MATHEMATICS : A JOY RIDE

1
MATHEMATICS A JOY RIDE
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
Mathematical Crossword
Across 1 an exterior angle of any angle
lt180 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
2
TRY TRY, DONT CRY
WELCOME
01 March 2011
8-15 am to 10 a.m
MATHS IS FUN JOY
3
THREE RS
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 GETUP
4
HAPPY WISE
EARLY TO BED, EARLY TO RISE MAKES THE PERSON
HAPPY WISE
TIME TO SLEEP
5
RESULT
REPORT CARD
ENGLISH
GOOD
HINDI
FAIR
SST
POOR
SCIENCE
SATISFACTORY
MATHS
Oh! GOD!
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FEAR/MENTAL BLOCK/DISLIKE?
Who is responsible for creating MATHSPHOBIA in
the childs mind?
MOTHER ?
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.
7
Lack of practice?
MATHS IS LEARNT ONLY BY DOING. DOING DEVELOPES
UNDERSTANDING SUCH A BEAUTIFUL LOGIC, NO
MUGGING FIND SO EASY, FOR EVER RECALLING.
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.
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INDIAN GENIUS
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?
9
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 dont 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 1001992,------5051) One gets 50 such
  pairs. Hence the answer is 101x505050. 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.

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
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Internet blogs
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.comvideomathtutor.com
articlesbase.com mathworks.in,futureschannel.co
m many more. Just type mathphobia or remedial
teaching in math in Google search
12
From a strictly mathematical viewpointWhat
Equals 100? What does it mean to give MORE than
100?
IfA 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 as1 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.IfH-A-R-D-W-O-R- K8118423151811
98AndK-N-O-W-L-E-D-G-E11141523125475
96ButA-T-T-I-T-U-D-E120209202145
100 L-O-V-E -O-F- G-O-D / FAITH
12152251567154 101
Therefore, one can conclude with mathematical
certainty thatWhile 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!
13
LEARN WHILE YOU PLAY

• PAPER FOLDING
• CRAFT WORK
• TEACHING AIDS
• ADDITIONAL INFORMATION
• FALLACIES/PUZZLES

14
LEARN TO ANSWER WHY HOW ?
C
B
A
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SIMPLE RESULTS
Pascal triangle
Some Algebraic Facts
(101)0
(ab)2
a2 2ab b2
1 1
1 1 2 1 1 3 3 1
1 4 6 4 1 1 5 10 10 5 1

Sequence of the numbers of the Pascals triangle
represent the binomial coefficients in the
expansion of (xy)n
(ab)2 geometrically gives area of a square whose
sides are (ab) units.
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AL-G-BAR
Some Algebraic Facts
(abc)2
a2b2c22ab2bc2ac
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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
3 180 (3-2) 180 180(3-2) 3 60
4 180 (4-2) 360 180(4-2) 4 90
5 180 (5 -2) 540 180(5-2) 5 108
6 180(6-2) 720 180(6-2) 6 120
n 180(n -2) 180(n-2) 180(n -2) n 180(n-2) n
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MATHS CRAFT 1
Mathematics stimulates the imagination, anchors
speculation, and promotes an awareness of
reality.
Helpful website www.scribd.com/doc/2726617/chapte
r-11
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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
r
hr
2 ? r
Area of a ? ½ base X height 1/2 X 2?r X r
? r2 Area of a circle
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l length
Area l X b sq.units
b breadth
r
Total surface area of a solid cylinder
2 ?rh 2 ?r2 sq.units
l 2 ? r
bh, height
CSA l Xb 2 ? r h
21
Volume of a cylinder
Volume of a cuboid lXbXh?r . r . h ? r2
h volume of a cylinder
? r
h
h
r
? r
22
Making a Cube
Making a Triangular Prism
4
5
3
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CRAFT
To make a cone and find its surface area and
volume
12cms

• Materials required
• A square piece of thin cardboard of side 12 cm
• A thick square cardboard of side
• 36 cm each
• Scissors, Adhesive, Compasses
• Bring the edges OA OB together .Stick
  them.Attach the circular piece above to the
  bottom of the cone formed.
• Length of the arccircumference of the circle as
• 2 ? x6 2 ? x18 x120/360 12 ?cm
• l slant height 18cms.
• CSA ? r l ? x6x18108? sq.cms.
• TSA ? x6x6 108 ? 144 ? sq.cms.

6
o
o
36
120
120
18
18
18
O
120
18
36cms.
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UNDERSTAND BETTER

• SQUARE PYRAMID

• HEXAGONAL PYRAMID

25
MATHS THROUGH CRAFT ACTIVITY
HEXAGONAL PRISM
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Sharpen your reasoning with puzzles
Change the direction of the fish moving 3 sticks.
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?
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FATHER OF ALGEBRA
Linear equations
The riddle begins, Diophantus youth lasted 1/6
of his life.
5 years later he had a son
He grew a beard after 1/12 more
after 1/7 more of his life he married
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.
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
28
ACHILLES FOOT
Achilles and tortoise
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?
100
0
(A 100, T 110) (A 110, T 111) (A 111,
T 111.1)(A111.1,T111.11 tortoise will be
always ahead of the Achilles, even if by a mere
eyelash.
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Scratch ur head

• Let x2 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 x11112321,1111x11111234321 what next?
• 371 3 3 7 3 1 3 407 4 3 o 3 7 3
• Palindromes 56765 both ways read same
• e.g.5775132231363

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Numeral NUMBER
4
7
WHICH NUMERAL IS SMALLER? WHICH NUMBER IS SMALLER?
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FIBONACCI
Fibonacci Numbers
New borne
One month old
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.
32
GOLDEN RECTANGLE
Calling someone a SQUARE is an insult but
calling them a GOLDEN RECTANGLE isnt so bad.

This construction which is used in many temples,
mosques fits into golden rectangles.
This old man portrait of Leonardo da Vinci shows
a picture with a square subdivided into
rectangles having golden ratio.
In each of the square if you put a quarter circle
then it represents the pattern which we see in
some seashell
The ratio AGAB represent the golden ratio and is
donated by
B
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 1.41 and 1.81,credit cards,TV
,monitors etc.
A

G
1.6 1
33
RELATION FUNCTION
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.

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CONVERGENCE
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 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 bulls eye along the line R.

V2
R
V1
37
The great Galileo Isac newton Gravitational
force g32ft/sec
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.y16t2 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.
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.
39
MOBIUS STRIP
Not even Picasso could paint this ring in two
different colours. It proves the strip has only
one side
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.
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Beauty of Math!
1 x 8 1 912 x 8 2 98123 x 8 3
9871234 x 8 4 987612345 x 8 5
98765123456 x 8 6 9876541234567 x 8 7
987654312345678 x 8 8 98765432123456789 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
look at this symmetry1 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 111111111123456789876
54321
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
Brilliant, isn't it?
42
U KNOW HIM
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
43
HELLO,HOPE U R WITH ME. THEN JUST READ IF THESE
INTEREST U.
John Napier a Scottish mathematician invention of
log table. He also is known for an invention of a
slide rule.
1550-1617
44
580-500a.c.
Pythagoras, Greek mathematician, formulated the
Pythagoras, theorem.
45
1642-1727
Sir Isaac Newtons greatest contribution to
mathematics was the invention of calculus.
The lines show average growth rate for successive
periods. But for the instant it is shown by a
gradient of the tangent.
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.
46
1596-1650
Rene Descartes, a French mathematician and
philosopher, invented analytic(co-ordinate)
geometry.
Cartesian plane is named after him.
47
1777-1855
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.
1791-1871
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

50
INTERESTING !!! If U are AWAKE.
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.

• 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.

51
THANK I MUST
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.

• 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 .

52
Across 1 an exterior angle of any angle lt180 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
53
MATHEMATICS A JOY RIDE
X
1
Mathematical Crossword
2
3
X
4
5
X
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)
6
7
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 xv-1y,
where x and y both are real .
54
MATHEMATICS A JOY RIDE
Across 2. 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)
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)
Mathematical Crossword
Time 5 mts.
55
Solns to the crossword
Across 2. 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
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
The winner is----