self-instructional material

Self-Instructional Material

i

KEY STAGE-III

Self-Instructional Materials

Key-stage III

(Classes VII and VIII)


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KEY STAGE-III

Published by

Ministry of Education in collaboration with Royal Education Council, Paro

Copyright © Ministry of Education, Bhutan

Advisors

1. Karma Tshering, Officiating Secretary, Ministry of Education

2. Kinga Dakpa, Director General, Royal Education Council, Paro

3. Phuntsho Lhamo, Education Specialist, Advisor to the Department of School

Education, Ministry of Education

SIM Developers

1. Yeshi Dorji, Principal EMO (Key-stage Coordinator and Science)

2. Lobzang Nima, Teacher, Dangchu PS (English Subject Coordinator)

3. Yeshi Jamtsho, Teacher, Bjemina PS (English)

4. Chechong Tshering, Teacher, Tashidingkha CS (Dzongkha)

5. Tshering Wangmo, Teacher, Changangkha MSS (Dzongkha)

6. Pem Choden Tamang, Teacher, Zillnoen Namgyelling LSS (Mathematics)

7. Tara Gajmer, Teacher, Loseling MSS (Mathematics)

8. Sukmith Lepcha, Teacher, Drukgyel LSS (Science)

9. Tshering Lhamo, Teacher, Changangkha MSS (Science)

10. Passang Dema, Teacher, Jigme Namgyal LSS (Mathematics)

11. Ngawang Drakpa, Teacher, Zilukha MSS (History)

Content Editors

1. Lobzang Nima, Teacher, Dangchu PS

2. Antony Joshy, Teacher, Yangchenphu HSS

3. Samdrup Tshering, Teacher, Lamgong MSS

4. Dechen Choden, Teacher, Trashiyangtse LSS

Layout and Design:

Sangay Jamtsho, Teacher, Lungtenzampa MSS

Cover Design:

Samdrup Tshering, Teacher, Lamgong MSS

Overall Coordinator:

Phuntsho Lhamo, Education Specialist, Advisor to the Department of School Education,

Ministry of Education


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KEY STAGE-III

TABLE OF CONTENTS

English

1. How to write a Narrative Essay……………………………………..………...1

2. Past Tense …………………………………………………………………….6

3. Present Tense ………………………………………………………………...11

4. Future Tense …………………………………………………………………15

5. Conversion of Direct to Indirect Speech ……………………………………..20

རྫོང་ཁ། ༡. འབྲི་རྩོམ། རྒྱུད་སྐུལ་དང་ འཆར་སྣང་འབྲི་རྫོམ། …………………………………………………………………………….25 ༢. ཡི་གུའི་སྫོར་བ། ལྷག་བཅས། ……………………………………………………………………………………………………...31 ༣. ཡི་གུའི་སྩོར་བ། འབྲེལ་སྒྲ་དང་ བྱེད་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ། ……………………………………………........................37

༤. ལྫོ་རྒྱུས་འབྲི་རྫོམ།……………………………………………………………………………………………………………………….44 Mathematics

1. Circumference and Area of Circle.…………………………….....................47

2. Describing and Solving Linear Relationship ……………………………….51

3. Linear Polynomials: Addition and Subtraction ……………………………..56

4. Graphical Representation of Data ………………………………………......60

5. Integers………………………………………………………………………67

Science

1. Reproduction in the Animals and Plants ……………………………………70

2. Work, Power and Energy ……………………………………………..….. ..81

3. Acid and Base. ……………………………………………....………...........87

4. The Formation of Images ………………………………………………... . .94

5. Elements and their Symbols………………………………………………..107

6. Force and Pressure………………………………………………………....112

History

1. The Young Jigme Namgyel………………………………………………..117


English-Class VII-VIII 1

KEY STAGE-III

Lesson No: 1 Subject: English Class: VII-VIII Time: 50 mins

Theme: Writing

Topic: How to write a Narrative Essay

Background

Narrative essays are told from a defined point of view, often the author's, so there is feeling as well

as specific and often sensory details provided to get the reader involved in the elements and

sequence of the story. The verbs are clear and precise. The narrative essay makes a point and that

point is often defined in the opening sentence, but can also be found as the last sentence in the

opening paragraph.

Think about how you wrote an essay. What were some of the conventions you used to write a

narrative essay?

Here are the steps for writing a narrative essay. Look at the examples in each step.

✓ Pick a relevant topic- Example: My favorite Pet.

✓ Then brainstorm or gather points on the topic.

Figure: Brainstorming (Mind Mapping)

My favourite

pet

protective and

friendly

play frisbee/

pool

incident at school

chewing on my shoes

good appetite-feed on

everything

playful

✓ Recognize the features of a narrative essay.

✓ Write a narrative essay following the steps.

https://essayinfo.com/essays/narrative-essay/



KEY STAGE-III

A topic sentence should give us the main idea that one wants to convey.

In the next paragraph we should narrate events that will support your topic sentence. For

instance, the second paragraph should;

✓ Show how Migser is playful.

✓ Pick a series of events to support the main idea-answers how, why, and when questions.

Each paragraph should talk only about one idea. Then the second paragraph should;

✓ Show how your favorite pet is easy to feed and the third, how is she protective.

Example of topic sentence

A pet is an animal that we keep at home and is considered as the family member. My

favorite pet is Migser. She is a playful dog which is easy to feed and always protective.

Example of paragraphing and supporting details of topic sentence.

My dog Migser is a playful dog because there is not a single event that I can remember her

being angry. She loves to play fetching Frisbee. I still remember how she once dove into

the pool to fetch the Frisbee where everyone thought she was drowning but when she came

out with the Frisbee in her mouth, I was so happy. She is a friendly pet as she always wags

her tail and initiates the play whenever she comes across other dogs. Therefore, Migser

indeed is a playful dog. (Paragraph 1)

Example of supporting details.

Migser has quite an appetite. She can feed on anything. It was on one of the Monday

morning, I was in hurry as I was getting late because I couldn’t find my shoes. You know

what? I saw Migser busy chewing on my shoe and I had to wear my old shoes that day.

Migser is always hungry and eats almost everything. That is why she is easy to feed.

It was on a rainy day I was returning from my school. I came across a group of big boys

on my way. I was so scared because they had their attention on me as I had the umbrella

and they didn’t. Then they stopped and asked for the umbrella but I refused to give. So,

they tried to take it with force. Suddenly we heard a snarl of an angry dog with its big teeth

flashing to them, “Grrrr…” I looked back and was so happy to see it was Migser. She

protected me from those bully. She is a protective dog.

(Paragraph 2 & 3)



KEY STAGE-III

Finally conclude the essay by restating the topic sentence why Migser is your favorite pet.

✓ The conclusion can also be a summary of the essay.

✓ There should not be the addition of any new idea

Activity 1

Instruction: Read the following essay and identify the features of a narrative essay.

Example paragraph on conclusion

Migser is my best friend with whom I play every day. She will never be hungry as she

feeds on everything that comes on her way because her stomach has a huge grinding

machine. Her protection over me is so amazing that makes Migser, the best pet in this

whole wide world. (Conclusion)

Friendship

A dictionary contains a definition of friendship somewhere in the F’s between the words “fear” and

“Friday.” An encyclopedia supplies interesting facts on friendship. But all the definitions and facts

do not convey what friendship is really all about. It cannot be understood through words or

exaggerations. The only way to understand friendship is through experience. It is an experience that

involves all the senses.

Friendship can be seen. It is seen in an old couple sitting in the park holding hands. It is the way

they touch, a touch as light as a leaf floating in the autumn air, a touch so strong that years of living

could not pull them apart. Friendship is seen in a child freely sharing the last cookie. It is the small

arm over the shoulder of another as they walk on the playground. Seeing friendship is not casual.

It is watching for subtlety, but friendship is there for eyes that can see.

Friendship is felt in a touch. It is a pat on the back from a teammate, a high five between classes,

the slimy, wet kiss from the family dog. It’s a touch that reassures that someone is there, someone

who cares. The touch communicates more than words or gestures. It is instantly understood and

speaks volumes beyond the point of contact, to the heart.

Friendship has a taste. It tastes like homemade bread, the ingredients all measured and planned,

then carefully mixed and kneaded, then the quiet waiting as the dough rises. Hot from the oven, the bread tastes more than the sum of its ingredients. There is something else there, perhaps the thoughts

of the baker as her hands knead the dough, or her patience as she waits for the dough to rise. Unseen

and unmeasured, this is the ingredient that makes the difference. Warm, fresh from the oven with a

little butter, the difference you taste is friendship.

Finally, more than the other senses, friendship is an experience of the heart. It is the language of

the heart—a language without words, vowels, or consonants; a language that, whether seen, felt,

heard, or tasted, is understood by the heart. Like air fills the lungs, friendship fills the heart, allowing us to experience the best life has to offer: a friend.

•

https://k12.thoughtfullearning.com/studentmodels/friendship



KEY STAGE-III

Summary

✓ Pick a relevant topic. Brainstorm or gather points on the topic.

✓ The topic sentence should tell us the main idea which one wants to convey.

✓ In the next paragraph you should narrate events that will support your topic sentence.

✓ Pick a series of events to support the main idea-answers how, why, and when questions.

✓ There should be three paragraphs in the body part of the essay.

✓ Each paragraph should talk about only one idea.

✓ Finally conclude the essay by restating the topic sentence and there should not be the

addition of any new ideas.

Self-check for Learning

Instruction: Using the above summary points and the steps mentioned, write a narrative essay

in about 150 words on any one of the following topics in your notebook.

✓ A difficult decision that you had to make.

✓ A random act of kindness.

✓ Loyalty



KEY STAGE-III

Friendship

A dictionary contains a definition of friendship somewhere in the F’s between the words

“fear” and “Friday.” An encyclopedia supplies interesting facts on friendship. But all the

definitions and facts do not convey what friendship is really all about. It cannot be understood through words or exaggerations. The only way to understand friendship is

through experience. It is an experience that involves all the senses.

Friendship can be seen. It is seen in an old couple sitting in the park holding hands. It is

the way they touch, a touch as light as a leaf floating in the autumn air, a touch so strong

that years of living could not pull them apart. Friendship is seen in a child freely sharing

the last cookie. It is the small arm over the shoulder of another as they walk on the

playground. Seeing friendship is not casual. It is watching for subtlety, but friendship is

there for eyes that can see.

Friendship is felt in a touch. It is a pat on the back from a teammate, a high five between

classes, the slimy, wet kiss from the family dog. It’s a touch that reassures that someone is there, someone who cares. The touch communicates more than words or gestures. It is

instantly understood and speaks volumes beyond the point of contact, to the heart.

Friendship has a taste. It tastes like homemade bread, the ingredients all measured and

planned, then carefully mixed and kneaded, then the quiet waiting as the dough rises. Hot

from the oven, the bread tastes more than the sum of its ingredients. There is something

else there, perhaps the thoughts of the baker as her hands knead the dough, or her patience as she waits for the dough to rise. Unseen and unmeasured, this is the ingredient that makes

the difference. Warm, fresh from the oven with a little butter, the difference you taste is

friendship.

Finally, it is the language of the heart—a language without words, vowels, or consonants;

a language that, whether seen, felt, heard, is understood by the heart. Like air fills the lungs,

friendship fills the heart, allowing us to experience the best life has to offer, that is an un-

failing friend. Experiences of all sorts makes us understand what friendship really is.

Answer for Self-check for Learning

Conclusion

Supporting detail

Supporting detail

Conclude with an impactful sentence

Supporting detail

Topic Sentence

Introduction



KEY STAGE-III


Theme: Writing

Topic: Past Tense

Background:

A tense expressing an action that has happened or a state that previously existed. The past

tense refers to event that has happened in the past. The basic way to form the past tense in

English is to take the present tense of the word and add the suffix -ed.

For example, to turn the verb "walk" into the past tense, add -ed to form "walked."

However, not all the words follow this general rule of adding the suffix -ed. For example; go,

begin, drive, become, swing, teach, take, etc. These words are called ‘irregular verbs’ in the

English language.

There are four different types of tenses under Past Tense. They are:

✓ Simple Past Tense.

✓ Past Continuous Tense.

✓ Past Perfect Tense.

✓ Past Perfect Continuous Tense.

Now let us look at each of the above tenses in detail.

1. Simple Past Tense

The simple past tense shows that you are talking about something that has already happened. The

simple past tense emphasizes that the action is finished. Let us look at the formula.

Simple Past Subject+ past form of verb+ adverb of time I watched TV.

I watched TV last night.

✓ Name all tenses under past tense.

✓ Study the formula and carry out the activities under past

tense.



KEY STAGE-III

Example:

✓ Madam Pem asked children to write.

✓ Sangay went home.

✓ I studied hard for exams.

✓ Last year, I travelled to Japan.

Activity 1

Instruction: Which of the following sentences are in simple past tense?

a) Did you go home?

b) Dema is asking her book back.

c) We saw some beautiful rainbows.

2. Past Continuous Tense

The past continuous tense, also known as the past progressive tense, refers to a continuing

action or state that was happening at some point in the past. ... There are many situations in which

this verb tense might be used in a sentence. For example, it is often used to describe conditions

that existed in the past. Let us look at the formula.

Past

Continuous

Subject + was/were + ing form of verb+ a

specific time

She was watching TV when I

called her.

Example:

✓ The audience was applauding until he fell off the stage.

✓ I was making dinner when she arrived.

✓ The children were laughing at my cleverness.

Activity 2

Instruction: Identify the correct from of the verbs in the following sentences.

a) I……………dinner when she arrived. (was making/am making)

b) What ……… you ………… when the alarm went off last night? (were-doing/have-

done)

c) We ……… if she was able to meet us at noon. (was wondering/were wondering)



KEY STAGE-III

3. Past Perfect Tense

The past perfect tense indicates that an action was completed (finished or "perfected") at some

point in the past before something else happened. This tense is formed with the past tense form of

"to have" (had) plus the past participle of the verb (which can be either regular or irregular

in form). Let us look at the formula below.

Past Perfect Subject+ had + Past participle

She had Watched TV.

Examples:

✓ She had met him before the party.

✓ I had written the letter before he arrived.

✓ I had fallen asleep before eight o'clock.

Activity 3


a) I thought I ………………..(see) her before. (have seen/had seen)

b) He ………………………..(left) when I arrived. (had left/have left)

c) She………………………..(sell) her car. (have sold/had sold)

4. Past Perfect Continuous Tense

The past perfect continuous (also called past perfect progressive) is a verb tense which is used

to show that an action started in the past and continued up to another point in the past. Let us look

at the formula and examples for some insight.

Past Perfect

Continuous

Subject + had + been + ing form of

verb

She had been watching TV

for an hour.

Examples:

✓ She had been watching the movie for two hours.

✓ Tshering had been playing football since 10 o’ clock.

✓ I had been applying for a job since 2018.



KEY STAGE-III

Activity 4


a) They (wait)…………..at the station for 90 minutes when the bus arrived. (have been

waiting/had been waiting)

b) He (drive)…………..less than an hour when he ran out of petrol. (had been driving/have

been driving)

c) How long (had/she) ……………..English before she went to London? (had she been

learning/have she been learning)

Summary

Let us now look at the formula for Past Tense and its types.

Tense Forms Rules Examples

Pas

t T

ense

Simple Past

Subject + past form of verb +

adverb of time

I watched TV.

I watched TV last night.

Past Continuous

Subject + was/were + ing form of

verb + a specific time

She was watching TV

when I called her.

Past Perfect

Subject + had + Past participle

She had Watched TV.

Past Perfect

Continuous

Subject + had + been + ing form of

verb

She had been watching

TV for an hour.



KEY STAGE-III


Instruction: Fill in the spaces below with correct verbs following the instructions provided.

1. We…….. to the cinema last week. (Make the sentence simple past)

2. A bird pooed on the window that I ………… only a minute before. (Change to past

perfect)

3. Yesterday at nine he ………… in front of his computer. (Change into past continuous)

4. When their mum got home, the boys …………… TV for two hours. (Change into past

perfect continuous)

Activity 1

c. We saw some beautiful rainbows.

Activity 2

a.was making

b.were you

c.were wondering

Activity 3

a.had seen

b.had left

c.had sold

Activity 4

a.had been waiting

b.had been driving

c.had she been learning

Answer for Activities

Answer for Self-check for Learning 1.went

2.had cleaned

3.was sitting

4.had been watching



KEY STAGE-III


Theme: Language and Grammar

Topic: Present Tense

Background

What is a tense?

A tense is a verb form that shows the time of an action, event or state, by a change in its form

and/or the use of a helping verb. Examples: works, see, will-call, is standing, have gone, looked.

English verbs can refer to the present, past, or future time.

In this lesson, you will learn four forms of simple present tense. They are:

✓ Present Simple

✓ Present Perfect

✓ Present Continuous

✓ Present Perfect Continuous

Now, let us look at four forms of simple present tense and its rule in detail.

1. Present Simple

The simple present tense expresses an action regularly happening or a universal truth.

Rule: [Subject +Verb (s/es form with 3rd person singular)]

Example:

✓ Students learn through the BBS lesson every day. (Habitual action)

✓ Honey is sweet. (Universal truth)

Example: For 3rd person singular.

✓ He- He drives a car.

✓ She- She washes her clothes.

✓ It- It eats rice.

✓ Differentiate four forms of present tense based on its

degree of completeness.

✓ Use each of the forms correctly.



KEY STAGE-III

Example: when the subject of the sentence isn’t in 3rd person singular,

✓ We go to the Dzong.

✓ I read every evening.

2. Present Continuous

It expresses an action going on at present.

Rule: [Subject + am/is/are + ing form of the verb]

Example:

✓ I am teaching.

✓ Bhutan is developing.

✓ We are staying at home.

3. Present Perfect

It expresses an action that has just been completed.

Rule: [Subject + have/has + past participle form of verb]

Examples:

✓ I have finished my project.

✓ The plane has just landed.

Activity 1

Instruction: Make the following sentences into the present perfect tense.

1. I study English.

2. They go to America.

3. She eats octopus.

4. We read that book.

5. You know Tenzin for 20 years.

6. I lose my books.

7. She passed the exam.

4. Present Perfect Continuous

It expresses an action that had begun in the past and is still going on.

Rule: [ Subject + have/has + been + ing form of verb]

Example:

✓ The schools in Bhutan have been closing since the first week of March.

✓ She has been reading for seven hours.



KEY STAGE-III

Activity 2

Instruction: Make the following into Present Perfect Continuous Tense.

1. I (stand) here for 15 minutes.

2. Pema (read) all day.

3. He (play) football, so he’s tired.

4. They (learn) Korean for two years.

5. It (rain). So, the pavement is wet.

Summary

Study the rules for the present tense.

✓ Subject +Verb (s/es) ✓ Subject + am/is/are + ing form of the verb

✓ Subject+ have/has+ past participle form of verb

✓ Subject+ have/has+ been+ ing form of verb


Instruction : Fill in the space below with correct verbs following the instructions given in the

bracket.

1. I usually __________ (go) to school. (Change to Present Simple)

2. Pema _____________(visit) us often. (Change to Present Simple)

3. It is ______________(get) late. We must go home. (Change to Present Continuous)

4. I cannot ask her now. She is ___________(pray). (Change to Present Continuous)

5. She __________(have/has) already finished my homework. (Change to Present

Perfect)

6. (Have/Has) you taken the dog for a walk? (Change to Present Perfect)

7. We/ sit/ on the chair. (Change into Present Perfect Continuous)

8. It /rain/ all day. (Change into Present Perfect Continuous)



KEY STAGE-III

1.go

2.visits

3.getting

4.praying

5.has

6.have

7.have been sitting

8.has been raining

Answers for Self-check for Learning

Activity 1

1.I have studied English.

2.They have gone to America.

3.She has eaten octopus.

4.We have read that book.

5.You have known Tenzin for 20 years.

6.I have lost my books.

7.She has passed the exam.

Activity 2

1.I have been standing for 15 minutes.

2.Pema has been reading all day.

3.He has been playing football, so he’s tired.

4.They have been learning Korean for two years.

5.It has been raining. So, the pavement is wet.

Answers for Activities



KEY STAGE-III



Topic: Future Tense

Background

The future tense is the verb tense used to describe a future event or state of being.

1. Simple Future Tense

Simple Future Tense describes an action that has not taken place, but will take place

sometime in the future.

To make the concept clear, let us look at the rules of how Simple Future Tense is formed:

Rule: Subject +will/shall+ going to +root form verb

Note: ‘Shall’ is usually used with the first person singular and plural (I and We) whereas ‘will’

is used with all persons (I, we, he, she, it, they, you).

Example:

✓ I shall wash my hands.

✓ Tshogyel will walk next year.

✓ Lekzin is going to write a story.

2. Future Continuous Tense

It expresses an action that is likely to happen in the future.

Rule: Subject+shall/will/(be+going to) +be+ing form of verb

Example:

✓ We shall be eating breakfast at 8 am.

✓ They will be playing football tomorrow.

✓ Ugyen is going to be studying this evening.

✓ Differentiate four forms of future tense based on its

degree of completeness.

✓ Use each of the forms correctly.



KEY STAGE-III

Subject Future Continuous

Tense

We shall be eating

They will be playing

Ugyen is going to be studying

Activity 1

Instruction: Identity, Simple Future Tense, and Future Continuous Tense, from the following

sentences.

1. I shall dance tonight.

2. Ugyen will be working hard this year.

3. It will be raining tomorrow.

4. You are going to be staying at home.

3. Future Perfect Tense

It expresses an action that will be completed at some point of time in the future

Rule: Subject + shall /will/ (be+going to) + have + Past participle

Example:

✓ I shall have learned English by the end of this year.

✓ We will have shifted to our new home by next week.

✓ She is going to have finished her homework by dinner time.

Activity 2

Instruction: Change each verb in the brackets to future perfect tense.

1. By this time tomorrow, I (finish) the project.

2. Ugyen (sells) her car by next Sunday.

3. She (cleans) the entire house by lunch.

4. You (understand) this lesson by the end of my presentation.

5. We (finish) our homework by tomorrow.



KEY STAGE-III

4. Future Perfect Continuous Tense

It expresses an action that will be completed at some point in time in the future but will

be continuing until then.

Rule: Subject + shall/will/ + have + been + ing form of verb

Example:

✓ By January next year, I shall have been teaching for eleven years.

✓ At five o'clock, we will have been listening to the English lesson for twenty-five

minutes.

✓ When Chungku turns fifteen, she will have been playing football for eleven years.

Activity 3

Instruction: Underline the verbs in each of the following sentences. All sentences are in

Future Perfect Continuous Tense.

1. Karma will have been living in Paro for eight years by this summer.

2. We shall have been studying at this school for four years by this October.

3. You are going to have been waiting for more than two hours when her plane finally

arrives.

4. Dechen will have been talking for an hour by the time she sleeps.

5. Dema is going to have been praying for three hours by the time she goes for a walk.

Summary

Future tense describes an action that will take place sometime in the future. The four types of

future tenses are;

1. Simple Future Tense

✓ It describes an action that will take place sometime in the future.

2. Future Continuous Tense

✓ It expresses an action happening at a stated time in the future.

3. Future Perfect Tense

✓ It expresses an action that will be completed at some point in time in the future.

4. Future Perfect Continuous Tense

✓ It expresses an action that will be completed at some point of time in future but

will be continuing until then.



KEY STAGE-III

Instruction: Study the rules for the Future Tense.

✓ Subject + am/is/are] + going to + root form verb] (Simple Future)

✓ Subject + shall/ will/ (be+going to) + be + ing form of verb (Future Continuous)

✓ Subject + shall /will/ (be+going to) + have + Past participle (Future Perfect)

✓ Subject + shall/will/ + have + been + ing form of verb (Future Perfect Continuous)


Instruction : Rewrite the sentences as per the instruction given in the brackets.

1. Tshomo plays guitar today. (Change to Simple Future tense)

2. I will meet Deki this Saturday. (Change to Future Continuous tense)

3. By the end of this week, he is going to complete his assignment. (Change to Future

Perfect tense)

4. They will fly to London for 4 hours by this time tomorrow. (Change to Future Perfect

Continuous Tense)

1.Tshomo will/shall play guitar today. 2.I shall/will be meeting Deki this Saturday.

3.By the end of this week, he will have

completed his assignment. 4.They will have been flying to London for 4

hours by this time tomorrow.




KEY STAGE-III

Activity 1

1.Simple future tense.

2.Future continuous tense



Activity 2

1.By this time tomorrow, I(shall/will/am going to

have finished) the project.

2.Ugyen (will/is going to have sold) her car by

next Sunday.

3.She (will/is going to have cleaned) the entire

house by lunch.

4.You (will/are going to have understood) this

lesson by the end of my presentation.

5.We (shall/will/are going to have finished) our

homework by tomorrow.

Activity 3

1.will have been living

2.shall have been studying

3.are going to have been waiting

4.will have been talking

5.is going to have been praying

Answers for Activity



KEY STAGE-III



Topic: Conversion of Direct to Indirect Speech

Background

Direct Speech

Direct speech is a sentence in which the exact words spoken are reproduced within quotation

marks or inverted commas.

Example:

✓ She said to me, "I am looking for my keys."

✓ "He misses his friend," said Pema.

Indirect Speech

Indirect speech is a report on what someone else said or wrote without using that person's exact

words. It is also called indirect discourse or reported speech. Reports on what someone said or

wrote

Example:

✓ She told me that she was looking for her keys.

Changed/transformed version

Instruction: Carefully study the table given below and remember; when you change a direct

speech into indirect speech or vice-versa, for example a direct speech under Simple Present will

change into Simple Past and vice-versa. Similarly, this applies to all the other tenses as

mentioned in the table below.

Direct Speech Indirect Speech

Present simple:

✓ Deki said, “I always wear Kira.”

✓ “I write poetry,” she said.

Past simple:

✓ Deki said (that) she always wore Kira.

✓ She said (that) she wrote poetry.

Present continuous:

✓ He said, “I am looking for a dog.”

✓ “I am doing my homework,” said the

girl

Past continuous:

✓ He said (that) he was looking for a dog.

✓ The girl said that she was doing her

homework.

✓ Study the information on Direct and Indirect speech.

✓ Convert Direct speech to Indirect speech relating to

tenses.



KEY STAGE-III

Activity 1

Instruction: Study the following direct speech. Out of four alternatives, select the one which

best expresses the same sentence in indirect speech.

1. Penjor asked me, ‘Did you see the cricket match on TV last night?’

a) Penjor asked me if I had seen the cricket match on TV the previous night.

b) Penjor asked me if I saw the cricket match on TV the previous night.

c) Penjor asked me did I see the cricket match on TV last night.

d) Penjor asked me whether I had seen the cricket match on TV last night.

2. Dawa said to his mother, ‘I am leaving for New York tomorrow.’

a) Dawa told his mother that he was leaving for New York tomorrow.

b) Dawa told his mother he is leaving for New York tomorrow.

c) Dawa told his mother that he was leaving for New York the next day.

d) Dawa told his mother he would be leaving for New York the next day.

Present perfect simple:

✓ Karma said, “Where have they gone?

✓ “You have seen that movie many

times,” said her father.

Past perfect simple:

✓ Karma wondered where they had gone.

✓ Her father said I had seen that movie

many times.

Present perfect continuous:

She said, "I've been teaching English for

seven years."

Past perfect continuous:

She said she had been teaching English for

seven years.

Past simple:

She said, "I taught online yesterday."

Past perfect: She said she had taught online

yesterday.

Past continuous:

✓ We were living in Bjemina during

those days,” they said to me.

✓ Dawa asked, “Were you studying

when she called?”


✓ They told me that they had been living

in Bjemina during those days.

✓ Dawa asked whether he had been

studying when she called.

Past perfect:

“I had gone to visit my mother,” he explained

Past perfect: NO CHANGE –

He explained (that) he had gone to visit his

mother


The teacher said, “He had been watching

you.”

Past perfect continuous: NO CHANGE –

The teacher said he had been watching you.



KEY STAGE-III

3. I said to him, ‘Why don’t you work hard?’

a) I asked him why didn’t you work hard.

b) I asked him why he didn’t work hard.

c) I asked him why he wouldn’t work hard.

d) I asked him why he wasn’t working hard.

4. He said to her, ‘What a hot day!’

a) He exclaimed sorrowfully that it was hot day.

b) He told her that it was a hot day.

c) He exclaimed that it was a hot day.

d) He said that it was a hot day.

5. The Lama said, ‘Be quiet and listen to my words.’

a) The Lama said them to be quiet and listen to his words.

b) The Lama told them that they should be quiet and listen to his words.

c) The Lama urged them to be quiet and to listen to his words.

d) The Lama said they should be quiet and listen to him.

Summary

Direct Speech

✓ Direct speech is a sentence in which the exact words spoken are reproduced within

quotation marks or inverted commas.

Indirect Speech

✓ Indirect speech is a report on what someone else said or wrote without using that person's

exact words. It is also called indirect discourse or reported speech. Reports on what

someone said or wrote



KEY STAGE-III


Instruction : Complete the sentences in reported speech.

1. Karma said, "I love this town."

2. "Are you sure?" He asked me.

3. "I can't drive a car," he said.

4. "Be nice to your brother," he said.

5. "Don't be naughty," he said.

6. "What have you decided to do?" she asked him.

7. "I always wake up early," he said.


1. a) Penjor asked me if I had seen the cricket match on TV the

previous night.

2. c) Dawa told his mother that he was leaving for New York the next

day.

3. b) I asked him why he didn’t work hard.

4. c) He exclaimed that it was a hot day.

5. c) The Lama urged them to be quiet and to listen to his words.



KEY STAGE-III

1.Karma said that he loved that town.

2.He asked me if/whether I liked soccer.

3. He said (that) he couldn’t drive a car.

4. He asked me to be nice to my brother.

5. He urged me not to be naughty.

6. She asked him what he had decided to do.

7. He said (that) he always woke up early.


རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 25

གནས་རིམ་ ༣ པ།

རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས། འཆར་གཞི་ཨང.་ ༡ ཆོས་ཚན་ རྩོང་ཁ། སྩོབ་རིམ་ བདུན་པ་དང་བརྒྱད་པ། དུས་ཡུན་ སྐར་མ་ ༥༠

དྩོན་ཚན་ འབྲི་རྩོམ། ནང་གསེས་དྩོན་ཚན་ རྒྱུད་སྐུལ་དང་ འཆར་སྣང་འབྲི་རྫོམ།

ངོ་སྩོད།

འབྲི་རྩོམ་ཟེར་མི་འདི་ སྤྱིར་བཏང་གནད་དྩོན་ཅིག་ལུ་ གཞི་བཞག་ཞིནམ་ལས་ ངོ་སྩོད་དང་ བར་གྱི་གནད་དྩོན་ དེ་ལས་ མཇུག་

བསྡུ་ཚུ་ཡྩོད་པའི་ འབྲི་བཀོད་ཅིག་གི་ཐྩོག་ལས་ ལྷག་མི་ཚུ་ ཡིད་ཆེས་བསྐྱེད་ཚུགས་པའི་ ཚིག་དྩོན་གྱི་རྣམ་འགྱུར་བཙུགས་ཏེ་

རྩོམ་སྒྲིག་འབད་ཡྩོད་པའི་ རྩོམ༌རིག་ཅིག་ལུ་སབ་ཨིན།

འབྲི་རྩོམ་གྱི་དབྱེ་བ་ལེ་ཤ་ཡྩོད་རུང་ འབྲི་རྩོམ་ལུ་སྤྱིར་བཏང་ དངོས་འབྱུང་འབྲི་རྩོམ་དང་ འཆར་སྣང་འབྲི་རྩོམ་གཉིས་ནང་ལུ་

བསྡུཝ་ཨིན། དངོས་འབྱུང་འབྲི་རྩོམ་ཟེར་མི་འདི། དངོས་སུ་འབྱུང་བའི་གནད་དྩོན་ཚུ་ ཡིག་ཐྩོག་ལུ་བཀོད་མི་གི་འབྲི་རྩོམ། དཔེར་

ན། རྒྱལ་རབས་བཟུམ་ཅིག་དང་། འཆར་སྣང་འབྲི་རྩོམ་ཟེར་མི་འདི་ ངོ་མ་མེན་པར་ རང་གི་སེམས་ཀྱིས་བཟྩོ་སྟེ་ ཡིག་ཐྩོག་ལུ་

བྲིས་མི་ཅིག་ལུ་སབ་ཨིན། དཔེར་ན། ཨམ་སྲིན་མྩོ་གི་སྲུང་བཟུམ་ཅིག་ལུ་སབ་ཨིན།

འབྲི་རྩོམ་ལུ་ དབྱེ་བ་ལེ་ཤཱ་ཡྩོད་རུང་ ད་ལྩོའི་དྩོན་ཚན་ནང་ལུ་ རྒྱུད་སྐུལ་དང་ འཆར་སྣང་འབྲི་རྩོམ་གྱི་སྐོར་ལས་ ལྷབ་ནི་ཨིན།

✓ རྒྱུད་སྐུལ་དང་ འཆར་སྣང་འབྲི་རྩོམ་ཟེར་བའི་གོ་དྩོན་ གསལ་ཏྩོག་ཏྩོ་འབད་སབ་ཚུགས།

✓ འབྲི་རྩོམ་གཉིས་ཀྱི་ཁྱད་ཆོས་ཚུ་ རེ་རེ་བཞིན་དུ་ ངོས་འཛིན་འབད་དེ་བྲི་ཚུགས།

✓ ཁྱད་ཆོས་ཚང་བའི་རྒྱུད་སྐུལ་དང་ འཆར་སྣང་འབྲི་རྩོམ་རེ་ བྲི་ཚུགས།

ལས་དྩོན།



རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས། འབྲི་རྩོམ་ག་ཅི་ར་བྲི་དགོ་རུང་ སྤྱིར་བཏང་ འབྲི་རྩོམ་གྱི་ཁྱད་ཆོས་གསུམ་ཚང་དགོཔ་ཨིན།

སྩོང་ལཱ་ ༡ པ།

བཀོད་རྒྱ། འྩོག་ལུ་ རྒྱུད་སྐུལ་དང་འཆར་སྣང་འབྲི་རྩོམ་གྱི་ གོ་དྩོན་དང་དཔེ་གཉིས་ ལེགས་ཤྩོམ་སྦེ་ལྷག།

རྒྱུད་སྐུལ་འབྲི་རྫོམ།

གནད་དྫོན་ག་ཅི་ཨིན་རུང་ འདི་ ཐབས་ཤེས་ཀྱི་ཐྫོག་ལས་ མི་གཞན་གྱི་སེམས་ བཅོས་ཁ་རྐྱབ་ཚུགས་པའི་ བདེན་པ་གཟང་སྟེ་

འབྲི་སབ་འབད་མི་ཅིག་ལུ་སླབ་ཨིན། དཔེར་ན་ ཆང་དང་ཏམ་ཁུ་གི་ཉེས་དམིགས་ བཟུམ་ཨིན།

རྒྱུད་སྐུལ་འབྲི་རྩོམ་ བྲི་བའི་སྐབས་ལུ་ ཚང་དགོ་པའི་ཁྱད་ཆོས་ཚུ་ཡང་།

✓ ཡིད་ཆེས་སྐྱེད་ཚུགས་པའི་ རྒྱུད་སྐུལ་གྱི་ཚིག་དྫོན་ཚུ་བཙུགས་དགོ།

✓ ཡིད་ཆེས་སྐྱེད་ཐབས་ལུ་ ཁུངས་དང་དགོས་པ གཏམ་ དཔེ་གཏམ་ཚུ་བཙུགས་དགོ།

✓ རྒྱུད་སྐུལ་གྱི་ཚིག་ཚུ་ བསྐོར་ཏེ་མེན་པར་ ཕྲངམ་ཕྲང་ས་ར་ དྩོན་དག་ཧ་གོ་ཚུགསཔ་འབད་ རྒྱུད་སྐུལ་འབད་དགོ།

འཆར་སྣང་འབྲི་རྫོམ།

འཆར་སྣང་འབྲི་རྫོམ་ཟེར་མི་འདི་ གནད་དྩོན་ག་ཅི་འབད་རུང་ཅིག་གི་སྐོར་ལས་ རང་གི་སེམས་ཀྱིས་བཟྫོ་སྟེ་ཡྩོད་མི་འདི་ ཡིག་

ཐྫོག་ལུ་བྲི་མི་ཅིག་ལུ་སླབ་ཨིན། དཔེར་ན་ ལྫོ་བཅོ་ལྔ་གི་ཤུལ་ལས་ ངེ་གི་མི་ཚེ་ ཟེར་དྩོ་བཟུམ་ཨིན།

འཆར་སྣང་འབྲི་རྫོམ་གྱི་ཁྱད་ཆོས།

✓ དངོས་སུ་འབད་མ་བྱུང་མི་ གནད་དྫོན་ཅིག་ལུ་གཞི་བཞག་སྟེ་བྲི་དགོ།

✓ མ་འྫོངས་པའི་འཆར་སྣང་ལུ་ གཞི་བཞག་བཞགཔ་ཅིག་དགོ།

✓ སེམས་ཀྱིས་བཟྫོ་སྟེ་བྲིས་བྲིསཝ་ཅིག་དགོ།

༡༽ ངོ་སྩོད། ༢༽ བར་གྱི་གནད་དྩོན། ༣༽ མཇུག་བསྡུ།



རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས། རྒྱུད་སྐུལ་འབྲི་རྫོམ་གྱི་དཔེ།

༉ དུས་ཀྱི་འགྱུར་བ་དང་འཁྲིལ་ཏེ་ འཛམ་གླིང་རྒྱལ་ཁབ་ག་ཏེ་ལུ་ཡང་ རང་སེམས་བདག་འཛིན་འབད་མ་ཚུགས་མི་ ག་ར་གིས་ འཚྩོར་སྣང་ཚུ་ མ་པ་ལས་རང་མེད་པར ཉལ་རུང་མ་ཆགས་ ལྩོང་རུང་མ་ཆགས་པར་ དེ་ཚུ་ ལྫོངས་སྫོད་བའི་སྒང་ལས་ རང་གིས་རང་ ག་ཨིན་ན་ཡང་མ་ཤེསཔ་འགྱོ་སྟེ་ ཚེ་སྫོག་ལུ་བར་ཆད་རྐྱབ་ ལུས་དང་སྫོག་གཉིས་ ཁ་འཕྱལ་ཏེ་བཏང་མི་ རས་སྫོར་ངན་པ་ཅིག་ལུ་ སྫོ་རས་ཟེར་སླབ་ཨིན།

དང་པ་ སྫོ་རས་ཚུ་ལྫོངས་སྫོད་བ་ཅིན་ མི་སྡེ་ནང་ལུ་ ལས་རྒྱུ་འབྲས་ཡྫོད་པའི་སྣང་བ་མེདཔ་ལས་ དུད་འགྲོ་སེམས་ཅན་ཚུ་ འཚེར་སྣང་མེད་པར་བསད་ནི་དང་ ཕམ་དང་སྤུན་ཆ་ ལྟ་ལྟྫོ་ཚང་ཚུ་ལུ་ཡང་ འདུ་ཤེས་མེད་པའི་སྒོ་ལས་ གཅིག་གིས་གཅིག་ལུ་ རྡུང་རྫོབ་དང་འཐབ་འཛིང་འབད་དེ་ གོངམ་དཔྫོན་གཡྫོག་ཚུ་ལུ་ ངོ་རྒོལ་འབདཝ་མ་ཚད་ གནམ་ཉི་མ་ སང་ཁྱི་བཟུམ་སྦེ་ ཁྲོམ་བཤལ་རྐྱབ། ཕྱི་རུ་ཁྲོམ་ཁར་ལས་ཕར་ ཚུལ་མིན་གྱི་སྐད་རྐྱབ་སྟེ་ མི་སྡེ་དང་ རྒྱལ་ཁབ་ནང་ལུ་ཡང་ སྟབས་མ་བདེཝ་སྫོམ་བཟྫོཝ་མས་ཟེར་ཞུ་ནི་ཨིན།

གཉིས་པ་ སྫོ་རས་འདི་ལས་བརྟེན་ཏེ་ རང་གི་གཟུགས་ཁམས་འཕྫོད་བསྟེན་ལུ་ གནྫོད་པ་ག་དེ་སྦེ་ཡྫོདཔ་ཨིན་ན་ ཟེར་བ་ཅིན དེཡང་ ལྫོངས་སྫོད་མི་ མི་འདི་ དུས་རྒྱུན་དུ་ལག་ལེན་འཐབ་ནི་འདི་གིས་ ཀླད་ར་ལུ་གནྫོད་པ་རྐྱབ་སྟེ་ གཟུགས་ཀྱི་སྟྫོབས་ཤུགས་ཚུ་ མར་ཉམས་འགྱོཝ་ལས་ ལྟྫོ་བཟའ་ནི་ལས་ལྷག་སྟེ་ སྫོ་རས་ལྩོངས་སྩོད་ནི་ལུ་དགའ་སྟེ་ ཉིནམ་གཅིག་ཡང་ སྩོ་རས་མ་བཟའ་བར་ སྩོད་མ་ཚུགསཔ་མ་ཚད་ འཆོལ་ནི་བཟུམ་སྦེ་ ས་མཐྫོ་ས་ལས་མཆོངསཔ་དྲག་ག་ རང་སྫོང་གཅདཔ་དྲག་ག་ ཟེར་བའི་ མནྩོ་བསམ་ངན་པ་བཏང་སྟེ་ ག་ཐྫོབ་གུ་ཐྫོབ་ བཟའ་ནིའི་ཉེན་ཁག་ཡྫོདཔ་ལས་ རང་གི་གཟུགས་ཁམས་འཕྫོད་བསྟེན་ལུ་ གནྫོད་པ་སྫོམ་ཡྫོད་ཟེར་ཞུ་ནི་ཨིན།

མཇུག་ར་ རས་ངན་སྫོ་རས་ལྫོངས་སྫོད་བ་ཅིན་ རང་དང་གཞན་ལུ་ གནྫོད་པ་ག་ཅི་བཟུམ་ར་ཡྫོདཔ་ཨིན་ན་ གོང་ལུ་བཤད་དེ་ཡྫོད་པའི་ གནད་དྫོན་ཚུ་ དབྱེ་དཔྱད་འབད་དེ་ ད་ལས་ཕར་ འདི་བཟུམ་མིའི་ རས་ངན་པ་ཚུ་ རང་གི་སྫོག་ལུ་ཐུག་སྟེ་འབད་རུང་ ལྫོངས་མ་སྩོད་བར་ མི་ཚེ་དྫོན་དང་ལྡནམ་ཅིག་ བཟྫོ་ནི་ཟེར་བའི་མནྫོ་བསམ་བཏང་སྟེ་ འཕལ་ཕུགས་གཉིས་ལུ་ཕན་པའི་ ལཱ་འབད་ནིའི་འཆར་གཞི་བརམ་དགོཔ་འདི་ ག་ཅི་དེ་ གལ་ཆེ་བས་ཟེར་ཞུ་ནི་ཨིན།



རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས། འཆར་སྣང་འབྲི་རྫོམ་གྱི་དཔེ།

ང་ལུ་མངོན་ཤེས་ཅིག་ཡྫོད་པ་ཅིན།

༉ ང་བཅས་མི་ མང་ཤྫོས་ར་ རང་གི་རྒྱུ་དང་སྤུ་གིས་མ་ལྕོགས་རུང་ སེམས་ཀྱི་རེ་བ་འདི་ སྫོམ་འབད་ར་བསྐྱེད་དེ་ སྫོད་

མི་ཙང་ཙ་ཨིན། དེ་དང་འདྲཝ་འབད་ ང་ལུ་ཡང་ མངོན་ཤེས་ཅིག་ཡྫོད་པ་ཅིན་ཟེར་ དུས་ཨ་རྟག་ར་ མནྫོ་བསམ་གཏངམ་

གཏང་ས་ར་སྫོད་དེ་ རང་གི་མགུ་ལུ་སྐྱེ་བའི་སྐྱ་ཡང་དཀརཔྫོ་ལུ་གྱུར། ཁ་ནང་གི་སྫོ་ཡང་ཉིན་ལྟར་བཞིན་དུ་ བུད་དེ་འགྱོཝ་

ཨིནམ་ མ་པ་ལས་མ་ཤེས་པས།

དང་པ་ ང་ལུ་མངོན་ཤེས་ཅིག་ཡྫོད་པ་ཅིན་ རང་གི་ཕམ་དང་བུ་གཞི་ གཉེན་ཉེཝ་དང་ལྟ་ལྟྫོ་ཚང་ འཆམ་མཐུནམ་ཚུ་

ལུ་ ཁོང་གིས་བསྐྱེད་དེ་ཡྫོད་པའི་རེ་བ་དང་འཁྲིལ་ཏེ་ རྒྱུ་དང་ཡྫོན་ཏན། ཐྫོབ་གོ་ས་ཚུ་ ག་ཅི་དགོ་རུང་ ཁོང་ནམ་ཁག་ཆེ་

བའི་སྐབས་ བྱིན་ཆོག་ཆོག་འབད་བཞག་སྟེ་ ཁོང་གི་མནྫོ་དྩོན་ཚུ་ ག་ཨིནམ་འབད་ར་ འགྲུབ་ཏེ་འབྱིན་ཚུགས་པའི་རེ་བ་

ཨིན།

གཉིས་པ་ རྒྱབ་ཁབ་དང་གཞུང་ལུ་ ནད་མ་འྫོངམ་ལས་རིམ་འགྲོ། །ཆུ་མ་འྫོངམ་ལས་གཡུར་བ། །ཟེར་དྫོ་བཟུམ་ ད་

རེས་ནངས་པ་ དེ་བཟུམ་གྱི་ནད་གཞི་གདུག་དྲགས་ཚུ་ མ་འཐྫོན་པའི་སྔ་གོང་ལས་ སྔོན་འགོག་འབད་ནིའི་ཐབས་ལམ་དང་

འཆར་གཞི་ཚུ་བརམ་ཏེ་ བྱ་སྟབས་བདེ་ཏྫོག་ཏྫོ་བཟྫོ་ཞིནམ་ལས་ རྒྱལ་ཁབ་འདི་ ཞི་བདེ་གི་ཐྫོག་ལུ་བཞག་ནི་ཨིན་ཟེར་བའི་

མནྩོ་བསམ་ཡང་གཏང་སྟེ་འྫོངམ་མས།

མཇུག་ར་ རང་གི་རེ་བ་ དེ་འབད་བསྐྱེད་རུང་ ཚེ་སྔོན་ཚྫོགས་བསགས་ཀྱི་འབྲས་བུ་ཆུངམ་ལས་བརྟེན་ཏེ་ མནྫོ་མནྫོ་

བའི་ཤིང་ཁར། བསམ་བསམ་པའི་བྱ་འཁོར་ཚུགས་པར་ ལཱ་ཁག་འདུག་ཟེར་ཞུ་ནི་ཨིན།



རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས།

སྩོང་ལཱ་ ༢ པ།

བཀོད་རྒྱ། འྫོག་ལུ་ཡྫོད་པའི་ འབྲི་རྫོམ་གྱི་དྫོན་ཚན་གཉིས་ལས་ གཅིག་གདམ་ཁ་རྐྱབ་སྟེ་ ཚིག་འབྲུ་ ༢༠༠ ལས་མ་ཉུངམ་

ཅིག་བྲིས།

ཀ༽ རྒྱུད་སྐུལ་འབྲི་རྩོམ་གྱི་དྩོན་ཚན་ ལམ་ལུགས་སྩོལ་བདག་འཛིན་འབད་དགོ།

ཁ༽ འཆར་སྣང་འབྲི་རྫོམ་གྱི་དྫོན་ཚན་ ཁྱོད་ལུ་ རི་ཡང་བརྡལ་ཚུགས་པའི་ ཁེ་ཀོ་ཡྫོད་པ་ཅིན་ ཁྱོད་ཀྱིས་ག་ཅི་འབད་འྫོང་གོ?

བཅུད་བསྡུས།

འབྲི་རྩོམ་གྱི་དབྱེ་བ་ལེ་ཤ་ཡྩོད་རུང་ འབྲི་རྩོམ་ལུ་སྤྱིར་བཏང་ དངོས་འབྱུང་འབྲི་རྩོམ་དང་ འཆར་སྣང་འབྲི་རྩོམ་གཉིས་ནང་ལུ་

བསྡུཝ་ཨིན། རྒྱུད་སྐུལ་འབྲི་རྩོམ་བྲི་བའི་སྐབས་ལུ་ གཞན་ཕར་ལྩོགས་མའི་མི་གི་ སེམས་འགྱུར་ཚུགསཔ་ཅིག་འབད་ བྲི་དགོཔ་

ཨིན། དེ་ལས་ འཆར་སྣང་འབྲི་རྩོམ་ཟེར་མི་འདི་ ངོ་མ་མེན་པར་ རང་གི་སེམས་ཀྱིས་བཟྩོ་སྟེ་ བྲིས་མི་ཅིག་ལུ་སབ་ཨིན། སྤྱིར་

བཏང་ འབྲི་རྩོམ་འབྲི་བའི་སྐབས་ ཚང་དགོ་པའི་ ཁྱད་ཆོས་ཚུ་ཡང་ ངོ་སྩོད། བར་གྱི་གནད་དྩོན། མཇུག་བསྡུ་ཚུ་ཨིན།

རང་ཉིད་དབྱེ་ཞིབ།

༡༽ འཆར་སྣང་འབྲི་རྩོམ་དང་ རྒྱུད་སྐུལ་འབྲི་རྩོམ་གཉིས་ཀྱི་ཁྱད་པར་ ག་ཅི་ར་འདུག?

༢༽ འཆར་སྣང་འབྲི་རྫོམ་བྲིཝ་ད་ ཚང་དགོ་པའི་ཁྱད་ཆོས་ ག་ཅི་ཡྩོདཔ་ཨིན་ན་ ཚངམ་འབད་བྲིས།

༣༽ རྒྱུད་སྐུལ་འབྲི་རྩོམ་ བྲི་བའི་སྐབས་ལུ་ ཚང་དགོ་པའི་ཁྱད་ཆོས་ཚུ་ ཐྩོ་བཀོད།





ལྷག་ནིའི་སྩོང་ལཱ་ཨིནམ་ལས་ དྩོན་ཚན་འདི་ ལེགས་ཤྩོམ་འབད་ལྷག་དགོཔ་ཨིན།


འབྲི་རྩོམ་དྩོན་ཚན་ གཉིས་ལས་ གཅིག་གདམ་ཁ་རྐྱབ་སྟེ་བྲི་དགོ།

རང་ཉིད་དབྱེ་ཞིབ་ཀྱི་ལན་གསལ་དཔེ།

༡༽ འཆར་སྣང་འབྲི་རྫོམ་འདི་ དངོས་སུ་མེན་པར་ རང་གི་སེམས་ཀྱིས་བཟྩོ་སྟེ་ བྲིས་མི་ཅིག་ལུ་གོ་ནི་དང་ རྒྱུད་སྐུལ་ཟེར་མི་འདི་ ཕར་ལྫོགས་མའི་སེམས་འགྱུར་ཚུགས་པའི་ བདེན་ཁུངས་གཟང་སྟེ་བྲིས་མི་ཅིག་ལུ་སླབ་ཨིན། ༢༽ འཆར་སྣང་འབྲི་རྫོམ་བྲིཝ་ད་ ཚང་དགོ་པའི་གྱི་ཁྱད་ཆོས།

✓དངོས་སུ་འབད་མ་བྱུང་མི་ གནད་དྫོན་ཅིག་ལུ་གཞི་བཞག་དགོ།

✓མ་འྫོངས་པའི་འཆར་སྣང་ལུ་ གཞི་བཞག་བཞགཔ་ཅིག་དགོ།

✓སེམས་ཀྱིས་བཟྫོ་སྟེ་བྲིས་འབྲིཝ་ཚུ་ འྩོང་དགོཔ་ཨིན།

༣༽ རྒྱུད་སྐུལ་འབྲི་རྩོམ་ བྲི་བའི་སྐབས་ལུ་ ཚང་དགོ་པའི་ཁྱད་ཆོས་ཚུ་ཡང་

✓ཡིད་ཆེས་སྐྱེད་ཚུགས་པའི་ རྒྱུད་སྐུལ་གྱི་ཚིག་དྫོན་ཚུ་ཚང་དགོ།

✓ཡིད་ཆེས་སྐྱེད་ཐབས་ལུ་ ཁུངས་དང་དགོས་པ གཏམ་ དཔེ་གཏམ་ཚུ་བཀོད་དགོ།

✓རྒྱུད་སྐུལ་གྱི་ཚིག་ཚུ་ བསྐོར་ཏེ་མེན་པར་ ཕྲངམ་ཕྲང་ས་ར་ དྩོན་དག་ཧ་གོ་ཚུགསཔ་འབད་ རྒྱུད་སྐུལ་

འབད་དགོཔ་ཚུ་ཨིན།

ལན་གསལ་དཔེ།



རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས། འཆར་གཞི་ཨང་ ༢ ཆོས་ཚན་ རྩོང་ཁ། སྩོབ་རིམ་ བདུན་པ་དང་བརྒྱད་པ། དུས་ཡུན་ སྐར་མ་ ༥༠

དྩོན་ཚན་ ཡི་གུའི་སྫོར་བ། ནང་གསེས་དྩོན་ཚན་ ལྷག་བཅས།


ལྷག་བཅས། ལྷག་བཅས་ཟེར་མི་འདི་ ཚིག་ལྷག་མ་ག་ཅི་ར་འབད་རུང་ སླབ་མ་ཚར་བར་ཡྫོད་མི་ཚུ་ ཡར་འདྲེན་ཚུགས་པའི་ནུས་པ་ཡྫོད་པའི་ཕད་ཅིག་ལུ་སླབ་ཨིན།

ལྷག་བཅས་ཀྱི་ཕད་ ཡང་ན་ རྐྱེན། སྟེ་ ཏེ་ དེ་ གསུམ་དང་ རང་དབང་ཅན་གྱི་ཕད་ སྦེ་ རྩིསཝ་ད་ བཞི་ཡྫོདཔ་ཨིན། ཕྲད་རང་དབང་ཅན་ཟེར་མི་འདི་ ཕྲད་ག་ཅི་ར་འབད་རུང་ རྗེས་འཇུག་དང་འཁྲིལ་མ་དགོ་པར་ རྗེས་འཇུག་ག་ར་གི་ཤུལ་ལས་འཇུག་མི་ལུ་སབ་ཨིན། དཔེར་ན་ སྦེ། ཕྲད་འདི་ རྗེས་འཇུག་ག་དང་ཡང་ འཁྲིལ་མ་དགོ་པར་ རྗེས་འཇུག་ག་ར་གིས་ ཤུལ་ལས་འགྱོ་བཏུབ་མི་ཅིག་ཨིན།

ལྷག་བཅས་ཀྱི་ཕྲད་ ལག་ལེན་འཐབ་ཐངས་ཀྱི་དཔེ། ✓ རྒྱང་མཐྫོང་ལྟ་སྟེ་ ཕན་ཐྩོགས་བྱུང་ཡི། ✓ ཁྱིམ་ནང་སྩོད་དེ་ དཔེ་ཆ་ལྷབ། ✓ འགྲུལ་འཕྲིན་བཏང་སྦེ་ བྩོ་སབ་ཅི། ✓ ཕྩོརཔ་བཏྩོན་ཏེ་ ཇ་འཐུང་།

✓ ལྷག་བཅས་ཀྱི་གོ་དྩོན་དང་ ཕྲད་ཚུ་ངོས་འཛིན་འབད་ཚུགས། ✓ ལྷག་བཅས་ཀྱི་ཕྲད་ ལག་ལེན་འཐབ་སྟེ་ དཔེ་བྲི་ཚུགས། ✓ ལྷག་བཅས་ཀྱི་ཕད་དང་གཅིག་ཁར་ བྱ་ཚིག་གི་འཇུག་ཚུལ་ཚུ་ ཧ་གོ་སྟེ་ ལག་

ལེན་འཐབ་ཚུགས།





ལྷག་བཅས་ཀྱི་ཕྲད་ཚུ་ རྗེས་འཇུག་གི་མཐའ་མར་ འཇུག་ཚུལ་གྱི་སྩོམ་ཚིག།

ལྷག་བཅས་ཀྱི་ཕྲད་ལུ་ རྗེས་འཇུག་གི་ཐྩོབ་ལམ་དང་འཁྲིལ་བའི་དཔེ།

རྗེས་འཇུག ཕད། དཔེར་བརྗོད། ག

སྟེ། སྦེ།

སྣུམ་འཁོར་བཀག་སྟེ་ འཛུལ་སྫོང་། སྣུམ་འཁོར་བཀག་སྦེ་ འཛུལ་སྫོང་། ང ཆུ་བཀང་སྟེ་བཞག། ཆུ་བཀང་སྦེ་བཞག། བ ཁ་སླབ་སྟེ་ འཆར་གཞི་བརམ། ཁ་སླབ་སྦེ་ འཆར་གཞི་བརམ། མ ཁ་འཆམ་སྟེ་ ལཱ་འབད། ཁ་འཆམ་སྦེ་ ལཱ་འབད། འ སེམས་དགའ་སྟེ་ ཁྱིམ་ནང་སྫོང་ཡི། སེམས་དགའ་སྦེ་ ཁྱིམ་ན་སྫོང་ཡི། མཐའ་མེད། ཁྱིམ་ན་འགྱོ་སྟེ་ ངལ་འཚྫོ། ཁྱིམ་ན་འགྱོ་སྦེ་ ངལ་འཚྫོ། ན

ཏེ།/སྦེ། སེམས་ཁར་དྲན་ཏེ་ བྲིས། སེམས་ཁར་དྲན་སྦེ་ བྲིས།

ར མེ་འབར་ཏེ་ ཚལ་མ་འཚིག། མེ་འབར་སྦེ་ ཚལ་མ་འཚིག། ལ ཉལ་ཏེ་ གཉིད་ལམ་མཐྫོང་། ཉལ་སྦེ་ གཉིད་ལམ་མཐྫོང་། ས ས་བསྲེས་ཏེ་ བཞག། ས་བསྲེས་སྦེ་ བཞག། ད དེ།/སྦེ། དད་པ་བསྐྱེད་དེ་ དབང་ཞུ། དད་པ་བསྐྱེད་སྦེ་ དབང་ཞུ།


བཀོད་རྒྱ། བྱ་ཚིག་གི་ གོ་དྩོན་དང་ ལྷག་བཅས་ཀྱི་ཕད་ བྱ་ཚིག་ལུ་འཇུག་པའི་དཔེ་ཚུ་ ལེགས་ཤྩོམ་འབད་ལྷག།

བྱ་ཚིག་གི་གོ་དྩོན། བྱ་ཚིག་ཟེར་མི་འདི་ ལཱ་ཅིག་འབད་བའི་དྫོན་སྟྫོན་པའི་ཚིག་ཅིག་ལུ་ སླབ་ཨིན།

སྟེ་ཏེ་དེ་གསུམ་ལྷག་བཅས་ཏེ། །ག་ང་བ་མ་འ་དང་ནི། །མཐའ་མེད་མཐའ་མར་སྟེ་ཐྫོབ་ཨིན། །ན་ར་ལ་ས་ཏེ་དང་ནི། ། རྗེས་འཇུག་ད་མཐར་དེ་ཐྫོབ་ཨིན། །རྫོང་ཁའི་སྐབས་ཀྱི་ཕད་སྦེ་འདི། །རྗེས་འཇུག་ག་རའི་མཐའ་མར་འཇུག །



རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས། ལྷག་བཅས་ཀྱི་ཕད་ བྱ་ཚིག་ལུ་འཇུག་ཚུལ།

༡༽ མིག་ཏྫོ་ལྟ་སྟེ་ ལཱ་འབད། ༢༽ ཡི་གུ་བཏང་སྟེ་ ལྩོག་འབྩོ། ༣༽ ལགཔ་བསྣར་ཏེ་ ཅ་ལ་ལེན།

༤༽ པར་བྲིས་ཏེ་ གྱང་གུ་སར། ༥༽ ས་ཁར་སྫོད་དེ་ བྩོ་སབ།

དཔེར་ན།

བྱ་ཚིག་ ལྷག་བཅས། ཚིག་ལྷག་མ། མིག་ཏྫོ་ལྟ་ སྟེ་ ལཱ་འབད། ཡི་གུ་བཏང་ སྟེ་ ལྩོག་འབྩོ།

ལྷག་བཅས་ཕད་ཀྱི་ཤུལ་ལས་ བྱ་ཚིག་འཇུག་པའི་དཔེ།

ལྷག་བཅས་ཕད་ཀྱི་ཤུལ་ལས་ བྱ་ཚིག་འཇུག་ནི་ཡྫོད། དེ་ཡང་ དུས་ག་ཅི་ལུ་འཇུགཔ་ཨིན་ན་ དབྱེ་བ་དཔྱད་དེ་བལྟ་དགོ།

དཔེར་ན། མིག་ཏྩོ་ལ་སྟེ་ བྲིས་ཡི། ཟེར་མི་ནང་ མིག་ཏྩོ་ ༼ལ་༽ བྱ་ཚིག། ༼སྟེ་༽ ཕྲད། ༼བྲིས་༽ བྱ་ཚིག།

༼ཡི་༽ དུས་འདས་པ་སྩོན་པའི་ཚིག་གྲོགས་ཨིན།

ལྷག་བཅས་ཕྲད་ཀྱི་ཤུལ་ལས་ བྱ་ཚིག་ དུས་གསུམ་དང་འཁྲིལ་འཇུག་ཐངས་ཀྱི་དཔེ།

དུས་འདས་པ་ དུས་མ་འྫོངས་པ་ དུས་ད་ལྟ་བ་ མིག་ཏྫོ་ལྟ་སྟེ་ བྲིས་ཡི། མིག་ཏྫོ་ལྟ་སྟེ་ བྲི་ནི། མིག་ཏྫོ་ལྟ་སྟེ་ འབྲི་དྫོ། པར་བྲིས་ཏེ་ བཏང་ཡི། པར་བྲིས་ཏེ་ གཏང་འྫོང་། པར་བྲིས་ཏེ་ གཏང་དེས།

ལགཔ་བསྣར་ཏེ་ བླུགས་ཅི། ལགཔ་བསྣར་ཏེ་ བླུག་གེ། ལགཔ་བསྣར་ཏེ་ བླུག་དྫོ།

འཛྩོལ་བ་འབད་བྲི་ནི་ཚུ་སྤང་དགོཔ།

ཁ་ལས་སབ་པའི་སྐབས་ ཕྲད་ཚུ་ སབ་ཐངས་སྩོ་སྩོ་འབད་སབ་རུང་ ཡིག་ཐྩོག་ལུ་བྲིཝ་ད་ ཕྲད་ཚུ་འཛྩོལ་བ་མེད་པར་བྲི་དགོཔ་ཨིན། དཔེར་ན་




འཛྫོལ་བ་ཨིན་མི། འཛྫོལ་བ་མེན་མི། ས་ཁར་སྫོད་འདི་བྲིས། ས་ཁར་སྫོད་དེ་བྲིས། ཡར་ལྫོང་འདི་བལྟ། ཡར་ལྫོང་སྟེ་བལྟ།

སྐད་སྒྱུར་འབད་འདི་བཞག། སྐད་སྒྱུར་འབད་དེ་བཞག། ཁྱིམ་ནང་སྩོད་འདི་ ངལ་འཚྩོ། ཁྱིམ་ནང་སྩོད་དེ་ ངལ་འཚྩོ། དཔེ་ཆ་ལྷབ་འབད་སྩོད། དཔེ་ཆ་ལྷབ་སྦེ་སྩོད།


བཀོད་རྒྱ། འྫོག་གི་དཔེར་བརྗོད་ཚུ་ལུ་ ལྷག་བཅས་ཀྱི་ཕད་ འཛྫོལ་བ་ཡྫོད་ག་མེད་ག་ དབྱེ་དཔྱད་འབད་དེ་ འཛྫོལ་བ་ཡྫོད་མི་ ཚུ་ ལེགས་བཅོས་འབད་དེ་བྲིས། ༡༽ རྐངམ་བརྐྱང་སྟེ་སྫོད། ༢༽ ལཱ་འབད་འདི་འུ་སྡུག། ༣༽ ཡི་གུ་འབྲི་སྟེ་བསྐྱལ། ༤༽ ཕར་བཏང་འབད་ལྫོག་ནི་མེད། ༥༽ ས་ཁར་སྫོད་དེ་ཉན། ༦༽ ཕར་འཕུལ་སྟེ་མ་བཞག། ༧༽ ཁུར་ཆ་འབག་དེ་འགྱོ། ༨༽ ལྷམ་ཕུད་སྟེ་ བཀོ་ད།

སྩོང་ལཱ་ ༣ པ།

བཀོད་རྒྱ། ལྷག་བཅས་ཀྱི་ཕད་ལུ་ རྗེས་འཇུག་གི་ཐྩོབ་ལམ་དང་འཁྲིལ་ཏེ་ དཔེ་རེ་རེ་བྲིས།

དཔེར་ན་ སྩོབ་གྲྭ་ནང་སྩོད་ དེ་ དཔེ་ཆ་ལྷབ།

ཁུར་ཆ་འབག་སྟེ་ དགོན་པ་སྩོང་།

མ་ འ་ མཐའ་མེད་

ག་ ང་ བ་

རྗེས་འཇུག། ཕྲད། རྗེས་འཇུག། ཕྲད་




ན་ ར་ ལ་

ས་ ད་


ལྷག་བཅས་ཟེར་མི་འདི་ ཚིག་ལྷག་མ་ག་ཅི་ར་ཨིན་རུང་ སླབ་མ་ཚར་བར་ཡྫོད་མི་ཚུ་ ཡར་འདྲེན་ཚུགས་པའི་ནུས་པ་ཡྫོད་པའི་ཕད་ཅིག་ལུ་སླབ་ཨིན། ལྷག་བཅས་ཀྱི་ཕད་ ཡང་ན་ རྐྱེན། སྟེ་ ཏེ་ དེ་ གསུམ་དང་ རང་དབང་ཅན་གྱི་ཕད་ སྦེ་ རྩིསཝ་ད་ བཞི་ཡྫོདཔ་ཨིན། བྱ་ཚིག་ཟེར་མི་འདི་ ལཱ་ཅིག་འབད་བའི་དྫོན་སྟྫོན་པའི་ཚིག་ལུ་ སླབ་ཨིན། ལྷག་བཅས་ཀྱི་ཕྲད་ ལག་ལེན་འཐབ་ཐངས་ཀྱི་དཔེ་ཚུ་ཡང་ ལམ་འགྱོ་སྟེ་ འུ་སྡུག། དཀའ་ངལ་འཐྩོན་ཏེ་ སྐྱིད་སྡུག་ཞུ། འྩོག་ལུ་བཀོད་དེ་བཞག་ནུག། ཟེར་དྩོ་བཟུམ་ཨིན།


བཀོད་རྒྱ། འྫོག་ལུ་ཡྫོད་པའི་རྗོད་ཚིག་ཚུ་ནང་ ལྷག་བཅས་ཀྱི་ཕད་ སྟེ་ ཏེ་ དེ་ གསུམ་ལས་ ག་འྫོས་འབབ་ཡྫོད་མི་འདི་ ལག་ལེན་འཐབ་སྟེ་བྲིས།

རང་ལུ་དགོ་པའི་ཡྫོན་ཏན་འདི་ དུས་ཚྫོད་འཕྫོ་བརླག་མ་གཏང་པར་ ཚ་ངེར་བཏྫོན་༡་་་་་་་་་་་་་ལྷབ་དགོ། དེ་མེན་ རང་ལུ་ ཡྫོན་ཏན་ཅིག་མེད་པ་ཅིན་ རང་ ངོ་ཚ་ ༢་་་་་་་་སྩོད་ནི་མ་གཏྩོགས་ གཞན་མེདཔ་ཨིན། ཐ་ན་གཡུས་ཁར་ལྷྫོད་་་༣་་་་་་་་་་་་འབད་རུང་ རང་ལུ་ ཁོག་པའི་ནང་ ཡྫོན་ཏན་ཅིག་མེད་པ་ཅིན་ གཞན་གྱིས་སྨད་པ་རྐྱབ་་༤་་་་་་་་་་་བཞགཔ་ཨིན། དེ་འབདཝ་ལས་ གཞུང་གིས་ ཤེས་ཡྫོན་སྟྫོང་པ་གནང་་་་༥་་་་་་་་་་་་ ཡྫོད་མི་ལུ་ དྲིན་ལན་འཇལ་ཚུགསཔ་ཅིག་འབད་དགོ།




སྩོང་ལཱ་༡ པ།

ལྷག་ནིའི་སྩོང་ལཱ་ཨིན།


༡༽ རྐངམ་བརྐྱང་སྟེ་སྫོད། ༢༽ ལཱ་འབད་དེ་འུ་སྡུག། ༣༽ ཡི་གུ་འབྲི་སྟེ་བསྐྱལ། ༤༽ ཕར་བཏང་སྦེ་ལྫོག་ནི་མེད། ༥༽ ས་ཁར་སྫོད་དེ་བཟའ། ༦༽ ཕར་འཕུལ་ཏེ་མ་བཞག། ༧༽ ཁུར་ཆ་འབག་སྟེ་འགྱོ། ༨༽ ལྷམ་ཕུད་དེ་ བཀོ་ད།

སྩོང་ལཱ་ ༣ པ།

དཔེ་ཚུ་ ཨ་ལྩོ་ཁོང་ར་གིས་ བྲི་དགོཔ་ཨིན།


༡༽ ཏེ། ༢༽ སྟེ། ༣༽ དེ། ༤༽ སྟེ། ༥༽ སྟེ།




རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས། འཆར་གཞི་ཨང.་ ༣ ཆོས་ཚན་ རྩོང་ཁ། སྩོབ་རིམ་ བདུན་པ་དང་བརྒྱད་པ། དུས་ཡུན་ སྐར་མ་ ༥༠ དྩོན་ཚན་ ཡི་གུའི་སྩོར་བ། ནང་གསེས་དྩོན་ཚན: འབྲེལ་སྒྲ་དང་ བྱེད་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ།

ངོ་སྩོད། འབྲེལ་སྒྲའི་གོ་དྫོན། འབྲེལ་སྒྲ་ཟེར་མི་འདི་ གང་ཟག་དང་དངོས་པྫོ་ཚུ་གི་བར་ན་ འབྲེལ་བ་སྟྫོན་པའི་ ཕྲད་ཅིག་ལུ་སླབ་ཨིན།

འབྲེལ་སྒྲའི་ཕད། གི། ཀྱི། གྱི། འི། ཡི།

འབྲེལ་སྒྲའི་ཕྲད་ཚུ་ རྗེས་འཇུག་གི་མཐའ་མར་ ཐྩོབ་ཐངས། རྗེས་འཇུག། ཕྲད།

ད་ བ་ ས་ གསུམ་གྱི་མཐའ་མར་ ཀྱི། ན་ མ་ ར་ ལ་ བཞི་གི་མཐའ་མར་ གྱི། ག་ ང་ འ་ མཐའ་མེད་ཀྱི་མཐའ་མར་ གི། འ་ དང་ མཐའ་མེད་ཀྱི་མཐའ་མར་ འི། ཡི།

མཐའ་མེད་ཀྱི་མཐའ་མར་ ཚིག་ཧེང་སྐལ་བཀལ་དགོ་པ་ཅིན་ ཡི་བྲི་ནི། མཐའ་མེད་ཀྱི་མཐའ་མར་ ཚིག་ཧེང་སྐལ་བཀལ་མ་དགོ་པ་ཅིན་ འི་བྲི་ནི། རྩོང་ཁའི་སྐབས་ལུ་ འི་དང་ཡི་གི་ཚབ་ལུ་ གི་བྲི་དགོཔ་ཨིན།


✓ འབྲེལ་སྒྲ་དང་ བྱེད་སྒྲའི་གོ་དྩོན་ཚུ་ལྷག་ཚུགས། ✓ འབྲེལ་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ་གྱི་གོ་དྩོན་དང་ དབྱེ་བ། དཔེ་ཚུ་ མ་འཛྩོལ་བར་བྲི་ཚུགས། ✓ བྱེད་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ་གི་ དབྱེ་བ་དང་གོ་དྩོན་ དཔེ་ཚུ་བྲི་ཚུགས།



རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས། བྱེད་སྒྲའི་གོ་དྩོན། བྱེད་སྒྲ་ཟེར་མི་འདི་ གང་ཟག་དང་ དངོས་པྩོ་གཉིས་ལས་ ལཱ་འབད་མི་ ག་ཨིན་ན་ སྩོན་པའི་ཚིག་ཅིག་ལུ་ སབ་ཨིན། ཡང་ན་ ག་གིས་ ག་ཅི་འབད་ཡི་ག་ སྩོན་མི་ཅིག་ལུ་ཡང་སབ་ཨིན།

བྱེད་སྒྲའི་ཕྲད། གིས། ཀྱིས། གྱིས། འིས། ཡིས།

བྱེད་སྒྲའི་ཕྲད་ཚུ་ རྗེས་འཇུག་གི་མཐའ་མར་ཐྩོབ་ཐངས།

རྗེས་འཇུག། བྱེད་སྒྲའི་ཕྲད། ད་ བ་ ས་ གི་མཐའ་མར་ ཀྱིས། ན་ མ་ ར་ ལ་ གི་མཐའ་མར་ གྱིས། ག་ ང་ འ་ མཐའ་མེད་ཀྱི་མཐའ་མར་ གིས། འ་དང་ མཐའ་མེད་ གཉིས་ཀྱི་མཐའ་མར་ འིས། ཡིས།

འིས་དང་ ཡིས་ཀྱི་ཚབ་ལུ་ རྩོང་ཁའི་སྐབས་ གིས་ ལག་ལེན་འཐབ་ཨིན།

འབྲེལ་སྒྲ་དང་བྱེད་སྒྲའི་ཁྱད་པར། འབྲེལ་སྒྲ། བྱེད་སྒྲ།

འབྲེལ་བ་སྟྫོནམ་ཨིན། ལཱ་འབད་མི་སྟྫོནམ་ཨིན། ཕད་ལུ་ རྗེས་འཇུག་ས་མི་ཐྫོབ། དཔེར་ན་ གི།

དབང་ཕྱུག་གི་ཨ་པ། ཕད་ལུ་ རྗེས་འཇུག་ས་འཐྫོབ། དཔེར་ན་ གིས།

དབང་ཕྱུག་གིས་ལྟྫོ་འབད།

ཕད་ གི་ ཀྱི་ གྱི་ འི་ ཡི། ཕད་ གིས་ ཀྱིས་ གྱིས་ འིས་ ཡིས།

སྫོར་ཚུལ་ན་མ་ར་ལ་གྱི། །ད་བ་ས་ཀྱི་ག་ང་གི། ། འ་དང་མཐའ་མེད་འི་དང་ཡི། །རྫོང་ཁའི་སྐབས་ལུ་གི་འཇུགཔ་ཨིན། །

འབྲེལ་སྒྲའི་སྫོམ་ཚིག།



རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས། སྩོང་ལཱ་ ༡ པ།

བཀོད་རྒྱ། འྩོག་ལུ་ འབྲེལ་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ་གྱི་དབྱེ་བ་དང་དཔེ་ བྱེད་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ་གྱི་དབྱེ་བ་དང་ དཔེ་ཚུ་ ལེགས་ཤྩོམ་སྦེ་ལྷག་ཞིནམ་ལས་ ཁྱད་པར་ཕྱེ།

འབྲེལ་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ་ལུ་དབྱེ་བ་དྲུག་ཡྩོད། ༡༽ ངོ་བྩོ་བདག་གཅིག་གི་འབྲེལ་བ། ༢༽ དེ་ལས་དེ་འབྱུང་གི་འབྲེལ་བ།

༣༽ ཡན་ལག་དང་ཡན་ལག་ཅན་གྱི་འབྲེལ་བ། ༤༽ ཁྱད་གཞི་དང་ཁྱད་ཆོས་ཀྱི་འབྲེལ་བ།

༥༽ རྟེན་དང་བརྟེན་པའི་འབྲེལ་བ། ༦༽ ནྩོར་དང་བདག་པྩོའི་འབྲེལ་བ།

འབྲེལ་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ་གྱི་དབྱེ་བ་དང་དཔེ། ངོ་བྩོ་བདག་གཅིག་གི་འབྲེལ་བ། ཤིང་གི་རྐང་ཁྲི། ཟེར་བའི་སྐབས་ ཤིང་དང་རྐང་ཁྲི་གཉིས་ གཞི་ ཡང་ན་ ངོ་བྩོ་ཤིང་དེ་ར་ཨིནམ་མ་གཏྩོགས་ ཤིང་མེན་པའི་རྐང་ཁྲི་ སྩོ་སྩོ་ཅིག་ ག་ནི་ཡང་མེདཔ་ལས་བརྟེན་ ངོ་བྩོ་བདག་གཅིག་གི་འབྲེལ་བ་ཟེར་སབ་ཨིན། དཔེར་ན་ གསེར་གྱི་བུམ་པ། ཤིང་གི་རལ་གྲི། ཟེར་དྩོ་བཟུམ་ལུ་སབ་ཨིན།

དེ་ལས་དེ་འབྱུང་གི་འབྲེལ་བ།

བ་གི་ཨོམ་ ཟེར་བའི་སྐབས་ འབྱུང་སའི་ཡུལ་ བ་འདི་ལས་ དངོས་པྩོ་ཨོམ་འབྱུང་དྩོ་བཟུམ་ འབྱུང་ཡུལ་ག་ཅི་འབད་རུང་ཅིག་ལས་ དངོས་པྩོ་དང་གང་ཟག་ ག་ཅི་འབད་རུང་ཅིག་འཐྩོན་མི་ལུ་སབ་ཨིན། དཔེར་ན་ བྱམྩོ་གི་སྒོང་རྩོག། སག་གི་ཕྱུག་གུ། ཟེར་དྩོ་བཟུམ་ལུ་སབ་ཨིན།

ཡན་ལག་དང་ ཡན་ལག་ཅན་གྱི་འབྲེལ་བ། ནྩོར་གྱི་ལགཔ། ཟེར་བའི་སྐབས་ ཡན་ལག་ཅན་ནྩོར་ལུ་ ཡན་ལག་ལགཔ་ཡྩོདཔ་འབད་ སྩོན་མི་ལུ་སབ་ཨིན། དཔེར་ན་ རྣམ་རྒྱལ་གྱི་རྐངམ། ཤིང་གི་འདབ་མ། ཟེར་དྩོ་བཟུམ་ལུ་སབ་ཨིན།



རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས། ཁྱད་གཞི་དང་ ཁྱད་ཆོས་ཀྱི་འབྲེལ་བ། ཉིམ་གི་འྩོད། ཟེར་བའི་སྐབས་ ཁྱད་གཞི་ཉིམ་འདི་ལས་ ཁྱད་ཆོས་འྩོད་ བྱུང་དྩོ་བཟུམ་སྦེ་ ཁྱད་གཞི་ གང་ཟག་དང་དངོས་པྩོ་ ག་ཅི་ཨིན་རུང་ གཞན་དང་མ་འདྲ་བའི་ ཁྱད་ཆོས་ཀྱི་ཡྩོན་ཏན་ ཡྩོད་མི་ཅིག་ལུ་སབ་ཨིན། དཔེར་ན་ གྱི་ཅུ་གི་རྣྩོས། གསེར་གྱི་མདངས། ཟེར་མི་བཟུམ་ཨིན།

རྟེན་དང་ བརྟེན་པའི་འབྲེལ་བ། སྣུམ་འཁོར་ནང་གི་མི། ཟེར་བའི་སྐབས་ རྟེན་སྣུམ་འཁོར་གྱི་ནང་ན་ བརྟེན་པ་མི་ གནས་ཏེ་ཡྩོད་པའི་དྩོན་སྩོན་མི་ལུ་སབ་ཨིན། དཔེར་ན་ ལྷ་ཁང་ནང་གི་སྐུ། རྩོང་ནང་གི་དགེ་འདུན་པ། ཟེར་མི་བཟུམ་ལུ་སབ་ཨིན།

ནྩོར་དང་ བདག་པྩོའི་འབྲེལ་བ། སྩོབ་དཔྩོན་གྱི་འགྲུལ་འཕྲིན། ཟེར་བའི་སྐབས་ ནྩོར་ འགྲུལ་འཕྲིན་འདི་གི་ བདག་པྩོ་ སྩོབ་དཔྩོན་ཨིནམ་འབད་ སྩོན་མི་ཅིག་ལུ་སབ་ཨིན། དཔེར་ན་ སངས་རྒྱས་ཀྱི་སྣུམ་འཁོར། དབང་ཕྱུག་གི་ཁྱིམ། ཟེར་མི་བཟུམ་ལུ་སབ་ཨིན།

བྱེད་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ་གྱི་དབྱེ་བ། ༡༽ བྱེད་པ་པྩོ་གཙྩོ་བྩོ། ༢༽ བྱེད་པ་པྩོ་ཕལ་པ། ༣༽ རང་བཞིན་གྱི་བྱེད་པ་པྩོ། ༤༽ རྒྱུ་མཚན་གྱི་དྩོན་ལུ་འཇུག་པའི་བྱེད་སྒྲ།

བྱེད་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ་གྱི་གོ་དྩོན་དང་ དབྱེ་བ་ དཔེ། བྱེད་པ་པྩོ་གཙྩོ་བྩོ། སྩོབ་དཔྩོན་གྱིས་ཡི་གུ་བྲིས་ནུག། ཟེར་ བྱེད་པ་པྩོ་ སེམས་ཡྩོད་པའི་ གང་ཟག་དང་ སེམས་ཅན་ཚུ་གིས་ ལཱ་ཅིག་འབད་བའི་དྩོན་སྩོན་མི་ལུ་ བྱེད་པ་པྩོ་གཙྩོ་བྩོ་ཟེར་སབ་ཨིན། དཔེར་ན་ དབང་ཕྱུག་གིས་ལྩོ་འབད། ཕུན་ཚྩོགས་ཀྱིས་མདའ་རྐྱབ། ཟེར་དྩོ་བཟུམ་ལུ་སབ་ཨིན། བྱེད་པ་པྩོ་ཕལ་པ། སྟྭ་རི་གིས་ཤིང་བཀག། ཟེར་ བྱེད་པ་པྩོ་ཕལ་པ་ སེམས་མེད་པའི་ ལག་ཆས་ཅིག་གིས་ ལཱ་ཅིག་འབད་བའི་དྩོན་སྩོན་མི་ལུ་་ བྱེད་པ་པྩོ་ཕལ་པ་ཟེར་སབ་ཨིན། དཔེར་ན་ ཏྩོག་ཙེ་གིས་ས་བརྐོ། གྱི་གིས་ཤིང་བཅད། ཟེར་མི་བཟུམ་ཨིན།



རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས། རང་བཞིན་གྱི་བྱེད་པ་པྩོ། རླུང་གིས་འབག། ཟེར་བའི་སྐབས་ ལཱ་འབད་མི་ གང་ཟག་དང་དངོས་པ་ ག་ཡང་མེད་པར་ རང་བཞིན་ཤུགས་ཀྱིས་ ལཱ་འབད་བའི་ཚིག་ཅིག་ལུ་སབ་ཨིན། དཔེར་ན་ དྲྩོད་ཀྱིས་སྐམ། བསིལ་གྱིས་གྱང་། ཟེར་དྩོ་བཟུམ་ དྲྩོད་དང་ བསིལ་གཉིས་ཀྱིས་ རང་བཞིན་ལུ་བརྟེན་ཏེ་ ལཱ་འབད་འགྱོ་མི་ཅིག་ལུ་གོ་དགོཔ་ཨིན།

རྒྱུ་མཚན་གྱི་དྩོན་ལུ་འཇུག་པའི་བྱེད་སྒྲ། དཔེ་ཆ་ལྷབ་ནི་འདི་གིས་ཤེས་ཅི། ཟེར་བའི་སྐབས་ ལཱ་ག་ཅི་ཨིན་རུང་ རྒྱུ་མཚན་ལཱ་འདི་ལས་བརྟེན་ཏེ་ དྩོན་དག་ཅིག་བསྒྲུབ་ཚུགས་པའི་ རྒྱུ་མཚན་སྩོན་པའི་ཚིག་ཅིག་ལུ་སབ་ཨིན། དཔེར་ན་ ཇ་འཐུང་ནི་འདི་གིས་ ཁ་སྐོམ་སངས་ཡི། མགྱོགས་པར་འགྱོ་ནི་འདི་གིས་ལྷྩོད་ཅི། ཟེར་མི་བཟུམ་ཨིན། སྩོང་ལཱ་ ༢ པ། བཀོད་རྒྱ། འབྲེལ་སྒྲ་དང་ བྱེད་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ་གྱི་དཔེ་ཚུ་ མ་འཛྩོལ་བར་བྲིས།

འབྲེལ་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ་གྱི་དབྱེ་བ། དཔེ། ༡༽ ངོ་བྩོ་བདག་གཅིག་གི་འབྲེལ་བ། དཔེར་ན་ གསེར་གྱི་མཛུབ་དཀྱི།

་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་ ༢༽ དེ་ལས་དེ་འབྱུང་གི་འབྲེལ་བ། ༣༽ ཡན་ལག་དང་ཡན་ལག་ཅན་གྱི་འབྲེལ་བ། ༤༽ ཁྱད་གཞི་དང་ཁྱད་ཆོས་ཀྱི་འབྲེལ་བ། ༥༽ རྟེན་དང་བརྟེན་པའི་འབྲེལ་བ། ༦༽ ནྩོར་དང་བདག་པྩོའི་འབྲེལ་བ།

བྱེད་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ། དཔེ། ༡༽ བྱེད་པ་པྩོ་གཙྩོ་བྩོ། སྩོབ་དཔྩོན་གྱིས་དཔེ་ཆ་སྩོན།

་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་་ ༢༽ བྱེད་པ་པྩོ་ཕལ་པ། ༣༽ རང་བཞིན་གྱི་བྱེད་པ་པྩོ། ༤༽ རྒྱུ་མཚན་གྱི་དྩོན་ལུ་འཇུག་པའི་བྱེད་སྒྲ།





འབྲེལ་སྒྲ་ཟེར་མི་འདི་ གང་ཟག་དང་ དངོས་པྫོ་ཚུ་གི་བར་ན་ འབྲེལ་བ་སྟྫོན་པའི་ ཕྲད་ཅིག་ལུ་སླབ་ཨིན། འབྲེལ་སྒྲའི་ཕད། གི་ ཀྱི་ གྱི་ འི་ ཡི། ལྔ་ཡྩོད། འབྲེལ་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ་ལུ་ དབྱེ་བ་དྲུག་ཡྩོད། བྱེད་སྒྲ་ཟེར་མི་འདི་ གང་ཟག་དང་ དངོས་པྩོ་གཉིས་ལས་ ལཱ་འབད་མི་ ག་ཨིན་ན་ སྩོན་མི་ཚིག་ཅིག་ལུ་སབ་ཨིན། ཡང་ན་ ག་གིས་ ག་ཅི་འབད་ཡི་ག་ སྩོན་མི་ཅིག་ལུ་ཡང་སབ་ཨིན། བྱེད་སྒྲའི་ཕྲད། གིས། ཀྱིས། གྱིས། འིས། ཡིས། ལྔ་ཨིན། བྱེད་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ་ལུ་ དབྱེ་བ་བཞི་ཡྩོད།

འབྲེལ་སྒྲ་དང་ བྱེད་སྒྲའི་ཁྱད་པར། འབྲེལ་སྒྲ། བྱེད་སྒྲ།

འབྲེལ་བ་སྩོནམ་ཨིན། ལཱ་འབད་མི་སྩོནམ་ཨིན། ཕྲད་ལུ་ རྗེས་འཇུག་ས་མི་འཐྩོབ། དཔེར་ན་ གི། དབང་ཕྱུག་གི་ཨ་པ།

ཕྲད་ལུ་ རྗེས་འཇུག་ས་འཐྩོབ། དཔེར་ན་ གིས། དབང་ཕྱུག་གིས་ལྩོ་འབད།

ཕྲད། གི་ ཀྱི་ གྱི་ འི་ ཡི། ཕྲད། གིས་ ཀྱིས་ གྱིས་ འིས་ ཡིས།

རང་ཉིད་དབྱེ་ཞིབ། བཀོད་རྒྱ། འྩོག་གི་དྲི་བ་ཚུ་གི་ལན་བྲིས། ༡༽ འབྲེལ་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ་གྱི་དབྱེ་བ་ ག་དེམ་ཅིག་ཡྩོདཔ་ཨིན་ན? རེ་རེ་བཞིན་བྲིས། ༢༽ བྱེད་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ་ལུ་ དབྱེ་བ་ག་དེམ་ཅིག་ཡྩོདཔ་ཨིན་ན? ཚངམ་སྦེ་བྲིས།




སྩོང་ལཱ་གི་ལན་གསལ་དཔེ། སྩོང་ལཱ་ ༡ པ། ལྷག་སྟེ་ ཁྱད་པར་ག་དེ་སྦེ་འདུག་ག་བལ་དགོ།

སྩོང་ལཱ་༢ པ། རང་གིས་ ག་ཤེས་མི་དཔེ་རེ་རེ་བྲི་དགོཔ་ཨིན།

རང་ཉིད་དབྱེ་ཞིབ་ཀྱི་ལན་གསལ་དཔེ། ༡༽ འབྲེལ་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ་ལུ་ དབྱེ་བ་དྲུག་ཡྩོད། དེ་ཡང་ ངོ་བྩོ་བདག་གཅིག་གི་འབྲེལ་བ། དེ་ལས་དེ་འབྱུང་ གི་འབྲེལ་བ། ཡན་ལག་དང་ཡན་ལག་ཅན་གྱི་འབྲེལ་བ། ཁྱད་གཞི་དང་ཁྱད་ཆོས་ཀྱི་འབྲེལ་བ། རྟེན་དང་བརྟེན་ པའི་འབྲེལ་བ། ནྩོར་དང་བདག་པྩོའི་འབྲེལ་བ། ཚུ་ཨིན།

༢༽ བྱེད་སྒྲ་དྩོན་གྱི་འཇུག་ཚུལ་ལུ་དབྱེ་བ་ བཞི་ཡྩོད་མི་ཚུ་ཡང་ བྱེད་པ་པྩོ་གཙྩོ་བྩོ། བྱེད་པ་པྩོ་ཕལ་པ། རང་བཞིན་གྱི་ བྱེད་པ་པྩོ། རྒྱུ་མཚན་གྱི་དྩོན་ལུ་འཇུག་པའི་བྱེད་སྒྲ། ཚུ་ཨིན།




རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས། འཆར་གཞི་ཨང.་ ༤ ཆོས་ཚན་ རྩོང་ཁ། སྩོབ་རིམ་ བདུན་པ་དང་བརྒྱད་པ། དུས་ཡུན་ སྐར་མ་ ༥༠

དྩོན་ཚན་ འབྲི་རྩོམ། ནང་གསེས་དྩོན་ཚན་ ལྫོ་རྒྱུས་འབྲི་རྫོམ།


འབྲི་རྩོམ་ཟེར་མི་འདི་ སྤྱིར་བཏང་ གནད་དྩོན་ཅིག་ལུ་ གཞི་བཞག་ཞིནམ་ལས་ ངོ་སྩོད་དང་ བར་གྱི་གནད་དྩོན་ དེ་ལས་ མཇུག་བསྡུ་ཚུ་ཡྩོད་པའི་ འབྲི་བཀོད་ཅིག་གི་ཐྩོག་ལས་ ལྷག་མི་ཚུ་ ཡིད་ཆེས་བསྐྱེད་ཚུགས་པའི་ ཚིག་དྩོན་གྱི་རྣམ་འགྱུར་བཏྩོན་ཏེ་ རྩོམ་སྒྲིག་འབད་ཡྩོད་པའི་ རྩོམ༌རིག་ཅིག་ལུ་སབ་ཨིན།

སྤྱིར་བཏང་འབྲི་རྩོམ་ལུ་ དབྱེ་བ་ལེ་ཤ་ཡྩོད་རུང་ དངོས་འབྱུང་འབྲི་རྩོམ་དང་ འཆར་སྣང་འབྲི་རྩོམ་གཉིས་ནང་ལུ་བསྡུཝ་ཨིན། དེ་བཟུམ་སྦེ་ འབྲི་རྩོམ་ལུ་ནང་གསེས་ཀྱི་དབྱེ་བ་ ལེ་ཤ་ཡྩོད་དེ་འབད་རུང་ ནཱ་ལུ་ ལྩོ་རྒྱུས་འབྲི་རྩོམ་གྱི་སྐོར་ལས་ ལྷབ་ནི་ཨིན།

ལྩོ་རྒྱུས་འབྲི་རྩོམ་གྱི་གོ་དྩོན།

ལྫོ་རྒྱུས་འབྲི་རྫོམ་ཟེར་མི་འདི་ གནད་དྫོན་ཅིག་གི་སྐོར་ལས་ ལྫོ་རྒྱུས་ཅིག་འབྲིཝ་ད་ འབྱུང་རིམ་དང་འཁྲིལ་བའི་ གོ་རིམ་དང་དུས་རིམ་གཉིས་ཆ་ར་ཡྫོདཔ་འབད་ བྲི་དགོ་པའི་ཁར་ དེ་ཡང་ གཞན་ལུ་ཚྫོར་བ་ ངོ་མ་མྩོང་ཚུགས་པའི་ ཚིག་གི་ཉམས་དང་ལྡནམ་འབད་ བྲིས་མི་ཅིག་ལུ་སླབ་ཨིན།

✓ འབྲི་རྩོམ་ཟེར་བའི་གོ་དྩོན་ གསལ་ཏྩོག་ཏྩོ་འབད་སབ་ཚུགས།

✓ ལྩོ་རྒྱུས་འབྲི་རྩོམ་གྱི་གོ་དྩོན་ མ་འཛྩོལ་བར་སབ་ཚུགས། ✓ ལྩོ་རྒྱུས་འབྲི་རྩོམ་ནང་ ཚང་དགོ་པའི་ཁྱད་ཆོས་ཚུ་ རེ་རེ་བཞིན་དུ་ ངོས་འཛིན་

འབད་ཚུགས། ✓ ལྩོ་རྒྱུས་འབྲི་རྩོམ་གཅིག་ ཁྱད་ཆོས་ཚངམ་སྦེ་བཙུགས་ཏེ་ བྲི་ཚུགས། །

༡༽ ངོ་སྩོད། ༢༽ བར་གྱི་གནད་དྩོན། ༣༽ མཇུག་བསྡུ།

འབྲི་རྩོམ་འབྲིཝ་ད་ ཁྱད་ཆོས་གསུམ་ཚང་དགོ།




✓ སྔོན་མར་འབད་འབདཝ་དང་ བྱུང་བྱུངམ་ཅིག་ལུ་ གཞི་བཞག་དགོ། ✓ ལྩོ་རྒྱུས་ཀྱི་འབྱུང་རིམ་ཚུ་ གོ་རིམ༌བསྒྲིག༌ཏེ་བྲི་དགོ། ✓ གནམ་ལྩོ་ ཟླ་ཚེས་ ཆུ་ཚྩོད་ ལ་སྩོགས་པའི་ དུས་ཚྩོད་ཚུ་ གོ་རིམ་བཞིན་དུ་ ཚུད་དགོཔ་ཨིན།


བཀོད་རྒྱ། དུས་ཅི་ སྤྱི་ལྩོ་༢༠༢༠ ལྩོའི་ མི་དབང་བདག་རིན་པྩོ་ཆེའི་ འཁྲུངས་སྐར་དུས་སྩོན་འདི་ རང་སྩོའི་སྩོབ་གྲྭ་ནང་ ག་དེ་སྦེ་ བརྩི་སྲུང་ཞུ་ཡི་ག་ དེ་གི་སྐོར་ལས་ ལྩོ་རྒྱུས་འབྲི་རྩོམ་ ཚིག་འབྲུ་ ༢༥༠ ལས་མ་ཉུངམ་ཅིག་བྲིས།

༡ དུས་སྩོན་འདི་ ས་གནས་ག་ཏེ་ལུ་ བརྩི་སྲུང་ཞུ་ཡྩོདཔ་ཨིན་ན? ༢ འཁྲུངས་སྐར་དུས་ཆེན་ཐེངས་ ག་ཅི་ཨིན་ན? ༣ སྐུ་མགྲོན་གཙྩོ་བྩོ་ ག་བྱྩོན་ཏེ་ཡྩོདཔ་ཨིན་ན? ༤ དུས་སྩོན་སྐབས་སུ་ སྩོ་སྩོན་གྱི་ལས་རིམ་ཚུ་ ག་ཅི་ར་ཡྩོདཔ་ཨིན་ན? ༥ དུས་སྩོན་འདི་ མཇུག་ག་དེ་སྦེ་བསྡུ་ཡྩོདཔ་ཨིན་ན?

བཅུད་བསྡུས། ✓ འབྲི་རྩོམ་གྱི་དབྱེ་བ་ལེ་ཤ་ཡྩོད་རུང་ འབྲི་རྩོམ་ལུ་སྤྱིར་བཏང་ དངོས་འབྱུང་འབྲི་རྩོམ་དང་ འཆར་སྣང་འབྲི་རྩོམ་གཉིས་

ནང་ལུ་བསྡུཝ་ཨིན། ✓ ལྫོ་རྒྱུས་འབྲི་རྫོམ་ཟེར་མི་འདི་ གནད་དྫོན་ཅིག་གི་སྐོར་ལས་ ལྫོ་རྒྱུས་ཅིག་བྲིཝ་ད་ འབྱུང་རིམ་དང་འཁྲིལ་བའི་ གོ་རིམ་

དང་ དུས་རིམ་གཉིས་ཆ་ར་ཡྫོདཔ་འབད་ བྲི་དགོ་པའི་ཁར་ དེ་ཡང་ གཞན་ལུ་ཚྫོར་བ་ ངོ་མ་མྫོང་ཚུགས་པའི་ ཚིག་གི་ཉམས་དང་ལྡནམ་འབད་ བྲིས་མི་ཅིག་ལུ་སླབ་ཨིན།

✓ སྤྱིར་བཏང་ འབྲི་རྩོམ་བྲི་བའི་སྐབས་ ཚང་དགོ་པའི་ ཁྱད་ཆོས་ཚུ་ཡང་ ངོ་སྩོད། བར་གྱི་གནད་དྩོན། མཇུག་བསྡུ་ཚུ་ཨིན།

ལྩོ་རྒྱུས་འབྲི་རྩོམ་ བྲི་བའི་སྐབས་ལུ་ ཚང་དགོ་པའི་ཁྱད་ཆོས།





༡) ལྩོ་རྒྱུས་འབྲི་རྩོམ་ནང་ ཚང་དགོ་པའི་ཁྱད་ཆོས་ ག་ཅི་ར་སྩོ?

༢) ཁྱོད་ཀྱིས་འབད་བ་ཅིན་ ཉིནམ་ཨ་རྟག་ར་ དྲན་ཐྩོ་བཞག་པ་ཅིན་ ལྩོ་རྒྱུས་འབྲི་རྩོམ་བྲི་ནི་ལུ་ ཕན་ཐྩོགས་ག་དེ་སྦེ་ར་འྩོང་ནི་ མས? བསམ་འཆར་བྲིས། ༣) སྤྱིར་བཏང་ འབྲི་རྫོམ་འདི་ དབྱེ་བ་ག་ཅི་ནང་བསྡུཝ་ཨིན་ན?


སྩོང་ལཱ་༡ པའི་ལན་གསལ་དཔེ།

ལྩོ་རྒྱུས་འབྲི་རྩོམ་ ཚིག་འབྲུ་ ༢༥༠ ལས་མ་ཉུངམ་ཅིག་བྲི་དགོཔ་ཨིན།


༡) ལྩོ་རྒྱུས་འབྲི་རྩོམ་ནང་ ཚང་དགོ་པའི་ཁྱད་ཆོས་ཚུ་ཡང་་་ ✓སྔོན་མར་འབད་འབདཝ་དང་ འབྱུང་བྱུངམ་ཅིག་ལུ་ གཞི་བཞག་དགོ། ✓ལྩོ་རྒྱུས་ཀྱི་འབྱུང་རིམ་ཚུ་ གོ་རིམ༌བསྒྲིག༌ཏེ་བྲི་དགོ། ✓གནམ་ལྩོ་ ཟླ་ཚེས་ ཆུ་ཚྩོད་ ལ་སྩོགས་པའི་ དུས་ཚྩོད་ཚུ་ གོ་རིམ་བཞིན་ ཚུད་དགོཔ་ཨིན། ༢) ཉིནམ་ཨ་རྟག་ར་ དྲན་ཐྩོ་བཞག་པ་ཅིན་ ལྩོ་རྒྱུས་འབྲི་རྩོམ་ནང་ འབྱུང་རིམ་དང་འཁྲིལ་བའི་ གོ་རིམ་དང་དུས་ རིམ་གཉིས་ཆ་ར་ཡྫོདཔ་འབད་ བྲི་དགོཔ་ལས་ འབྱུང་རིམ། དུས་ཚྩོད། ཉིནམ་ཚུ་མ་འཛྩོལ་བར་ རིམ་པ་བཞིན་དུ་ གོ་རིམ་བསྒྲིག་ཏེ་ བྲི་ཚུགས་ནིའི་ཕན་པ་ཡྩོདཔ་ཨིན། ༣) སྤྱིར་བཏང་ལུ་ འབྲི་རྫོམ་འདི་ དབྱེ་བ་ དངོས་འབྱུང་འབྲི་རྩོམ་དང་ འཆར་སྣང་འབྲི་རྩོམ་ནང་བསྡུཝ་ཨིན།


Mathematics-Class VII-VIII 47

KEY STAGE-III

Lesson No: 1 Subject: Mathematics Class level: VII - VIII Time: 50 mins

Theme: Measurement

Topic: Circumference and Area of Circle.

Introduction

✓ Circle is defined as the set of all points that are equidistance or equal distance from

another single point.

✓ The diameter is the length of the line passes

through the center that divides the circle into

two equal parts.

✓ Radius is the half of the length of the diameter.

✓ RadiusDiameter = 2

✓ Circumference of a circle is the perimeter of a circle. Perimeter is the distance around the

shape.

✓ Since circle is a special shape, the perimeter of a circle gets a special name of

circumference.

PI (π)

✓ In math the word pi is a very special number with Greek letter π as a symbol.

✓ Pi is the ratio of a circle’s circumference to its diameter.

✓ circle theacross distance

circle a around distance)( =pi

diameter

ncecircumfere=

✓ The value of a7

2214.3)( == telyApproprimapi .

✓ Formula to find the circumference and area of any circle

diameternceCircumfere =

diameterC =

)2(2 radiusdiameterSincerC ==

✓ Tell the parts of circle.

✓ Identify the formula to find the circumference of a circle.

✓ Identify the formula to find the area of a circle.

✓ Differentiate between the area of the circle and

circumference of the circle.

✓ Apply the formula to solve the real-world problems.

Figure: Parts of circle

https://www.mathsisfun.com/geometry/circle.html



KEY STAGE-III

rnceCircumfere 2=

Area of circle = Area of Rectangle = Base × Height

Area of Circle https://pythagoreanmath.com/complete-explanation-for-area-of-a-circle-formula/

Let us look at the figures to derive the formula for the Area of a Circle:

1. In first figure, the circle is divided into four equal sections and

arranage them into rectangular formation.

2. The formation does not look rectangular so let us divide the

circle into 8 sections and arrange them in the same formation.

3. The shape begins to resembles a parallelogram, but not a

rectangle. Let us keep dividing the circle into smaller pieces.

4. Everytime we divide the circle into smaller pieces the formation

looks more like a rectangle.

5. If we divide the circle infinitely many times, then the shape

eventually becomes a perfect rectangle.

6. We can now find the area of the circle by finding the area of the

rectangle.

7. Therefore, the base of the rectangle is equal to the half of the circumference of the circle

8. Finally, we can find the area of the rectangle by multiplying the base and height.

Height = Radius

Base = Half the Circumference rr == 22

1

Figure: Finding the Area of Circle

Area of Semi-circle (Half of the circle) =

Area of Quadrant (One Fourth of the circle) =

Use these formulas to

do further calculations.



KEY STAGE-III

Activity 1

Instruction: Let us look at the following example to find circumference and area of the circle.

Write all the answers in the notebook.

Example: Solution: Radius= 8cm

mC

C

rnceCircumfere

24.50

814.32

2

=

=

=

2

2

2

96.200

6414.3

6488

mArea

A

r

rArea

=

=

==

=

* r2 and 2r are completely different.

Question 1: Calculate the area of given circles.

a) b)

Activity 2

Instruction: Let us look at the diagram to calculate the area of shaded part.

Example:

2

2

54.10535.10

465.3849

5.35.314.377

m

rss

CircleofAreaSquareofAreapartshadedtheofArea

=

−=

−=

−=

−=

Question 2: Calculate the area of the shaded part for the shape given below.

a) b)

8 m

3.5 m

10mm

7 cm

10 cm

2m

2m

7 m

7 m

Hint:

✓ Side of a square is

equal to diameter

of a circle.



KEY STAGE-III

Summary

✓ Circle is defined as the set of all points that are equidistance or equal distance from

another single point.

✓ The formula for the area of circle is2rA = , where r represents the radius of the circle.

✓ The Diameter is line segment that goes straight across the circle, through the center and

is twice the radius.

✓ The Circumference is the distance around the circle.

✓ The Formula for rcircleaofnceCircumfere 2= .


Instruction: Answer the following questions.

1. You walked around a circle which has a diameter of 100m, how far have you walked?

2. A track is made of two semi-circles attached

to opposite sides of a 70 m square. What is the

total area inside the track?

3. A round post is cut from a square piece of wood with a side of 20 cm. What is the area of

the base of the post? ( 14.3= )

Answers for the Activity

Activity 1: a) , b)

Activity 2: a) b)


1.

2.

3.

70 m



KEY STAGE-III

Lesson No: 2 Subject: Mathematics Class level: VII-VIII Time: 50 mins

Theme: Representing Relationships

Topic: Describing and solving Linear Relationship

Introduction

✓ An equation that describes a linear relationship is called a linear equation.

✓ Example; V = 10n – 6 or V = 105 – 5n.

✓ Each variable in a linear equation has an exponent of 1. The exponent does not need to be

written because x1 = x.

✓ 3x + 2 = 8 is a linear equation because the exponent of variable x is 1.

✓ x2 = 9 is not a linear equation because the exponent of the variable x is 2.

✓ You can use table, graph or algebraic equation to solve problems related to the pattern of

relationship.

✓ When you plot points to graph a relationship, if it forms a straight line, the relation is linear.

✓ Both the graph and the table can be used to predict whether the relationship is linear or not.

✓ You can see when x -values change by a

constant amount, the

y –values also change by

another constant amount.

For example:

Activity 1

Instruction: Look at the pattern given below to create and complete the table as follows.

x-value 1 2 3 4 5

y-value 7 15 23 31 39

✓ Describe linear relationship.

✓ Use algebraic equation to describe linear relationship.

✓ Define linear equation.

✓ Solve linear equation using inverse operation.

+8 +8 +8 +8

+1 +1 +1 +1

Figure 1 Figure 2 Figure 3



KEY STAGE-III

You can create a table of values.

The table makes it easy to see that the number of dots in the pattern is 3, 6, 9…while the figure

number is 1, 2, 3,… This means that the number of dots increases by 3 as the figure number

increases by 1.

Question 1: Copy and complete the Table.

Activity 2

Instruction: Let us use the same pattern given above to determine the number of dots in any

figure by using:

a) Table form:

✓ We observe that we multiply figure number by 4 and add 6

to get the number of dots. Therefore, 6 is constant and 4 is

termed as numerical co-efficient.

d = 4 f + c. Therefore, the equation for the relationship is;

b) Algebraic equation:

✓ Use the equation d = 4f +6, where d is the number of dots and f is the figure number to

determine the number of dots in any given figure number:

i. For figure 4, substitute f = 4; d = 4 4 + 6 = 22

ii. For figure 5, substitute f = 5; d = 4 5 + 6 = 26

iii. For figure 20, substitute f = 5d = 4 20 + 6 = 80 + 6 = 86

Figure Number Number of dots

1 3

2 6

3 9

4 ?

Number of grey squares Number of white squares

1 8

2 10

3 ?

4 ?

5 ?

Figure Number Number of dots

1 10

2 14

3 18

4 ?

+3

+3

+3

9 + 3 =12, So ? = 12

d = 4f +6

Co-efficient

Constant

Variable

+4

+4

+4



KEY STAGE-III

c) Graph:

✓ Create a graph using the information in

the table to plot each row in the table as

a point.

✓ The figure number is the x -coordinate

and the number of dots is the

y-coordinate. The points are (1, 10), (2, 14), and

(3, 18).

✓ Use the pattern to include the number

of dots for figures 4 and 5.

Question 2: Create an algebraic equation to describe the relationship between the term value and

its position in the pattern given below.

Term number Term value

1 3

2 12

3 21

4 30

Activity 3

Instruction: Now let us look on how to find out the inverse operation by using symbols:

✓ Inverse operations are opposite operations that undo each other.

Addition and subtraction are inverse operations. Multiplication and division are inverse

operations.

3 x + 2 8

x x x

3 x + 2 + (-2) 8 + (-2)

x x x

3x 6

x x x

=

=

=

=

1. One side has 3bags of x balls plus 2

more balls.The other side has 8 balls.

Since each bag holds x balls, you can

solve the equation by finding out how

many balls are in one bag.

2. Undo adding 2 by subtracting 2:

3. Undo multiplying by 3 by dividing by3:

3x = 6



KEY STAGE-III

Let us look at another way to solve the equation: Isolation of the variable when variable appears

on both sides of the equation. Example on Isolation of variables:

✓ You can isolate it to one side by

addition or subtraction to solve the

equation.

Question 3: Solve each equation given below.

a) 3145 =−x b) xx −=+ 5243



1. Copy and complete the table to create a graph. Is it a Linear?

Term number Term Value

1 8

2 13

3 ?

4 ?

5 28

2. Use a table and an equation to describe this pattern. How many dots are there in figure 4?

3. Solve each equation.

a) xx 348 −=+ b) 1725 =+x


before. mentioned as solved becan Equation

327

2234272

3472

+=

−+=−+

+=+

x

sidesbothfromxSubtractxxxx

xx

x 2

x x is now alone on one side of the equation:

x = 2.

=



KEY STAGE-III

Summary

✓ An equation that describes a linear relationship is called linear equation.

✓ When we are asked to solve the equation, we need to find the value of x that makes the

equation true.

✓ When you plot points to graph a relationship, if it forms a straight line, the relation is

linear.

✓ Each variable in a linear equation has an exponent of 1. The exponent does not need to be

written because x1 = x.

.


Activity 1: 12, 14, 16

Activity 2: V = 9n – 6

Activity 3: a) 7 b) 12


1.18 and 23. It is a linear graph.

2.d=3f+3, where d is the number of dots and f is the figure number.

Figure 4 has 15

3.a) -1 b) 3



KEY STAGE-III

Lesson No: 3 Subject: Mathematics Class level: VII-VIII Time: 50 mins

Theme: Linear Polynomials

Topic: Linear Polynomials: Addition and Subtraction

Introduction

Polynomials

A linear polynomial is an algebraic expression that includes a variable with an exponent of 1 and

no other powers. It usually involves more than one terms.

Types of Polynomial with example:

i. One term – Monomial: 22xx

ii. Two terms – Binomial: yx 343 −+

iii. Three terms –Trinomial: 232 ++ yx

iv. Higher terms polynomial: 352 23 +++ xxx

What are linear polynomials? Consider the following expressions:

a. 𝒙

b. 𝟑𝒙 + 𝟏

c. 𝟐𝒏 − 𝒏 + 𝟏

d. 𝟗 − 𝟒 + 𝟑𝒂

e. 𝟓𝒚 + 𝟑 − 𝟐𝒚

Algebra Tiles representation of number:

✓ The tiles consist of two colors; black tiles represent negative values and white tiles

represent positive values.

✓ Define linear polynomials.

✓ Identify the different tiles.

✓ Add and subtract expressions using tiles and without tiles.

What can you say about the exponents of ?,, yandanx

= 1 - Therefore, a polynomial with exponent 1 is called linear

polynomial.

- The standard form is (ax + b) where ‘a' is numerical

coefficient, ‘ x ’ is a variable and b is a constant term.



KEY STAGE-III

Representations of polynomials using tiles

Tile representation for numbers (Zero property)

✓ Any integer added to its opposite has a value of zero. This is called the Zero Property.

tile1+ tile1−

tilex+ tilex−

1. Addition of polynomials using tiles

Example: (5 – 4x) + (2x – 3)

Step 1: Model the polynomials using tiles

Step 2: Combine like tiles (terms) and apply zero property

x

x2

23 +x

23 +−nn

35 −− a

233 −+c

(5 − 4𝑥) + (2𝑥 − 3) (5 − 4𝑥)

(2𝑥 − 3)

Step 3: Write the simplified expression

(5 − 4𝑥) + (2𝑥 − 3) = (𝟐 − 𝟐𝒙)



KEY STAGE-III

Grouping or Combining method (Without tiles)

Step 1: Write down the expression (5 – 4x) + (2x – 3)

Step 2: Combine/group the like terms

Step 3: Write down the simplified form

2. Subtraction of Polynomials using tiles

Subtraction is also adding the opposites.

Example: (1 + 2x) – (2 – 3 𝒙)

Step 1: Add the opposite of the second polynomial to the first one.

Step 2: Model polynomial and apply

Zero Property.

Step 3: Write the simplified expression.

Symbolically (without using tiles):

Step 1: Write the expression. (𝟏 + 𝟐𝒙) − (𝟐 + 𝟑𝒙)

Step 2: Add the opposite of the second = (𝟏 + 𝟐𝒙) + (−𝟐 + 𝟑𝒙) (Adding opposite)

polynomial and add. = (𝟐𝒙 + 𝟑𝒙) + (𝟏 − 𝟐) (Arrangement of like

terms) = 𝟓𝒙 − 𝟏 (Simplified form)

Step 3: Write the simplified form. = 𝟓𝒙 − 𝟏 𝒐𝒓 − 𝟏 + 𝟓𝒙

(5 – 4x) + (2x – 3) = (−4x + 2x) + (5 – 3) = −2𝑥 + 2

(5 – 4x) + (2x – 3) = -2x + 2 OR 2 – 2x

(1 + 2𝑥)– (2 – 3𝑥) = 5𝑥 − 1

(1 + 2𝑥)– (2 – 3𝑥) = (𝟏 + 𝟐𝒙) + (−𝟐 + 𝟑𝒙)

(𝟏 + 𝟐𝒙) + (−𝟐 + 𝟑𝒙)

(𝟏 + 𝟐𝒙) + (−𝟐 + 𝟑𝒙) = 𝟓𝒙 − 𝟏



KEY STAGE-III

Activity 1

Instruction: Answer all the following questions. a) )23()39( xx +−+−−

b) )27()72( −−− xx

c) (3−4x) − (7x+2)

d) )23()15( xx +−+−

Summary

✓ You can use different colored shapes to represent positive and negative copies of a

variable or constant.

✓ Like terms are terms that represent different multiples of the same variable. You can

collect them to simplify expressions.

✓ Any integer added to its opposite has a value of zero. This is called the Zero

Property.

✓ You can apply the zero principle to help simplify expressions.



1. Model: k37 −

2. Simplify: )43()62()34( −−−++− xxx

Answer for Activity

Activity 1:

a)

b) −14x + 4

c)

d) 7x − 4

Self-check for learning

1.

2. 9x + 7



KEY STAGE-III

Lesson No: 4 Subject: Mathematics Class level: VII - VIII Time: 50 mins

Theme: Data

Topic: Graphical Representation of Data

Introduction

✓ Data is a collection of facts such as numbers, words, measurement, and observation of

even just description of things.

Marks 0 -10 10 -20 20-30 30-40 40-50

No. of students 6 7 13 6 4

✓ Circle graph shows the parts that make up a

set of data.

✓ You can use a circle graph to compare:

i. The parts (each part is sector of the

circle).

ii. Each part to the whole set of data

(represented by the whole circle).

✓ Circle graphs are also called as pie chart.

A circle graph shows the relationship

✓ between a whole and its part. The whole circle is divided into sectors. The size of each

sector is proportional to the activity or information it represents.

✓ A box and whisker plot, or box plot

divides a set of data into fourths, or

quartiles, in the order of the least to

the greatest. Each quartile contains

25% of the data values.

✓ The dividing lines between the

quartiles are called the Lower quartile (Q1), the median (Q2), and the upper quartile (Q3)

✓ Represent data using circle graph.

✓ Construct box and whisker plot and scatter plot.

✓ Use information from tables, pictures, diagrams, graphs or

equation to describe change.

https://byjus.com/circle-graph-formula/



KEY STAGE-III

Activity 1

Instruction: Let us look at the following table to draw a pie chart step by step. Write all the

answers in the notebook.

Example: The time spent by a student during a day.

Sleep — 8 hours, School — 6 hours, Homework — 4 hours, Play — 4 hours and Others — 2

hours

Solution:

Total hours are 24 hours. Now we need to find fraction of each of the activity with respect to

whole day and also the angle subtended by that activity to draw the pie chart

Follow the steps to draw a pie chart:

i. Find the central angle each component by using 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡

𝑇𝑜𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒× 360°.

ii. If the values are given in percentage the above formula changes as % 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡

100× 360°.

iii. Draw a circle with any convenient radius.

iv. Draw a horizontal radius.

v. Starting with a horizontal radius, draw another radius making central angle corresponding

to the value of first co component.

vi. Repeat the process for all the components.

vii. These different radii divide the whole circle into various sectors.

viii. Shade with the different colors to show various components and title them.

Activity Hours Fraction Central Angle

Sleep 8 3

1

24

8=

1360 120

3 =

School 6 4

1

24

6=

1360 90

4 =

Homework 4 6

1

24

4=

1360 60

6 =

Play 4 6

1

24

4=

1360 60

6 =

Others 2 12

1

24

2=

1360 30

12 =

https://physicscatalyst.com/class-6/fractions.php



KEY STAGE-III

Question 1: Bhutan has four ecosystems. Create a circle graph to represent the information

below.

Activity 2

Instruction: Let us look at the example to convert the data into 360 degree and also to percent.

Question 2: In a class there are 36 students. Draw a circle graph for the marks group given

below.

Types of ecosystem Area (millions of hectares)

Forests 3400

Agriculture 240

Grasslands 800

Barren (snow and ice) 190

Marks group No. of

Students Converting to 360 Percent[100%]

0 10− 6 6

360 6036

= 6

100 17%36

=

10 20− 7 7

360 7036

= 7

100 19%36

=

20 30− 13 13

360 13036

= 13

100 36%36

=

30 40− 6 6

360 6036

= 6

100 17%36

=

40 50− 4 4

360 4036

= 4

100 11%36

=

Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50

No. of students 5 8 12 7 4

3600 500 800 1200 700 400

https://physicscatalyst.com/class8/data-handling.php#C0



KEY STAGE-III

33, 41, 43, 45, 56, 59, 65, 66, 69, 72, 76, 79, 88

3rd Quartile (Q3) 3 2nd Quartile (Q2) 1st Quartile (Q1,)

X-coordinates Y-coordinates

Activity 3

Instruction: Let us use following the steps to create a box and whisker plot.

Example: The following are the marks of 13 students [out of 100]

45, 76, 78, 98, 43, 66, 41, 33, 76, 56, 59, 66, 65

Step 1: Arrange the data from the least to the greatest.

Step 2: Find:

i. Minimum and Maximum values of the data.

ii. Median (Q2) – The middle value of the set of data.

iii. Lower quartile (Q1) – The middle value of the first or lower half of the data.

iv. Upper quartile (Q3) – The middle value of the second or upper half of the data.

Step 3: Use Minimum, Maximum, Q1, Q2 and Q3 values to draw the box and whisker plot.

Activity 4

Instruction: Looking at the pattern below draw a scatter plot to represent the data.

Example:


Solution:

Figure No. Love sign

1 3

2 5

3 7

Min value Max value

0 10 20 30 40 50 60 70 80 90

Q1 Q2 Q3

33, 41, 43, 45, 56, 59, 65, 66, 69, 72, 76, 79, 88



KEY STAGE-III

0

2

4

6

8

0 1 2 3 4

Num

ber o

f Lo

ve S

ign

Figure Number

Figure no. Vs. Love sign

Question 4: Create a table of values that relates the figure number to the number of sticks in the

figure.

Summary

✓ A systematic record of facts or different values of a quantity is called data.

✓ Circle graph or pie chart shows the values of components as the sectors of a circle.

✓ The dividing lines between the quartiles are called the Lower quartile Q1, the median Q2,

and the upper quartile Q3.

- The lower quartile is the median of the lower half of the data. It includes the median

if there is an odd number of a piece of data.

- The upper quartile is the median of the upper half of the data. It includes the median,

if there is an odd number of pieces of data.

Self -check for Learning

Instruction: Solve the questions given below.

1. The chart shows the results of a survey of students’ favourite sport as a school. Create the

circle graph.

Favourite sport Percent of students

Archery 75%

Football 15%

Basketball 5%

Badminton 5%




KEY STAGE-III

2. Dorji shoots 50 arrows every time he practices. The following scores represent the

number of times he hit the target each time he practiced. Create a box and whisker plot to

display the data.

8 13 12 11 12

11 10 3 12 13

18 12 12 13 15

11 11 22 12 8

3. Create a table of values and draw a scatter plot to represent the data given.

Figure: 1 Figure: 2 Figure: 3

Anwers for Activity

Activity 1: Activity 2:

Activity 3:

Activity 4:

Figure Number Number of sticks

1 3

2 5

3 7

4 9

5 11

6 13

7 15

8 17



KEY STAGE-III


1.

2.

3.



KEY STAGE-III

Lesson No: 5 Subject: Mathematics Class: VII-VIII Time: 50 mins

Theme: Numbers

Topic: Integers

Introduction

✓ Integers are defined as the set of positive and negative numbers including zero.

Examples: ...4,3,2,1,0,1,2,3,4 −−−−

✓ To add numbers having like signs, add the numerical value and assign the common sign

to the sum. Examples: i) 18612 =+ ii) 761 −=−+−

✓ To add numbers having unlike signs, subtract the numbers by assigning the sign of the

bigger value. Example:

23427 −=+−

✓ Integers can be represented or

modeled by using number line.

Activity 1

Instruction: Observe the example given below carefully and answer the questions that

follow. Write all the answers in your notebook.

Example: Order the integers from least to greatest.

4,0,3,5,2 −++−

So, from least to greatest are 5,3,0,2,4 ++−−

Question 1: Replace each ∆ with < or > to compare each pair of integers;

a) 2− 5− b) 3− 1+

0 -4 +3 +5 -2

✓ Define integers.

✓ Place the integers on the number line.

✓ Compare integers using symbols.

✓ Solve the problems using the order of operations.

Figure: Positive and Negative Integers

https://www.onlinemathlearning.com/integer-number-line.html



KEY STAGE-III

Activity 2

Instruction: Look at the example and answer the questions that follow.

Order of operation rules;

Step 1: If there are brackets, first calculate anything inside them

Step 2: Divide and multiply numbers next to each other, in order from left to right

Step 3: Add and Subtract numbers next to each other, in order from left to right.

Example ( ) ( ) ( ) ( )4253 −−+−−−

Step 1 = ( ) ( ) ( )473 −−−−

Step 2 = ( ) 283 −−

Step 3 = 31−

Question 1: Calculate: a) ( ) ( ) 3524 +−−+− b) ( ) ( ) ( ) 2563 −−+−

Activity 3

Instruction: Look at the example and answer the questions that follow.

Example 1: Find the value of ( ) ( )34 ++−

( ) ( ) 134 −=++−

✓ Equal values of opposite signs cancel each other is called Zero Property.

Question 1: Solve the following using models:

a) ( ) ( )54 +++ b) ( ) ( )75 ++− c) ( ) ( )75 −+−

Summary

✓ Integers are defined as the set of positive and negative numbers including zero.

✓ To solve questions on ‘order of operation’, we can use BEDMAS to solve it correctly.

✓ 1, 2, 3, 4, 5…are positive integers.

✓ -1, -2, -3, -4, -5…are negative integers.

✓ 0 is neither positive nor negative integer.

✓ To add numbers having like signs, add the numerical value and assign the common sign

to the sum.

✓ Equal values of opposite signs cancel each other is called Zero Property.

0 0 0



KEY STAGE-III



1. Use a number line model to add each.

a) ( ) ( )83 −++ b) ( ) ( )45 −+−

2. a) Calculate; ( ) ( ) ( ) 4832 +−−+−

3. Which integer in each pair is greater?

a) 2112 −+ or b) 2017 −+ or


Activity 1: a) -2 > -5 b) -3 < +1

Activity 2: a) 0 b) 12

Activity 3: a) 9 b) 2 c) -12


1.a) -5 b) -1

2.a) 10

3.a) b)


Science-Class VII-VIII 70

KEY STAGE-III

Lesson No: 1 Subject: Science Class level: VII-VIII Time: 50 mins

Theme: Life Processes

Topic: Reproduction in the Animals and Plants

Background

All living organisms can reproduce. Reproduction is the process of producing offspring by their

parents. It is also defined as the ability of an organism to produce young ones of its kind. It ensures

the survival of species. Now, you are the children of your parents and in future, you will have your

children and similarly, your children will have their children and the cycle continues.

Types of Reproduction

Figure 1: Sexual and Asexual Reproduction.

✓ Define reproduction.

✓ Differentiate sexual and asexual reproduction.

✓ Explain the changes that occur during puberty.

✓ Identify the parts of male and female reproductive systems.

✓ Explain the process of fertilization in human.

✓ Describe the methods of natural and artificial vegetative

propagation.

Reproduction

Sexual Reproduction Asexual Reproduction

•Sex cells are

involved.

Sperm + Ovum

• It requires sex

cells from two

parents.

•Sex cells are

not involved.

• It requires sex

cell from one

parent.



KEY STAGE-III

Table 1: Differences between Sexual and Asexual Reproduction.


• During the sexual contact, the male sex cell

(sperm) travels to the female gamete (ovum),

fuse to form a new cell called a zygote.

• This process of the fusion of sperm with the

ovum is called fertilization.

• The zygote will divide and re-divide to form

an embryo which further leads to the

development of a baby.

• During the asexual reproduction, the parent

cell divides and replicates to form the

offspring identical to their parents.

• Fertilization can happen in the absence of

any of the sex cells (male and female

gametes).

A human can only produce new ones of their kind when they attain their reproductive age, that is

both the male and female have to reach puberty. Puberty is the onset of sexual maturity in an

individual. It usually starts at around 11 to 13 years of age. During puberty, there is the

development of secondary sexual characteristics in both genders.

Table 2: Secondary Sexual Characteristics in Male and Female.

Secondary Sexual Characteristics in

Male

Secondary Sexual Characteristics in

Female

• The growth of pubic hair, beard and

moustache on the face.

• Deepening of voice.

• Development of muscles.

• Broadening of shoulders.

• Development of breasts.

• High-pitched voice.

• Widening of hips.

• Growth of pubic hair.

• Start of menstruation (monthly bleeding).

https://byjus.com/biology/sexual-and-asexual-reproduction



KEY STAGE-III

Reproduction in Human: The Male Reproductive System

Table 3: Male Reproductive Parts and their Functions

Male Reproductive

Parts

Characteristics Functions

A pair of testes A pair of oval-shaped which are

located outside the body in the

scrotum.

It produces sperms (male gametes)

and male hormones.

Scrotum It is the loose sac of skin. It contains and protects the testes.

Sperm duct A pair of a long tube connected

from testes to the urethra.

They carry sperms from testes to

the urethra.

Accessory glands The collection of three glands

Cowper’s gland, seminal

vesicles, and prostate gland.

These glands produce fluids that

mixed with sperm and a mixture

called semen is formed. The fluid

lubricates the duct system and

nourishes the sperm.

Urethra A small duct that extends from

the urinary bladder to the

outside of the body through the

penis.

It is a tube for the passage of both

urine and semen.

Penis It is cylindrical and projected

outside the body.

It helps to deposit sperms in the

female cervix during sexual

intercourse and to pass urine

outside the body.

Figure 2: Male Reproductive System



KEY STAGE-III

The Female Reproductive System

Table 4: Female Reproductive Parts and their Functions

Female

Reproductive Parts

Characteristics Function

A pair of ovaries The ovaries are small, oval-shaped

glands that are located on either

side of the uterus.

Each ovary produces one

ovum every month

alternatively.

They also produce hormones.

Fallopian tube Two narrow tubes that are attached

to the upper part of the uterus on

either side.

They are the pathway for ova

(egg cells) to travel from the

ovaries to the uterus.

Fertilization of an egg by a

sperm occurs here.

Uterus A hollow, pear-shaped muscular

organ. It is also called the womb.

The implantation of blastula

and the development of the

embryo takes place here.

Cervix The lower part of the uterus that

opens into the vagina.

The sperms are deposited here

during sexual intercourse. It

allows sperms to enter into the

uterus and menstrual blood to

flow out.

Vagina A muscular canal that joins the

cervix to the outside of the body. It

is also known as the birth canal.

It receives the sperms during

sexual intercourse.

Figure 3: Female Reproductive System



KEY STAGE-III

Fertilization and Development of Foetus

During sexual intercourse, millions of sperms are deposited into the vagina with the help of the

penis. The sperms travel through the vagina and into the uterus and reach the fallopian tube where

fertilization occurs. Only one sperm fuse with the ovum. This fusion of sperm and ovum is called

fertilization. It results in the formation of a single-celled structure called a zygote.

The zygote then begins to divide and forms a cluster of cells called a blastula. It travels down to

the uterus and fixes itself to the wall of the uterus. The fixing of blastula on the wall of the uterus

is called implantation. The blastula develops into an embryo and the embryo starts to grow into

a fully developed baby by the process of cell division. The wall of uterus becomes thick with

increased blood supply to nourish the growing embryo.

The period of complete development of the foetus until the birth of the baby is called the gestation

period. It is about 280 days almost nine months in human. The state of carrying the foetus in the

uterus of a woman is called pregnancy. The coming out of a baby from the body of the mother is

called birth.

What happens if the ovum is not fertilized by a sperm?

The ovum will disintegrate (break down) within a few days while still in the fallopian tube. Then

it is discharged along with the lining of the uterus and blood. The outflow of blood together with

the lining of the uterus is called menstruation.

Activity 1

Instruction: Answer the following questions in your notebook.

1. The figure below shows a diagram of the human reproductive system. Study it carefully and

answer the following questions.

i. In which label does the development of the

embryo take place?

ii. Write the function of the part labelled B.

iii. Name the organ system.

iv. What would happen if the part labelled A is cut

off?

2. Fill in the blanks.

The ……………… is the male sex cell. It is produced in the ……………… The testes are held

outside the body in a bag of skin called……………… This keeps the sperms at the right

……………… The sperm travel up the……………… where liquids are added from

the……………… glands. The mixture is called ……………… The semen flows out of the

……………… through a tube called ………………



KEY STAGE-III

Reproduction in Plants

Let us learn how plants reproduce and find out how it differs from the reproduction in human.

Plants reproduce by two methods namely sexual and asexual reproduction.

Table 5: Sexual and Asexual Reproduction in Plants


• The sex cells or gametes are involved.

• In flowering plants, gametes are produced

in the reproductive parts of the flowers.

• The female and male gametes fuse to form

a zygote.

• The zygote undergoes several divisions to

form an embryo, which later develops into

a mature plant.

• No gametes are involved.

• In asexual reproduction, plants multiply

through vegetative parts such as roots,

stems, leaves and buds.

• It is called vegetative reproduction or

vegetative propagation.

Vegetative propagation is grouped into natural and artificial based on how the plants reproduce.

Figure 4: Types of Vegetative Propagation

A. Natural Vegetative Propagation: Some plants produce new plants from vegetative parts like

stem, leaves and roots. The new plants are exactly similar to the parent plants.

i. Vegetative propagation by the stem: The underground stems of some plants produce buds,

which grow into new plants.

Examples: Potato tuber is a modified stem. You may have noticed some marks on potatoes

called “eyes” which are buds that later grow into new plants. Other plants such

as onion bulbs, rhizome of ginger and turmeric show a similar mode of

reproduction.

Natural Vegetative Propagation Artificial Vegetative Propagation

Vegetative Propagation

By Stem By Root By Leaves Stem Cutting Layering Grafting

Mound Layering Aerial Layering



KEY STAGE-III

ii. Vegetative propagation by roots: The roots of some plants grow into new plants.

Examples: The root tuber of sweet potato remain buried in the soil and during favourable

condition it gives rise to a new plant.

iii. Vegetative propagation by leaves: These plants

produce buds at the margin of the leaves, which

grow into new plants.

Example: Bryophyllum

Figure 6: Vegetative Propagation by Root

https://www.toppr.com/content/concept/natural-vegetative-propagation-201518/

Figure 7: Bryophyllum

https://www.toppr.com/content/concept/natural-vegetative-propagation-201518/

https://www.qsstudy.com/biology/asexual-reproduction

Figure 5: Vegetative Propagation by the Stem



KEY STAGE-III

B. Artificial Vegetative Propagation: The parts of the plant like stem and buds are used to

develop new plants by the human.

i. Stem Cutting: A stem or a branch of a plant is cut and planted in moist soil. This planted

stem gives rise to roots and buds which grows into a new plant. The stem cut should

have one or more nodes. Examples: sugar cane, rose, china rose, and bougainvillea.

ii. Layering: The two types of layering are mound layering and aerial layering.

a. Mound Layering: The lower branch of the plant is bent close to the ground and

covered with moist soil keeping its

growing tip above the soil surface. This

bent branch is called a layer. Once the

layer produces roots, it is cut from the

parent plant and grown separately.

Examples: Lemon, rose, jasmine.

b. Aerial layering: This method is

practiced in plants having its branches

away from the soil. A ring of the bark is

removed from the base of the aerial

branch. It is covered with moist clay

and wrapped in polythene sheet to

prevent evaporation. After a week, the

covered part of the branch develops

roots which are cut along with roots and

planted into the soil.

Examples: Mango,

litchi, lemon, orange,

guava, apple, etc.

Figure 8: Stem Cutting in Rose https://www.youtube.com/watch?v=gUwnaubQIig

Figure 9: Types of Layering https://www.brainkart.com/article/Artificial-Vegetative-methods_38187/



KEY STAGE-III

iii. Grafting: The stem of a plant is cut and fitted on another plant of same species or allied

species. The join is bound

together with tape and covered

with wax to keep it moist and

prevent infection. The plant

receiving the bud or shoot is

called stock, while the bud or

shoot fixed on the stock is called

the scion. Later the scion grows

into a new plant.

Examples: Orange and lemon

Activity 2


1. Carefully observe the figure given at the side and

answer the following questions.

i. Identify the type of propagation.

ii. Name two plants in which such a method can be

practiced.

iii. Why is such a method not practiced in rose?

2. Identify the part of the following plants which can be

used for vegetative propagation.

(Potato, sweet potato, mint, dahlia, sugarcane, begonia flower)

Summary

✓ Reproduction is the process by which living organism produce young ones of their kind.

✓ Two types of reproduction in living beings are asexual reproduction and sexual

reproduction.

✓ The onset of sexual maturity in an individual is called puberty.

✓ The human male reproductive system consists of a pair of testes, sperm ducts (vas

deferens), accessory glands, urethra and penis.

✓ In the female, the reproductive systems consist of a pair of ovary, fallopian tube, uterus,

cervix and vagina.

✓ The fusion of male gamete and female gamete is called fertilization.

Figure 10: Grafting https://www.jagranjosh.com/general-knowledge/gk-questions-and-answers-on-artificial-propagation-of-plants-1521461519-1

https://irrecenvhort.ifas.ufl.edu/plant-prop-glossary/08-layering/



KEY STAGE-III

✓ The fixing of blastula to the wall of the uterus is called implantation.

✓ The period of development of the foetus in the uterus is called the gestation period.

✓ The vegetative reproduction is the production of new plants from parts of the plant other

than seeds.

✓ Cutting, grafting, layering and budding are artificial methods of vegetative propagation.



1. Explain the importance of reproduction in an organism.

2. The figure below shows the bacteria’s mode of reproduction. How is the reproduction different

from that of human?

3. Match the structures with its functions.

Structure Functions

Fallopian tube A skin bag that protects testes and regulates its temperature.

Testes The site for fertilization in mammals.

Accessory glands Carry sperms from testes to the urethra.

Scrotum Produce fluids to lubricate and nourish the sperms.

Sperm duct Produce sperms and the hormone testosterone.

4. Before fertilization occurs, the sperms have to travel from the testes to ovum in the female

organs. The pathway shown in the figure is incorrect.

What is wrong with the path of the sperm shown in the figure? Explain your points by

putting it in the correct order.



KEY STAGE-III

Answers for Activities

Activity 1

i.i. C

ii. Produces female gamete (ovum).

iii. Female reproductive system.

iv. Fertilization cannot take place and the female cannot become pregnant.

ii.Sperm, testes, scrotum, temperature, sperm duct (vas deferens), accessory, semen,

penis, urethra.

Activity 2

1.i. Aerial layering

ii. Orange and Mango

iii. It is because the stem of the rose plant is closer to the ground. It can be bent for

mound layering.

2.Potato-tuber, sweet potato-root and tuber, mint-stem, dahlia-root and tuber,

sugarcane-stem, begonia flower-root


1.Reproduction helps to increase the number of individuals, provides continuity of life

and form new species or bring evolution in a species.

2.Bacteria undergo the asexual mode of reproduction whereas human undergo sexual

reproduction. No sex gametes are involved.

3.

Structure Functions

Fallopian tube The site for fertilization in mammals.

Testes Produce sperms and hormone testosterone.

Accessory glands Produce fluids to lubricate and nourish the sperms.

Scrotum A skin bag that protects testes and regulates its temperature.

Sperm duct Carry sperms from testes to the urethra.

4. The uterus serves as the site for embryo development. The vagina is the tube which

receives the sperms. The cervix connects the uterus to the vagina. The oviduct is the

tube which connects the ovary to the uterus. Therefore, the correct path of the sperm

is sperm duct, vagina, cervix, uterus and oviduct.



KEY STAGE-III


Theme: Physical Processes

Topic: Work, Power and Energy

Background

Work

Scientifically, work is said to be done when a force is applied on a body and the body has moved

over a distance along the direction of the motion of the body. If the body does not move when

the force is applied to it, no work is done.

Work is said to be done when a force acting on a body produces displacement.

Activity 1

Instruction: Answer the following questions in your notebook. The first question is done for

you.

1. If a force of 10 N acting on a body produces a displacement of 0.3 m. What will be the

work done?

Solution:

✓ Define work, power and energy.

✓ State the units of work, power and energy.

✓ Relate work, force and displacement.

✓ Calculate work, power and energy.

✓ Explain the relevance of energy in our day to day life.

Work = Force x Displacement

W= F x d

Unit of work is joule (J) or Newton meter (Nm)

W= F x d

F=

d=

W

d

W

F

F = 10 N

d = 0.3 m

W = ?

W = F x d

= 10 N x 0.3 m

= 3 Nm or 3 J



KEY STAGE-III

2. A bulldozer does a work of 50,000 J to move a boulder through a distance of 15 m.

Calculate the force applied by it.

3. Sonam has done a work of 1000 J while pushing a table using 300 N force. Find the

distance covered by the table along the direction of the force.

Now let us look at another topic.

Power

Power depends on the amount of work done and the time taken to complete the work.

Power is the amount of work done in unit time. It is also defined as the rate of doing work.

Activity 2

Instruction: Answer the following questions in your notebook. The first question is done for

you.

1. A box is pushed across 5 m by a force of 30 N in 10 seconds. Calculate power.

Solution:

2. A table is pushed 15 m across a room with the force of 50 N.

a. What is the work done?

b. If it takes 20 seconds to push the table across the room. What is power?

Power =

P =

Unit of power is joule per second (J/s) or watt (W)

Work done

time

W

t

F = 30 N

d = 5 m

t = 10 s

W = F x d

= 30 N x 5 m

= 150 J

P=

P=

P= 15 W

W

t

150 J

10 s



KEY STAGE-III

Energy

From the time we get up in the morning till the time we sleep, we do lots of work. What made it

possible for us to do all this work? It is due to the energy that we have.

Energy is the ability to do work.

Let us learn about the common sources of energy by carrying out the activity given below.

Activity 3

Instruction: Complete the table given below by filling in the last column. Check whether or

not the energy source is renewable or non-renewable.

Energy Source Definition

Renewable/

Non-

renewable

Hydropower

The production of

electrical energy

through the use of

flowing water.

Fossil fuels

The fuels produced

from the dead remains

of plants and animals

that lived millions of

years ago.

Example: Coal, petrol,

diesel, kerosene,

methane (LPG)

Wind

The energy possessed

by the wind that helps

to do mechanical

work.



KEY STAGE-III

Biomass

The organic matter

used as a fuel.

Example: firewood,

ethanol and biogas/

gobar gas.

Geothermal

The heat inside the

earth that can be

utilized as a source of

energy.

Nuclear

The energy produced

using radioactive

substances like

Uranium.

Solar

The energy derived

from the Sun in the

form of solar

radiation.

Summary

✓ Work is said to be done when a force acting on a body produces displacement.

✓ Unit of work is Newton meter or joules.

✓ Power is the amount of work done in unit time.

✓ Unit of power is joule per second or watt.

✓ Energy is the ability to do work.

✓ Different sources of energy are hydropower, wind, solar, biomass, nuclear, fossil fuels

and geothermal energy.

https://www.shutterstock.com/search/

https://www.shutterstock.com/search/



KEY STAGE-III



1. An ant is dragging a housefly and an elephant is pushing a big tree which is not moving.

Who is doing work, the ant or the elephant? Justify.

2. Is work the same as power? Justify your statement.

3. A bull pulls a plough with a constant force of 2000 N along a field through a distance of

10 m in 50 s. What is the power of the bull?

4. Our government wants to construct more wind energy plant in the country. Which place

would you recommend for the construction? Why?

Activity 1 2. 3.

Activity 2

2. .




KEY STAGE-III

Activity 3

Energy

Source

Renewable/

non-renewable

Hydropower Renewable

Fossil fuels Non-renewable

Wind Renewable

Biomass Renewable

Geothermal Renewable

Nuclear Non-renewable

Solar Renewable


1.The ant is doing work because it is applying force as well as displacing the object

(housefly).

2.No, work and power are different from each other. Work is applying force on an

object and displacing it whereas power is work done in a unit time.

3.

4.I would recommend Wangdi Phodrang for the construction of wind energy plant

because this place is always windy. Wind energy plant requires a place with

continuous wind flow.

Answer for Activity



KEY STAGE-III


Theme: Materials and their Properties

Topic: Acid and Base

Background

General Characteristics of an Acid General Characteristics of a Base

o It dissolves in water to produce hydrogen

ion.

HCl H+ + Cl-

H2SO4 2H+ + SO42-

o It turns blue litmus paper red.

o It turns methyl orange to red.

o Phenolphthalein remains colourless in

acid.

o It has a sour taste.

o Inorganic acids are highly corrosive.

o It dissolves in water to produce hydroxide

ion.

NaOH Na+ + OH-

Ca(OH)2 Ca2+ + 2OH-

o It turns red litmus paper blue.

o It turns methyl orange to yellow.

o It turns phenolphthalein pink.

o It has a bitter taste.

o Some bases are highly corrosive.

o It is slippery to touch.

o If the base is soluble in water, it is called

an alkali.

✓ Define acid and base.

✓ Differentiate between acid and base.

✓ Define neutralization with an example.

✓ State some applications of neutralization.

✓ Explain the reaction of acids with metals, metal carbonate

and metal bicarbonate with examples.

+H2O

+H2O

+H2O

+H2O



KEY STAGE-III

Activity 1

Instruction: Answer the following questions in your notebook. Question 1 can be done in the

booklet.

1. Complete the table given below by writing the colour change of the indicator in the acid

and base. The first one is done for you.

Indicator Colour in Acid Colour in Base

Blue litmus paper Red Remains blue

Red litmus paper

Methyl orange

Phenolphthalein

2. Show how acid and base given below dissociates in water.

i. HNO3

ii. KOH

Types of Acids

Acids

Organic

Citric acid

Maleic acid

Lactic acid

Oxalic acid

Ascorbic acid

Inorganic/ Mineral

Sulphuric acid

Hydrochloric acid

Nitric acid

Phosphoric acid

Carbonic acid



KEY STAGE-III

Acid and Alkali in Foods

Acids in Food Alkalis in Food

Asparagus Broccoli

Cucumber Avacado

Okra/ Ladyfinger

Reactions between Acid and Base

http://fashiontrendsnow.com/organic-

acids-market-overview-manufacturers-

profiles-competition-revenue-by-

countries/

https://trans4mind.com/nutrition/pH.htm

l

https://medium.com/@virgs/https-medium-com-lopidio-transacao-de-dados-pt-1-2617985ae55d



KEY STAGE-III

Neutralization is a reaction between acid and base to form salt and water.

Acid and base react to form salt and water.

Example:

NaOH + HCl → NaCl + H2O

KOH + HNO3 → KNO3 + H2O

Application of neutralization reaction

Reaction between Acid and Metal

The metal reacts with acids to form salt and hydrogen gas.

Example:

1. Zn + 2HCl → ZnCl2 + H2

Sodium

hydroxide Hydrochloric

acid

Sodium

chloride

Water

Acid + Base → Salt + Water

Potassium

hydroxide Nitric

acid

Potassium

nitrate Water

Zinc Hydrochloric

acid

Zinc

chloride

Hydrogen

• Chemical waste must be neutralized before disposing of

it.

• Antacid neutralizes the effect of HCl in the stomach.

• The acidity of the soil is neutralized by adding lime or

ashes.

• Compost neutralizes the alkalinity of the soil.

• Use soap or baking soda on bee sting as it contains

formic acid.

• Use vinegar or lemon on wasp sting as it contains

alkali.

• Toothpaste neutralizes the acids in our mouth produced

by bacteria.

• Astronaut uses lithium hydroxide to neutralize the

exhaled CO2.

Wasp

Bee

https://www.thesun.co

.uk/tech/10399465/nas

a-blood-clot-

backwards-jugular-

vein-astronauts-iss/)

https://www.addisonpestcontrol.co

m/services/bees-wasps-and-

hornets

Metal + Acid → Salt + Hydrogen



KEY STAGE-III

2. Ca + H2SO4 → CaSO4 + H2

Reaction between Acids and Metal Carbonates/ Bicarbonates

When metal carbonate or metal bicarbonate reacts with the acid, it produces salt, water and

carbon dioxide.

Example:

1. CaCO3 + 2HCl → CaCl2 + H2O + CO2

2. 2NaHCO3 + H2SO4 → Na2SO4 + 2H2O + 2CO2

Activity 2


1. How is the neutralization reaction used in the field of agriculture?

2. All acids are corrosive. Do you agree? Explain.

Summary

✓ An acid is a chemical substance that produces hydrogen ion when dissolved in water.

✓ The base is a chemical substance that produces hydroxide ion when dissolved in the

water.

✓ A neutralization reaction is a reaction between acid and base which produces salt and

water.

✓ An acid reacts with metal producing hydrogen and salt.

✓ An acid reacts with metal carbonates or bicarbonates producing salt, water and carbon

dioxide.

Calcium Sulphuric

acid

Calcium

Sulphate

Hydrogen

Calcium

Carbonate Calcium

Chloride

Hydrochloric

acid

Water Carbon

dioxide

Sodium

Bicarbonate

Sodium

Sulphate

Water Carbon

dioxide Sulphuric

acid

Metal Carbonate/ Metal Bicarbonate + Acid → Salt + Water + Carbon dioxide



KEY STAGE-III



1. When we have stomach disorders, we take antacids to solve the problem. How does it

help? Support your answer with an equation.

2. A Chemistry laboratory assistant noticed labels missing from two reagent bottles

containing hydrochloric acid and sodium hydroxide. As a science student, how can you

help him to place back the correct labels?

3. Calcium carbonate is the major component of marble. Sulphuric acid is one of the major

components of acid rain. Write a balanced chemical equation to show the corrosion of

marble statue by the acid rain.



KEY STAGE-III

Activity 1

1….

Indicator Colour in Acid Colour in Base

Blue litmus paper Red Remains blue

Red litmus paper Remains red Blue

Methyl orange Red Yellow

Phenolphthalein Remains colourless Pink

2….

i.HNO3 → H+

+ NO3-

ii.KOH → K+ + OH

-

Activity 2

1.Neutralization reaction is used in the field of agriculture:

•By adding lime or ashes to neutralize the acidity of the soil.

•By adding manure or compost to neutralize the alkalinity of the soil.

2.No, all acids are not corrosive in nature. Organic acids are mild. They are also

consumed as they are present in the foods we eat.


1.For stomachache, we must eat antacid since it contains a base called

magnesium hydroxide. Magnesium hydroxide neutralizes the effect of

hydrochloric acid in our stomach and relieves the pain.

Mg (OH)2 + 2HCl → MgCl2 + 2H2O

2.In both hydrochloric acid and sodium hydroxide bottle, I will dip both blue and

red litmus paper. The substance that turns blue litmus red is HCl and the one

that turns red litmus blue is NaOH.

3.…..

CaCO3 + H2SO4 → CaSO4 + H2O + CO2




KEY STAGE-III


Theme: Physical Properties

Topic: The Formation of Images

Background

You have already learnt about the properties of light in lower grades. Light is a form of energy

which helps us to see the objects. Have you ever wondered why we can see the different objects

around us? This is due to the reflection of light.

Laws of Reflection

The bouncing back of light into the same medium after striking a surface is called reflection of

light. It depends on the nature of a surface.

Incident ray: The light ray falling on the surface.

Reflected ray: The light ray bouncing back in the

same medium after striking the reflecting surface.

Point of incidence (P): The point on the mirror

surface, where the incident ray, the reflected ray and

the normal meets.

Normal ray: It is the line drawn perpendicular to the reflecting surface at the point of incidence.

Angle of incidence (𝒊): The angle between the incident and the normal.

Angle of reflection (r): The angle between normal and the reflected ray.

The law of reflection states that:

✓ The incident ray, the reflected ray and the normal all lie in the same plane.

✓ The angle of incidence is equal to the angle of reflection.

✓ Define reflection.

✓ Differentiate types of reflection.

✓ Draw ray diagrams to show how spherical mirror forms image

of an object placed at different positions.

✓ State applications of spherical mirrors.

✓ Draw ray diagrams for the image formed by lenses.

✓ Identify the uses of lenses in optical instruments and devices.

✓ Define dispersion.

Figure 1: Reflection of Light

https://byjus.com/physics/reflection-of-light/



KEY STAGE-III

Types of Reflection

Table 1: Differences between Regular and Irregular Reflection

Regular Reflection Irregular Reflection

• It is a phenomenon in which the light rays

are reflected parallel to each other after

striking a surface.

• It occurs only if the rays are falling on a

smooth and even surface like a plane mirror.

• It is a phenomenon in which light rays are

scattered in different directions after striking

a surface.

• It occurs if the rays are falling on a rough

surface.

Spherical Mirrors

A mirror in which the reflecting surface is a part of a sphere is called a spherical mirror. There

are two types of spherical mirrors- a concave mirror and a convex mirror.

Table 2: Differences between Concave and Convex Mirror

Concave Mirror Convex Mirror

-The inner surface is the reflecting surface.

-The outer surface is the reflecting surface.

-The image can be a real or virtual, erect or

inverted and magnified, diminished or same

size as that of an object, all depending on the

position of the object from the mirror.

-The image formed is always virtual, erect

and smaller in size than the object, but gets

larger as it comes towards the mirror.

-It is also called converging mirror because a

parallel beam of light falling on the mirror

converges at a point after reflection.

-It is also called diverging mirror because a

parallel beam of light falling on the mirror

appears to diverge from a point after

reflection.

https://www.toppr.com/content/concept/regular-and-

diffused-reflection-210160

http://byjus.com/physics/concave-convex-mirrors



KEY STAGE-III

Terms Used in Spherical Mirror

Pole (P): It is the midpoint of a mirror.

Centre of curvature (C): It is the centre of the sphere of which the mirror forms a part.

Radius of curvature(R): It is the distance between the pole and the centre of curvature. It is

twice the focal length of the mirror.

Principal axis: An imaginary line that passes through the pole and the centre of curvature.

Aperture: It is used to denote the size of the mirror.

Focus: It is the point on the principal axis, where the light rays parallel to the principal axis will

converge or diverge after reflection from the mirror.

Focal length: The distance between the pole and the focus of the mirror.

Rules for Drawing Ray Diagrams in a Concave Mirror

1. The ray of light travelling parallel to

the principal axis after reflection will

pass through the focus.

2. The ray of light travelling through

focus will reflect parallel to the

principal axis.

Figure 2: Concave and convex mirrors shown as a part of complete hollow sphere.

http://physicscatalyst.com/class10/light-reflection-andrefraction.php.



KEY STAGE-III

3. The ray of light passing through the

centre of curvature will reflect along

the same path.

4. The ray of light incident on the pole

of the mirror will reflect, following

the laws of reflection.

Figure 3: Rules for Drawing Ray Diagrams for Concave Mirror

Formation of an Image by a Concave Mirror-Ray Diagram

1. When the object is at infinity

Characteristics of the image:

• Real

• Inverted

• Highly diminished

• Located at the focus

2. When the object is placed beyond the center of curvature


• Real

• Inverted

• Diminished

• Located between the centre of curvature and

focus

3. When the object is placed at the centre of curvature


• Real

• Inverted

• Same size as object

• Located at the centre of curvature

4. When the object is between focus and centre of curvature.


• Real

• Inverted

• Enlarged

• Located beyond the centre of curvature.

Figure 4: Image Formed by the Concave Mirror



KEY STAGE-III

Uses of Concave Mirror

Concave mirrors are used

• as shaving mirrors

• as make-up mirrors

• as a dentist’s mirror

• in searchlights

• in floodlights

• in headlights of vehicles

• in solar heating devices

Figure 5: Uses of Concave Mirror

Rules for Drawing Rays in a Convex Mirror

1. Ray of light travelling parallel to the

principal axis after reflection appears

to diverge from the focus.

2. When a light ray appears to pass

through focus, it will reflect parallel

to the principal axis.

3. Ray of light appearing to pass

through the centre of curvature will

reflect in the same path.

4. Ray of light incident on the pole of

the mirror will reflect, following the

laws of reflection.

Figure 6: Rules for Drawing Ray Diagram in a Convex Mirror

https://slideplayer.com/slide/3563454/



KEY STAGE-III

Formation of an Image in a Convex Mirror-Ray Diagram

1. When the object is placed in front of a mirror


• Always virtual

• Upright

• Diminished

• Located between the pole and the focus

Uses of Convex Mirror

A convex mirror is used

• as a rear-view mirror in vehicles.

• as a reflector in the street light.

• in shops to detect shoplifters.

• at sharp bends to give a view of oncoming traffic.

Figure 7: Uses of Convex Mirror

Activity 1


1. You are given three mirrors of different types: mirror used at home, concave and convex. How

will you identify each one of them?

2. In the ray diagrams of concave and convex mirrors, we see that the image formed is either real

or virtual. Give three differences between a real image and a virtual image.

Lenses

A lens is a transparent medium with a spherical surface, which refracts light. There are several

types of lens. The basic types of lens are the concave lens and the convex lens.

Figure 6: Image Formed by the Convex Mirror

https://socratic.org/questions/what-are-some-examples-of-convex-mirrors



KEY STAGE-III

Table 3: Differences between Convex and Concave Lens

Convex Lens Concave Lens

• It is thicker in the middle and thinner at the

edges.

• Light rays tend to converge after refraction

from the lens.

• It can form a real and virtual image.

• The image formed may be the enlarged or

same size or diminished.

• It is thinner in the middle and thicker at

the edges.

• Light rays tend to diverge from the lens

after refraction.

• It forms virtual images only.

• The image formed is always diminished.

Convex Lens: Rules for the Construction of the Ray Diagram

1. Ray of light travelling parallel to the principal axis

converges at principal focus after passing through the

lens.

2. Ray of light passing through the optical centre of

the lens emerges from the lens without deviation.

3. Ray of light emerging from the principal focus

travels parallel to the principal axis.

Figure 8: Rules for the Construction of Ray Diagrams in the Convex Lens

https://www.pinterest.com/pin/248683210648484520/



KEY STAGE-III

Formation of an Image in a Convex Lens- Ray Diagram

1. When the object is kept at infinity and the light rays coming from the object passes through

the convex lens.


• Formed at the principal focus F2

• Real

• Inverted

• Highly diminished

2. When the object is beyond 2F1


• Formed in between F2 and 2F

2

• Real

• Inverted

• Diminished

3. When the object is at 2F1


• Formed at 2F2

• Real.

• Inverted.

• Same size as the object

4. When the object is in between 2F1

and F2


• Formed beyond 2F2

• Real

• Inverted

• Magnified

5. When the object is at F1


• Formed at infinity

• Real

• Inverted

• Highly magnified

Image

Image

Object

Image

Object

Image

Object

Object



KEY STAGE-III

6. When the object is in between F1 and optical centre O


• Formed beyond F1

• Virtual

• Erect

• Magnified

Concave Lens: Rules for the Construction of the Ray Diagram

1. An incident ray of light travelling parallel

to the principal axis diverges from the lens

after refraction. The refracted ray appears

to come from the principal focus.

2. Ray of light that appears to pass through

the principal focus travels parallel to the

principal axis after refraction.

3. Ray of light passing through the optical

centre of the lens emerges from the lens

without deviation.

Object

Image

Figure 9: Image formed by the Convex Lens

Figure 11: Rules for the Construction of

Ray Diagrams in the Concave Lens



KEY STAGE-III

Formation of an Image in a Concave Lens- Ray Diagram

1. When the object is at infinity


• Formed at the Focus (F1)

• Virtual

• Erect

• Diminished

2. When the object is between F1 and optical centre (O)


• Formed between the O and F1

• Virtual

• Erect

• Diminished

Uses of Concave and Convex Lens

Table 4: Uses of Concave and Convex Lens

Device Name Lens

Used

Device Name Lens

Used

Binocular

Convex

lens

Flash

Light

Convex lens

and

Concave

Lens

Projector Convex

lens

Spectacles Convex lens

and

Concave

Lens

Magnifying

glass

Convex

lens

Contact

Lens

Convex lens

and

Concave

Lens

Microscope Convex

lens

Telescope Convex lens

and

Concave

Lens

Image

Figure 12: Image formed by the Concave Lens

Image

Object



KEY STAGE-III

Spy hole in

the door

Convex

lens

Camera Convex lens

and

Concave

Lens

Activity 2


1. Observe the figures given below and identify the lenses X and Y. Give reason to support your

answer.

2. It was observed that when the distance between an object and a lens decreases, the size of the

image increases. What is the nature of this lens?

Dispersion of White Light

So far, we have learnt about the types of mirrors and lens, and how the images are formed

according to the position of the objects. Now let us learn about the composition of the white light.

The light coming from the sun is not

colourless, but it is made up of seven

colours. They are violet, indigo, blue,

green, yellow, orange and red. These

lights are collectively called VIBGYOR.

When we pass white light through a prism,

we can see the light splitting into seven

colours as shown in the figure. The

process of white light separating into the

seven colours is called a dispersion. The

band of light formed on the screen is called the

spectrum.

https://www.teachoo.com/10840/3118/Uses-of-Concave-and-Convex-Lens/category/Concepts

https://www.toppr.com/content/concept/dispersion-of-light-by-prism-

210300/

Figure 13: Dispersion of White Light



KEY STAGE-III

Summary

✓ The bouncing back of light into the same medium after striking a surface is called reflection

of light.

✓ The incident ray, the normal and the reflected ray at the point of incidence lie on the same

plane.

✓ A spherical mirror whose reflecting surface is curved inside is called a concave mirror or

converging mirror.

✓ A spherical mirror whose reflecting surface is bulging outside is called a convex mirror or

diverging mirror.

✓ A concave mirror forms either a real or a virtual image, whereas a convex mirror always

forms a virtual image.

✓ A lens is a transparent medium with a spherical surface, which refracts light.

✓ There are two main types of lenses that are convex lens and concave lens.

✓ The convex lens is thicker at the center than at the edge. It is also called the converging

lens.

✓ A concave lens is thinner at the center than the edges. It is also called the diverging lens.

✓ White light is composed of seven different colours that are violet, indigo, blue, green,

yellow, orange and red.



1. Show with a diagram that a concave lens always forms a virtual image of an object placed

anywhere on the principal axis.

2. What are some benefits of learning ray diagram in the scientific world?

3. Which sides of the spoons are behaving like a concave and convex mirror? Why?

4. What type of mirror is used as a side mirror in a scooter? Why?



KEY STAGE-III

Activity 1

1. We can identify the mirrors by observing the image formed by each:

Plane mirror: Image is virtual, erect and of same size.

Convex mirror: Image formed will always be virtual, erect and diminished.

Concave mirror: Image may be real or virtual, inverted or erect and magnified or

diminished depending on the position of object.

2.

Real Image Virtual Image

•The image is formed when light rays

meet.

•It can be obtained on the screen.

•The image formed is inverted/ upside

down.

Example: The image formed on the

cinema screen.

•The image is formed when light rays

appear to meet.

•It cannot be obtained on the screen.

•The image formed is erect/ upright.

Example: The image formed by plane

mirror or concave mirror.

Activity 2

1. X is convex lens because the rays are converging after the refraction.

Y is concave lens because the rays are diverging after the refraction.

2. It is a convex lens.

Self-check for learning

1.

or

2. Benefits of learning ray diagrams:

•Construction of contact lens for different eye defects.

•Binoculars for looking at the faraway objects.

•Telescope to learn about the space.

•Camera for photography.

3. The outer surface of spoon (A) acts as convex mirror because the image formed is

upright. Inner surface of spoon (B) acts as a concave mirror because the image formed

is inverted.

4. Concave mirror are used as the side mirror in a scooter because the image formed is

spread over a large area as light gets diverted. This will help drivers to see the large

area behind.




KEY STAGE-III


Theme: Materials and their Properties

Topic: Elements and their Symbols

Background

The universe is made up of a large number of substances. These substances are classified either as

pure substances or mixtures depending upon their composition. A pure substance is the one in

which all the molecules or atoms are of the same kind. A pure substance can be either an element

or a compound.

What is an Element?

A pure substance made up of only one type of atoms is called an element. All the atoms of an

element are identical. Most of the elements occur naturally, while others are obtained artificially.

Hydrogen, oxygen, carbon, nitrogen, iron, copper, gold and silver are common examples of

elements. At present, there are about 118 elements. Each of the elements is given a name and a

symbol unique to it. A symbol is a short form or abbreviated name of an element. The symbol

represents the atom of an element. Along with the symbol, we use atomic number and mass

number to represent an element.

zXA

✓ Define the term element and symbol.

✓ Identify the atomic number and mass number of an element.

✓ Write symbols of the first 30 elements and arrange them in the

periodic table.

✓ Classify elements into metals and non-metals.

✓ Describe some of the properties of metals and non-metals.

Mass number Element/ symbol

Atomic number

Substance

Pure Substance

Element

Metal Non-metal Metalloid

Compound

Mixture



KEY STAGE-III

Rules for writing the symbols:

1. A symbol always starts with a capital letter. Eg: O, N, H, Hg, Mg, etc.

2. Usually, the first letter of the element is the symbol.

3. If the elements are represented by two letters, the second should be a small letter. Eg: Hg,

Zn, Fe, etc.

4. Symbols of some elements are based on their Latin names. Eg; the symbol of gold is Au

not Go as it is called Aurum in Latin.

First 30 Elements in the Periodic Table

Element Symbol Atomic

number

Mass

number

Element Symbol Atomic

number

Mass

number

Hydrogen H 1 1 Sulphur S 16 32

Helium He 2 4 Chlorine Cl 17 35.5

Lithium Li 3 7 Argon Ar 18 40

Beryllium Be 4 9 Potassium K 19 39

Boron B 5 11 Calcium Ca 20 40

Carbon C 6 12 Scandium Sc 21 45

Nitrogen N 7 14 Titanium Ti 22 48

Oxygen O 8 16 Vanadium V 23 51

Fluorine F 9 19 Chromium Cr 24 52

Neon Ne 10 20 Manganese Mn 25 55

Sodium Na 11 23 Iron Fe 26 56

Magnesium Mg 12 24 Cobalt Co 27 59

Aluminium Al 13 27 Nickle Ni 28 59

Silicon Si 14 28 Copper Cu 29 63.5

Phosphorus P 15 31 Zinc Zn 30 65

https://www.jobilize.com/course/section/the-arrangement-of-atoms-in-the-periodic-table-by-openstax



KEY STAGE-III

Metals and non-metals

Elements are further classified into metals and non-metals based on their properties. We have

been using metals and non-metals in our daily lives. Their usefulness depends on their properties.

Properties of Metals Properties of Non-metals

Usually solid May be solid, liquid or gas

Usually hard Usually soft

Ductile→It can be made into thin wires. Non-ductile→It cannot be made into thin wires.

Malleable→It can be hammered into

different shapes without breaking.

Non-malleable→It cannot be hammered into

different shapes without breaking.

Lustrous→It has a shiny surface. Non-lustrous→It doesn’t have a shiny surface.

Sonorous→It produces a ringing sound. Non-sonorous→It doesn’t produce a ringing

sound.

Good conductors of heat and

electricity

Non-conductors of heat and electricity

Non-brittle→It doesn’t break easily. Brittle→It breaks easily.

High melting point Low melting point and boiling point

Eg: Fe, Cu, Al, Zn, Au(gold),

Ag(silver), Sn(tin), Pb(lead), etc…

Eg: C, S, N, O, Cl, I(iodine), etc…

Do You Know?

✓ Non-metals are usually soft except diamond. It is the hardest naturally occurring

substance on earth.

✓ Non-metals are bad conductors of heat and electricity except graphite.

✓ Although zinc is metal, it is brittle (neither malleable nor ductile).

✓ Bromine is a liquid non-metal.

✓ Some elements have both the properties of metals and non-metals, they are called

metalloids. (Examples: Boron, silicon, germanium, arsenic, antimony…)

Activity 1


1. An element with symbol ‘Y’ is represented as 30Y65. What is the atomic number and mass

number of this element? Name the element ‘Y’.

2. Fill in the blanks with an appropriate word(s):

a. The pure substance made up of only one type of atoms is called ___________.

b. The hardest substance on earth is ___________.

c. The only non-metal that is a good conductor of heat and electricity is __________.

d. The ______________ of the element always starts with capital letter.



KEY STAGE-III

Summary

✓ An element is a pure substance made up of the same kind of atoms.

✓ A symbol is a short form of representing an element.

✓ Elements can be classified into metals and non-metals based on their properties.

✓ Metals are usually hard, solid, ductile, malleable, sonorous and conducts heat and

electricity.

✓ Non-metals are usually soft, brittle and non-conductor of heat and electricity. It can be

solid, liquid or gas.



1. Sort the following elements into metals and non-metals using their symbol.

(Zinc, Copper, Sulphur, Oxygen, Iodine, Sodium, Aluminium)

2. Why is copper used in household wirings?

3. Select the most suitable answers from the elements given in the box.

i. A metal which is expensive and used to make ornaments.

ii. Two non-metals combine to form water.

iii. A metal which is used in making cans to store foods.

iv. A non-metal present in pencil lead.

v. A metal widely used in the construction of the building.

Gold Oxygen Iron Hydrogen

Carbon Sulphur Diamond Tin



KEY STAGE-III

Activity 1

1.Atomic number=30 Mass Number=65 Element=Zinc

2.a. element

b. diamond

c. graphite

d. symbol


1.…

Metals Non-metals

Zn, Cu, Al S, O, I, Na

2.This is because copper is malleable and ductile. It can be beaten into any shapes

or sizes without breaking. It is also a good conductor of electricity.

3.i. Gold

ii. Hydrogen and Oxygen

iii. Tin

iv. Carbon

v. Iron




KEY STAGE-III


Theme: Physical Processes

Topic: Force and Pressure

Background

Relationship between Pressure, Force and Area

The pressure is the amount of force acting perpendicular on a unit surface. When an object is

placed on a surface, it exerts a force equal to its weight. The pressure acting on a surface can be

increased by increasing the weight and decreasing the surface area. Let us investigate pressure and

its relationship with force and surface area.

Activity 1

Instruction: Carry out the following investigations.

Materials required: 2 bottles of different sizes filled with

water, 2 cups, 1 flat board

Investigation 1

1. Place the 2 cups upside down and on it place the flat

board.

2. Place the small bottle on the board and observe how

far the board is bending.

3. Place the big bottle on the board and observe how far

the board is bending.

How is pressure related to the weight (force) of the object?

In investigation 1, we observed that a bigger water bottle

exerts more pressure than a smaller water bottle. So, we

can conclude that more weight, more pressure.

✓ Define Pressure.

✓ Construct a relationship between force, area and pressure.

✓ Calculate pressure using force and area.

✓ Explain the applications of pressure in our daily lives.

Figure 1: Relationship between

Force and Pressure



KEY STAGE-III

Investigation 2

1. Place the big bottle upright on the board and

observe how far the board is bending.

2. Place the big bottle sideways on the board and

observe how far the board is bending.

How is pressure related to the surface area of the object?

In investigation 2, we observed that bottle standing upright

exerts more pressure than bottle lying down. So, we can

conclude that more surface area, less pressure.

From the 2 investigations above, we learnt that:

i. The pressure is directly proportional to the force

(weight).

• More force, more pressure.

• Less force, less pressure.

ii. The pressure is inversely proportional to the

surface area.

• More surface area, less pressure.

• Less surface area, more pressure.

Combining statement (i) and (ii) we get:

Pressure =

The unit of Pressure is Newton per meter square (Nm-2) or

pascal (Pa)

Application of Pressure

• Nails have sharp pointed tips (less surface area) so that

pressure increases with a decrease in surface area.

• Sharp knife cuts better than a blunt knife as sharp knife

has less surface area thereby increases the pressure.

• In Southern Bhutan people carry the loads in a bamboo

basket using a flat rope resting on their head. A flat

rope has a larger surface area thus reducing the

pressure.

Force

Area

Figure 2: Relationship between

Surface Area and Pressure

Figure 3: Flat rope reduces

pressure.

https://www.travel-images.com/nepal/photo-

nepal437.html



KEY STAGE-III

• School bags have broad straps or belts to reduce pressure.

• Camels have broad hooves to increase the

surface area on sand thus preventing them

from sinking in the sand.

• The foundation of the dzongs are broad to

increase the surface area and the stability of

the dzongs.

• Trucks have double rear wheels to reduce

the pressure exerted by the load on the road.

Activity 2

Instruction: Look at the solved examples and solve the following questions in your notebook.

Example 1

What will be the pressure exerted by a force of 100N on a surface area of 10m2?

F = 100 N

A = 10 m2

P = ?

P =

=

= 10 Nm-2 or 10 Pa

F

A

100 N

10 m2

Formula

P=

A=

F= P x A

F

A

F

P

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KEY STAGE-III

1. Dorji weighs 1500N. If the total surface area of the soles of his feet is 0.5m2, what is the

pressure exerted by his body on the ground?

2. The pressure exerted by a block of wood is 40 Pa. If the force exerted by the block is 80N,

what is the surface area of the wood?

3. A cube of wood exerts a pressure of 2Pa when it is placed on a floor. What is the force

exerted by the cube if its surface area is 5m2?

Summary

✓ The pressure is the perpendicular force acting on a unit surface area.

✓ The pressure is directly proportional to force and inversely proportional to the surface

area.

✓ The unit of pressure is the pascal (Pa) or newton per meter square (Nm-2)

✓ Formula



1. Define pressure.

2. Given below are the four bodies of 100kg each.

a. Arrange the above blocks in terms of pressure exerted by them on the plank, from the

least to the greatest.

b. Identify the block that exerts the maximum pressure? Explain.

c. Identify the block that exerts the least pressure? Explain.

3. A wooden block of weight 12 N kept on a table having a surface area of 4 m2. Calculate

the pressure exerted on the table.

4. High heel shoes are more likely to damage floors than flat shoes. Do you agree? Explain.

100kg

A

100 kg

B 100 kg C

100 kg

D

P= F

A

A=

F

P

F= P x A



KEY STAGE-III

Activity 2

1.F= 1500N A=0.5m2 P=?

P=F/A

P=1500N/0.5m2

P= 3000Pa

2.P=40Pa F=80N A=?

A=F/P

A=80N/40Pa

A=2m2

3.P=2Pa A=5m2 F=?

F=P x A

F=2 Pa x 5m2

F=10N


1.Pressure is the perpendicular force acting on a unit surface area.

2.a. C, A, D, B

b. B exerts maximum pressure because it has less surface area.

c. C exerts minimum pressure because it has more surface area.

3.F= 12N A=4m2 P=?

P=F/A

P=12N/4m2

P= 3Pa

4.Yes, I agree because high heel shoes have less surface area so it exerts more pressure

on the floor than flat shoes.



History-Class VII-VIII 117

KEY STAGE-III

Lesson No: 1 Subject: Bhutan History Class: VII-VIII Time: 50 mins

Topic: The Young Jigme Namgyel

Introduction

Jigme Namgyel was one of the greatest national

figures in Bhutan. He brought to an end to the civil

wars, successfully mediated between the rivals,

and united the country after two centuries of

instability. He is rightly regarded as the architect of

the united Bhutan. It was Jigme Namgyel who had

made the position of the Trongsa Poenlop the most

important throughout the country.

He had paved the way to peace and laid the foundation of monarchy that was established in 1907

by his son Gongsa Ugyen Wangchuck who became the First Druk Gyalpo. The institution of the

monarchy had ushered an unprecedented peace in Bhutan. In this lesson, let us learn about the

early life of Jigme Namgyel, his engagement in political affairs, and his emergence as the

undisputed leader in Bhutan.

✓ Describe the early life of Jigme Namgyel.

✓ Explain the prophecy that made Jigme Namgyel leave

his home for Trongsa.

✓ Explain why Jigme Namgyel was given rapid

promotion by Trongsa Poenlop Tshokye Dorji.

✓ Narrate the events in the western regions of Bhutan

where Jigme Namgyel displayed his diplomatic skills

and military strategies.

✓ Explain the role of Jigme Namgyel in the Battle of

Lingmithang.

✓ Discuss how the Battle of Samkhar helped Jigme

Namgyel emerge as an undisputed leader.

1. Have you ever dreamt where you were asked to leave your home and go

to an unknown destination?

2. Who was the father of the first Druk Gyalpo Ugyen Wangchuck?

A Biography of Jigme Namgyel (Centre for Bhutan Studies)



KEY STAGE-III

He was born to Pila Goenpo Wangyal, a descendant of

Tertoen Pema Lingpa and Sonam Pelzom. The Early Life of

Jigme Namgyel

Jigme Namgyel was born in 1825 into the Dungkar Choeje

family in Kurtoe, Lhuentse.

From a young age, he was known to be active, brave,

intelligent and lively child. He was also a devoted follower

of religious teachings.

It took him several months to reach Trongsa. Upon his arrival at

Naru village in Tang, Bumthang, he is said to have worked as a

sheepherder for his survival.

When he was quite young, he used to have strange dreams

which told him to go the west (Trongsa) where he would find

his destiny. Believing in his recurrent dreams, he left his home

for Trongsa. Jigme

Namgyel’s

Dreams and

His

Departure to

Trongsa

When he reached Chumey valley, he met Buli Lama Shakya

Namgyel who provided him shelter and food. When Jigme

Namgyel proceeded to Trongsa, the Lama sent his servant

Urukpa Dondrup as his companion and to show him the way to

Trongsa.

Jigme Namgyel’s

Service in

Trongsa

On reaching Trongsa, he met the Trongsa Poenlop

Ugyen Phuntsho at the archery ground. The Poenlop

admitted him as tozep (common retainer), the lowest

rank in the court of Trongsa.

When he started his career in the service of Trongsa

Poenlop, he was 18 years old.



KEY STAGE-III

In 1843, Trongsa Poenlop Ugyen Phuntsho retired and Tshokye

Dorji of Tang Ugyen Choling, Bumthang succeeded to the post of

the Trongsa Poenlop.

It was under the new Poenlop Tshokye Dorji that Jigme

Namgyel was rapidly promoted to various posts such as

Zinggup (Superintendent of tozep), Zimnang (junior

chamberlain), Darpoen (chief of attendants), Trongsa

Tshongpoen (trade officer), Trongsa Zimpoen (chamberlain)

and Trongsa Dronyer (guest master).

As a Trongsa Tshongpoen, he was required to travel to Tibet

for trade. On one of the journeys, he met his future wife, Pema

Choeki, the daughter of the former Trongsa Poenlop Ugyen

Phuntsho. She was at the Lhalung Monastery in Tibet with

her elder brother, Kuenzang Tenpai Nyima, who was the

Sungtrul incarnation of Tertoen Pema Lingpa

The quick promotion given to Jigme Namgyel indicated that

he was a man of wide-ranging abilities. He worked tirelessly

and carried out the responsibilities assigned to him without

fail. He proved his dedication, diligence and loyalty to the

new Poenlop.

Jigme

Namgyel’s

Services

Rewarded



KEY STAGE-III

Activity 1

Instruction: Write down one responsibility for the following posts held by Jigme Namgyel in

the table given below:

Posts Responsibility

Tozep

Zinggup

Zimnang

Darpoen

Tshongpoen

Zimpoen

Dronyer

For this act of courage, bravery and loyalty, Jigme

Namgyel was rewarded with the additional post of

Lhuentse Dzongpoen. Poenlop Tshokey Dorji was so

grateful to Jigme Namgyel that he also promised him the

post of Trongsa Poenlop after his retirement.

Jigme Namgyel

saved Trongsa

Poenlop Tshokye

Dorji

In 1849, the Punakha Dzong was destroyed by fire. Jigme

Namgyel was sent to Punakha leading a large group of

workmen from Trongsa to help in the restoration of the

dzong. He spent the whole year in Punakha supervising

the workers.

In 1850, the Trongsa Poenlop Tshokye Dorji visited

Punakha to check the progress of the Dzong construction

where he became the target of assassination. There was a

plan by the leaders of western regions to assassinate him

at an archery match. Jigme Namgyel is said to have

remained alert and watchful. He ensured that the Poenlop

was well guarded and protected from his enemies. He

escorted him back to Trongsa safely.



KEY STAGE-III

Reunification of Sharchog Khorlo Tsibgye- The Battle of Lingmithang

1. Have you heard about the Sharchog Khorlo Tsibgye? Which are the

dzongkhags that comprise the Sharchog Khorlo Tsibgye?

The Dzongpoens of these four regions were secretly supported

by the central government in Punakha.

In 1850, the Dzongpoens of Zhongar, Trashigang,

Trashiyangtse and the Gyadrung of Dungsam Pemagatshel

planned to revolt against the Trongsa Poenlop.

The rebel Dzongpoens prepared to march on to Trongsa with

military support expected to come from western Bhutan.

Cause of the

Battle

Course of the

Battle

Jigme Namgyel was promoted to the post of Trongsa Dronyer. The

Trongsa Poenlop collected a large force of troops from Trongsa,

Bumthang, Lhuentse and Zhemgang. They were sent towards the

east under the command of Jigme Namgyel.

The rebel Dzongpoens have gathered at Lingmithang. Before they

embarked their journey towards Trongsa, Jigme Namgyel reached

there and the battle was fought throughout the winter of 1850.



KEY STAGE-III

Outcome of the

Battle

Jigme Namgyel defeated the rebel Dzongpoens and taken as

prisoners to Trongsa.

The four dzongs of Zhongar, Trashigang, Trashiyangtse and

Dungsam were brought under the control of the Trongsa

Penlop.

These eight eastern provinces of central and eastern Bhutan

collectively were known as the Sharchhog Khorlo Tsibgye.

These regions were reunified once again and brought under

the direct control of the Trongsa Poenlop who had, until then,

the effective jurisdiction only over four provinces of Trongsa,

Bumthang, Lhuentse and Zhemgang.

2. Bumthang Dezhi (Four Divisions of

Bumthang)

3. Kurtoe Dozhi (Four Valleys of Kurtoe)

Sharchog Khorlo

Tsibgye

(Eight Provinces of the

Eastern Circle)

4. Yangtse Tshonga (Five Blocks of

Yangtse)

5. Khenrig Namsum (Three Regions of

Kheng)

1. Mangde Tshozhi (Four Blocks of

Mangde)

6. Zhongar Tshoduen (Seven Blocks of

Zhongar)

8. Dungsam Dosum (Three Valleys of

Dungsam)

7. Trashigang Tshochu (Ten Blocks of

Trashigang)



KEY STAGE-III

Activity 2

Instruction: Sketch a map of Bhutan in your notebook and shade the exact location of

Sharchog Khorlo Tsibgye using the colours mentioned below.

1. Red - Mangde Tshozhi 2. Green- Bumthang Dezhi

3. Black - Kurtoe Dozhi 4. White - Khenrig Namsum

5. Blue- Zhongar Tshoduen 6. Yellow –Trashigang Tshochu

7. Pink- Dungsam Dosum 8. Brown- Yangtse Tshonga

Power Struggles in the Western Regions

In 1851 trouble began in western Bhutan. After the 39th Desi Zhabdrung

Thugtruel Jigme Norbu retired from the post, the ambitious Wangdue

Phodrang Dzongpoen Chakpa Sangay seized the throne and proclaimed

himself as the 40th Desi. The Central Monk Body and the supporters of

the Zhabdrung turned to Trongsa Poenlop for armed assistance against

the Desi. Trongsa Poenlop Tshokye Dorji sent Jigme Namgyel leading

the troops from Trongsa to fight against the central government. On

arrival in Punakha no major battle was fought as the Desi had moved his

base to Norbugang. However, Jigme Namgyel killed the Desi’s Nyagoe

(Champion fighter) called Mikthoem in an ambush. Jigme Namgyel

returned to Trongsa leaving Chakpa Sangay still on the throne, who was

assassinated by Agay Haap (Tshulthrim Namgyel), the former Paro

Poenlop. Through this military venture into western Bhutan, he gained

the knowledge of political affairs in the west which proved useful later

in his career.

Conflict

of 1851



KEY STAGE-III

Activity 3

Instruction: Answer the question below in your note book.

1. Jigme Namgyel did not take revenge against Kuenga Palden who took over the post of Desi

after murdering his nominee Uma Dewa. If you were Jigme Namgyel, what actions would

you have taken against the Desi?

Conflict

of 1854

In 1854, there was a power struggle in the west. Thimphu Dzongpoen

Uma Dewa and Wangdue Phodrang Dzongpoen Kuenga Palden were

contending for the post of Desi. The reigning 41st Desi, Jamtruel

Jamyang Tenzin, was besieged by the Thimphu Dzongpoen. Jigme

Namgyel arrived in Punakha with his army. After carefully judging the

situation, he opted for settlement through peaceful negotiation through

which the Desi retained the post and the rival Dzongpoens withdrew.

This was a diplomatic victory for Jigme Namgyel and it helped him

strengthen his political influence in western Bhutan.

In appreciation and as a reward for the timely intervention and peaceful

mediation, the Trongsa Poenlop was given the power to appoint all

Dzongpoens in the eastern regions. Besides, he was allowed to keep the

entire land tax of Kumarikata (Assam) paid by the British. These

arrangements made the Trongsa Poenlop independent of the central

authority in Punakha.

Conflict

of 1857

In 1857, when Desi Jamtruel Jamyang Tenzin died, the old feud between

the two rivals, Thimphu Dzongpoen Uma Dewa and Wangdue

Phodrang Dzongpoen Kuenga Palden, broke out again. This incident

called for the Trongsa Poenlop’s intervention. Jigme Namgyel helped

the Thimphu Dzongpoen and nominated him as the Desi. However, in

the same year, he was assassinated by Kuenga Palden who declared

himself as the Desi with support from the Lhengye Tshog and the

Central Monk Body. Despite the murder of his nominee, Jigme

Namgyel did not take revenge against Kuenga Palden. Instead, he

endorsed him as the new Desi.



KEY STAGE-III

Battle of Samkhar

In 1853, when Jigme Namgyel was appointed as Trongsa

Poenlop, there was an agreement that he would vacate the post

after three years in favour of the Jakar Dzongpoen Tsondrue

Gyeltshen, son of the former PoenlopTshokye Dorji.

After three years, Tsondrue Gyeltshen claimed for the post of

Trongsa Poenlop but Jigme Namgyel did not honour the

agreement considering the political situation in the country.

Cause of the

Battle

Course of the

Battle

In 1857, The battle was fought at Samkhar below Jakar Dzong in

Bumthang.

Desi Kuenga Palden and the central government forces joined the

battle on the Jakar Dzongpoen’s side.

Outcome of the

Battle

The Je Khenpo and Zhabdrung’s Zimpoen settled the disputes

through peaceful negotiation.

Tsondrue Gyaltshen was promoted to the rank of Jakar Poenlop

and given the administrative control over some of the eastern

regions.

Jigme Namgyel retained the post of Trongsa Poenlop.

The eastern region was divided between the two Poenlops of

Trongsa and Jakar.

Jigme Namgyel built the Palace at Wangduechoeling to

commemorate his victory. Though the battle was indecisive,

Jigme Namgyel considered it a victory for him since he did

not lose the post of Trongsa Poenlop.



KEY STAGE-III

Summary

✓ Jigme Namgyel was born to the noble family of Dungkar Choeje in Kurtoe.

✓ He left for Trongsa believing his dreams that foretold his destiny.

✓ He started his career in the service of Trongsa Poenlop at the age of 18.

✓ He was hard working, dedicated, diligent and loyal. These qualities earned him

recognition from the Trongsa Poenlop Tshokye Dorji who promoted him to various posts

within a short period of time.

✓ He brought the entire region of Sharchhog Khorlo Tsibgye under the jurisdiction of the

Trongsa Poenlop after the Battle of Lingmithang.

✓ His military venture and intervention into affairs of western Bhutan proved useful in his

career.

✓ The Battle of Samkhar was important for Jigme Namgyel because he could retain the

post of Trongsa Poenlop for himself through the peaceful mediation by the Je Khenpo

and the Zhabdrung’s Zimpoen.


1. If you were Jigme Namgyel, would you have believed in your dreams and left your

home? Give reasons to support your answer.

2. What would have been the situation in Bhutan had Jigme Namgyel not intervened in the

political affairs of the western Bhutan?

3. Explain the significance of the Battle of Samkhar.

4. Discuss the role of Jigme Namgyel in the Battle of Lingmithang.



KEY STAGE-III

`


1.Open ended

2.There would have been chaos and disorder in the country characterized by

continuous civil wars and bloodshed.

3.The Battle of Samkhar was important for Jigme Namgyel because he could

retain the post of Trongsa Poenlop for himself. It established peace between the

Trongsa Poenlop Jigme Namgyel and the Jakar Dzongpoen Tsondrue Gyaltshen

through the peaceful negotiation initiated by the Je Khenpo and the Zhabdrung’s

Zimpoen.

4.Jigme Namgyel commanded the troops of Trongsa Poenlop who were mobilized

from Mangde, Zhemgang, Lhuentse and Bumthang. He fought the war with the

forces of Zhongar, Trashigang, Tashiyangtse and Dungsam. He defeated the rebel

Dzongpoens and brought the entire regions (Sharchog Khorlo Tsibgye) under the

jurisdiction of Trongsa Poenlop whose power base was ultimately strengthened.


Posts Responsibility

Tozep To fetch water and firewood, running errands and sweeping

courtyards.

Zinggup To act as bodyguard and soldier.

Zimnang To guard the master’s chamber.

Darpoen Head of the attendants.

Tshongpoen Responsible for Trongsa Poenlop’s trade.

Zimpoen Responsible for the personal welfare of the Poenlop.

Dronyer To look after the welfare of guests.

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