal• Unconnected problems PLANTED• Simple things are made mysterious from mars• & more ....

In the followingpages

A selection ofmaterial fromtext-books aregiven verbatim

on the left.

The same work in the traditional

way is givenin green on the

right.

You compare


1. FOUNDATION2. ‘MODERN(!) TABLES’3. TEXT-BOOKS TEACH in Class

(Not Teachers)

NCERT Guidelines (For Text-books):

Teachers to initiate and guide a discussion

Children to identify ideas, Relationships& patterns evolving in the discussion and togenerelise these in their own language,aided by teacher if needed.

In this scenarioIS THERE ROOM, REALLY,

FOR A text-book?

Crores of teachers use these bloated terror-books in class? HOW? WHY?

What are theMATHS EDUCATION

PEOPLEdoing?

Teach with a

lively discussioninvolving all children

intheir own LanguageKeep text-books away

at a distanceSee the

CheerHappiness

EnthusiasmInterest.

Now

Ask thesechildren

ifmaths

is difficult

Suggestions & Model

Lesson inhttp://

www.magicmaths.org/

FORMULAE

TAMILNADU STATE BOARD VIII STANDARD - 2011FORMULAE CREATED FOR PROFIT & LOSSORIGINALLY NO FORMULACHILDREN ARE EXHORTED TO LEARN THESE TO SOLVE PROBLEMS ANDENJOY MATHEMATICS.

(i) Profit or Gain = Selling price – Cost price

(ii) Loss = Cost price – Selling price

(iii) Profit % =Pr ofit x 100C.P.

(iv) Loss % =Loss x 100C.P.

(v) Simple Interest (I) =Principal x Time x Rate

100 =

Pnr100

(vi) Amount = Principal + Interest

(vii) Percentage of increase =Increase in amount x 100

Original Amount

(viii) Percentage of decrease =Decrease in amount x 100

Original Amount

(ix) S.P = C.P. + Profit

(x) Selling price (S.P.) =(100 + Profit %) x C.P

100

(xi) C.P. =100 x S.P

(100 + Profit %)

(xii) When there is profit C.P. =100 x S.P

(100 + Profit %)

(xiii) When there is a loss C.P. =100 x S.P.

(100 - Loss %)

(xiv) When there is profit S.P. =(100 + Profit %) x C.P

100

(xv) When there is a loss S.P. =(100 - Loss %) x C.P

100

(xvi) C. P. (of the air-cooler) = Real Cost + Conveyance Charges

(xvii) Cost price (of the car) = Real Cost price + Overhead expenses

Discount is the reduction on the Marked Price or List Price of the article.

The normal price attached to the article before the discount

made is called as Marked Price (M.P.) or List Price of the article.

(xviii) Discount = Marked Price - Selling Price

(xix) Selling Price = Marked Price - Discount

(xx) Marked Price = Selling Price + Discount

(xxi) M.P. =100 x S.P

(100 - Discount %)

(xxii) M.P. =100 + Gain% x C.P.

(100 - Discount %)

(xxiii) C.P. =(100 - Discount %) x M.P.

100 + Gain%

FORMULAE

NCERT VIII STANDARD - 2004 TO 2006FORMULAE CREATED FOR PROFIT & LOSSORIGINALLY NO FORMULACHILDREN ARE EXHORTED TO LEARN THESE TO SOLVE PROBLEMS ANDENJOY MATHEMATICS.

1. In case of profit or gain (i.e., if S.P. > C.P.),

(i) Profit = S.P. – C.P.

(ii) S.P. = Profit + C.P.

(iii) C.P. = S.P. – Profit

(iv) Profit % =Pr ofit x 100C.P.

(v) Profit =C.P. x Pr ofit %

100

(vi) S.P. = C.P. x 100 + Pr ofit %

100

(vii) C.P. =100 x S.P.

100 + Profit %

2. In case of loss (i.e., if S.P. < C.P.),

(i) Loss = C.P. – S.P.

(ii) S.P. = C.P. – Loss

(iii) C.P. = Loss + S.P.

(iv) Loss % =Loss x 100C.P.

(v) Loss =C.P. x Loss %

100

(vi) S.P. = C.P. x 100 Loss %

100

(vii) C.P. =100 x S.P.

100 Loss %

3. Discount

(i) Discount = M.P. – S.P.

(ii) Rate of Discount = Discount % = Discount x 100

M.P.

(iii) S.P. = M.P. – Discount

(iv) S.P. = M.P. – Discount % x M.P.

100

(v) S.P. = M.P. x Discount %1

100

(vi) S.P. = M.P. x 100 Discount %

100

(vii) M.P. =100 x S.P.

100 Discount %


Convention: Reducing Calculations is GOOD mathsN.C.E.R.T (1) Std. XExample 4: (page 231) In figure, two circular flower beds have been shown ontwo sides of a square lawn ABCD of side 56 m. If the centre of each circular flowerbed is the point of intersection O of the diagonals of the square lawn, find the sumof the areas of the lawn and the flower beds.

Note that the Solution below is exactly the same as on the left.I have just simplified the 6 un-simplified results as per convention.SEE how SIMPLE the solution has become!

Results (1) to (6) of the left page are reduced. (Values in GREEN) See how simple the solution is.

Solution: Area of the square lawn ABCD = 56 x 56 = 3136 (1)Let OA = OB = x metresSo, x2 + x2 = 562

or, 2x2 = 56 x 56or, x2 = 28 x 56 = 1568 (2)

Now, area of sector OAB = 21 x x4

= 1 224 7

x x 28 x 56

= 22x56 = 1232 (3)

Also, Area of OAB = 14

x 56 x 56

= 14 x 56 = 784 (4)So, area of flower bed AB = 1232 – 784 = 448 (5)

Similarly, area of other flower bed = 448 (6)

Therefore total area is 3136 + 448 + 448 = 4032 m2

Conventional Work:

4. TEXT BOOKS are TERROR BOOKSN.C.E.R.T. Std. X (Question on right)

Solution:Area of the square lawn ABCD = 56 x 56 m2 (1)Let OA = OB = x metresSo, x2 + x2 = 562

or, 2x2 = 56 x 56or, x2 = 28 x 56 (2)

Now, area of sector OAB 2 290 1= x x = x x360 4

= 1 224 7

x x 28 x 56m2 [From (2)] (3)


x 56 x 56 m2 [as 9 5 9 33÷ = x22 33 22 5

27 = 10

7 = 210

AOB = 900] (4)

So, area of flower bed AB21 22 1= x x28x56 x56x56 m

4 7 4

[from (3) and (4)]

21 22= x 28 x 56 2 m4 7

21 8= x 28 x 56 x m4 7

(5)

Similarly, area of other flower bed 21 8= x 28 x 56 x m4 7

(6)

Therefore total area21 8 1 8= 56x56+ x28x56x + x28x56x m

4 7 4 7

[From (1), (5) and (6)]

22 2= 28 x 56 2+ + m7 7

218= 28x56x m7

2= 4032 m Compare with next page also

The 6 Red boxesbuild upto the

Terrible Black Box


Good Maths on right

The 6 Red boxesbuild upto the

Terrible Black Box

Convention: Reducing Calculations is GOOD mathsN.C.E.R.T (1) Std. XExample 4: (page 231) In figure, two circular flower beds have been shown ontwo sides of a square lawn ABCD of side 56 m. If the centre of each circular flowerbed is the point of intersection O of the diagonals of the square lawn, find the sumof the areas of the lawn and the flower beds.

If you care forMaths, Children,Aptitude Developement,See the solution below.

Below I give a SMARTER method!Encourage children to think differentlyBright children will be happy

Solution:Required area = 2 sectors + 2 triangles

= half circle + half squareDB = 56 x 2 (diagonal of sq. ABCD)

OB = 28 x 2 ; OB2 = 784 x 2 = 1568

Half circle area =12

x 227

x OB2

a =117

x 1568 = 11 x 224 = 2464

Half sq. area =12

x 56 x 56

= 28 x 56 = 2 x 282 = 2 x 784 = 1568

Req. area = 2464 + 1568 = 4032 m2

Normal Good Maths:

4. TEXT BOOKS are TERROR BOOKSN.C.E.R.T. Std. X (Question on right)

Solution:Area of the square lawn ABCD = 56 x 56 m2 (1)Let OA = OB = x metresSo, x2 + x2 = 562

or, 2x2 = 56 x 56or, x2 = 28 x 56 (2)

Now, area of sector OAB 2 290 1= x x = x x360 4

= 1 224 7

x x 28 x 56m2 [From (2)] (3)


x 56 x 56 m2 [as 9 5 9 33÷ = x22 33 22 5

27 = 10

7 = 210

AOB = 900] (4)

So, area of flower bed AB21 22 1= x x28x56 x56x56 m

4 7 4

[from (3) and (4)]

21 22= x 28 x 56 2 m4 7

21 8= x 28 x 56 x m4 7

(5)

Similarly, area of other flower bed 21 8= x 28 x 56 x m4 7

(6)

Therefore total area21 8 1 8= 56x56+ x28x56x + x28x56x m

4 7 4 7

[From (1), (5) and (6)]

22 2= 28 x 56 2+ + m7 7

218= 28x56x m7

2= 4032 m


4. TEXT BOOKS are TERROR BOOKSN.C.E.R.T. Std. IX has the following step

2 225 7 m 625 49 m = 576 m = 24m

Comments:How do the children

calculate 252 androot of 576?

Mentally!?

Normal Work:N.C.E.R.T. Std. IX has the following step

2 225 7 m 625 49 m = 576 m = 24m

How about using the identity? 2 225 7 = 32 x 18 = 16 x 36 = 4 x 6 = 24m

Our own Sri Bhascaracharya gave this inhis Leelavati of 1150 A.D.!


Normal Work:N.C.E.R.T. Std. VIIIExample 5 (Page 77)

Find the compound interest on Rs.25600 for 2 yearsat 6.25% per annum.

Solution:

P = Rs.25600, n = 2 yrs, r = 6.25% = 1

16

A21= 25600 x 1

16

2

2

17= 25600 x 16

= 100 x 289 [as 162 = 256 & 172 = 289]= 28900

C. I. = 28900 – 25600 = Rs.3300

Comment:

A = P 1100

nr

is the formula for the Amountby Compound Interest.

If necessary use C.I. = A – P

4. TEXT BOOKS are TERROR BOOKSN.C.E.R.T. Std. VIIIExample 5 (Page 77)

Find the compound interest on Rs.25600 for 2 yearsat 6.25% per annum.

Solution: P = Rs.25600, n = 2, r = 6.25

2

2

Compound Interest= 1 1100

6.25= Rs 25600 1 1100

1= Rs 25600 1 116

17 17= Rs 25600 116 16

289 256= Rs 25600256

nrP

25600x33= Rs 3300256

Rs

Comment:

A formula is to make thework easy, short & sweetand fast.

But the ‘formula’ on the left is

fabricatedto prolong, confuse andcomplicate the work andthereby terrorise thechildren.

The Terror-Books are full ofsuch terrible fabrications!


Normal Work:N.C.E.R.T. Std. VII

Express 1000 as a product of powers of primefactors.

Solution:1000 = 103

= (2 x 5)3

= 23 x 53

4. TEXT BOOKS are TERROR BOOKSN.C.E.R.T. Std. VII

Express 1000 as a product of powers of primefactors.

Solution: 1000= 2 x 500

= 2 x 2 x 250= 2 x 2 x 2 x 125= 2 x 2 x 2 x 5 x 25= 2 x 2 x 2 x 5 x 5 x 5= 23 x 52.

A student, Atul, does like this: 1000= 10 x 100

= 10 x 10 x 10= (2 x 5) x (2 x 5) x (2 x 5) (since 10 = 2 x 5)= 2 x 5 x 2 x 5 x 2 x 5= 2 x 2 x 2 x 5 x 5 x 5

or 1000 = 23 x 53 (Required Form)

In Std. 7,you give a hint that10 = 2 x 5?!

NCERT & CBSEare teaching

orCHEATING

OUR CHILDRENandthe

NATION


Fractions to be reducedfirst and then next step.

4. TEXT BOOKS are TERROR BOOKSTAMILNADU Std. VII (2009)

2) A Simplification.

9 5 9 3322 33 22 5

x

= 297110 why

297110 ? Is it not

2710 ?

= 772

110

= 72

10

Fractionsnot reduced

but

Bloated!Unnatural simplification.

This is the maths weteach our

CHILDREN.

Normal Work:TAMILNADU Std. VII (2009)

2) A Simplification.

9 5 9 33÷ = x22 33 22 5

27 = 10

7 = 210

2

3


Normal Work:N.C.E.R.T. Std. VIII

Mohit bought a CD for Rs.750 and sold it for Rs.875. Find his gain per cent.

Solution: Bought for = Rs.750; Sold for = Rs.875

Profit = 875 – 750 = 125This profit 125 is out of the cost: 750

Profit percent is 125 100 2 x 100 = = 16 %750 6 3

Note: An VIII Std. student to know• 6 x 125 = 750

•100

6 is a sixth of 100; = 216 %3

Capable children should be encouraged to work:

Profit 125 out of 750

This is a sixth and so is 216 %3

4. TEXT BOOKS are TERROR BOOKSN.C.E.R.T. Std. VIII

Mohit bought a CD for Rs.750 and sold it for Rs.875.Find his gain per cent.

Solution: CP = Rs.750 and SP = Rs.875. Since (SP) > (CP), Mohit makes a gain. Gain = Rs.(875 – 750) = Rs.125

Gain% = %gain x 100CP

[From where &

why is this formula?]

125 50 2= x 100 % = % = 16 %750 3 3

Note:These chapters• Percentages• Profit, Loss• Interest (Simple and

Compound)had only 2 formulae.

1.pnrI = 100

2. A = P 1100

nr

Now aTamilnadu Govt.

book for Std. VIIIlists 38 results to bemastered by children withwhich they can do sumsvery fast!


Normal Work:TAMILNADU Std. VI (2009)

Convert 8.37 into an ordinary fraction.

Solution: 8.37 means 8 and 37 hundredths

8.37 = 378

100 =

837100

or Better still:

8.37 = 837100

4. TEXT BOOKS are TERROR BOOKSTAMILNADU Std. VI (2009)

Convert 8.37 into an ordinary fraction.

Solution:

1 18.37 = 8 x 1 + 3 x + 7 x 10 100

3 7= 8 + + 10 100

8 x 100 3 x 10 7= + + 1 x 100 10 x 10 100800 30 7= + + 100 100 100837= 100

ARare Piece

ofMaths!

Must bepreserved

for posterity!!

What a depth ofknowledge

ofdecimal fractions

to help & guide children!

Note:We haveCommon Fractions & Decimal Fractions!

What is‘ordinary fraction’?



Example 2: (page 263)A metallic cylindrical pipe has thickness 0.5cm and outside diameter 4.5cm. If 1cm3 of the metal has mass of 8g find the mass of 77cm long pipe.

SmartCalc Solution:Outer diameter = 4.5 cm,thickness of pipe = 0.5 cmMass of 1 cm3 of metal is 8g.

Radius: Outer (R) = 2.25cm, inner (r) = 1.75cm, h = 77cm

Volume of metal in pipe = h (R2 – r2)

= 227

x 77 x (2.252 – 1.752)

= 22 x 11 x 4 x 0.5= 22 x 11 x 2= 484

Volume of metal= 484 cm3.Mass= 484 x 8 = 3872 g = 3.872 kg

4.5 cm

0.5 cm

77 cm


Example 2: (page 263)A metallic cylindrical pipe has thickness 0.5cm and outside diameter 4.5cm.If 1cm3 of the metal has mass of 8g find the mass of 77cm long pipe.

Solution:We first find the vloume of the metallic part of the cylinderical pipe. This is thedifference of the volume of two solid cylinders one of diameter 4.5 cm and theother of diameter (4.5 – 1.0) cm or 3.5 cm.

Where is the Diagram?

For outer cylinder, radius = 1 4.52

x and height = 77 cm

Volume = 2

3 322 4.5 4.5 4.577cm 242 cm7 2 2 2

x x x x (1)

For inner cylinder, radius = 4.5 3.50.5 cm= cm2 2

, and height = 77 cm

Volume = 2

3 322 3.5 3.5 3.577 cm 242 cm7 2 2 2

x x x x (2)

The required bolume of the pipe =Volume of the outer cylinder – Volume of the inner cylinder

2 23

3

3 3

4.5 3.5242 cm2 2

4.5 3.5 4.5 3.5242 cm2 2 2 2

242 4 0.5 cm 484cm

x

x x

x x

Mass of the pipe = 484 x 8g [Since 1 cm3 of the metal has mass 8g]= 3872g=3.872kg



Example 5: (page 161) Convert the given decimals to per cents: (a) 0.75, (b) 0.09, (c) 0.2

Solution:

0.75 is, in fact, 75 hundredths and so is 75% (by definition of percentageRule of thumb: Just move the decimal point 2 places to the right.

(1) 0.75 = 75%

(2) 0.09 = 9%

(3) 0.2 = 20%


Example 5: (page 161) Convert the given decimals to per cents: (a) 0.75, (b) 0.09, (c) 0.2

Solution:

( ) 0.75 0.75 100%75 100% 75%

100

a x

x

What a messy job?

9( ) 0.09 9%100

b

2( ) 0.2 100% 20%10

c x

Another messy job!

If b) is correct then why method a) {and c)?}


4. TEXT BOOKS are TERROR BOOKSN.C.E.R.T. Std. X

Example 7: (page 247)A toy is in the shape of a right circular cone on top of a hemisphere as in thediagram. The radius of the sphere, as well as the base of the cone is 2 cm andheight of the toy is 4 cm. Determine the volume of the toy.(= 3.14)

Solution:

3 2

3 2 3

3

2 1Volumeo of toy = r r h3 32 1= x 3.14 x (2) + x 3.14 x (2) x 2 cm3 3

= 25.12 cm

Normal Work:N.C.E.R.T. Std. X

Example 7: (page 247)A toy is in the shape of a right circular cone on top of a hemisphere as in thediagram. The radius of the sphere, as well as the base of the cone is 2 cm andheight of the toy is 4 cm. Determine the volume of the toy.(= 3.14)

Solution:

Volume of the toy h3 22 1= π r + π r3 32 1= π x 8 + π x 83 3

= 8= 8 x 3.14= 25.12 cm3.



Example 122: (page 62) The price of 30 pens is Rs.172.50. Find the price of one pen.

Solution:

Price of 30 pens = Rs.172.50 5.75Price of 1 pen = 172.50 ÷ 30 30)172.50

= Rs.5.75 150 . 225 210 . 150 150 0 .

The price of 1 pen is Rs.5.75

MENTAL MATHSLong multipl ication &division is basic work

These may be resorted towhen working with largenumbers only.

Mental maths to be taught.


Example 122: (page 62) The price of 30 pens is Rs.172.50. Find the price of one pen.

Solution:30 pens cost Rs.172.50

1 pen costs172.50 17.25 = = 5.75

30 3

Price of 1 pen is Rs.5.75

Do not needLong Division

fordividing by 3.



Example 117: (page 61) Multiply: 2.1 x 1.3 x 1.2

Solution: SmartCalc Solution

1.3 x 1.2 = 1.56 (12 x 13 is easier)1.56 x 2.1 = 31.2176 (By ‘Quickmaths method’)

So 2.1 x 1.3 x 1.2 = 3.276


Example 117: (page 61) Multiply: 2.1 x 1.3 x 1.2

Solution: First multiply: 21 x 13 x 12

_____2__1__x__13 6 3 2_ 1_____ 2__7__3__

___2__7 3__x__12 5 4 62 7_ 3_____3_ 2 _7__6__

We have, 21 x 13 x 12 = 3276 Total number of decimal places in all the three

numbers is 3 2.1 x 1.3 x 1.2 = 3.276

MENTAL MATHSShocking lack of

Mental Maths

VISIT:http://

www.magicmaths.org

See theQuickmaths techniques

Any calculation in ONEline without paper-work

Free, Easy, Indian

MagicmathsWorkshops

I teachQuickmaths Techniques

See thenear total response

All HandsUp

brighter & not so bright

Total Participation

.Really

Is Maths Difficult?

ChildrenEnjoy & Participate

even in the hot sun!

Compare these withany normal maths

class in any school!

2800 Children (10 Schools) - Kumbakonam

Queen Mary’s, Rohini - New Delhi

Govt. Girls’ School, Kunnathur (Erode)

MAGICMATHS PROJECTfor Excellence in Mathematics

Any of the following calculations can be doneMentally, in around 5 to 10 secondsNo finger-counting, No guessingNo Paper-work

Multiply by 11

Multiply 2 x 2 digits

Square no. ending in 1

Square no. ending in 5

Multiply from Left

QuickmathsTechniques

1) 47 x 3 = 1412) 87 x 6 = 5223) 43 x 11 = 4734) 4273 x 11 = 470035) 824 x 5 = 41206) 473 x 5 = 23657) 31 x 22 = 6828) 25 x 73 = 18259) 322 = 1024

10) 32 x 33 = 105611) 872 = 756912) 2372= 5616913) 21542 = 463971614) 213 = 926115) 323= 3276816) Sq rt of 784 = 2817) 299 x 300 x 301 = 2699970018) Cube root of 13824 = 2419) Twelve and a half percent of 840 is 10520) If longer sides of rt triangle are 52 & 48,

other side is 2021) 942 + 1062 = 2007222) 2874 x 57 = 16381823) 5862 x 273 = 1600326

SRM University - Chennai

Kumaran (CBSE) - Bangaluru

MAGICMATHS PROJECTfor Excellence in Mathematics

Magicmaths Programme isdeveloped and propagated byme since late 2001.

The aim is to facilitateExcellence in Maths

by making mathseasy, efficient, enjoyable & inexpensive.

I offer:1. Easy & Fast Mental Addition Programme

(30 days at 10 minutes a day)

2. One-step, Paperless Calculation Techniques(Multiplication, Division, Square, Cube, Roots Any calculation in one line; No rough work; Any calculation in under 10 seconds)

3. Develop Lateral Thinking & Aptitude(Solve CAT level problems in 10 seconds

by unconventional methods)

I write these in books; Conduct (nearly 600)workshops in India, Abu Dabhi, Sri Lanka, Malaysia

Maths is not, but is made, difficult;Clean up the mess; See smiles all over

Engg Maths Lecturers - Navi Mumbai

Bhakthas, Karur

St. Michael’s,Coimbatore

Bishop Cotton Girls,Bangaluru

SASTRAKUMBAKONAM

I am sure some one with thepower & dynamism

is still out there!

Prof. Doss

Ambani Vidyalaya, Surat MATHEMATICS! Clean Upmagicmaths.org/pdf/cleanUp 051014.pdf · CLEAN UP THE...

Documents

Transcript of Ambani Vidyalaya, Surat MATHEMATICS! Clean Upmagicmaths.org/pdf/cleanUp 051014.pdf · CLEAN UP THE...