NCERT Solutions

Chapter 1 Patterns in Mathematics

Exercise 1.5

NCERT Solutions Class 6 Maths Chapter 1 Patterns in Mathematics Exercise 1.5

Chapter 1 of NCERT Solutions Class 6 Maths, "Patterns in Mathematics," is fundamental in honing a student's observational and logical reasoning skills. This chapter introduces the diverse world of patterns, laying a crucial groundwork for advanced mathematical concepts. For students aspiring for academic excellence, understanding these patterns is not just about scoring marks but about developing a sharp mathematical mind.

Exercise 1.5 specifically builds on the earlier understanding of patterns, often introducing more intricate sequences or problems that require a deeper level of analytical thinking. It challenges students to not only identify but also to explain the rules behind complex patterns, enhancing their problem-solving capabilities. ALLEN's solutions are designed to simplify these challenges, offering clear, step-by-step guidance that makes learning effective and engaging for every student.

1.0Download NCERT Solutions of Class 6 Maths Chapter 1 Patterns in Mathematics Exercise 1.5: Free PDF

Download the complete and easy-to-understand NCERT Solutions for Class 6 Maths Chapter 1 Exercise 1.5 in PDF format.

NCERT Solutions Class 6 Maths Chapter 1 Ex 1.5

Key Concepts of Exercise 1.5

Identifying more advanced patterns in numbers and shapes.
Learning how to extend and complete more advanced patterns.
Creating new patterns according to rules
Seeing symmetry and regularity in designs.
Making connections to real-life experiences and structures.

2.0NCERT Exercise Solutions Class 6 Chapter 1- Patterns in Mathematics : All Exercises

NCERT Solutions for Class 6 Maths Chapter 1: Exercise 1.1

NCERT Solutions for Class 6 Maths Chapter 1: Exercise 1.2

NCERT Solutions for Class 6 Maths Chapter 1: Exercise 1.3

NCERT Solutions for Class 6 Maths Chapter 1: Exercise 1.4

NCERT Solutions for Class 6 Maths Chapter 1: Exercise 1.5

NCERT Solutions for Class 6 Maths Chapter 1: Exercise 1.6

3.0NCERT Class 6 Chapter 1 Patterns in Mathematics Exercise 1.5 : Detailed Solutions

1.5 Patterns In Shapes

1. Can you recognize the pattern in each of the sequences in the table given below?

Sol. Regular Polygons: Triangle, quadrilateral, pentagon, hexagon, heptagon, etc. Pattern: The number of sides increases by 1 each time, forming a polygon with an additional side. Complete Graphs: K2, K3, K4, K5, etc. Pattern: The number of vertices increases by 1 , and the lines connecting every vertex form a complete graph. The number of edges increases accordingly. Stacked Squares: Squares are stacked upon each other, with additional layers of smaller squares. Pattern: More squares are added as layers, increasing the total number of smaller squares. Stacked Triangles: Triangles stacked upon each other, increasing the number of small triangles in the structure. Pattern: As new layers are added, the number of smaller triangles increases. Koch Snowflake : As fractal pattern where each line segment is replaced by smaller "bumps" in the shape of an equilateral triangle. Pattern: Each iteration adds more bumps along the edges, increasing the complexity and the number of line segments.

2. Try and redraw each sequence in the table given in question 1, 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. Sol. Regular Polygon: The next shape after the Decagon ( 10 sides) is the Hendecagon ( 11 sides). Rule: Increase the number of sides by 1

Complete graphs: After K6 (6 vertices), the next complete graph is K7 Rule: Add one more vertex and connect every vertex to all others,

Stacked Squares: The next shape will have an additional layer of squares stacked below or around the existing structure Rule: Add another layer with additional small squares, expanding the structure.

Stacked Triangles: The next shape will have one more layer of triangles at the base, increasing the total number of triangles. Rule: Add another row of triangles to form a larger slacked structure.

Koch Snowflake: The next shape will have more intricate and smaller triangular "bumps" added to each side of the snowflake. Rule: Each line segment is replaced with 4 smaller segments (one segment for the bump), increasing the total number of segments exponentially.

4.0Key Features and Benefits Class 6 Maths Chapter 1 Patterns in Mathematics: Exercise 1.5

Promotes logical reasoning and observation skills
Develops foundational skills for higher-order concepts in mathematics like algebra and geometry
Builds engagement through engaging practice and creative pattern
Provides clarity in reasoning and problems with clear step-by-step solutions
Allows students to build confidence in their abilities to solve complex problems.

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