# Play and fun with mathematics

Post on 09-Jan-2016

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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 PresentationTRANSCRIPT

Play and fun with mathematicsA subject also be a part of life Mrs. Seema RamakrishnaSHARP INSTITUTEWe sharpen the brains MathematicsPlay and fun with mathematicsA subject also be a part of life Mrs. Seema RamakrishnaSHARP INSTITUTERedefining the learning process MathematicsMagic squares of order 3x3Magic squares of order 5x5Magic squares of order 6x6Diabolic Magic Square of KhajurahoSuper magic square(s) 1 5 8 3 7 2 6 9 4Magic SquareAn oldest Magic Square of China31439144Index 7859786 X 4 = ?10 70 80 50 90 70 80 621 4 1 6 1 0 1 8 1 4 1 6 1 2 32 12 41 52 72 12 41 842 8 3 2 2 0 3 6 2 8 3 2 2 4 53 54 02 54 53 54 03 064 24 83 05 44 24 83 674 95 63 56 34 95 64 285 66 44 07 25 66 44 896 3 7 2 4 5 8 1 6 3 7 2 5 4 107 08 05 09 07 08 06 0 Multiplication of 9 by using fingeresMultiplication of 6 to 10 by using fingers 7 X 8 = 50 + 6 = 56Example18 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 40Another 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 = 99,99,99,9991, 3, 6, 10, .1, 4, 9, 16, 25, .TRY yourself for other patterns.1+3+5+7+9+11+13 = 49 =72Geoboard?Fig.3Fig.1Fig.2Fig.4a2a.bb2a.b( a + b ) 2 = a2 + 2ab + b2 Algebraic Identity(a - b)2a.bb2a.b( a - b ) 2 = a2 - 2ab + b2 Algebraic Identityabbb2aAREA of a Triangle = 1/2 BASE x Corresponding ALTITUDEADEBChbAA 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 = GAE also DAC = GA F Therefore , GAE + EBC = GB C = 90 and GAF + FCB = GCB = 90 So GBC + GCB = 180 => A+ B+C = 180 Thus we verified the sum of the interior angles of a triangle is 180. Now again, EF = EG + FG = BC, Hence , BC = GG and clearly AG = AG & AG // AG => GBCG is a rectangle. AREA of a rectangle = BASE x Corresponding ALTITUDE= BC x BA= b x DEBC hbAA h ar (ABC ) = ar (rect GBCG) Why ? = BC x GB = BC x AD ( since GB = GB = AG ) = BC x AD = Base x Altitude. Thus we verified that Area of a triangle = Base x Altitude Now we have to show that area of rectangle GBCG = ar.( ABC)126910117823451876543211211109 On arranging sectors, we get a parallelogram as follow: - (A limiting case)Area of a circle = Area of ||gm = base x altitude= circumference x radius= x 2 R x R= R2 .EDCBAbccbaa Baudhyayan Sulva SutraProof : ar.( trap.) = ar.(1 ) + ar.(2 ) + ar.(1) (a+b) (a+b) = a.b + a.b + c2 a2 + b2 + a.b = a.b + c2 a2 + b2 = c2 321CBSE 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 USEMAIL: sharpinstitute@gmail.com

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