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
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
5 closed rectilinear
figure
6 first counting machine
9 Equation represents
a straight line
7 centroid is point of
intersection of –
10 graph representing
the data
8 amount of space taken
up by a 3D object
11 triangle with all
sides unequal .
12 mean of a statistical
data
13 Father of the coordinate geometry
15 points on the same line
are ----
14 shape of a box
17 Point of intersection of
altitudes of a triangle
16 another name for
indices
18 3X4 = 4X3
1
MATHS IS FUN & JOY
TRY TRY, DON’T CRY
2
THREE R’S
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
3
HAPPY & WISE
EARLY TO BED, EARLY TO RISE
MAKES THE PERSON HAPPY & WISE
TIME TO SLEEP
4
RESULT
5
R/MENTAL BLOCK/DISLIKE?
Who is responsible for
creating MATHSPHOBIA
in the child’s 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.
TEACHER ?
6
Lack of practice?
“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.
7
INDIAN GENIUS
WHY GO SO FAR? STORY OF THE SON OF OUR OWN
SOIL SIR RAMANUJAN
Who was Srinivasa Ramanujan?
A famous Indian mathematician
1729?
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.
8
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
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
11
From a strictly mathematical viewpoint:
What Equals 100%?
What does it mean to give MORE than 100%?
If:
ABCDEFGHIJKLMNOPQRST
UVWXYZ
Is represented as:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Therefore, one can conclude
18 19 20 21 22 23 24 25 26.
with mathematical certainty that:
If:
While Hard Work and Knowledge
H-A-R-D-W-O-R- K
will get you close, and Attitude
8+1+18+4+23+15+18+11 = 98%
And:
will get you there,
K-N-O-W-L-E-D-G-E
It's the Love of God /Faith that
11+14+15+23+12+5+4+7+5 = 96%
will put you over the top!
But:
A-T-T-I-T-U-D-E
1+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%
12
LEARN WHILE YOU PLAY

PAPER FOLDING

CRAFT WORK

TEACHING AIDS

ADDITIONAL INFORMATION

FALLACIES/PUZZLES
13
LEARN TO ANSWER
WHY & HOW ?
A
C
A
B
B
C
B
A
C
B
A
C
14
SIMPLE RESULTS
Some Algebraic Facts
(a+b)2 = a2 + 2ab+ b2
a
ab
a
a2
b
b2 b
Pascal triangle
= (10+1)0
= (10 + 1)1
1 1
= (10 + 1)2
1 2 1
1 3 3 1
= (10 + 1)3
1 4 6 4 1 = (10 + 1)4
1 5 10 10 5 1 = (10 + 1)5
1
b
ab
(a+b)2 geometrically gives area
of a square whose sides are
(a+b) units.
Sequence of the numbers
of the Pascal’s triangle
represent the binomial
coefficients
in
the
expansion of (x+y)n
15
AL-G-BAR
Some Algebraic Facts
(a+b+c)2 = a2+b2+c2+2ab+2bc+2ac
a
b
c
a2
ab
ac
ab
b2
bc
ac
bc
c2
16
SUM OF THE ANGLES OF REGULAR POLYGONS
Shape of the
regular polygon
No. of
sides &
angles
3
Rule of
Sum of
the
angles
180 (3-2)
Sum of the
angles
180
Rule for
measure
of each
angle
Degree
measure
of each
angle
180(3-2)
3
60
180(4-2)
4
4
180 (4-2)
360
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
17
MATHS CRAFT 1
Helpful website:
www.scribd.com/doc/2726617/chapter-11
Mathematics
stimulates the
imagination,
anchors
speculation, and
promotes an
awareness of
18
reality.
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
h=r
2∏r
Area of a ∆ = ½ base X height =1/2 X 2∏r X r
= ∏ r2
= Area of a circle
19
l= length
b=
breadth
Area= l X b sq.units
r
b=h,
height
Total surface area of a solid
cylinder =
l =2 ∏r
2 ∏rh + 2 ∏r2 sq.units
CSA =l Xb =2 ∏ r h
20
Volume of a cylinder =
Volume of a cuboid = lXbXh=∏r . r . h= ∏ r2 h=
volume of a cylinder
∏r
h
h
r
∏r
21
Making a Cube
Making a Triangular
Prism
4
5
3
22
CRAF
T 12cms
To make a cone and find its
surface area and volume
Materials required:
o
6
o
1. A square piece of thin cardboard of
side 12 cm
2.
A thick square cardboard of side
36 cm each
1.
`36
18
18
120
18 120
O
120
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
18
36cms.
Scissors, Adhesive, Compasses
5. l = slant height =18cms.
∏ r l = ∏ x6x18=108∏ sq.cms.
6.
CSA =
7.
TSA = ∏ x6x6 + 108 ∏ =144 ∏ sq.cms.
UNDERSTAND BETTER
• SQUARE PYRAMID
• HEXAGONAL PYRAMID
24
MATHS THROUGH CRAFT
ACTIVITY
HEXAGONAL PRISM
25
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?
26
FATHER OF ALGEBRA
Linear equations
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
5 years later he
had a son
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
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
x = x/6 + x/12 + x/7 + 5 + x/2 + 4,
which reduces to 3x/28 = 9 telling us
27
Diophantus was 84 years old when he
died.
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)
(A=111.1,T=111.11 tortoise will be always ahead of the
28
Achilles, even if by a mere eyelash.
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
29
Numeral & NUMBER
WHICH NUMERAL IS SMALLER?
WHICH NUMBER IS SMALLER?
30
FIBONACCI
Fibonacci Numbers
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
Every ratio of the
Fibonacci
numbers
starting from 3/2, 5/3,
8/5, ….. is called golden
ratio more about it
Fibonacci numbers.
in the next slide.
New borne
One month old
31
GOLDEN RECTANGLE
Calling someone a “SQUARE” is an insult but calling
them a “GOLDEN RECTANGLE” isn’t so bad.
This old man
portrait of
Leonardo da
Vinci shows a
picture with a
square
subdivided into
rectangles
having golden
ratio.
The ratio AG:AB
represent the
golden ratio and
is donated by
B
A
G
1+ 5
=
2
=1.6 :1
This construction
which is used in
many temples,
mosques fits into
golden
rectangles.
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 ,monitors32etc.
RELATION & FUNCTION
33
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
CONVERGENCE
35
Vector analysis
V2
R
V1
• 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.
36
The great Galileo & Isac newton : Gravitational force
g=32ft/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.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.
37
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
38
horizon.
MOBIUS STRIP
Not even Picasso could paint this ring in
two different colours. It proves the strip
has only one side
39
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
Beauty of Math!
1x8+1=9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111
look at this symmetry:
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
1x1=1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=12345678987654321
Brilliant, isn't it?
41
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
E = mc2
ALBERT EINSTEIN
42
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
43
580-500a.c.
Pythagoras, Greek
mathematician, formulated
the Pythagoras, theorem.
44
1642-1727
Sir Isaac Newton’s
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.
45
1596-1650
Rene Descartes, a French
mathematician and
philosopher, invented
analytic(co-ordinate)
geometry.
Cartesian plane is
named after him.
y
(3,5)
x
46
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.
47
Charles Babbage
British Mathematician
& Engineer develop an
early computer.
1791-1871
48
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
49
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 story50
goes.
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
51
MATH AND HELP REDUCE THE FAIL %.
MATHEMATICS : A JOY RIDE
Mathematical 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 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)
Time 5 mts. Made by Alka Damle
54
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
55