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.

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.

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.

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.

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.

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.

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.

Eka:ZZero, do you know what 2D and 3D mean?
Zzero:Are they the classes in which Neela and Suresh study, Eka?

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!

Eka:Very smart, Zzero!

“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.

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:

On television.

in a Newspaper

Charts and Statistics.

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?

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.

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 )

“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.

‘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.

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.

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.

“Yes, Sankhya. Now call Ganith and I’ll teach you how to make rotis.”

Sankhya’s roti looked like this. (An Oblong)

Amma’s roti looked like this.(Perfect Circle)

Ganith’s roti looked like this. (Shapeless)

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.

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.

Sankhya and Ganith now enjoy reading the newspaper!

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

You can do it too!