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Happy Maths 2: Shapes and Data

Module by: Mala Kumar, Angie Upesh. E-mail the authors

A picture of the book title.
Happy Maths 2: Shapes and Data

Logo reading: Read India, an Imprint of Pratham Books
This series is sponsored by Pals for Life


Original Story (English)
Happy Maths - 2
Shapes and Data by Mala Kumar
©Pratham Books, 2007

First Edition 2007
Illustrations: Angie & Upesh
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.

Introduction

A picture of two children happily writing in a book.
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.

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.

A picture of two children playing. A girl is jumping rope.

The Funny Cricket Ground

A picture of of a cartoon one and zero waving and smiling.
Zzero: 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.

Sometimes, when one of the boys is a bit lazy and does not measure the distance between two pegs carefully, the shape of the field changes. When a match is boring, the crowd stays away.

A picture of A picture of an empty cricket field with boundary.
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!

A picture of a picture of a cricket field with a game in progress and a crowd pushing against the boundary, distorting it.
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.

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.

A picture of a picture of three cricket players giving their opinions on the type of field shape they prefer.

Exercise 1

Draw cricket fields in different shapes. Do all these shapes have names?

Solution

A picture of five standard shapes.
Some shapes do not have names. In mathematics, a section of study is called geometry. Under this section we study shapes called triangles, squares, rectangles, parallelograms, circles and some others.

Exercise 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?

Solution

A picture of five standard shapes.
Three straight lines on a single plane will form a triangle. So we need at least three straight lines to form a closed figure like a cricket ground. Try to see what happens when you keep extending the triangular shape by adding one more straight line to the formation. (You get a square, a pentagon, a hexagon…. and finally a circle!) And one curved line is enough to form a closed figure… a circle!

Exercise 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?

Solution

A picture of five more shapes.
Zzero would like to play in a field whose boundary makes a circle. That way every point on the boundary rope would be approximately the same distance from him.

Exercise 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?

Solution

Pitch length = 20m, Midpoint 4. t=202=10m t 20 2 10m . Radius of circle= 10+65=75 10 65 75 m Circumference of a circle= 2πr 2 r where 227 22 7 , r=radius, Circumference = 2×22775=471 2 22 7 75 471 metres (approximately)

A picture of a cricket player ready for his pitch.

Example 1: Try This:

In a circle, the centre O is equidistant from every point on the circle.

A picture of a circle and its radius representing the pitch length from the mound.
Pitch length = 20m Radius of circle= 10+65=75 10 65 75 m Circumference of a circle is given by the formula - Circumference 2πr 2 r

What's π π?

Pi is a value. When you divide the circumference of a circle by its diameter, you always get 227 22 7 .

Take any circle. Measure its circumference. Measure its diameter. Divide the circumference by its diameter. Answer 227 22 7 .

A picture of a cartoon one and zero smiling holding a cricket bat and ball.
Eka:What if I take a BIG circle, Zzero?
Zzero:Try it, Eka, or take a tiny circle. The answer will always be the same!

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.”

A picture of a young boy and girl on the floor looking at floor designs.
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.

A picture of two concentric square designs on the floor.
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.

A picture of a young girl placing flowers in the square design on the floor as a boy watches.
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.

Sankhya picked up some more white powder and started humming 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.

Exercise 5

Do you like to do freehand drawing? Can you draw this figure without lifting your pencil off the paper or retracing your lines?

A picture of a freehand rangoli design pattern on the ground.

Solution

There are 3 steps to this rangoli.

A picture of a 3 step by step process in drawing the previous rangoli pattern without removing your pencil from the ground.

Exercise 6

Draw the rangoli that Sankhya and Ganith drew and then decorated with flowers.

Solution

Hope you enjoyed drawing a design and decorating it with flowers!

A picture of the floor pattern decorated with flowers.

Exercise 7

How many sharp ‘corners’ does this figure have?

Solution

8 corners. In geometry, these are called angles.

A picture of two concentric squares with all 8 internal angles labeled 1-8.

Exercise 8

How many flowers did Sankhya use to decorate the rangoli?

Solution

16. She arranged four flowers in a row. In a square, the sides 4. are equal. So if there were four flowers in a row, there would be four in a column. 4+4+4+4=16 4 4 4 4 16 . A simpler method is to multiply 4 (in a row) by 4 (in a column). 4×4=16 4 4 16 .

Exercise 9

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!)

A picture of a complex floor design featuring a flower.

Solution

Solution not present.

Zzeros Chatter

A picture of of a cartoon one asking zero a tricky question.
Eka:ZZero, do you know what 2D and 3D mean?
Zzero:Are they the classes in which Neela and Suresh study, Eka?

A picture of a cartoon one explaining what 2 and 3D mean to the cartoon zero.
Eka:No, no, Zzero. 2D stands for two dimensions. Length, and height and width are all dimensions. We use them to measure the size of an object.
Zzero:So 3D means three dimensions!

A picture of a cartoon one complimenting the smiling zero.
Eka:Very smart, Zzero!

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.

A picture of a young boy Ganith jumping in jubilation in from of the television.

Data

Data is nothing but information.

Actually, the singular of data is datum. Funny word!

We use data to form opinions, to make arrangements, to organise matters and to inform others.

Sankhya and her family used the data from the news on television to organise their time. Mathematical data is very useful too.

We use mathematical data, also called statistics, in many ways.

Different forms of data:

A picture of a newspaper and television.
On television.

A picture of a pie chart.
in a Newspaper

A picture of bar graph.
Charts and Statistics.

A picture of a girl presenting a report on averages in front of a blackboard.
Sankhya likes writing tests. Her marks indicate 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 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!

Mode

What have most students in Sankhya's class scored?
A picture of a chart of students scores and their frequency.
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.

A picture of number line showing the scores of the students and the median of the scores, 63.
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+652=1262=63 61 65 2 126 2 63 )

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 answersheets,” requested Amma.

A picture of a girl reading a newspaper.
‘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.

A picture of a confused girl helping her mother sort through paperwork in a worried state.
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.

Example 2

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.

Now, lets go back to the newspaper.

Schools send their lists with the names of students to a Central Board. After the papers are corrected, the Central Board makes a list with the names of all the students and their marks.

People called Analysts or Statisticians read this information, understand it, and write it in the form of tables so that we can understand the information easily.

The table is given to newspapers, television channels and to all the schools in the country immediately.

Over 6,00,000 students wrote the Class 10 examinations in the CBSE Board in 2006.

“And lakhs of students must have written the Class 10 exams of other Boards too, isn’t it ?” asked Sankhya.

A picture of a diagram showing how data is analyzed and interpreted into media by statisticians.
“Yes, Sankhya. Now call Ganith and I’ll teach you how to make rotis.”

A picture of Sankhya rolling rotis.

A picture of an oblong roti. Sankhya’s roti looked like this. (An Oblong)

Amma’s roti looked like this.(Perfect Circle) A picture of a roti in a perfect circle.

A picture of a shapeless roti. Ganith’s roti looked like this. (Shapeless)

Exercise 10

If the full roti represents the 100 percent of students who took up the Class X CBSE examination, what part of the roti would represent the pass percentage?

Solution

Half a roti.
A picture of a face in a roti, half smiling, half frowning.

Exercise 11

Students write examinations either in Urban Centres or Rural Centres. What part of the roti would represent the percentage of students who have passed from Rural Centres?

Solution

90%.
A picture of a roti divided into 90% and 10%.

Exercise 12

Take another roti. Can you show the percentage of boys who have secured a first class?

Solution

70%. 30 % of those who passed did not get a first class.
A picture of divided into 70% and 30%.

A picture of Ganith holding a shapless roti.

A picture of Ganith molding his roti into a star shape.

Reading a Picture

A picture of Eka and Zzero holding up a chart.
A chart can be of many kinds.

It is an easy-to-understand representation of information. A chart in mathematics can be very helpful. Take a look at the chart presented here. The vertical line shows average marks of a class, 0 to 100. Average = Sum of the marks of all the students in the class divided by the number of students.

  • If the sum of marks of 40 students is 2800, then • the class average is 70 marks.
  • The coloured blocks represent the four Quarterly (Qtr) Examination marks obtained by each class.
  • Just by looking at the picture, what are the things that you can learn about the three classes?

Exercise 13

Which class has shown the most improvement?

Solution

Class 3 showed the best improvement of the three classes, from an average of below 40 marks to over 80 marks.
A picture of a bar graph that charts Class 3's progress throughout the year.

Exercise 14

Have students of Class 4 improved?

Solution

Students of Class 4 have improved from getting an average of 42 marks to over 70 marks.
A picture of a chart showing Class 4's progress throughout the year.

Exercise 15

What can you say about Class 5 students?

Solution

Class 5 students did not do as well in the final exam as in the previous examination.
A picture of a chart showing Class 5's progress throughout the year.

When you see different shapes around you, study them. See if there is anything special about these shapes. Then you can record your observations in the form of charts.

Example 3: Different types of charts

A picture of pie chart.
Pie Chart

A picture of divided bar graph.
Divided Bar Graph

A picture of bar graph.
Bar Graph

A picture of line graph.
Line Graph

Conclusion

Sankhya and Ganith now enjoy reading the newspaper!

They try to convert several news items into graphs or drawings!

You can do it too!

A picture of Sankhya and Ganith drawing charts and graphs on the wall.

A picture of a young boy, Ankit.
I am Ankit. I study in class 7 and want to become a lawyer when I grow up because the law is equal for everybody. You will never see me lagging behind in disco dancing and cricket also! Thank you for buying this book. My friends and I will get to read many more books in our library because you bought this book.

Mala Kumar is a journalist, writer and editor based in Bangalore. Her stories for children have won awards from Children’s Book Trust. She discovered her love for teaching while conducting non-formal workshops in Mathematics in schools, using the day’s newspaper instead of text-books.

Angie is a graphic designer and in her spare time loves to keep busy with ceramic. Upesh is an animator who collects graphic novels and catches up with odd films in his spare time. Together they form ‘The Other Design Studio’.

A picture of Sankhya and Ganith working in a maths book.
This is a Mathematics book with a difference. There are more stories here than problems! So read the stories, take in the mixture of facts and fiction and enjoy teasing your brain.

Titles in this series

Happy Maths 1 : Numbers
Happy Maths 2 : Shapes and Data
Happy Maths 3 : Measurements
Happy Maths 4 : Time and Money

For more information on all our titles please visit www.prathambooks.org

Our books are available in English, Hindi, Tamil, Telugu, Kannada, Marathi, Gujarati, Bengali, Punjabi, Urdu and Oriya.

Pratham Books is a not-for-profit publisher that produces high-quality and affordable children’s books in Indian languages.

Age Group: 11 - 14 years
Happy Maths - 2 Shapes and Data (English)
MRP: Rs. 25.00

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