Play and fun with mathematics

1. Mathematics A subject …also be a part of life Play and fun with mathematics Mrs. Seema Ramakrishna SHARP INSTITUTE We sharpen the brains…

2. Mathematics A subject …also be a part of life Play and fun with mathematics Mrs. Seema Ramakrishna SHARP INSTITUTE Redefining the learning process

3. Magic Squares Power of Maths Magic squares of order 3x3 Magic squares of order 5x5 Magic squares of order 6x6 Diabolic Magic Square of Khajuraho Super magic square(s)

4. Magic Square 6 8 1 7 3 5 An oldest Magic Square of China 4 9 2

5. Napier Multipliation strips

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7. Multiplication of 9 by using fingeres

8. 7 X 8 = 50 + 6 = 56 Multiplication of 6 to 10 by using fingers

9. Another way of multiplication 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…………

10. 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

11. 1, 3, 6, 10, …. 1, 4, 9, 16, 25, …. 1+3+5+7+9+11+13 = 49 =72 TRY yourself for other patterns……….

12. Geoboard Fig.2 Fig.1 Fig.4 Fig.3 ?

13. General 8. Can you arrange 12 match sticks in three different rectilinear figures with areas 6 sq.units, 5 sq. units and 4 sq. units? 1 1 1 2 1 1 5 4 1 1 1 2 3 1 2 1 AREA = 6 Sq. units AREA = 5 Sq. units AREA = 4 Sq. units

14. Algebraic identities ... Jolm-8

15. Algebraic Identity a2 a.b a.b b2 ( a + b ) 2 = a2 + 2ab + b2

16. Algebraic Identity (a - b)2 a.b a a.b b2 b b2 b a ( a - b ) 2 = a2 - 2ab + b2

17. Jolm-3 Can mathematics be fun ?

18. AREA of a Triangle = 1/2 BASE x Corresponding ALTITUDE A D h E A’ A” ½ h B C b

19. 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.

20. AREA of a rectangle = BASE x Corresponding ALTITUDE = BC x BA’ = b x ½ h D E A’ A” ½ h B C b

21. Now we have to show that area of rectangle G’BCG” = ar.(  ABC) 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

22. Jolm-7 Area of a circle 3 4 2 5 1 6 12 7 11 8 10 9

23. On arranging sectors, we get a parallelogram as follow: -(A limiting case) 11 7 1 3 5 9 2 4 8 12 6 10 Area of a circle = Area of ||gm = base x altitude = ½ circumference x radius = ½ x 2 R x R = R2 .

24. Pythagoras Theorem

25. Baudhyayan Sulva Sutra A E a 3 c c b 1 2 B D Indian Proof of Pythagoras Therorm a b C 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

26. CBSE board makes that the mathematics laboratory and the projects are the compulsory for the academic. Setting up the mathematics laboratory and making mathematics projects are not as easy as physics and chemistry. • We are very glad to inform you that our institute ‘SHARP INSTITUTE’ is conducting various mathematics workshops and programs by which we can train and guide your teachers and students in setting up mathematics laboratory and projects. CONTACT US EMAIL: sharpinstitute@gmail.com