NCERT Solutions for Class 6 Maths Chapter 1 Exercise 1.5 Patterns in Mathematics - FREE PDF Download
NCERT Solutions for Class 6 Maths Chapter 1, Exercise 1.5, "Patterns in Shapes," are designed to help students understand how shapes form patterns. This exercise focuses on recognizing and creating patterns using different shapes, which enhances spatial reasoning and visual understanding. It aligns with the CBSE Class 6 Maths Syllabus and offers clear, step-by-step guidance on identifying and analysing patterns in shapes. It helps students recognize and apply these patterns effectively, making learning more manageable and systematic.
- 4.1Table 3: Examples of Shape Sequences
Students can download these NCERT Solutions as a FREE PDF, providing a convenient way to practice and improve problem-solving skills. NCERT Solutions for Class 6 Maths include useful tips and straightforward methods to make learning engaging and effective, preparing students for more advanced topics in mathematics.
Glance on NCERT Solutions Maths Chapter 1 Exercise 1.5 Class 6 | Vedantu
This exercise helps students recognize and describe patterns formed by shapes.
Students learn to identify sequences and repetitions in shapes, such as squares, triangles, and circles.
The solutions guide students on how to draw and continue patterns with different shapes.
Students practice creating their patterns using a variety of shapes.
The exercise includes problems that challenge students to apply their understanding of shape patterns to solve.
Exercise 1.5
Table 3: Examples of Shape Sequences
1. Can you recognise the pattern in each of the sequences in Table 3?
Ans:
(a) Regular Polygons: Examples include triangle, quadrilateral, pentagon, and hexagon. In these shapes, the number of sides increases by 1 with each step, starting from 3. This forms a continuous number sequence where each polygon has one more side than the previous one.
(b) Complete Graphs
The number of lines in the sequence is as follows:
For K2 = 1, K3 = 3, K4 = 6, K5 = 10, and K6 = 15. The resulting series is 1, 3, 6, 10, 15,…. This forms a triangular number sequence, where each term represents the total number of lines that can form a triangle. Triangular numbers are generated by adding consecutive natural numbers, making this sequence grow in a predictable pattern.
(c) Stacked Squares:
The number of small squares in each layer follows the pattern: 1, 4, 9, 16, 25, and so on. This sequence represents square numbers, where each term is the result of squaring a natural number ($1^{2}$, $2^{2}$, $3^{2}$, etc.).
The arrangement visually forms a perfect square, showing how the number of small squares increases as the layers grow, perfectly fitting into a square grid. Hence, it’s a clear representation of a square number sequence.
(d) Stacked Triangles:
The number of small triangles in each layer follows the pattern:
Thus, it is also a square number sequence represented through triangular formations.
(e) Koch Snowflake:
Number of sides in each becomes 4 times.
The number of sides in each increases by a factor of 4.
2. Try and redraw each sequence in Table 3 in your notebook. Can you draw the next shape in each sequence? Why or why not? After each sequence, describe in your own words what is the rule or pattern for forming the shapes in the sequence.
Ans: (a) Regular Polygon
A polygon with 11 sides, is known as a hendecagon.
(b) K6
The image shows a complete graph with 7 vertices (K7), where every point is connected to every other point with straight lines.
(c) Stacked Squares
The total number of squares is 6 × 6 = 36. This calculation represents a perfect square, showing how the number of small squares forms a 6x6 grid.
(d) Stacked Triangles
The total number of triangles is 1 + 3 + 5 + 7 + 9 + 11 = 36. This sum represents the sequential addition of odd numbers, resulting in the total number of triangles in the arrangement.
(e) Koch Snowflake
The shape is a Koch snowflake, created by repeatedly adding triangular bumps to each side of an equilateral triangle.
Benefits of NCERT Solutions for Class 6 Maths Chapter 1 Exercise 1.5 Patterns in Mathematics
Students learn to recognize and describe different patterns made with shapes, improving their ability to work with geometric figures.
The exercise helps students spot and understand various patterns, making it easier to identify relationships between shapes.
Working with shapes and patterns improves student’s ability to visualise geometric concepts and solve related problems.
By creating and continuing patterns, students practice thinking creatively and applying math in new ways.
The problems in this exercise challenge students to use their knowledge of shapes to find solutions, enhancing their problem-solving skills.
Learning about patterns in shapes lays the groundwork for understanding more advanced geometry concepts later on.
Class 6 Maths Chapter 1: Exercises Breakdown
Important Study Material Links for Class 6 Maths Chapter 1 - Patterns in Mathematics
Conclusion
NCERT Solutions for Class 6 Maths Chapter 1, Exercise 1.5, "Patterns in Shapes," from the chapter "Patterns in Mathematics," helps students understand how different shapes form patterns. The clear explanations in the solutions make it easier to recognize and create these patterns. Practising these exercises enhances student’s ability to visualise and work with geometric patterns, improving their problem-solving skills. With the solutions available as a FREE PDF download, students can study and review at their own pace, making learning both convenient and effective.
Chapter-wise NCERT Solutions Class 6 Maths
The chapter-wise NCERT Solutions for Class 6 Maths are given below. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.
Related Important Links for Class 6 Maths
Along with this, students can also download additional study materials provided by Vedantu for Maths Class 6.
FAQs on NCERT Solutions for Class 6 Maths Chapter 1 - Patterns in Mathematics Exercise 1.5
1. What is the focus of Exercise 1.5 in NCERT Solutions for Class 6 Maths Chapter 1?
Exercise 1.5 in NCERT Solutions for Class 6 Maths Chapter 1 focuses on understanding and working with patterns in shapes. It teaches how different shapes form patterns and how to create and continue these patterns.
2. How can I download the NCERT Solutions for Exercise 1.5 in Chapter 1?
You can download the NCERT Solutions for Exercise 1.5 from Class 6 Maths Chapter 1 as a FREE PDF from educational websites or the NCERT official site. Simply search for the exercise or chapter to find the download link.
3. What types of patterns are covered in Exercise 1.5 of Class 6 Maths?
Exercise 1.5 covers patterns made with various shapes, such as squares, triangles, and circles. It helps students recognize and create different geometric patterns.
4. How do I identify patterns in shapes in Exercise 1.5?
To identify patterns in shapes, look for repeating sequences or arrangements of shapes. Exercise 1.5 guides you through finding and describing these patterns step-by-step.
5. What is the benefit of understanding patterns in shapes from NCERT Solutions for Class 6?
Understanding patterns in shapes helps students improve their spatial reasoning and visualisation skills. It makes it easier to work with geometric concepts and solve related problems.
6. How do NCERT Solutions for Exercise 1.5 help with problem-solving?
NCERT Solutions for Exercise 1.5 provides clear explanations and examples of how to recognize and create patterns in shapes. This helps students apply these concepts to solve various problems.
7. Are there any specific tips for solving patterns in shape problems?
When solving patterns in shape problems, focus on identifying repeating sequences and consistent arrangements. Use the examples in the solutions to guide your approach.
8. What kind of problems are included in Exercise 1.5 of Chapter 1?
Exercise 1.5 includes problems where students need to identify, create, and continue patterns using different shapes. It tests their ability to recognize and work with geometric patterns.
9. How does Exercise 1.5 relate to real-life situations?
Patterns in shapes can be seen in everyday objects and designs, such as tiles, wallpapers, and art. Understanding these patterns helps students apply mathematical concepts to real-world scenarios.
10. How do patterns in shapes in Class 6 Maths help with future math topics?
Learning patterns in shapes helps with future geometry topics. It improves spatial awareness and problem-solving skills, which are important for understanding more complex geometric concepts.
11. How can I practice patterns in shapes effectively using NCERT Solutions?
To practice effectively, work through each problem in Exercise 1.5 carefully. Use the step-by-step solutions to understand each pattern and apply these methods to new problems for better understanding.
