self-instructional material
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Self-Instructional Material
i
KEY STAGE-III
Self-Instructional Materials
Key-stage III
(Classes VII and VIII)
Self-Instructional Material
ii
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
Self-Instructional Material
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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
Self-Instructional Material
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/
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English-Class VII-VIII 2
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)
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English-Class VII-VIII 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
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English-Class VII-VIII 4
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
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English-Class VII-VIII 5
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
Self-Instructional Material
English-Class VII-VIII 6
KEY STAGE-III
Lesson No: 2 Subject: English Class: VII-VIII Time: 50 mins
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.
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English-Class VII-VIII 7
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)
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English-Class VII-VIII 8
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
Instruction: Identify the correct from of the verbs in the following sentences.
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.
Self-Instructional Material
English-Class VII-VIII 9
KEY STAGE-III
Activity 4
Instruction: Identify the correct from of the verbs in the following sentences.
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.
Self-Instructional Material
English-Class VII-VIII 10
KEY STAGE-III
Self-check for Learning
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
Self-Instructional Material
English-Class VII-VIII 11
KEY STAGE-III
Lesson No: 3 Subject: English Class: VII-VIII Time: 50 mins
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.
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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.
Self-Instructional Material
English-Class VII-VIII 13
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
Self-check for Learning
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)
Self-Instructional Material
English-Class VII-VIII 14
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
Self-Instructional Material
English-Class VII-VIII 15
KEY STAGE-III
Lesson No: 4 Subject: English Class: VII-VIII Time: 50 mins
Theme: Language and Grammar
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.
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English-Class VII-VIII 16
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.
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English-Class VII-VIII 17
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.
Self-Instructional Material
English-Class VII-VIII 18
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)
Self-check for Learning
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.
Answers for Self-check for Learning
Self-Instructional Material
English-Class VII-VIII 19
KEY STAGE-III
Activity 1
1.Simple future tense.
2.Future continuous tense
3.Future continuous tense
4.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
Self-Instructional Material
English-Class VII-VIII 20
KEY STAGE-III
Lesson No: 5 Subject: English Class: VII-VIII Time: 50 mins
Theme: Language and Grammar
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.
Self-Instructional Material
English-Class VII-VIII 21
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?”
Past perfect continuous:
✓ 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
Past perfect continuous:
The teacher said, “He had been watching
you.”
Past perfect continuous: NO CHANGE –
The teacher said he had been watching you.
Self-Instructional Material
English-Class VII-VIII 22
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
Self-Instructional Material
English-Class VII-VIII 23
KEY STAGE-III
Self-check for Learning
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.
Answers for Activity
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.
Self-Instructional Material
English-Class VII-VIII 24
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.
Answers for Self-check for Learning
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།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 26
གནས་རིམ་ ༣ པ།
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།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 27
གནས་རིམ་ ༣ པ།
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།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 28
གནས་རིམ་ ༣ པ།
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།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 29
གནས་རིམ་ ༣ པ།
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།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 30
གནས་རིམ་ ༣ པ།
རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས།
སྩོང་ལཱ་ ༡ པ།
ལྷག་ནིའི་སྩོང་ལཱ་ཨིནམ་ལས་ དྩོན་ཚན་འདི་ ལེགས་ཤྩོམ་འབད་ལྷག་དགོཔ་ཨིན།
སྩོང་ལཱ་ ༢ པ།
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།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 31
གནས་རིམ་ ༣ པ།
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།
ངོ་སྩོད།
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།
ལས་དྩོན།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 32
གནས་རིམ་ ༣ པ།
རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས།
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།
སྩོང་ལཱ་ ༡ པ།
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 །
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 33
གནས་རིམ་ ༣ པ།
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་
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 34
གནས་རིམ་ ༣ པ།
རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས།
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།
སྩོང་ལཱ་ ༢ པ།
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་
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 35
གནས་རིམ་ ༣ པ།
རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས།
ན་ ར་ ལ་
ས་ ད་
བཅུད་བསྡུས།
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།
རང་ཉིད་དབྱེ་ཞིབ།
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།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 36
གནས་རིམ་ ༣ པ།
རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས།
སྩོང་ལཱ་༡ པ།
ལྷག་ནིའི་སྩོང་ལཱ་ཨིན།
སྩོང་ལཱ་ ༢ པ།
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།
རང་ཉིད་དབྱེ་ཞིབ་ཀྱི་ལན་གསལ་དཔེ།
༡༽ ཏེ། ༢༽ སྟེ། ༣༽ དེ། ༤༽ སྟེ། ༥༽ སྟེ།
ལན་གསལ་དཔེ།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 37
གནས་རིམ་ ༣ པ།
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།
ལས་དྩོན།
✓ 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།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 38
གནས་རིམ་ ༣ པ།
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།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 39
གནས་རིམ་ ༣ པ།
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།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 40
གནས་རིམ་ ༣ པ།
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།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 41
གནས་རིམ་ ༣ པ།
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།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 42
གནས་རིམ་ ༣ པ།
རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས།
བཅུད་བསྡུས།
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།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 43
གནས་རིམ་ ༣ པ།
རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས།
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།
ལན་གསལ་དཔེ།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 44
གནས་རིམ་ ༣ པ།
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།
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་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།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 45
གནས་རིམ་ ༣ པ།
རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས།
✓ 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།
སྩོང་ལཱ་ ༡ པ།
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།
རྩོང་ཁ། སྩོབ་རིམ་༧-༨ པ། 46
གནས་རིམ་ ༣ པ།
རང་ཉིད་སྩོབ་སྩོན་མཁོ་ཆས།
རང་ཉིད་དབྱེ་ཞིབ།
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?
ལན་གསལ་དཔེ།
སྩོང་ལཱ་༡ པའི་ལན་གསལ་དཔེ།
ལྩོ་རྒྱུས་འབྲི་རྩོམ་ ཚིག་འབྲུ་ ༢༥༠ ལས་མ་ཉུངམ་ཅིག་བྲི་དགོཔ་ཨིན།
རང་ཉིད་དབྱེ་ཞིབ་ཀྱི་ལན་གསལ་དཔེ།
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།
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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
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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.
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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.
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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= .
Self-check for Learning
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)
Self-check for Learning
1.
2.
3.
70 m
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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
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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
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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
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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
Self-check for Learning
Instruction: Answer the following questions.
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
Figure 1 Figure 2 Figure 3
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.
=
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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.
.
Answers for Activity
Activity 1: 12, 14, 16
Activity 2: V = 9n – 6
Activity 3: a) 7 b) 12
Self-check for Learning
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
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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.
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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)
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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
Self-Instructional Material
Mathematics-Class VII-VIII 59
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.
Self-check for Learning
Instruction: Answer the following questions.
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
Self-Instructional Material
Mathematics-Class VII-VIII 60
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/
Self-Instructional Material
Mathematics-Class VII-VIII 61
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 =
Self-Instructional Material
Mathematics-Class VII-VIII 62
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
Self-Instructional Material
Mathematics-Class VII-VIII 63
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:
Figure 1 Figure 2 Figure 3
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
Self-Instructional Material
Mathematics-Class VII-VIII 64
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%
Figure 1 Figure 2 Figure 3
Self-Instructional Material
Mathematics-Class VII-VIII 65
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
Self-Instructional Material
Mathematics-Class VII-VIII 66
KEY STAGE-III
Self-check for Learning
1.
2.
3.
Self-Instructional Material
Mathematics-Class VII-VIII 67
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
Self-Instructional Material
Mathematics-Class VII-VIII 68
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
Self-Instructional Material
Mathematics-Class VII-VIII 69
KEY STAGE-III
Self-check for Learning
Instruction: Answer the following questions.
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
Answers for Activity
Activity 1: a) -2 > -5 b) -3 < +1
Activity 2: a) 0 b) 12
Activity 3: a) 9 b) 2 c) -12
Self-check for Learning
1.a) -5 b) -1
2.a) 10
3.a) b)
Self-Instructional Material
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.
Self-Instructional Material
Science-Class VII-VIII 71
KEY STAGE-III
Table 1: Differences between Sexual and Asexual Reproduction.
Sexual Reproduction 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
Self-Instructional Material
Science-Class VII-VIII 72
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
Self-Instructional Material
Science-Class VII-VIII 73
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
Self-Instructional Material
Science-Class VII-VIII 74
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 ………………
Self-Instructional Material
Science-Class VII-VIII 75
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
Sexual Reproduction Asexual Reproduction
• 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
Self-Instructional Material
Science-Class VII-VIII 76
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
Self-Instructional Material
Science-Class VII-VIII 77
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/
Self-Instructional Material
Science-Class VII-VIII 78
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
Instruction: Answer the following questions in your notebook.
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/
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Science-Class VII-VIII 79
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.
Self-check for Learning
Instruction: Answer the following questions in your notebook.
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.
Self-Instructional Material
Science-Class VII-VIII 80
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
Self-check for Learning
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.
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KEY STAGE-III
Lesson No: 2 Subject: Science Class level: VII-VIII Time: 50 mins
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
Self-Instructional Material
Science-Class VII-VIII 82
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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
Self-Instructional Material
Science-Class VII-VIII 83
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.
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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/
Self-Instructional Material
Science-Class VII-VIII 85
KEY STAGE-III
Self-check for Learning
Instruction: Answer the following questions in your notebook.
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. .
Answers for Activity
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Activity 3
Energy
Source
Renewable/
non-renewable
Hydropower Renewable
Fossil fuels Non-renewable
Wind Renewable
Biomass Renewable
Geothermal Renewable
Nuclear Non-renewable
Solar Renewable
Self-check for Learning
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
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Lesson No: 3 Subject: Science Class level: VII-VIII Time: 50 mins
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
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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
Self-Instructional Material
Science-Class VII-VIII 89
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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
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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
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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
Instruction: Answer the following questions in your notebook.
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
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Self-check for Learning
Instruction: Answer the following questions in your notebook.
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.
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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.
Self-check for Learning
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
Answers for Activity
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Lesson No: 4 Subject: Science Class level: VII-VIII Time: 50 mins
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/
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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
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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.
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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
Characteristics of the image:
• Real
• Inverted
• Diminished
• Located between the centre of curvature and
focus
3. When the object is placed at the centre of curvature
Characteristics of the image:
• Real
• Inverted
• Same size as object
• Located at the centre of curvature
4. When the object is between focus and centre of curvature.
Characteristics of the image:
• Real
• Inverted
• Enlarged
• Located beyond the centre of curvature.
Figure 4: Image Formed by the Concave Mirror
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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/
Self-Instructional Material
Science-Class VII-VIII 99
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Formation of an Image in a Convex Mirror-Ray Diagram
1. When the object is placed in front of a mirror
Characteristics of the image:
• 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
Instruction: Answer the following questions in your notebook.
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
Self-Instructional Material
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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/
Self-Instructional Material
Science-Class VII-VIII 101
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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.
Characteristics of the image:
• Formed at the principal focus F2
• Real
• Inverted
• Highly diminished
2. When the object is beyond 2F1
Characteristics of the image:
• Formed in between F2 and 2F
2
• Real
• Inverted
• Diminished
3. When the object is at 2F1
Characteristics of the image:
• Formed at 2F2
• Real.
• Inverted.
• Same size as the object
4. When the object is in between 2F1
and F2
Characteristics of the image:
• Formed beyond 2F2
• Real
• Inverted
• Magnified
5. When the object is at F1
Characteristics of the image:
• Formed at infinity
• Real
• Inverted
• Highly magnified
Image
Image
Object
Image
Object
Image
Object
Object
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6. When the object is in between F1 and optical centre O
Characteristics of the image:
• 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
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Formation of an Image in a Concave Lens- Ray Diagram
1. When the object is at infinity
Characteristics of the image:
• Formed at the Focus (F1)
• Virtual
• Erect
• Diminished
2. When the object is between F1 and optical centre (O)
Characteristics of the image:
• 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
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Spy hole in
the door
Convex
lens
Camera Convex lens
and
Concave
Lens
Activity 2
Instruction: Answer the following questions in your notebook.
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
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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.
Self-check for Learning
Instruction: Answer the following questions in your notebook.
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?
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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.
Answers for Activity
Self-Instructional Material
Science-Class VII-VIII 107
KEY STAGE-III
Lesson No: 5 Subject: Science Class level: VII-VIII Time: 50 mins
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
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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
Self-Instructional Material
Science-Class VII-VIII 109
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
Instruction: Answer the following questions in your notebook.
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.
Self-Instructional Material
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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.
Self-check for Learning
Instruction: Answer the following questions in your notebook.
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
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Activity 1
1.Atomic number=30 Mass Number=65 Element=Zinc
2.a. element
b. diamond
c. graphite
d. symbol
Self-check for Learning
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
Answers for Activity
Self-Instructional Material
Science-Class VII-VIII 112
KEY STAGE-III
Lesson No: 6 Subject: Science Class level: VII-VIII Time: 50 mins
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
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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
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• 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
https://stillunfold.com/animal/camel-feet-amazing-facts
Figure 4: Broad hooves of camel
Figure 5: Double rear wheel of heavy vehicle
https://www.alamy.com/stock-photo/double-rear-tires.html
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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
Self-check for Learning
Instruction: Answer the following questions in your notebook.
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
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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
Self-check for Learning
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.
Answers for Activity
Self-Instructional Material
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)
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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.
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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
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History-Class VII-VIII 120
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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.
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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.
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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)
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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
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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.
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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.
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History-Class VII-VIII 126
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.
Self-check for Learning
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.
Self-Instructional Material
History-Class VII-VIII 127
KEY STAGE-III
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Self-check for Learning
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.
Answers for Activity
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.