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Mathematics. A subject …also be a part of life. Play and fun with mathematics. Mrs. Seema Ramakrishna. SHARP INSTITUTE. We sharpen the brains…. Mathematics. A subject …also be a part of life. Play and fun with mathematics. Mrs. Seema Ramakrishna. SHARP INSTITUTE. - PowerPoint PPT Presentation
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Play and fun with Play and fun with mathematicsmathematics
A subject …also be a A subject …also be a part of lifepart of life
Mrs. Seema Mrs. Seema RamakrishnaRamakrishnaSHARP INSTITUTESHARP INSTITUTE
We sharpen the brains…We sharpen the brains…
MathematicsMathematics
Play and fun with Play and fun with mathematicsmathematics
A subject …also be a A subject …also be a part of lifepart of life
Mrs. Seema Mrs. Seema RamakrishnaRamakrishnaSHARP INSTITUTESHARP INSTITUTERedefining the learning processRedefining the learning process
MathematicsMathematics
Magic squares of order 3x3
Magic squares of order 5x5
Magic squares of order 6x6
Diabolic Magic Square of Khajuraho
Super magic square(s)
1
5
8
3 7
2
6
9 4
Magic Square
An oldest Magic Square
of China
IndeIndexx 7859786 X 4 = ?7859786 X 4 = ?
11 00
77
00
88
00
55
00
99
00
77
00
88
00
66
22 11
4 4
11
6 6
11
0 0
11
8 8
11
4 4
11
6 6
11
2 2
33 22
11
22
44
11
55
22
77
22
11
22
44
11
88
44 22
8 8
33
2 2
22
0 0
33
6 6
22
8 8
33
2 2
22
4 4
55 33
55
44
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22
55
44
55
33
55
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33
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66 44
22
44
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44
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66
77 44
99
55
66
33
55
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88 55
66
66
44
44
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77
22
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66
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3 3
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2 2
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5 5
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1 1
66
3 3
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2 2
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31439144
Multiplication of 9 by using fingeres
Multiplication of 6 to 10 by using fingers
7 X 8 = 50 + 6 = 56
Example 18 x 24 = ? 18 x 24 Cancel even (18) 9 x 48* Take 48 4 x 96 Cancel even (4) 2 x 192 Cancel even (2) 1 x 384* Take 384 Product of 18 & 24 is
48 + 384 = 432 Now You Try 32 x 40…………
Another way of multiplication
The interesting products
12345679 x 9 = 11,11,11,111 12345679 x 18 = 22,22,22,222 12345679 x 27 = 33,33,33,333 12345679 x 36 = 44,44,44,444 12345679 x 45 = 55,55,55,555 12345679 x 54 = 66,66,66,666 12345679 x 63 = 77,77,77,777 12345679 x 72 = 88,88,88,888 12345679 x 81 = 99,99,99,999
1, 3, 6, 10, …. 1, 4, 9, 16, 25, ….
TRY yourself for other patterns……….
1+3+5+7+9+11+13 = 49 =72
GeoboardGeoboard
?Fig.3
Fig.1
Fig.2
Fig.4
4
3 2
2
5
2
1
1
1 1
1
1
1
1
11
8. Can you arrange 12 match sticks in three different rectilinear figures with areas 6 sq.units, 5 sq. units and 4 sq. units?
AREA = 6 Sq. units AREA = 5 Sq. units AREA = 4 Sq. units
a2a.b
b2a.b
( a + b ) 2 = a2 + 2ab + b2
Algebraic Identity
(a - b)2a.b
b2a.b
( a - b ) 2 = a2 - 2ab + b2
Algebraic Identity
a
b
b
b2
a
AREA of a Triangle
= 1/2 BASE x Corresponding ALTITUDE
A
D E
B C
h
b
A’ A”
½ h
Theory :-
In fig.1.1 , In ADB, ADB = 90 , DAB + ABD = 90 Similarly in ADC , DAC + AC D = 90
But from fig1.1 & 1.2, we get DAB = G’A’E also DAC = G’’A’’ F
Therefore , G’A’E + EBC = G’B C = 90 and G”A”F + FCB = G”CB = 90 So G’BC + G”CB = 180 => A+ B+C = 180
Thus we verified the sum of the interior angles of a triangle is 180. Now again, EF = EG’ + FG” = ½ BC, Hence , BC = G’G” and clearly A’G’ = A”G” & A’G’ // A”G” => G’BCG” is a rectangle.
AREA of a rectangle = BASE x Corresponding ALTITUDE
= BC x BA’
= b x
D E
B C
½ h
b
A’ A”
½ h
ar (ABC ) = ar (rect G’BCG”) Why ?
= BC x G’B
= BC x ½ AD ( since G’B = GB = AG )
= ½ BC x AD
= ½ Base x Altitude.
Thus we verified that
Area of a triangle = ½ Base x Altitude
Now we have to show that
area of rectangle G’BCG” = ar.( ABC)
12
6
910
11
7
8
2
3 4
5
1
8
7
6
5
4
3
2
1
12
11
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9
On arranging sectors, we get a parallelogram as follow: - (A limiting case)
Area of a circle = Area of ||gm
= base x altitude
= ½ circumference x radius
= ½ x 2 R x R
= R2 .
E
DCB
A
bc
c
b a
a
Baudhyayan Sulva Sutra
Proof : ar.( trap.) = ar.(1 ) + ar.(2 ) + ar.(1)
½ (a+b) (a+b) = ½ a.b + ½ a.b + ½ c2
½ a2 + ½ b2 + a.b = a.b + ½ c2
a2 + b2 = c2
3
21
•CBSE board makes that the mathematics CBSE board makes that the mathematics laboratory and the projects are the compulsory for laboratory and the projects are the compulsory for the academic. Setting up the mathematics the academic. Setting up the mathematics laboratory and making mathematics projects are laboratory and making mathematics projects are not as easy as physics and chemistrynot as easy as physics and chemistry. .
We are very glad to inform you that our We are very glad to inform you that our institute ‘SHARP INSTITUTE’ is conducting institute ‘SHARP INSTITUTE’ is conducting various mathematics workshops and various mathematics workshops and programs by which we can train and guide programs by which we can train and guide your teachers and students in setting up your teachers and students in setting up mathematics laboratory and projects. mathematics laboratory and projects.
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