CBSE Mathematics

Lesson Plan Math Class 10 (Ch-9) | Applications of Trigonometry

2026-10-03T19:14:57.634+05:30

LESSON PLAN, math. CLASS-10
Ch-9, Application of Trigonometry

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Rmb dav centnary public school Nawanshahr
NAME OF THE TEACHER				DINESH KUMAR
CLASS	X	CHAPTERS	09	SUBJECT	MATHEMATICS
TOPIC	Application of Trigonometry			DURATION : 10 CLASS MEETINGS

PRE-REQUISITE KNOWLEDGE
Knowledge of Right-Angled Triangles and Pythagorean Theorem.
Concept of Trigonometric Ratios (sin, cos, tan, cosec, sec, cot) for acute angles.
Values of trigonometric ratios for standard angles (0°, 30°, 45°, 60°, 90°).
Basic algebraic simplification and ratio calculations.

TEACHING AIDS
Green Board, Chalk, Duster, Clinometer (angle measuring device), Charts showing trigonometric formulas and right triangle figures, Measuring Tape, Worksheets, Assignments.

TECHNOLOGY REQUIRED
Smart Board, Projector, Laptop, Internet, GeoGebra / Interactive Geometry Software for visual simulation of angles of elevation and depression.

METHODOLOGY
Demonstration, Activity-Based Learning (measuring height of school building/flagpole using clinometer), Lecture Method, and Problem-Solving Technique.

LEARNING OBJECTIVES
To understand real-world applications of trigonometry in finding heights and distances without actual measurement.
To define Line of Sight, Horizontal Level, Angle of Elevation, and Angle of Depression.
To formulate mathematical models and right-angled triangle representations from practical word problems.
To select and apply appropriate trigonometric ratios to solve heights and distances problems.
LEARNING OUTCOMES
After studying this lesson, students will be able to explain and demonstrate:
Line of Sight, Horizontal Line, Angle of Elevation, and Angle of Depression.
Drawing accurate diagrammatic representations for real-life situation word problems.
Calculating heights of objects (buildings, towers, trees) and distances between objects using trigonometric ratios.
Solving practical multi-step problems involving single and combined right-angled triangles.

RESOURCES
NCERT Text book of Mathematics
NCERT Exemplar Text Book
RESOURCE CENTRE at cbsemathematics.com
DAV Resource Material for class 10

KEY WORDS
Line of Sight, Angle of Elevation, Angle of Depression, Horizontal Level, Height, Distance, Trigonometric Ratios, Right Triangle, Clinometer.

CONTENT & PRESENTATION
Line of Sight and Horizontal Level
Angle of Elevation
Angle of Depression
Applications in calculating Heights and Distances
Trigonometric Ratio selection for single right-angled triangle
Trigonometric Ratio selection for combined right-angled triangles

LEARNING ACTIVITIES
INTRODUCTORY ACTIVITY
Visual observation activity where students look up at a high object (like a ceiling fan, wall clock, or tree top) and note the change in eye level and inclination angle compared to looking straight ahead.
EXPERIENTIAL ACTIVITY
Hands-on measurement of the height of the school flagpole or basketball hoop using a handmade Clinometer (protractor + string + plumb weight) and measuring tape to measure horizontal distance from the base.
ART INTEGRATED ACTIVITY
Students create an illustrated poster or 3D visual diagram mapping real-world structures (towers, lighthouses, kites, airplanes) with clearly marked angles of elevation/depression and corresponding right-angled triangles.
PROCEDURE
Begin the session by explaining why trigonometry was developed historically (astronomy, navigation, surveying, geography). Introduce practical contexts like finding the height of a tall mountain or tree without climbing it.
PRESENTATION OF THE TOPIC
Introduction
Line of Sight: The line drawn from the eye of an observer to the point in the object viewed by the observer.
Horizontal Level: The line drawn parallel to the ground from the eye of the observer.
Angle of Elevation: The angle formed by the line of sight with the horizontal line when the object is ABOVE the horizontal level (i.e. when we look up at an object).
Angle of Depression: The angle formed by the line of sight with the horizontal line when the object is BELOW the horizontal level (i.e. when we look down at an object). Note: Angle of Depression = Angle of Elevation by alternate interior angles.

Step-by-Step Problem Solving Strategy
Step 1: Read the problem carefully and draw a clear right-angled triangle diagram.
Step 2: Mark given lengths, given angles, and unknown quantities (height 'h' or distance 'd').
Step 3: Identify the right triangle containing the unknown side and known side/angle.
Step 4: Choose the correct trigonometric ratio (usually tan θ = Opposite/Adjacent or sin θ = Opposite/Hypotenuse).
Step 5: Substitute standard trigonometric values (e.g., tan 30° = 1/√3, tan 45° = 1, tan 60° = √3) and solve.
MIND MAP
Core Concepts
Line of Sight
Horizontal Level
Angle of Elevation (Looking UP)
Angle of Depression (Looking DOWN)

Key Ratios Used
tan θ = Opposite / Adjacent (Height / Distance)
sin θ = Opposite / Hypotenuse (Height / Slant Distance)
cos θ = Adjacent / Hypotenuse (Base Distance / Slant Distance)
Application Types

Single Triangle Problems (Direct height or distance)
Dual Triangle Problems (Two observers, moving objects, multi-level structures)

STUDENTS DELIVERABLES:

Review questions given by the teacher.

Students can prepare a Presentation on the topic “prove that given number is irrational number”.

Solve N.C.E.R.T. problems with examples,

Solve assignment of Multiple Choice Questions (MCQ) given by the teacher.

EXTENDED LEARNING:-

Students can extend their learning through the RESOURCE CENTRE and can find more valuable and interesting concepts on mathematics at cbsemathematics.com

Students can also extend their leaning by watching this topic on video.

SKILLS ENHANCED

Observation skill, analytical skill, critical & creative thinking, team work, constructive approach, interpersonal skill, engagement in learning process etc.

ASSESSMENT TECHNIQUES:

Assignment sheet will be given as home work at the end of the topic.

Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.

Class Test , Oral Test , worksheet and Assignments. can be made the part of assessment.

Re-test(s) will be conducted on the basis of the performance of the students in the test.

Competency based assessment can be taken so as to ensure if the learning outcomes have been achieved or not. e.g.

Puzzle

Quiz

Misconception check

Peer check

Students discussion

Competency Based Assessment link: M C Q

FEEDBACK:

All those students who performed well will be appreciated positively, and all those who can not perform up to the mark will again be given some important tips, guidance and positive motivation to go through the topic again and then re-evaluated again. If possible then provision of remedial classes can be made for batter results.

🙏

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Interdiciplinary & Experiantial Learning

2026-05-01T18:38:46.316+05:30

Interdiciplinary & Experiantial Learning

Interdisciplinary activities:

Interdisciplinary activities are learning experiences that connect two or more subjects to help students understand concepts in a holistic and practical way. Instead of studying each subject in isolation, students explore how different areas of knowledge relate to each other in real-life situations.

In the context of Central Board of Secondary Education, interdisciplinary learning is strongly encouraged under competency-based education and experiential learning approaches.

WARLI ART

Simple definition:

Interdisciplinary activities integrate concepts from different subjects to solve a problem or complete a task.

Key features

Connects different subjects.

Focuses on real-life situations.

Encourages critical thinking and creativity.

Makes learning meaningful and practical.

Promotes holistic understanding.

Examples of Interdisciplinary Activities

Mathematics + Science

Measuring speed, distance, and time in Physics experiments

Data handling and graph plotting in Science

Mathematics + Social Science

Population studies using statistics

Budget and taxation calculations

English + Science

Writing reports on experiments

Preparing project presentations

Art + Mathematics

Symmetry, patterns, and geometric designs (Rangoli, Mandala)

ICT + All Subjects

Creating presentations, coding projects, data analysis

Drawing rangoli, Mandal art or Warli art using symmetry, shapes, and patterns.

Why Interdisciplinary Activities are Important

Enhances Conceptual Understanding
Students learn concepts more deeply when they see connections between subjects.

Promotes Critical Thinking
Encourages analysis, reasoning, and problem-solving across disciplines.

Develops Real-Life Skills
Helps students apply knowledge to real-world situations.

Encourages Collaboration
Students often work in groups, improving teamwork and communication.

Conclusion

Interdisciplinary activities make learning meaningful, engaging, and application-oriented. They prepare students not only for examinations but also for real-world challenges, making education more relevant and effective.

Experiential Learning

Experiential Learning means learning by doing and reflecting on real experiences, rather than only learning from textbooks.

It helps students understand concepts deeply by observing, experimenting, practicing, and applying knowledge in real-life situations. It connects classroom concepts with real-life situations, making learning more meaningful and long-lasting.

Definition

Experiential learning is a student-centred approach where learners gain knowledge through direct experience, activity, and reflection.

Key idea in CBSE

CBSE follows the principle:
“I hear – I forget, I see – I remember, I do – I understand.”

Main features of experiential learning

Learning through hands-on activities

Focus on real-life application

Encourages critical thinking and problem-solving

Promotes active student participation

Experiential Learning Cycle

Experience – Students perform an activity (experiment/project)

Reflection – They think and discuss what happened

Conceptualization – They understand the concept/theory

Application – They apply learning in new situations

Examples

Mathematics

Measuring real objects to understand geometry
Collecting data and making graphs
Using maths lab activities

Types of experiential learning

Activity-based learning: Using models, charts, manipulatives, or experiments

Project-based learning: Long-term tasks integrating multiple subjects

Art-integrated learning: Learning concepts through drawing, music, drama, or craft Example: Understanding symmetry through rangoli patterns

Sports-integrated learning: Linking sports activities with academic concepts Example: Calculating speed and time using race data.

Learning happens through real experience, not rote calculation.

Role of teacher in experiential learning
Plan meaningful activities
Provide real-life contexts
Encourage discussion and reflection
Guide students instead of giving direct answers

Benefits of experiential learning
Improves conceptual clarity
Makes learning joyful and engaging
Develops life skills
Enhances retention and understanding
Aligns with NEP 2020 and CBSE competency-based education

Conclusion

Experiential Learning transforms classrooms into active learning spaces, where students do not just study subjects but experience them. It helps in developing knowledge, skills, and values, preparing students for real-life challenges.

Activity : Designing Hands-on Activities

(Duration: 45 minutes)

Pythagoras Theorem by Paper Folding (a Visual Connect)

Procedure:

Divide participants in groups. Provide a square sheet of paper and pencil to each group.Initiate a discussion on how they can use the material provided to them to prove Pythagoras theorem.

After discussing the responses, you may ask them to perform the following activity and clarify that it is one of the ways in which it may be done.

Step 1: Take a square sheet of paper fold it along the diagonal and press it to form a crease and unfold if. (Fig. 1)

Figure 1

Step 2: Fold the bottom of a right corner towards the crease of the diagonal and press it when the edge of the sheet is parallel to the diagonal Fig. 2.

Figure 2

Step 3: Now fold the adjacent side of the square and press, when it lies along the side of the right angle already folded. Fig. (3) and press it to make a crease.

Figure 3

Step 4: Similarly repeat the same step with the remaining two corners. [Fig. 4 and Fig. 5].

Figure 4

Figure 5

Step 5: We have a square with a square hole inside. Unfold and label the square as shown in given figure. Let ABCD be the original square with,

AP = a , AQ = b , PQ = c

Step 6: Now area of square ABCD= Area of 4 congruent triangles + area of square PQRS.

⇒ (a + b)² = 4(1/2ab) + c²

⇒ a² + b² + 2ab = 2ab + c²

⇒ a²+ b² = c²

Figure 6

This proves Pythagoras Theorem

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Bloom's Taxonomy Learning Domains

2026-04-10T21:11:00.006+05:30

BLOOM’S TAXONOMY
DIFFERENT LEARNING DOMAINS

Introduction to Bloom’s Taxonomy

Bloom’s Taxonomy is a structured framework used to classify educational learning objectives according to different levels of cognitive complexity. It helps in organizing learning goals from basic understanding to higher-order thinking skills.

Originally developed by Benjamin Bloom in 1956, the taxonomy was later revised in 2001 by Lorin Anderson and David Krathwohl to make it more relevant for modern education. The revised version emphasizes active learning through action-oriented verbs.

Bloom’s Taxonomy serves as a versatile tool in education. It supports:

Curriculum planning by aligning learning objectives with desired outcomes

Assessment design by creating questions across different cognitive levels

Lesson planning by structuring teaching strategies effectively

Differentiated instruction to meet diverse learner needs

Student-centered learning by promoting critical and creative thinking

Overall, Bloom’s Taxonomy provides a clear and practical approach for teachers and students to enhance the teaching–learning process in a meaningful and measurable way.

Categorizing Educational Goals

Bloom’s Taxonomy is a system that helps in organizing learning goals step by step. Each level depends on the level below it. It is often shown as a pyramid, similar to Maslow’s Hierarchy of Needs.

In this framework:

A student must remember before they can understand

They must understand before they can apply

They need to analyze before they can evaluate

Proper evaluation is needed before making a correct conclusion

Teachers use action words (verbs) to guide students through each level of thinking. This makes learning clear and helps in measuring student progress. Learning goals are divided into smaller parts and taught step by step during lessons.

Some common words like learn, understand, and know are difficult to measure. Bloom’s Taxonomy solves this problem by using clear action words such as define, explain, solve, and create, which can be easily assessed.

The main aim of education is that by the end of a lesson, students should gain:

Knowledge

Skills

Positive attitude towards the subject

Using Bloom’s Taxonomy in Teaching

Teachers can use Bloom’s Taxonomy to plan lessons and courses in a better way.

It helps them:

Focus on specific learning levels throughout the year

Design assignments and exams based on student ability

Ensure students master one level before moving to the next

Frame questions

Assess students effectively from basic thinking to advanced thinking skills

Helps in lesson planning

Improves question paper quality

Promotes higher-order thinking

Makes learning student-cantered

This approach gives students clear and achievable goals. It also helps in building strong thinking skills step by step, leading to deeper understanding and better learning outcomes.

Purpose and Significance

Bloom’s Taxonomy helps educators to:

Structure teaching in a logical progression
Design meaningful and measurable learning outcomes
Encourage critical and creative thinking
Improve the quality of assessment practices

Domains of Learning

The taxonomy identifies three major areas of learning:

Cognitive Domain –knowledge - related to knowledge and intellectual skills

Affective Domain – Attitude - related to attitudes, values, and emotions

Psychomotor Domain – Skill - related to physical and practical skills

Together, these domains aim at the holistic development of learners.

Evolution of Bloom’s Taxonomy

Original Version (1956):

Knowledge → Comprehension → Application → Analysis → Synthesis → Evaluation

Revised Version (2001):

Remember → Understand → Apply → Analyze → Evaluate → Create

The revised version emphasizes action-oriented learning and places “Create” at the highest level.

Comparison between old and new version of Bloom’s Taxonomy

Old Version (1956)

Developed by Benjamin Bloom

Revised Version (2001)

Updated by Anderson and Krathwohl

Knowledge

Comprehension

Application

Analysis

Synthesis

Evaluation

Remember

Understand

Apply

Analyze

Evaluate

Create

Key Change: “Create” is now the highest level (not Evaluation)

Six Levels of Bloom’s Taxonomy (With Explanation)

1. Remember (Smallest Level)

Meaning:

Recall facts and basic concepts

Action Words:

Define, list, name, identify

Example:

Define trigonometric ratios

List types of numbers

CBSE Trend: Mostly used in MCQs & objective questions

2. Understand

Meaning:

Explain ideas or concepts

Action Words:

Explain, describe, Summarizing concepts, interpreting information

Example:

Explain Pythagoras theorem

Summarize a chapter

CBSE Use: Short answer questions (2–3 marks)

3. Apply

Meaning:

Use knowledge in new situations

Action Words:

Solve problems, use, demonstrate, calculate

Example:

Solve a quadratic equation

Use formula in numerical

CBSE Use: Case-based & numerical questions

4. Analyze

Meaning:

Break information into parts and examine relationships

Action Words:

Compare, differentiate, analyze, classify

Example:

Compare democracy and monarchy

Analyze a graph

CBSE Use: Assertion–Reason questions

5. Evaluate

Meaning:	Justify a decision or opinion
Action Words:	Justify, argue, evaluate, defend
Example:	Justify the role of Gandhiji Evaluate a policy

CBSE Use: Long answer (5 marks)

6. Create (Highest Level)

Create (Highest Level)

Meaning:

Produce new or original work

Action Words:

Design, create, develop, construct

Example:

Design a project

Write a research-based answer

CBSE Use: Projects, competency-based questions

Present Educational Scenario (CBSE / NEP 2020)

Competency-Based Learning

Modern education emphasizes understanding, application, and problem-solving rather than memorization.

Assessment Pattern

Lower-order skills (Remember, Understand): Limited weightage

Application-based questions: Significant focus

Higher-order thinking (Analyze, Evaluate, Create): Increasing importance

Types of Questions

Objective questions test basic knowledge

Case-based questions assess application

Analytical questions develop reasoning skills

Teaching Strategies

Activity-based learning

Experiential methods

Use of digital tools and ICT

Collaborative learning

Rote learning is discouraged

Group discussion

Focus Areas under NEP 2020

Conceptual clarity

Skill development

Real-world relevance

Innovation and creativity

Creativity & innovation

How to use Bloom's Taxonomy in teaching

Example in Mathematics (Topic Trigonometry)

Remember: Recall basic formulas

Understand: Explain relationships between functions

Apply: Solve numerical problems

Analyze: Compare different methods

Evaluate: Verify correctness of solutions

Create: Develop real-life applications

Approximate Weightage

Level	Weightage
Remember + Understand	30–40 %
Apply	30 %
Analyze + Evaluate + Create	30–40 %

Question Types in Present Exams

MCQ	Remember/Understand
Case-based	Apply/Analyze
Assertion-Reason	Analyze
Competency Questions	HOTS

Conclusion

Bloom’s Taxonomy remains a foundational tool in education. It promotes a shift from rote learning to meaningful understanding and higher-order thinking.

In the current educational landscape, it plays a crucial role in developing learners who are analytical, creative, and capable of solving real-world problems.

In today’s education system (CBSE + NEP), higher-order thinking (HOTS) is the main focus.

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CBSE Mathematics

Lesson Plan Math Class 10 (Ch-9) | Applications of Trigonometry

LESSON PLAN, math. CLASS-10 Ch-9, Application of Trigonometry

Single Triangle Problems (Direct height or distance)Dual Triangle Problems (Two observers, moving objects, multi-level structures)

STUDENTS DELIVERABLES:

Interdiciplinary & Experiantial Learning

Bloom's Taxonomy Learning Domains

BLOOM’S TAXONOMYDIFFERENT LEARNING DOMAINS

LESSON PLAN, math. CLASS-10
Ch-9, Application of Trigonometry

Single Triangle Problems (Direct height or distance)
Dual Triangle Problems (Two observers, moving objects, multi-level structures)

BLOOM’S TAXONOMY
DIFFERENT LEARNING DOMAINS