Extra Curriculum Support
Enhanced Curriculum Support
This is a comprehensive educational resource designed to provide students with the tools and guidance necessary to excel. This support system is structured to cater to various aspects of learning, ensuring that students are well-prepared for academic challenges and practical applications of mathematical concepts. Some are the key benefits are mentioned below:
1.Comprehensive Learning: This holistic approach helps students gain a thorough understanding of the subject. Practical Application: The resources encourage students to apply mathematical concepts to real-life scenarios, enhancing their practical understanding and problem-solving skills.
2.Critical Thinking and Reasoning: Value-Based and HOTS questions promote critical thinking and reasoning abilities. These skills are crucial for students to tackle complex problems and make informed decisions.
3.Exam Preparedness: Sample Question Papers and NCERT Exemplar Solutions provide ample practice for exams. They help students familiarize themselves with the exam format and types of questions, reducing exam anxiety.
4.Ethical and Moral Development: Value-Based Questions integrate ethical and moral lessons into the learning process, helping in the overall development of students' character and social responsibility. By incorporating these diverse elements, Enhanced Curriculum Support aims to provide a robust and well-rounded knowledge, preparing students for both academic success and real-world challenges.
Sec A
1. Define line of symmetry. Give an example of a shape with one line of symmetry.
2. How many lines of symmetry does a square have? Draw and label them.
3. Identify the number of lines of symmetry in a circle.
4. State whether the letter "A" is symmetrical. If yes, draw its line of symmetry.
5. Name a shape with no line of symmetry and explain why.
6.What is rotational symmetry? Provide an example.
7. Write the order of rotational symmetry for an equilateral triangle.
8. How many lines of symmetry does a rectangle have? Justify your answer.
9. Identify the type of symmetry in the letter "X."
Sec B
1. Draw a regular hexagon and mark all its lines of symmetry.
2. Explain the difference between line symmetry and rotational symmetry with examples.
3. How many lines of symmetry does a regular pentagon have? Draw and explain.
4. Check whether the number 818 is symmetrical when written vertically. Explain.
5. Identify the order of rotational symmetry for the following shapes: square, rectangle, circle.
6. Draw the lines of symmetry for the letter "H" and "Z."
7. Explain why a parallelogram has no line of symmetry but has rotational symmetry.
Sec C
1. A figure has 6 lines of symmetry. What could the figure be? Justify your answer with a diagram.
2. Draw a scalene triangle and explain why it has no line of symmetry.
3. Find the order of rotational symmetry for the letters "S," "O," and "N." Justify your answers with diagrams.
4. A student claims that all quadrilaterals have at least one line of symmetry. Is this true? Explain with examples.
5. Draw a rectangle and a rhombus. Show how their lines of symmetry differ.
6. Create a symmetrical design using an axis of symmetry and explain your process.
Sec D
1. Design a symmetrical pattern with 4 lines of symmetry and explain its features.
2. Compare and contrast the lines of symmetry in a circle, an equilateral triangle, and a regular hexagon.
3. A clock face is an example of rotational symmetry. Explain how, and state the order of symmetry.
4. Create a step-by-step method to determine the lines of symmetry in any given polygon.
5. Explain the role of symmetry in art and design, giving at least three examples.
6. How is symmetry used in the creation of road signs? Illustrate with examples.
7. Analyze the symmetry in the English alphabet. Identify letters with no symmetry, one line of symmetry, and rotational symmetry.
Problem 1
A group of students is tasked with creating a symmetrical rangoli design for their school’s cultural event. They decide to work together, dividing the design into equal sections for each student to complete.
(a) How does symmetry make the rangoli design more appealing?
(b) Explain how teamwork and equal contribution in this activity reflect the importance of fairness and inclusivity.
(c) What values can students learn from participating in such collaborative activities?
Problem 2
A butterfly is a natural example of symmetry in nature. Butterflies are essential pollinators and play a vital role in maintaining the balance of ecosystems.
(a) Draw and label the line of symmetry of a butterfly.
(b) Explain how observing symmetry in nature can help us appreciate and protect the environment.
(c) Suggest two ways we can help conserve butterflies and their habitats.
Q1
A figure has both line symmetry and rotational symmetry. The order of rotational symmetry is 4, and the figure has 4 lines of symmetry.
(a) Identify the shape and draw it.
(b) Justify how the lines of symmetry and the rotational symmetry are related in this shape.
(c) Can a figure have more lines of symmetry than the order of rotational symmetry? Explain with an example.
Q2
An architect is designing a bridge and wants to incorporate symmetry to make it visually appealing and structurally balanced.
(a) Explain how symmetry can enhance both the aesthetic and functional aspects of the bridge.
(b) Suggest a symmetrical design for the bridge, indicating the type of symmetry used (line or rotational).
(c) Why is symmetry often used in engineering and construction?
Q3
A student observes that a regular hexagon has 6 lines of symmetry and an order of rotational symmetry of 6. The student claims that the same applies to all regular polygons.
(a) Verify the student’s claim by analyzing a square and a regular pentagon.
(b) Generalize a rule for the relationship between the number of sides, lines of symmetry, and rotational symmetry in a regular polygon.
(c) Explain why this rule does not apply to irregular polygons.
Questions
1. How many lines of symmetry does a regular hexagon have?
(a) 2 (b) 3 (c) 6 (d) 8
2. Identify the order of rotational symmetry of a square.
(a) 2 (b) 4 (c) 6 (d) 8
3. Which of the following letters has no line of symmetry?
(a) A (b) B (c) Z (d) H
4. Which of these shapes has infinite lines of symmetry?
(a) Circle (b) Square (c) Rectangle (d) Triangle
5. The letter "S" has:
(a) One line of symmetry
(b) Rotational symmetry of order 2
(c) Both line and rotational symmetry
(d) Neither line nor rotational symmetry
6. If a shape has rotational symmetry of order 1, it means:
(a) It has one line of symmetry
(b) It has no symmetry
(c) It coincides with itself only after a full rotation
(d) It has infinite lines of symmetry
7. Draw the lines of symmetry for an equilateral triangle. How many are there?
8. Explain the difference between line symmetry and rotational symmetry with one example for each.
9. Identify the number of lines of symmetry for the following shapes:
(a) Rectangle (b) Rhombus
10. Write the English alphabets that have both line and rotational symmetry.
11. A regular octagon has 8 sides. How many lines of symmetry does it have?
12. Draw the lines of symmetry for the letter "H" and explain why it has more than one line of symmetry.
13. Explain why a parallelogram has no line of symmetry but has rotational symmetry of order 2.
14. Create a symmetrical rangoli pattern with at least 4 lines of symmetry.
15. Write a step-by-step method to find the lines of symmetry in any given polygon.
16. A clock face is an example of rotational symmetry. State the order of rotational symmetry for the clock when the hands are in the 12 o'clock position.
Q1
Case Study:
The Taj Mahal, a famous monument in India, is known for its symmetrical design. The monument's main dome, minarets, and garden layout exhibit perfect symmetry. The central dome is surrounded by four minarets at equal distances, and the reflection of the Taj Mahal in the water body enhances its symmetrical appearance. Symmetry is not only used to enhance beauty but also to ensure balance and stability in architecture.
Question: Based on the given information, answer the following:
1. Identify the type of symmetry present in the Taj Mahal.
2. If the monument has one central line of symmetry, explain how it divides the structure.
3. Why is symmetry important in architecture, particularly for monuments like the Taj Mahal?
4. Draw a diagram of a symmetrical building layout with one line of symmetry.
Sol
Solution :
1. Type of Symmetry:
The Taj Mahal exhibits line symmetry as it has a central vertical line that divides the structure into two identical halves.
2. Explanation of Central Line of Symmetry:
The central line of symmetry divides the Taj Mahal into two identical halves, ensuring that the left and right sides mirror each other. This includes the dome, minarets, and garden layout.
3. Importance of Symmetry in Architecture:
Symmetry enhances the aesthetic appeal of structures, making them visually pleasing.
It ensures structural balance and stability, which is crucial for large monuments.
Symmetry in design often symbolizes harmony and order, reflecting cultural or religious significance.
4. Diagram:
(Students will draw a layout showing a symmetrical building with a central vertical line dividing it into two identical halves, including elements like domes, pillars, or gardens.)