Number Knowledge

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Welcome to Class 1 Number Knowledge lesson plan

Class 1 Lesson Plans in English
Lesson:1 Introduction to Mathematics
Lesson 2: Shapes
Lesson 3: Number Knowledge
Lesson 4: Place value System
Lesson 5: Addition
Lesson 6: Subtraction
Lesson 7: Measurement
Lesson 8: Time
Lesson 9: Whole and Parts
Lesson 10: Money

Learning Objectives

  1. Read, write and recall numbers (cardinal numbers) from 0 to 120
  2. Understand partitioning of numbers (introduction to place values)
  3. Counting forwards and backwards
  4. Know the position of numbers (ordinal numbers)
  5. Comparing two 2-digit numbers
  6. Recognize odd and even numbers (0 to 50)
  7. 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
एकम् ११ एकादश
द्वे १२ द्वादश
त्रीणि १३ त्रयोदश
चत्वारि १४ चतुर्दश
पञ्च १५ पञ्चदश
षट् १६ षोडश
सप्त १७ सप्तदश
अष्ट १८ अष्टादश
नव १९ नवदश
१० दश २० विंशतिः

Practice Writing Numbers

Writing exercise of Samskrit numbers.

Number knowledge - Sanskrit Number 1.PNG Number knowledge - Sanskrit Number 1.PNG
Number knowledge - Sanskrit Number 2.PNG Number knowledge - Sanskrit Number 2.PNG
Number knowledge - Sanskrit Number 3.PNG Number knowledge - Sanskrit Number 3.PNG
Number knowledge - Sanskrit Number 4.PNG Number knowledge - Sanskrit Number 4.PNG
Number knowledge - Sanskrit Number 5.PNG Number knowledge - Sanskrit Number 5.PNG

See the end of this chapter for more practice sheets.

Expanded forms of Numbers

Number Exercise: Partitioning a 2-digit number (20 to 99) An introduction to place-value system.

Activity: Find the 10s

Number exercise: Partitioning a 2-digit number.

Draw a line around 10 items and write the remaining numbers as shown in the example.

15 = 10 and 5 18 = _____ and _____
Number knowledge - BANANA 15 CIRCLE 10.png Number Knowledge - BRINJAL.png
19 = _______ and _______ 20 = _______ and _______
Number knowledge - CORN.png BHENDI.png
13 = _______ and _______ 11 = _______ and _______
Number knowledge - POTATO.png Number Knowledge - Bottle gourd.png
12 = _______ and _______ 14 = _______ and _______
Number Knoweledge - LEMON.png Number Knowledge - CARROT.png

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)

Number knowledge - Building blocks.png One stack here has 10 blocks.

There are 10 blocks below.

Number knowledge - block.png Number knowledge - block.png Number knowledge - block.png Number knowledge - block.png Number knowledge - block.png Number knowledge - block.png Number knowledge - block.png Number knowledge - block.png Number knowledge - block.png Number knowledge - block.png

How many stacks and blocks are needed for the following numbers. Find the missing spots.

76 Seventy - six Seven Stacks and Six Blocks
119 Ten Stacks and Nineteen Blocks
Ninety - five ________ Stacks and ________ Blocks
110 One hundred ten ________ Stacks and ________ Blocks
107 ________ Stacks and ________ Blocks
120 ________ Stacks and ________ Blocks
One hundred fourteen ________ Stacks and 4 Blocks
87 8 Stacks and ________ Blocks
102 ________ Stacks and ________ Blocks
90 ________ Stacks and ________ Blocks

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.

Number knowledge - Lotus flowers and circles with numbers.png

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.

Number knowledge - Sunflower connect the dots (E).png

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.

Number Knowledge - Small bird outline.png

Color 6 out of __________ birds

Number knowledge - Small hens outline.png

Color 8 out of __________ hens

Number knowledge - Banana Outline.png

Color 8 out of __________ bananas

Number knowledge - Orange Outline.png

Color 12 out of __________ oranges

Number knowledge - BEES OUTLINE.png

Color 11 out of __________ bees

Number knowledge - insects outline.png

Color 10 out of __________ insects

Number knowledge - LOTUS OUTLINE.png

Color 5 out of __________ lotuses

Number knowledge - flowers outline.png

Color 9 out of __________ flowers

Number knowledge - PURSES OUTLINE.png

Color 4 out of __________ purses

Number knowledge - PHOTO FRAMES OUTLINE.png

Color 5 out of __________ photoframes

Number knowledge - PENCILS OUTLINE.png

Color 17 out of __________ pencils

Number knowledge - BRINJAL OUTLINE.png

Color 13 out of __________ brinjals

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.

Number knowledge - Bank (E).png
Number knowledge - Four houses away.png

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.

Number knowledge - Train.jpg

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 air-conditioned 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

Number knowledge - Market Scene.jpg

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

Number knowledge - Rama with basket of oranges.png

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.

Number knowledge - orange.pngNumber knowledge - orange.pngNumber knowledge - orange.pngNumber knowledge - orange.pngNumber knowledge - orange.pngNumber knowledge - orange.pngNumber knowledge - orange.pngNumber knowledge - orange.pngNumber knowledge - orange.pngNumber knowledge - orange.pngNumber knowledge - orange.pngNumber knowledge - orange.pngNumber knowledge - orange.pngNumber knowledge - orange.pngNumber knowledge - orange.png

If Rama equally shared the oranges he had into two baskets...

Number knowledge - Basket of oranges.png Number knowledge - Basket of oranges.png
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.

Number knowledge - Latha with brinjals.png

Latha replied that they grew vegetables in their backyard and had grown many brinjal plants.

Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png

She had _______________ brinjals. The teacher then asked her to place one brinjal each into two heaps. She placed the brinjals in the following manner.

Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png
Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png Number knowledge - Brinjal.png
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.

25    18    9   23    6    28  34   10  39  11   41 30 15   21   1   29   7   32   43  19   24 17   35   12   46   3  20  13 16 37   49   31   26   8   36   2   14   22 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. Number knowledge- Butterfly bees and flowers.png

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 Number knowledge - equal sign.png 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 =

Number knowledge - Crocodile comparison (E).png

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

Number 1 Comparison Symbol Number 2
Rama had 15 oranges Rama had a less number than Latha Latha had 18 brinjals
15 Number knowledge - Less than sign.png 18
If Rama had 20 Oranges Rama has more number than Latha Latha had 18 brinjals
20 Number knowledge - greater than sign.png 18
If Rama had 18 Oranges Rama has same number as Latha Latha had 18 brinjals
18 Number knowledge - equal sign.png 18

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 2-digit numbers

Number Exercise: Comparing the quantity

Write the comparison sign between two numbers. Remember the following

Greater than Less than Equal to
Number knowledge - Symbols.png
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

Number-line

Number knowledge - numberline example.png

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 number-line. 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.

Krishna and govardhan mountain.jpg

E. He was seven years old when he lifted the Govardhana mountain to protect the people of Brindavan from the wrath of Indra.

Krishna and kalindi.jpeg

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.

Number knowledge - Number line krishna leela.png

  1. How many events took place before the age of 5? _________________
  2. How many events took place between the age of 10 and 20 years? _________________
  3. 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 place-value 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.     

Number knowledge - planets.jpg
  1. Bhuta means ‘a being’
  2. Samkhya means ‘a number’

In the Bhutasankhya system, numbers are represented using common words such as:

  1. The physical bodies such as earth, moon (1), planets (9), stars, oceans, mountain, fire, sky, directions etc.
  2. The parts of a human body such as eyes, ears (2), jaws, knees, hands, fingers, teeth etc.
  3. The animals such as serpents, horse, elephants etc.
  4. The names of the devatas, such as Shiva, Indra, Surya and sometimes historical persons such as Manu, Rama (3) etc. Number knowledge - Balram.png Number knowledge - Parashuram.png
Number knowledge - Brahma.gif

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

Numbers Word Form Word Numeral Images
एकम् Akasha (आकाश्) Number knowledge - sky.jpg
द्वे Netra (नेत्र)     Number knowledge - Eyes.png
त्रीणि Hara (हरः) Number knowledge - Shiva graphic.png
चत्वारि Vedas (वेदः) Number knowledge - Vedas.PNG
पञ्च Indriyas (इन्द्रियम्) Number knowledge - Pancha Indriyas.png
षट् Kartikeya (Six faces) (कार्तिकेयः) Number knowledge - Kartikeya.jpg
सप्त Ashva (Horses of Surya’s Chariot) अश्वाः Number knowledge - Sun's chariot.jpg
अष्ट Dik (Directions) (दिक्) Number knowledge - 8 DIRECTIONS (E).png
नव Ratnas (Gems) (रत्नानि) Number knowledge - Ratnas.jpg
१० दश Ravana (रावणः) Number knowledge - Ravana.png

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
Number knowledge - pandavas.jpg

Match the following

  • Pandavas
  • Asvini devatas
  • Grahas
  • Nakshatras
  •  Kauravas
  •  Brahma
  •  Ravana
  • Shiva
  1. दश
  2. पञ्च
  3. चत्वारि
  4. शतम्
  5. द्वे
  6. त्रीणि
  7. सप्तविंशतिः
  8. नव

Activities and Exercises

  1. 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.
    Number knowledge - Bhutasankhya clock.png
  2. 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.
  3. 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
एकम् प्रथम 26
द्वे द्वितीय
त्रीणि तृतीय
चत्वारि चतुर्थ
पञ्च पञ्चम
षट् षष्ट
सप्त सप्तम
अष्ट अष्टम
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

Number knowledge - Sanskrit Number 6.PNG Number knowledge - Sanskrit Number 6.PNG
Number knowledge - Sanskrit Number 7.PNG Number knowledge - Sanskrit Number 7.PNG
Number knowledge - Sanskrit Number 8.PNG Number knowledge - Sanskrit Number 8.PNG
Number knowledge - Sanskrit Number 9.PNG Number knowledge - Sanskrit Number 9.PNG
Number knowledge - Sanskrit Number 10.PNG Number knowledge - Sanskrit Number 10.PNG

References

  1. Rangacharya, M. (1912) Ganita-Sara-Sangraha of Mahaviracharya with English translation and notes. Madras: Government Press (Pages 6 and 7 from अथ सङ्ख्यासंज्ञा Shloka 53 to 62)