Number Knowledge
Welcome to Class 1 Number Knowledge lesson plan
Learning Objectives
 Read, write and recall numbers (cardinal numbers) from 0 to 120
 Understand partitioning of numbers (introduction to place values)
 Counting forwards and backwards
 Know the position of numbers (ordinal numbers)
 Comparing two 2digit numbers
 Recognize odd and even numbers (0 to 50)
 Understanding Bhutasankhya sytem
Introduction
Now that we know the importance of mathematics, let us learn to apply counting and calculations in our daily lives. First, we shall recall the numbers learnt till now and practice writing numbers.
Numbers  Word Forms  Numbers  Word Forms 

१  एकम्  ११  एकादश 
२  द्वे  १२  द्वादश 
३  त्रीणि  १३  त्रयोदश 
४  चत्वारि  १४  चतुर्दश 
५  पञ्च  १५  पञ्चदश 
६  षट्  १६  षोडश 
७  सप्त  १७  सप्तदश 
८  अष्ट  १८  अष्टादश 
९  नव  १९  नवदश 
१०  दश  २०  विंशतिः 
Practice Writing Numbers
Writing exercise of Samskrit numbers.
See the end of this chapter for more practice sheets.
Expanded forms of Numbers
Number Exercise: Partitioning a 2digit number (20 to 99) An introduction to placevalue system.
Activity: Find the 10s
Number exercise: Partitioning a 2digit number.
Draw a line around 10 items and write the remaining numbers as shown in the example.
15 = 10 and 5  18 = _____ and _____ 
19 = _______ and _______  20 = _______ and _______ 
13 = _______ and _______  11 = _______ and _______ 
12 = _______ and _______  14 = _______ and _______ 
Write each number identifying the number of groups of 10s
34 has 30 and 4  78 has 70 and 8  91 has ______ and ______ 
47 has ______ and ______  71 has ______ and ______  40 has ______ and ______ 
63 has ______ and ______  98 has ______ and ______  39 has ______ and ______ 
76 has ______ and ______  81 has ______ and ______  53 has ______ and ______ 
33 has ______ and ______  41 has ______ and ______  59 has ______ and ______ 
Write the missing number  
99 has 90 and 9  36 has 30 and 6  85 has ______ and 5 
66 has 60 and ______  ______ has 20 and 8  43 has ______ and 3 
______ has 20 and 4  67 has 60 and ______  ______ has 80 and 8 
Activity: Identifying and writing expanded forms
Number Exercise: Writing expanded forms (75 to 120)
Activity: Count forward and backward (1s, 2s, 3s, 5s)
Number Exercise: Count forward and backward 50 to 99 (by 1s, 2s, and 3s).
Count forward by 1 and colour that flower yellow. Count backward by 2 and colour that flower red. Write all the numbers in the circles given below.
Count by 5 and colour that box red. Count by 10 and colour that box yellow.
5  10  15  20  25  30  35  40  45  50 
23  28  33  38  43  48  53  58  63  68 
36  41  46  51  56  61  66  71  76  81 
17  22  27  32  37  42  47  52  57  62 
Count by 3 and circle the numbers starting from 1. Join the circled numbers. Colour the picture yellow.
Activity: How many of a Total
Number Exercise: Knowing how many in a total number.
Color as many things to match the number given in the box and write the total number on the line given below.
Cardinal and Ordinal Numbers
A cardinal number defines how many (number) of something are present. Example, my friend's house is 4 (four) houses away from my house.
An ordinal number defines where (position) is something located in a list. Example, my friend’s house is the fourth building from my house.
So, if we say there are five persons standing in the line in a bank and the fifth person is wearing a blue shirt, we are
 counting the number of persons, seen standing in a line
 identifying the position of a particular person
Activity: My Train Ride
Number Exercise: Using the cardinal word forms and Ordinal numbers.
During the summer holidays, I went to Manguluru from Bengaluru by a train. The engine is the ___________ (1) and the foremost carriage of the train. My mother told me that a train also has cars in which we all travelled. The engine of our train was very strong. It pulled our long train having _________(18) cars easily even in uphill places. Our car was in the middle, _________ (9) from the engine. I sat by the window and was counting the trains and the number of cars they had. The ______(3) train that sped by us was very long having _________ (22) cars. I was surprised to see that the _________ (6) car of a train standing in a station had the words “Medical Van” written on it. It started to move when the guard waved a green flag standing on the _______ (7) car which was also the train’s last car.
It was fun walking along with my father in a moving train crossing __________ (5) cars to reach the __________ (4) car. It was the food or the pantry car. As the train took a bend in the hills, I saw that the ladies’ car was just _________ (2) cars away from the engine. Our car was followed by three airconditioned cars which were in __________ (10), ___________ (11) and ____________ (12) places away from the engine. When I got off the train at Manguluru, as I walked towards the station, I saw the railway porters unloading many things from two cars in the rear. They were the ___________ (16) and _________ (17) cars. It was a joyous train ride and I was looking forward to visit my grandparents.
Activity: Pick a sweet mango
Number Exercise – Sorting, Ordinal numbers till 50, Making a number chart
Lakshmi likes sweet mangoes. So, her mother went to the wholesale market to buy mangoes for her to distribute to her friends on her birthday. She knew that ripe mangoes are yellow in color and they are sweet. Lakshmi’s mother wanted to make some mango pickle so she chose unripe mangoes from the carts. From the top row tell the number and position of the ripe and unripe mangoes.
Ripe Mangoes  Unripe mangoes  

Cardinal  Ordinal  Cardinal  Ordinal 
Odd and Even Numbers
Let’s talk about sharing now. Rama visited an orange farm when he went to his grandparents’ home. He brought 15 oranges home. And he wondered what he would do with so many oranges…
So, he decided to share them with his friends. He wanted to give the same number of oranges to both his friends.
Don’t we all share with whom we care for.
If Rama equally shared the oranges he had into two baskets...
Count and write how many oranges are in the basket _________.  Count and write how many oranges are in the basket _________. 
Rama split _____________ out of 15 oranges into two baskets of each and had __________ remaining with him which could not be shared with both his friends. He wondered why he could not share 15 oranges completely. However, he happily shared the rest and ate the one orange himself.
Then he gave the two baskets to his friends and asked his teacher about his activity. The teacher called all the class students. He asked each student what things they had more in number that could be shared with others.
Latha replied that they grew vegetables in their backyard and had grown many brinjal plants.
She had _______________ brinjals. The teacher then asked her to place one brinjal each into two heaps. She placed the brinjals in the following manner.
Count and write how many brinjals are present _________.  Count and write how many brinjals are present _________. 
She did not have anything left after making two equal groups of brinjals.
The teacher informed that, any
Number ending in 0 2 4 6 8 are called Even
Number ending in 1 3 5 7 9 are called Odd
Rama had 15 oranges, having _________ as an ending number. So, 15 is an ___________ number. After splitting them in to two baskets he had ________ remaining. Rama understood that he had an odd number of oranges.
Latha had 18 oranges having __________ as an ending number. So, 18 is an ___________ number. After splitting them in to two heaps she had _____ with her. Latha came to know that she had an even number of brinjals. Latha gave one heap of brinjals to her neighbour and took one home happily.
Any number that can be split into two equal quantities without any leftover is Even.
Any number that leaves behind something after being split into two sets of equal quantities is Odd.
Activity: Identifying even and odd numbers
Number Exercise – Visual identification of odd and even numbers (0 to 50)
Identify looking at the number and write if it is even or odd, strike out as you write. Place only even numbers in one box and odd into another box.
Write Even Numbers
18  
Write Odd Numbers
25 
Activity: Bees and Butterflies
Number Exercise: Counting by 2 for even and odd numbers.
Draw a line to lead the butterfly forwards by two flowers. Write the number and colour that flower yellow. Draw a line to lead the bee backwards by two flowers. Write the number and colour that flower orange.
Comparing Numbers
We saw that Rama had 15 oranges and that he wanted to share them such that both his friends get same number of oranges.
Friend 1  Sign  Friend 2  
Number of Oranges  7  7  
Equality Sign  7  7 
What is neither more not less is said to be equal in mathematical terms. It is said to be same. It is represented by the equal symbol =
It requires that two things are measured or compared before saying that they are “more” or “less” or “equal”. In mathematics, they are represented as shown below
Comparison can be between anything same or different. In our example we saw that Rama and Latha had different things namely, oranges and brinjals being compared for their number. We can compare many things for their sameness or differentness.
Activity: Comparison of two 2digit numbers
Number Exercise: Comparing the quantity
Write the comparison sign between two numbers. Remember the following
Greater than  Less than  Equal to 
Number  Write the sign  Number  Number  Write the sign  Number 
28  39  45  8  
14  14  19  16  
74  100  62  62  
10  99  53  86  
0  5  33  35  
25  0  91  91  
76  89  69  59  
22  7  44  22 
Find the missing numbers. An example is given in each section of the table.
Number  Numbers in between  Number 

43  44 45  46 
108  112  
87  91  
20 21 22  
53 54  
1 2 3  
99 100 101 
2 Less  Number  2 More  5 Less  Number  5 More 

27  29  31  80  85  90 
78  120  
103  105  
46  70  
55  114  
117  97 
Numberline
We can write whole numbers (and other kinds of numbers) on a horizontal straight line with numbers placed at equal intervals along its length infinitely extending on both sides. The numbers increase as we move from left to right and decrease as we move towards the right side. A number line can be made with numbers with a pattern, for example, a series of numbers differing by 3 can be written on the number line. It helps us compare numbers visually.
We can see that the numbers are increasing by 1 as we go along the number line.
Activity: Krishna Leela
Number Exercise: Introduction to numberline. Use a number line (visual of skip counting by 3) to mark the events.
A. Krishna was taken to Nanda's house in Gokula as soon as he was born. (represented as red dot on the number line)
B. When he was less than a month old, Putana the rakshasi, tried to poison him. (represented as red dot on the number line)
C. About the time of his first birthday, Krishna was carried up by Trinavarta, an other rakshasa.
D. Krishna was about five years old when he released Nalakubara and Manigriva from a curse.
E. He was seven years old when he lifted the Govardhana mountain to protect the people of Brindavan from the wrath of Indra.
F. At nine years of age Krishna danced on the hood of Kaliya, the snake.
G. At the age of eleven he killed Kamsa and had the upanayana samskara.
H. By the age of twenty, he destroyed Jarasandha's army and Kalayavana asura.
I. Krishna brought back the Syamantaka mani and married Satyabhama at the age of thirty years.
On the number line place a red point noting each age of Krishna's activities and answer the questions given below. Note that 0, 3 up to 30 (skip count by 3) are given on the number line.
 How many events took place before the age of 5? _________________
 How many events took place between the age of 10 and 20 years? _________________
 How many events took place between the age of 20 and 30 years? _________________
Word Numerals  Ancient Indian System of Representing Numbers
Till now we have seen that numbers have
 written symbols called as Anka
 arrangement method which is called as Decimal Place system
 value of numbers
 position
Now, in the early centuries in India, as mathematical system was evolving, our scholars developed a method of expressing numbers as words. They came up with Sankhya samjna (सङ्ख्यासंज्ञा), as mentioned in Ganitasaarasangraha^{[1]} or "word numerals". They arranged them just as we see in the placevalue notation.
These word numerals are expressed by names of things, beings or concepts, naturally or in accordance with the terms in Shastras. Thus, the number “one” is expressed by anything that is markedly unique such as the moon, earth etc and zero is expressed by words meaning sky, empty, complete etc. This system of representing numbers using words is called Bhutasankhya system. The word “Bhutasankhya” is a compound word. It is made up of the words bhuta and sankhya.
 Bhuta means ‘a being’
 Samkhya means ‘a number’
In the Bhutasankhya system, numbers are represented using common words such as:
 The physical bodies such as earth, moon (1), planets (9), stars, oceans, mountain, fire, sky, directions etc.
 The parts of a human body such as eyes, ears (2), jaws, knees, hands, fingers, teeth etc.
 The animals such as serpents, horse, elephants etc.
 The names of the devatas, such as Shiva, Indra, Surya and sometimes historical persons such as Manu, Rama (3) etc.
Thus, the Bhutasamkhya refers to the collection of set of ‘things’ denoted by that number. Our ancient mathematicians used these terms in their shlokas to mention the number they had in mind. Some numbers have multiple representations, such as
 Four 4 – Brahma (Chaturmukha) and Vedas (Chaturveda)
 2 – Eyes, Ears, Twins, Shoulders
 3 –
 6 –
 8 –
 9 –
Bhutasankhya System of representing number
Activity: Representation of numbers using words
Number Exercise: Identify the number given in the Bhutasankhya (word numerals)
Bhutasankhya  Circle one number to indicate the Bhutasankhya  
Puranas  23  45  18  89 
Masas (months)  33  12  10  64 
Bhuvanas (worlds)  10  4  14  33 
Rishis  7  34  17  54 
Kalas (arts)  46  39  14  64 
Vasus (a kind of devatas)  18  44  8  20 
Vidyas  10  14  56  72 
Bhutas (beings)  15  24  5  99 
Ratnas (gems)  19  9  49  66 
Adityas  12  34  22  10 
Manus (a ruler of earth)  14  52  100  74 
Chandra Kalas (moon’s phases)  10  26  56  16 
Number of Devatas  33  66  49  30 
Adri or Achala (mountains)  10  7  14  64 
Bhujas (shoulders)  90  2  100  53 
Danta (teeth)  10  24  32  30 
Visvedevas (a kind of devatas)  13  16  39  22 
Saagara (oceans)  10  37  4  7 
Match the following


Activities and Exercises
 Make a board or draw on ground numbers 1 to 30 in squares. The teacher calls out an odd and even number which should be located on the ground by the children for that many rubberbands.
 Every child collects 109 number of items like toothpicks, match sticks, icecream spoons (long and short wooden), small spent pencils etc. Every child must make bundles of 10 of these using rubberbands. After making 10 bundles 9 will be kept loose. Show your number work using these bundles. 4 bundles and 3 loose toothpicks make 43 .... and so... on.
 Make your own clock using the Bhutasankhya numbers you learnt.
Find the even or odd numbers between the two numbers given
Number  Even numbers  Number  Number  Odd number  Number 

47  48  50  18  19 21  23 
11  12 14  15  37  42  
13  19  23  29  
31  36  25  31  
17  22  42  48  
39  45  11  14  
29  33  32  36 
Identify and write the Bhutasankhya between two numbers given below
Number  Bhutasankhya  Number 

9  Dashanana or Ravana  11 
31  33  
63  65  
26  28 
Compare the numbers and write less than or more than or equal to symbols.
Bhutasankhya  Write the symbols  Bhutasankhya 

Chandra  Shiva  
Kalas (Arts)  Dantas  
Giri (mountains)  Svaras (music)  
Kartikeya  Vedas  
Rishis  Sagaras  
Vidyas  Puranas  
Aditya  Masas 
Practice writing numbers in Samskrit and English
Cardinal and Ordinal Number Chart (1 to 50)
See and learn to write numbers in Samskrit. Fill the charts with numbers in English (cardinal and ordinal)
Numbers  Word Forms  Position  Numbers  Word Forms  Position 

१  एकम्  प्रथम  26  
२  द्वे  द्वितीय  
३  त्रीणि  तृतीय  
४  चत्वारि  चतुर्थ  
५  पञ्च  पञ्चम  
६  षट्  षष्ट  
७  सप्त  सप्तम  
८  अष्ट  अष्टम  
९  नव  नवम  
१०  दश  दशम  
११  एकादश  एकादशतम  
१२  द्वादश  द्वादशतम  
१३  त्रयोदश  त्रयोदशतम  
१४  चतुर्दश  चतुर्दशतम  
१५  पञ्चदश  पञ्चदशतम  
१६  षोडश  षोडशतम  
१७  सप्तदश  सप्तदशतम  
१८  अष्टादश  अष्टादशतम  
१९  नवदश  नवदशतम  
२०  विंशतिः  विंशतितम  
२१  एकविंशतिः  एकविंशतितम  
२२  द्वाविंशतिः  द्वाविंशतितम  
२३  त्रयोविंशतिः  त्रयोविंशतितम  
२४  चतुर्विंशतिः  चतुर्विंशतितम  
२५  पञ्चविंशतिः  पञ्चविंशतितम  50 
Cardinal and Ordinal Number Chart (51 to 70)
Numbers  Word Forms  Position 
51  
Practice writing numbers in Samskrit
References
 ↑ Rangacharya, M. (1912) GanitaSaraSangraha of Mahaviracharya with English translation and notes. Madras: Government Press (Pages 6 and 7 from अथ सङ्ख्यासंज्ञा Shloka 53 to 62)