Number Knowledge

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Welcome to Class 1 Number Knowledge lesson plan

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
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

See the end of this chapter for more practice sheets.

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 _____
19 = _______ and _______	20 = _______ and _______
13 = _______ and _______	11 = _______ and _______
12 = _______ and _______	14 = _______ and _______

Activity : Expanded forms of Numbers

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

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)

One stack here has 10 blocks. There are 10 blocks below. 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.

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.

Color 6 out of __________ birds	Color 8 out of __________ hens
Color 8 out of __________ bananas	Color 12 out of __________ oranges
Color 11 out of __________ bees	Color 10 out of __________ insects
Color 5 out of __________ lotuses	Color 9 out of __________ flowers
Color 4 out of __________ purses	Color 5 out of __________ photoframes
Color 17 out of __________ pencils	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.

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 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

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.

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.

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

Number 1	Comparison Symbol	Number 2
Rama had 15 oranges	Rama had a less number than Latha	Latha had 18 brinjals
15		18
If Rama had 20 Oranges	Rama has more number than Latha	Latha had 18 brinjals
20		18
If Rama had 18 Oranges	Rama has same number as Latha	Latha had 18 brinjals
18		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	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

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
27	29	31
	78
	103
	46
	55
	117
5 Less	Number	5 More
80	85	90
	120
	105
	70
	114
	97

Number-line

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.

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.

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 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.     

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.

Bhutasankhya System of representing number

Numbers	Word Form	Word Numeral	Images
१	एकम्	Akasha (आकाश्)
२	द्वे	Netra (नेत्र)
३	त्रीणि	Hara (हरः)
४	चत्वारि	Vedas (वेदः)
५	पञ्च	Indriyas (इन्द्रियम्)
६	षट्	Kartikeya (Six faces) (कार्तिकेयः)
७	सप्त	Ashva (Horses of Surya’s Chariot) अश्वाः
८	अष्ट	Dik (Directions) (दिक्)
९	नव	Ratnas (Gems) (रत्नानि)
१०	दश	Ravana (रावणः)

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 –

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

Pandavas Asvini devatas Grahas Nakshatras  Kauravas  Brahma  Ravana Shiva

दश पञ्च चत्वारि शतम् द्वे त्रीणि सप्तविंशतिः 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.
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. Find the even or odd numbers between the two numbers given
4. Make your own clock using the Bhutasankhya numbers you learnt.
5. Identify and write the Bhutasankhya between two numbers given below
6. Compare the numbers and write less than or more than or equal to symbols.

Number	Even numbers	Number
47	48	50
11	12    14	15
13		19
31		36
17		22
39		45
29		33
Number	Odd number	Number
18	19   21	23
37		42
23		29
25		31
42		48
11		14

Number	Bhutasankhya	Number
9	Dashanana or Ravana	11
31		33
63		65
26		28

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 100)

Numbers	Word Forms	Position	Numbers	Word Forms	Position
51

Practice writing numbers in Samskrit

६	६
७	७
८	८
९	९