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1 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.

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Presentation on theme: "1 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."— Presentation transcript:

1 1 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 Point of intersection of altitudes of a triangle

2 TRY TRY, DONT CRY MATHS IS FUN & JOY 2 01 March am to 10 a.m

3 TIME TO GETUP THREE RS 3 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.

4 TIME TO SLEEP EARLY TO BED, EARLY TO RISE MAKES THE PERSON HAPPY & WISE HAPPY & WISE 4

5 RESULT 5

6 TEACHER ? MOTHER ? Who is responsible for creating MATHSPHOBIA in the childs 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? 6

7 Lack of practice? 7 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.

8 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 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 in ? INDIAN GENIUS 8

9 Story time Once the inspector visited the school. He entered the 4 th 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 dont you want to give It a try? Pat came the reply, sir, it's not a big deal. Answer is 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, ) 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

10 10 Of course, mathematical prodigies are born, not made. But it does beg the question: "If somebody who can't even read or write is able to perform these kinds of breathtaking calculations, what stops other people from doing even simple sums?" Clearly, something went wrong along the way. Young children naturally enjoy numbers. And even people who now have an intense dislike for math often say they once enjoyed it. What has happened to them is generally an unfortunate event in their past. Perhaps they were ridiculed for a mistake they made with numbers, in front of the entire class. Maybe they missed some crucial math lessons and never really caught up. perhaps they were taught to handle numbers mechanically - when what they really needed was some explanation of why the numbers work the way they do. Whatever the specific reason, bad experiences with numbers left an emotional scar, which developed into a phobia to keep the sufferer safe from further harm. So let us try to analyse this so called MATHPHOBIA

11 Internet blogs 11 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

12 12 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 Z Is represented as: If: H-A-R-D-W-O-R- K = 98% And: K-N-O-W-L-E-D-G-E = 96% But: A-T-T-I-T-U-D-E = 100% L-O-V-E -O-F- G-O-D / FAITH = 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%?

13 LEARN WHILE YOU PLAY PAPER FOLDING PAPER FOLDING CRAFT WORK CRAFT WORK TEACHING AIDS TEACHING AIDS ADDITIONAL INFORMATION ADDITIONAL INFORMATION FALLACIES/PUZZLES FALLACIES/PUZZLES 13

14 LEARN TO ANSWER WHY & HOW ? A B C B C A B C A B C A 14

15 Some Algebraic Facts (a+b) 2 a b a b b a b a2a2 b2b2 = a 2 + 2ab+ b 2 (a+b) 2 geometrically gives area of a square whose sides are (a+b) units. Pascal triangle 1 = = (10 + 1) 1 = (10 + 1) 2 = (10 + 1) 3 = (10 + 1) 4 = (10 + 1) 5 Sequence of the numbers of the Pascals triangle represent the binomial coefficients in the expansion of (x+y) n SIMPLE RESULTS 15 (10+1) 0

16 Some Algebraic Facts (a+b+c) 2 = a 2 +b 2 +c 2 +2ab+2bc+2ac AL-G-BAR a2a2 ab ac b2b2 c2c2 ab ac bc a b c 16

17 17 SUM OF THE ANGLES OF REGULAR POLYGONS Shape of the regular polygon No. of sides & angles Rule of Sum of the angles Sum of the angles Rule for measure of each angle Degree measure of each angle 3180 (3-2) (3-2) (4-2) (4-2) (5 -2) (5-2) (6-2) (6-2) n180(n -2) n 180(n-2) n

18 MATHS CRAFT 1 Mathematics stimulates the imagination, anchors speculation, and promotes an awareness of reality. 18 Helpful website:

19 19 2 r h=r Area of a = ½ base X height =1/2 X 2 r X r = r 2 = 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 2r

20 20 l= length b= breadth Area= l X b sq.units l = 2 r b=h, height CSA =l Xb =2 r h r Total surface area of a solid cylinder = 2 rh + 2 r 2 sq.units

21 21 Volume of a cylinder = r r Volume of a cuboid = lXbXh= r. r. h= r 2 h= volume of a cylinder h h r

22 Making a Cube Making a Triangular Prism

23 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 = x6x =144 sq.cms. 12cms 6 o o CRAF T ` cms. O 18

24 UNDERSTAND BETTER SQUARE PYRAMID HEXAGONAL PYRAMID 24

25 MATHS THROUGH CRAFT ACTIVITY HEXAGONAL PRISM 25

26 26 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.

27 Linear equations FATHER OF ALGEBRA 5 years later he had a son The riddle begins, Diophantus youth lasted 1/6 of his life. He grew a beard after 1/12 more after 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/ x/2 + 4, which reduces to 3x/28 = 9 telling us Diophantus was 84 years old when he died. 27

28 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= tortoise will be always ahead of the Achilles, even if by a mere eyelash

29 Scratch ur head Let x=2 ; x(x – 1) = 2 ( x – 1) ;x 2 - x = 2x -2 ; x 2 – x –x = 2x – 2 – x ; x 2 – 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= what next? 371= ; 407= 4 3 +o Palindromes: both ways read same e.g.57+75= =363 29

30 Numeral & NUMBER WHICH NUMERAL IS SMALLER? WHICH NUMBER IS SMALLER? 30

31 Fibonacci Numbers FIBONACCI One month old New borne Sequence is 1, 1, 2, 3, 5, 8, 13, ………if youve ever thought maths wasnt 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. 31

32 Calling someone a SQUARE is an insult but calling them a GOLDEN RECTANGLE isnt 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 = 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. A G B 32 =1.6 :1

33 RELATION & FUNCTION 33

34 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. 34

35 CONVERGENCE 35

36 Vector analysis VECTOR ANALYSIS Shooting at a target on a windy day is a problem illustrating one of Carl Gausss 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 V 1.The rifleman compensates by moving his gun slightly left of the target as represented by vector V 2.The bullet flies in a compromise pathway to the bulls eye along the line R. V1V1 V2V2 R 36

37 37 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=16t 2 ;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

38 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. 38

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

40 KLEIN BOTTLE Three 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. 40

41 41 1 x = 9 12 x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x 9 +10= x = x = x = x = x = x = x = x = Beauty of Math! Brilliant, isn't it? look at this symmetry: 1 x 1 = 1 11 x 11 = x 111 = x 1111 = x = x = x = x = x =

42 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 = mc 2 U KNOW HIM 42

43 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

44 Pythagoras, Greek mathematician, formulated the Pythagoras, theorem a.c. 44

45 Sir Isaac Newtons 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

46 Rene Descartes, a French mathematician and philosopher, invented analytic(co-ordinate) geometry. (3,5) x y Cartesian plane is named after him

47 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

48 Charles Babbage British Mathematician & Engineer develop an early computer

49 INDIA IS PROUD OF U & INDEBTED TO U FOR EVER Aryabhatta: gave the value of Pi. For his astronomical contributions Indias 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 49

50 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. 50

51 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 %. 51 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.

52 52 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 Point of intersection of altitudes of a triangle

53 ACROSS: 1) 1729, famous constant (8) 3) Numbers which are divisible by 2 4) The normal which is perpendicular to the osculating plane and a unit vector along it (8) 5) Point of intersection of perpendiculars drawn form the vertices of a triangle to the opposite sides (11) 7) Line joining the vertex to the midpoint of the opposite side of a triangle (6) 11) A straight line joining any two points on the circumference of a circle (5) 12) A subset of a sample space of a random experiment(5) 13) The rate of change of displacement (8) 14) Volume of this is 1/3 of the cylinder 15) Triangle having all its sides unequal(7) 16) Matrix obtained by interchanging rows and columns (9) MATHEMATICS : A JOY RIDE Mathematical Crossword DOWN: 1) A quadrilateral which has all its sides equal but its angles are not right angel. 2) The arrangement of elements in rows and columns in a rectangular bracket, (6). 6) Directed line segment having direction as well as magnitude.(6) 8) A set which contains no elements at all is called –set (4) 9) A set A { 1,2,3 …N} for some n N.(6) 10) The quantity x+ -1y, where x and y both are real X X X 53

54 Made by Alka Damle 54 Across 2. The result in multiplication (7) 5. Approximately equal to (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) Down 1. Rectlinear closed figure with three sides 3. 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 operation 11. 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 55 Across 2. The result in multiplication (7) 5. Approximately equal to (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 Down 1. Rectlinear closed figure with three sides 3. 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 operation 11. 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


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