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Original Story (English) Happy Maths - 2 Shapes and Data by Mala Kumar ©Pratham Books, 2007 First Edition 2007 This series is sponsored by Illustrations: Angie & Upesh Pals for Life ISBN 978-81-8263-907-2 Registered Office: PRATHAM BOOKS No.633/634, 4th “C” Main, 6th ‘B’ Cross, OMBR Layout, Banaswadi, Bangalore- 560043. & 080 - 25429726 / 27 / 28 Regional Offices: Mumbai & 022 - 65162526 New Delhi & 011 - 65684113 Typsetting and Layout by: The Other Design Studio Printed by: xxxxxxxxxxxxx Published by: Pratham Books www.prathambooks.org All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher.
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Sankhya and Ganith have been learning a lot of things in their mathematics class. Join Sankhya and Ganith in their happy discoveries about mathematics. Zzero and Eka are friends of Sankhya and Ganith. In this book, Sankhya and Ganith learn that different shapes have different properties. They also try to understand how to make sense of all the information that they gather. 2
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Sankhya likes to skip. The last time her brother Ganith counted, she skipped a hundred and ten times in five minutes! Ganith tried it too. He skipped thirty times… tripped and fell down. It’s fun to count sometimes. Numbers are just one part of mathematics. This book tells you how you can play with mathematics. You see it can be fun almost all the time. 3
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The Funny Cricket Ground Hello, my name is Zzero. And this is my friend, Eka.That makes two of us. With you for company, we will be three. And if you get all your friends to join us…. why we can be a cricket team, or a hockey team or even the entire stadium of football fans, or…. That reminds me, I have to be at the cricket match between Aryanagar and Bhaskaragram.You see, I’m the Umpire! I hope you will help me keep count. The cricket ground in Aryanagar is large. Its boundary is not clear. Sometimes, the boys put pegs around it at equal distances and they put a rope around the pegs. The rope becomes the boundary. If the pegs are put neatly, we get a circle. 4
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Sometimes,whenoneoftheboysisabitlazyanddoesnotmeasure the distance between two pegs carefully, the shape of the field changes. When a match is boring, the crowd stays away. But when there is an interesting match, the viewers come closer and closer to the pitch and the field takes on different shapes depending on which side of the crowd is pushing in stronger! Most professional cricket grounds should be large enough to mark an oval boundary measuring 65 metres from the stumps at either end of the wicket. Official cricket fields in the world usually measure about 90 to 150 metres across. 5
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At Aryanagar, rules keep changing. Ashwin, the tallest fellow in Aryanagar wants a square field. Little Meenu wants a small, circular field. Samir, the strongest boy in Aryanagar wants a large, pentagon shaped field. 6
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1. Draw cricket fields in different shapes. Do all these shapes have names? 2. If you had to have a cricket ground with straight lines as boundaries, what is the smallest number of straight lines that you would require to form a field? 3. If a batsman hits a boundary, he gets four runs. If you were a batsman, what shape of field would you like to play on? Why? 4. In a circular field, the stumps on either end of the pitch are 65m from the boundary. The pitch is 20m long. Would you be able to tell how long the rope of the boundary should be? 7
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Try This A 65m In a circle, the centre O is equidistant from every point on the circle. 10m O Pitch length = 20m Radius of circle=10m + 65m = 75m Circumference of a circle is given by the formula - B Circumference = 2πr What’s π? Pi is a value. When you divide the circumference of a circle by its diameter, you always get 22/7. Take any circle. Measure its circumference. Measure its diameter. Divide the circumference by its diameter. Answer = 22/7. What if I take a BIG Try it, Eka, or take a tiny circle, Zzero? circle. The answer will always be the same! 8
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Floor Designs Sankhya was making a rangoli on the floor. Ganith did not like it. “Akka, why do you always make rangolis that look like jalebis? See, I will make a new rangoli.” Ganith made some straight lines on the mud floor. Sankhya giggled. “Your rangoli looks like a lot of bricks. I don’t like that.” Ganith looked up at the mango tree nearby. He drew a square to represent the tree. Sankhya drew a smaller square inside the big square to show the base of the tree. 9
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Ganith went around the garden and brought a huge mound of flowers for her to decorate the rangoli with. Sankhya started keeping the flowers on the inner square. Four flowers fitted side-by-side on one side of the inside square. After Sankhya had filled the square with flowers, she put flowers on top of these. She repeated this four times. The rangoli now looked like a solid tower. Sankhyapickedupsomemorewhitepowderandstartedhumming to herself. As she sang, her hands flew on the floor and soon she had a beautiful figure that had many curves. It did not have any sharp corners. “Akka, you are an artist!” said Ganith. 10
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1. Do you like to do freehand drawing? Can you draw this figure without lifting your pencil off the paper or retracing your lines? 2. Draw the rangoli that Sankhya and Ganith drew and then decorated with flowers. 3. How many sharp ‘corners’ does this figure have? 4. How many flowers did Sankhya use to decorate the rangoli? 5. Instead of 4, if Sankhya had used 10 flowers along each line of the inner square, how many flowers would she have needed to make a ‘tower’ 10 floors high? (Or you could say, 10 flowers high!) 11
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Zzeros Chatter ZZero, do you know Are they the classes what 2D and 3D mean? in which Neela and Suresh study, Eka? No, no, Zzero. 2D stands for two So 3D means three dimensions! dimensions. Length, and height and width are all dimensions. We use them to measure the size of an object. Very smart, Zzero! 12
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So Much Information! “Today’s weather - warm and sunny throughout the day, heavy rain expected in the evening,” said a stylish newsreader on television. “You better carry your umbrella, Sankhya,” cautioned Amma. “I think I’ll cut the grass in the backyard tomorrow,” said Father. “I’m going to make paper boats of all kinds. Yippee!” danced Ganith. 13
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Data Data is nothing but information. Actually, the singular of data is datum. Funny word! Weusedatatoformopinions,tomakearrangements,toorganise matters and to inform others. Sankhyaandherfamilyusedthedatafromthenewsontelevision to organise their time. Mathematical data is very useful too. We use mathematical data, also called statistics, in many ways. 14
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What’s Average ? Sankhyalikeswritingtests.Hermarksindicate whether she has learnt her lessons well. When she gets ‘above average’ marks she feels happy. But what does average mean? Let’s see. These are the marks out of 100 that Sankhya and her 19 classmates got in the last mathematics examination. 74, 65, 35, 57, 59, 53, 44, 88, 97, 33, 86, 88, 88, 45, 61, 79, 88, 56, 57, 67. Let us add all these marks. 74+ 65+ 35+ 57+ 59+ 53+ 44+ 88+ 97+ 33+ 86+ 88+ 88+ 45+ 61+ 79+ 88+ 56+ 57+ 67=1320. The number we get when we divide the sum by the number of students is called Arithmetic Mean, or average. 1320 divided by 20=66. Mean score in Sankhya’s class in Mathematics is 66. Anyone who gets around this has scored average marks. Students who get higher marks than the mean have scored above average marks. Students who score much less than the mean need to do much better in the next examination! 15
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Mode What have most students in Sankhya’s class scored? Let’s put the marks in ascending order, that is, from the lowest to the highest. Mode is the figure that appears most often in the list. In the list 88 is the Mode. Median Median is the number that appears in the middle of the list after you have put it in descending or ascending order. 7 57 59 61 6 88 88 33 56 5 5 6 88 97 35 44 45 53 7 7 86 88 4 79 In a group of 20 numbers, the 10th and 11th numbers are in the middle. Median is the value between these two numbers that is between 61 and 65. Median in this example is 63. (61+65 / 2 =126 / 2=63) 16
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Sankhya is Confused “In the Class 10 Board examinations, 50% of students have passed. 10% of students who have passed are from the Urban centres in the State. While 80% of girls who have passed have scored first class marks only 70 % of boys have secured first class. …..” Sankhya read from the day’s newspaper. “How did the newspaper get so much information in one day? No one came to Aryanagar to find out. So how do they know how the boys and girls in our school have fared in the examinations?” asked a very confused Sankhya. “Forget that, Sankhi, come here and help me sort these answer- sheets,” requested Amma. ‘Percent’ comes from the Latin Per Centum. Centum means 100. Percentage means ‘number of parts per hundred’. The symbol for percentage is %.50% means 50 out of 100. 17
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Sankhya’s mother is a geography teacher in Aryanagar Vidyamandir. “Put all Class 5 papers here, Class 4 papers in this pile, and Class 6 papers here.” Mother and daughter counted the number of answer copies in each class. Sankhya spent the day helping her mother to fill up the record book that had columns for Name, Marks and Comments. At the end of the day, Sankhya could guess some things clearly: • There were more number of students in Class 4 than in Class 5. • The Class 6 answer papers were thicker than the answer papers of Class 4. • More girls in Class 6 had passed than boys. • Equal number of girls and boys had passed in Class 4. 18
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