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MATHEMATICS : A JOY RIDE

Mathematical Crossword Across

1 an exterior angle of any angle <180

2 perimeter of a circle

3 Indian genius ,a student of Prof. Hardy

5 closed rectilinear figure

9 Equation represents a straight line

10 graph representing the data

11 triangle with all sides unequal .

13 Father of the co-ordinate geometry

14 shape of a box

16 another name for indices

18 3X4 = 4X3

Down

2 Lines intersecting in the same point

4 figure formed by two rays originating at same point

5 this theorem was first used by Maharshi Bodhayan

6 first counting machine

7 centroid is point of intersection of –

8 amount of space taken up by a 3D object

12 mean of a statistical data

15 points on the same line are ----

17 Point of intersection of altitudes of a triangle

TRY TRY, DON’T CRYTRY TRY, DON’T CRY

MATHS IS FUN & JOYMATHS IS FUN & JOY

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01 M

arch

201

1 8-15 am to 10 a.m

TIME TO TIME TO GETUPGETUP

THREE R’S

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Teaching math is about providing an atmosphere of playful engagement with mathematical problems, where students feel confident in failing, in order to try again; a place where students become transformed by exercising their own mathematical powers of reasoning.

TIME TO SLEEPTIME TO SLEEP

EARLY TO BED, EARLY TO RISEMAKES THE PERSON HAPPY & WISE

HAPPY & WISE

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RESULT

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TEACHER ?

MOTHER ?

Who is responsible for creating MATHSPHOBIAin the child’s mind?

Dull teaching causes most people to shy away from maths. Understanding how children learn best is an important step towards improving maths learning.By providing conducive atmosphere.

FEAR/MENTAL BLOCK/DISLIKE?

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Lack of practice?

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“I hear and I forget. I see and I remember.

I do and I understand.”

1. Recognize you have an aversion to math, whether it's full-blown math phobia or just a few math blocks here and there.

2. Make a conscious decision to do something about it.

3. Give yourself a regular math workout, however small to start with.

You'll find it all gets easier, and you'll soon enjoy math once again.

WHY GO SO FAR? STORY OF THE SON OF OUR OWN SOIL SIR RAMANUJAN

Who was Srinivasa Ramanujan?A famous Indian mathematician who lived from 1887 to 1920. The theory of numbers brought worldwide fame to Ramanujan.

Some of us here know Sir Ramanujan worked at Cambridge University with the great mathematician, G.H. Hardy.His birth centenary was celebrated in1987.

1729?

INDIAN GENIUS

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Story time• Once the inspector visited the school. He entered the 4th std.

class where his favorite subject was being tought.He posed a small question to the children. He asked them the sum of first 100 counting numbers.. All the children got busy to find the answer. Some started writing in the notebook,some started counting fingers. One little boy on the last bench was sitting very quietly watching the rest of the children. Inspectors always have a bad habit of catching the back benchers as during inspection teachers make the dull children sit at the back. So he asked the child ,”sweetheart, why don’t you want to give It a try?” Pat came the reply, sir, it's not a big deal. Answer is 5050. Inspector was very impressed with the child & asked him to explain. Child confidently replied ,sir ,if one adds two numbers at the extreme, every time one gets a total of 101.

• (as 100+1;99+2,------50+51) One gets 50 such pairs. Hence the answer is 101x50=5050. Inspector knew that one day this child prodigy is going to be a high achiever in life. Yes, his prophecy was true. Till the date we know him as Sir Ramanujan. 9

Internet blogs

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Teaching math is about being a physician who with care & affection ,above all patience finds the remedy for the patient (student).Patient too cooperates & follows the treatment religiously. A place where students become transformed by exercising their own mathematical powers of reasoning Math inquiry lessons are student-focused. Teachers give students materials and minimal direction; students then explore the topic and construct their own meaning

. Movies with inquiry bases ,hands on math activities applications on the futureschannel.com

Visit the sites: mathtopper.com;videomathtutor.com;articlesbase.com;

mathworks.in,futureschannel.com & many more.

Just type mathphobia or remedial teaching in math in Google search

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If:A B C D E F G H I J K L M N O P Q R S T U V W X Y ZIs represented as:1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26.If:H-A-R-D-W-O-R- K8+1+18+4+23+15+18+11 = 98%And:K-N-O-W-L-E-D-G-E11+14+15+23+12+5+4+7+5 = 96%But:A-T-T-I-T-U-D-E1+20+20+9+20+21+4+5 = 100%

L-O-V-E -O-F- G-O-D / FAITH 12+15+22+5+15+6+7+15+4 = 101%

Therefore, one can conclude with mathematical certainty that:While Hard Work and Knowledge will get you close, and Attitude will get you there, It's the Love of God /Faith that will put you over the top!

From a strictly mathematical viewpoint:What Equals 100%?

What does it mean to give MORE than 100%?

LEARN WHILE YOU PLAYLEARN WHILE YOU PLAY

PAPER FOLDINGPAPER FOLDING

CRAFT WORK CRAFT WORK

TEACHING AIDSTEACHING AIDS

ADDITIONAL INFORMATIONADDITIONAL INFORMATION

FALLACIES/PUZZLESFALLACIES/PUZZLES13

LEARN TO ANSWER LEARN TO ANSWER WHY & HOW ?WHY & HOW ?

A

BC

B C

A

B C

A

B C

A

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Some Algebraic Facts

(a+b)2

a b

a b

ba b

a ba2

b2

= a2 + 2ab+ b2

(a+b)2 geometrically gives area of a square whose sides are (a+b) units.

Pascal triangle 1 = 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1

= (10 + 1)1

= (10 + 1)2

= (10 + 1)3

= (10 + 1)4

= (10 + 1)5

Sequence of the numbers of the Pascal’s triangle represent the binomial coefficients in the expansion of (x+y)n

SIMPLE RESULTS

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(10+1)0

Some Algebraic Facts

(a+b+c)2 = a2+b2+c2+2ab+2bc+2ac

AL-G-BAR

a2 ab ac

b2

c2

ab

ac

bc

bc

a b c

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SUM OF THE ANGLES OF REGULAR POLYGONSShape of the

regular polygonNo. of

sides & angles

Rule of Sum of

the angles

Sum of the angles

Rule for measure of each angle

Degree measure of each

angle

3 180 (3-2) 180180(3-2)

3 60

4 180 (4-2) 360180(4-2)

4 90

5 180 (5 -2) 540180(5-2)

5108

6 180(6-2) 720180(6-2)

6120

n 180(n -2) 180(n-2)180(n -2)

n180(n-2)

n

MATHS CRAFT 1

Mathematics stimulates the imagination, anchors speculation, and promotes an awareness of reality. 18

Helpful website: www.scribd.com/doc/2726617/chapter-11

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2 ∏ r

h=r

Area of a ∆ = ½ base X height =1/2 X 2∏r X r

= ∏ r2 = Area of a circle

To derive the formula for area of a circle

Recall circumference of a circle is 2∏r

Area of a triangle is = ½ base X height

2∏r

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l= length

b= breadth

Area= l X b sq.units

l = 2 ∏ rb=h,height

CSA =l Xb =2 ∏ r h

rTotal surface area of a solid cylinder = 2 ∏rh + 2 ∏r2 sq.units

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Volume of a cylinder =

∏ r

∏ r

Volume of a cuboid = lXbXh=∏r . r . h= ∏ r2 h=

volume of a cylinder

hhr

Making a Cube Making a Triangular Prism

3

4

5

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To make a cone and find its surface area and volume

Materials required:

1. A square piece of thin cardboard of side 12 cm

2. A thick square cardboard of side

36 cm each

1. Scissors, Adhesive, Compasses

2. Bring the edges OA & OB together .Stick them.Attach the circular piece above to the bottom of the cone formed.

3. Length of the arc=circumference of the circle as

4. 2 ∏ x6 = 2 ∏ x18 x120/360 =12 ∏cm

5. l = slant height =18cms.

6. CSA = ∏ r l = ∏ x6x18=108∏ sq.cms.

7. TSA = ∏ x6x6 + 108 ∏ =144 ∏ sq.cms.

12cms

6o o

CRAFT

`36

120

12018

120

36cms.

O

18

18

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UNDERSTAND BETTER

• SQUARE PYRAMID • HEXAGONAL PYRAMID

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MATHS THROUGH CRAFT ACTIVITY

HEXAGONAL PRISM 25

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Sharpen your reasoning with puzzles

Can you divide no.of 17 cows between three brothers so that elder one gets ½,middle one gets 1/3 & the youngest get 1/9 th of the total cows?

Change the direction of the fish moving 3 sticks.

Linear equations

FATHER OF ALGEBRA

5 years later he had a sonThe riddle begins, “Diophantus ” youth lasted 1/6 of his life. He grew a beard

after 1/12 moreafter 1/7 more of his life he married

The son lived exactly ½ as long as his father. And Diophantus died just 4 years after his son.

All this adds up to the years Diophantus lived

ALGEBRA SOLVES A RIDDLE

Little is known about the life of Diophantus the Greek father of algebra, except his age at death, which has been preserved in the famous 1,500-year-old riddle shown here. If we assume ‘x’ as his age at the time of death then we get the equation

x = x/6 + x/12 + x/7 + 5 + x/2 + 4, which reduces to 3x/28 = 9 telling us Diophantus was 84 years old when he died.

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Achilles and tortoise ACHILLES FOOT

Speed of Achilles is 10 times that of tortoise. However tortoise gets a head start of 100 meters. When will Achilles catch on with the tortoise?

(A = 100, T = 110); (A = 110, T = 111); (A = 111, T = 111.1)(A=111.1,T=111.11 tortoise will be always ahead of the Achilles, even if by a mere eyelash.

0

100

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Scratch ur head• Let x=2 ; x(x – 1) = 2 ( x – 1) ;x2 - x = 2x -2 ; x2 – x –x = 2x – 2 – x ; x2 – 2x = x -2 ; x (x – 2 ) = x – 2 ; x =1 But x= 2 hence 2 = 1 o If you jog half way from A to B at a steady rate of

2miles/hr ; how fast would you have to run the rest of the way in order to average 4 miles /hr for the entire trip.

BEWARE IT MIGHT BE A FALLACY• Have you noticed? 11 x 11 =121;111 x111=12321,1111x1111=1234321 what next?• 371= 3 3 + 7 3 + 1 3; 407= 4 3 +o 3 + 7 3

• Palindromes: 56765 both ways read same• e.g.57+75=132+231=363

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Numeral & NUMBER

WHICH NUMERAL IS SMALLER?

WHICH NUMBER IS SMALLER?

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Fibonacci Numbers FIBONACCI

One month old

New borne Sequence is 1, 1, 2, 3, 5, 8, 13, ………if you’ve ever thought maths wasn’t “natural,” think again. The numbers of many flowerpetals are Fibonacci numbers. The numbers of spirals in a pine cone, pineapple, and sunflower seed heads also tend to be Fibonacci numbers.

Every ratio of the Fibonacci numbers starting from 3/2, 5/3, 8/5, ….. is called golden ratio more about it

in the next slide.

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Calling someone a “SQUARE” is an insult but calling them a “GOLDEN RECTANGLE” isn’t so bad.

GOLDEN RECTANGLE

This old man portrait of Leonardo da Vinci shows a picture with a square subdivided into rectangles having golden ratio.

This construction which is used in many temples, mosques fits into golden rectangles.

The ratio AG:AB represent the golden ratio and is donated by

2=1 + 5

In each of the square if you put a quarter circle then it represents the pattern which we see in some seashell

This rectangle is the most harmonious & pleasing to the eye hence we have sheets of paper, book of pages, standard photo frame, monitor, credit cards, windows and so on in the shape of rectangle.

Usually ratio of all rectangular things is between 1.4:1 and 1.8:1,credit cards,TV ,monitors etc.

AG

B

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=1.6 :1

RELATION & FUNCTION

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THEORY OF CONVERGENCE • (using a shrinking ruler to measure the

unmeasurable)• A fundamental concept of calculus is ‘convergence of

limit’. The idea that an unknown value can be measured by ”closing in “through approximations that are made finer & finer until they are refined, in effect to a precise value.1) the tracks converging on the horizon appear to join at a particular point, though they actually never meet.2)Images of a boy holding a mirror photographed in another mirror, although actually never shrink, but they appear to be converging on such a small area that it is considered to be a point.3)The lines AE,AD,AC &AB show average growth rates for successively smaller periods of time. But for the instant A ,the growth rate is shown by the tangent at A.

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CONVERGENCE

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Vector analysis

• VECTOR ANALYSIS Shooting at a target on a windy day is

a problem illustrating one of Carl Gauss’s realm of mathematics known as ‘vector analysis’ The velocity of the wind blowing from west to east is represented by an arrow i.e. vector V1.The rifleman compensates by moving his gun slightly left of the target as represented by vector V2.The bullet flies in a compromise pathway to the bull’s eye along the line R.

V1

V2 R

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A parachuter in free fall drops faster every monent.Calculus finds his rate at any instant by in effect, measuring shorter & shorter time segments.In the first bracketed period he falls at an average speed of 88ft/sec for half a sec.In the next equal period 104 feet.In two shorter periods he drops 94.4 ft per sec & 97.6 ft.The ever narrowing range finally converge to 96 ft/sec at exactly 3 sec.

Timing an object as it falls from a given height is the most straight forward method of gauging the efects of gravity.It was this technique which Galileo used about 1585 to arrive at his free fall eqn.y=16t2 ;y representing the distance fallen in ft. and t the elapsed time I sec. after the first fall.Newton further proved that it is law of nature that every free falling object falls to earth with a constant acceleration of 32ft /sec every sec.

The great Galileo & Isac newton : Gravitational force

g=32ft/sec

THEODOLITE & SEXTANT

A theodolite is a surveying instrument used for measuring horizontal and vertical angles.

A Sextant is an instrument used to measure the angle of elevation of the sun above the horizon.

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MOBIUS STRIP

Not even Picasso could paint this ring in two different colours. It proves the strip has only one side 39

KLEIN BOTTLEThree diagrams at left illustrate how a stretchable glass tube can be transformed in to A

Klein bottle. One end becomes the neck, the other the base. The neck goes through the side of the bottle& the neck & the base join, making inside continuous with the outside.

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1 x 8 + 1 = 912 x 8 + 2 = 98

123 x 8 + 3 = 9871234 x 8 + 4 = 9876

12345 x 8 + 5 = 98765123456 x 8 + 6 = 987654

1234567 x 8 + 7 = 987654312345678 x 8 + 8 = 98765432

123456789 x 8 + 9 = 987654321

1 x 9 + 2 = 1112 x 9 + 3 = 111123 x 9 + 4 = 11111234 x 9 + 5 = 1111112345 x 9 + 6 = 111111123456 x 9 + 7 = 11111111234567 x 9 + 8 = 1111111112345678 x 9 + 9 = 111111111123456789 x 9 +10= 1111111111

9 x 9 + 7 = 8898 x 9 + 6 = 888987 x 9 + 5 = 88889876 x 9 + 4 = 8888898765 x 9 + 3 = 888888987654 x 9 + 2 = 88888889876543 x 9 + 1 = 8888888898765432 x 9 + 0 = 888888888

Beauty of Math!

Brilliant, isn't it?

look at this symmetry:

1 x 1 = 111 x 11 = 121111 x 111 = 123211111 x 1111 = 123432111111 x 11111 = 123454321111111 x 111111 = 123456543211111111 x 1111111 = 123456765432111111111 x 11111111 = 123456787654321111111111 x 111111111=12345678987654321

IN 1882 A GERMAN COUPLE WORRIED THAT THEIR THREE YEAR OLD CHILD HAD NOT LEARNT TO SPEAK A WORD . HOWEVER HE GREW UP WITH THE SIDE INTEREST OF OBSCURE MATHS. WHICH EARNED HIM A NOBLE PRIZE. TILL THE DATE THE WORLD REMEMBER S HIM AS

ALBERT EINSTEIN

E = mc2

U KNOW HIM

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John Napier a Scottish mathematician invention of log table. He also is known for an invention of a slide rule.

HELLO,HOPE U R WITH ME. THEN JUST READ IF THESE INTEREST U.

1550-1617

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Pythagoras, Greek mathematician, formulated the Pythagoras, theorem.

580-500a.c.

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Sir Isaac Newton’s greatest contribution to mathematics was the invention of calculus.

A picket fence is a simple key to integration. Calculus solves the problem by dividing the area in to small intervals so that the top becomes negligible.

The lines show average growth rate for successive periods. But for the instant it is shown by a gradient of the tangent.

1642-1727

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Rene Descartes, a French mathematician and philosopher, invented analytic(co-ordinate) geometry.

(3,5)

x

yCartesian plane is named after him.

1596-1650

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Carl Friedrich Gauss along with Archimedes and Newton, Carl Friedrich Gauss has been called the greatest mathematician ever. He contributed in the field of astronomy, surveying & electromagnetism.

1777-1855

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Charles Babbage British Mathematician & Engineer develop an early computer.

1791-1871

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INDIA IS PROUD OF U & INDEBTED TO U FOR EVER

• Aryabhatta: gave the value of Pi. For his astronomical contributions India’s first satellite was named after him.

• Brahmagupta: Developed a decimal system by giving Zero.

• Bhaskara: developed Trigonometry.

• Jayant Naralikar : Theory of relativity.

• S.N.Bose : an eminent statistician

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INTERESTING !!! If U are AWAKE.

• 1729? As I told you earlier at schol Ramanujan was a studnt star in Maths.He went beyond what was tought in class.Fascination for the beauties in maths overpowered him.1729 is the famous taxi no.which is often mentioned in narrating his love for nos.While in the U.K. Prof. Hardy visited him in the hospital as Ramanujan was lying ill.Hardy mentioned the no.of the taxi in which he came.At once Ramanujan gave out the property of 1729 as the smallest no.that can be expressed as a sum of two cubes in two different ways.This theory later helped immensly in solving indeterminate eqns.

Who was Leelavati? This unortunate daughter of Bhaskarachrya became a first woman mathematician as the going got tough for her. As we all know Bhaskaracharya was a great astronomer & had developed a science of astronomical calculations. He had calculated an auspicious muhurtam for his daughter to get married. However he also knew something which made him worry. What was that U want me to tell? THIS IS JUST TO SEE HOW MANY OF U ARE STILL AWAKE!!Ok so the story goes.

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• I HOPE THIS TALK PROMOTES THE LOVE FOR MATHEMATICS & DEVELOPES BETTER UNDERSTANDING.

• I AM GRATEFUL FOR YOUR PRESENCE AND INTERACTION.

• Hope this orientation helps in redefining maths

• I REQUEST YOU TO GIVE CANDID OPINION FOR FURTHER IMPROVEMENT ON THIS EFFORT TO PROMOTE LOVE FOR MATH AND HELP REDUCE THE FAIL %.

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This was a humble effort to demonstrate the power and sophistication of these ideas, and explore how mathematics teaching can be structured to resonate with children's sophisticated thinking.

Made by Alka Damle 54

Across2. The result in multiplication (7)5. Approximately equal to 3.1415 (2)7. Number added to another in addition (6)9. The bottom number in division (7)10. A positive or negative whole number (7)12. A sign used in subtraction (5)13. Amount of space taken up by a 3D object (6)18. 1/2 or 3/4, for example (8)20. This shape has all points at the same distance from its center (6)21. The 3 or the 2 in 3 X 2 = 6 (6)22. Is identical in value (6)23. Figure formed by two lines extending from the same point (5)24. Take away (8)

Down1. Rectlinear closed figure with three sides3. Angle greater than 90 degrees and less than 180 degrees is this (6)4. Longer dimension of a rectangle (6)5.  ____ sign is used in addition (4)6. Sharing a pizza between friends requires this kind of operation (8)8. For finding total you need to this operation11. To determine the product (8)14. A gram, a foot or 87 degrees (7)15. A three-sided figure having two equal sides (9)16. The answer in a division problem (8)17. A quadrilateral with four sides equal (6)19. An angle measuring less than 90 degrees (5)

MATHEMATICS : A JOY RIDE

Mathematical Crossword

Time 5 mts.

55

Across2. The result in multiplication (7)5. Approximately equal to 3.1415 (2)7. Number added to another in addition (6)9. The bottom number in division (7)10. A positive or negative whole number (7)12. A sign used in subtraction (5)13. Amount of space taken up by a 3D object (6)18. 1/2 or 3/4, for example (8)20. This shape has all points the same distance from its center (6)21. The 3 or the 2 in 3 X 2 = 6 (6)22. Is identical in value (6)23. Figure formed by two lines extending from the same point (5)24. Take away (8

Down1. Rectlinear closed figure with three sides3. Angle greater than 90 degrees and less than 180 degrees is this (6)4. Longer dimension of a rectangle (6)5.  ____ sign is used in addition (4)6. Sharing a pizza between friends requires this kind of operation (8)8. For finding total you need to this operation11. To determine the product (8)14. A gram, a foot or 87 degrees (7)15. A three-sided figure having two equal sides (9)16. The answer in a division problem (8)17. A quadrilateral with four sides equal (6)19. An angle measuring less than 90 degrees