NCERT Solutions Class 6 Maths Chapter 1 Patterns in Mathematics Exercise 1.3

In Class 6 Maths NCERT Solutions Chapter 1 Patterns in Mathematics, learners will identify that repeating or growing sequences can provide shortcuts to calculations, reduce complexity and structure their logical reasoning. Patterns may allow students to see the appeal in mathematics and serve as stepping stones to understanding future topics such as algebra and geometry. 

Exercise 1.3 takes the understanding of patterns a step further by introducing students to number sequences and how to identify the rules behind them. By recognizing, extending, and creating patterns, students develop their reasoning skills and problem-solving skills, making learning mathematics fun and engaging.

1.0Download NCERT Solutions of Class 6 Maths Chapter 1 Patterns in Mathematics Exercise 1.3: Free PDF

Obtain step-by-step solutions for each question in NCERT Solutions Class 6 Maths Chapter 1 Patterns in Mathematics Exercise 1.3.

Key Concepts of Exercise 1.3

• Recognising number sequences and knowing how and why a rule exists. 
• Completes and extends given patterns based on some fixed logic.
• Creates new patterns using addition, subtraction, or multiplication rules.
• Recognizing patterns in odd/even numbers and multiples.
• Strengthening the concept of regularity and symmetry in maths.

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

3.0NCERT Class 6 Chapter 1 Patterns in Mathematics Exercise 1.3 : Detailed Solutions

1.3 Visualising Number Sequences

1. Copy the pictorial representations of the number sequences in the table (given below) in your notebook, and draw the next picture for each sequence.

2. Why are $1,3,6,10,15$, called triangular numbers? Why are $1,4,9,16,25,\dots$ called square numbers or squares? Why are $1,8,27,64,125\dots \dots$ called cubes? Sol. Triangular numbers: Each term is the sum of first n consecutive counting numbers, $(1,3,6,10,15\dots )$. These numbers can form equilateral triangles when arranged in dots.

1, 4, 9, 16 are square numbers called so because they can form geometrical shape squares when arranged in dots.

Cubes ( $1,8,27,64\dots$ ) are called cubes because they form the geometrical shape cube (shape having same length, breadth and height) when these number of unit cubes are arranged in a particular way.

3. You will have noticed that 36 is both a triangular number and a square number! That is, 36 dots can be arranged perfectly both in a triangle and in a square. Make pictures in your notebook illustrating this! This shows that the same number can be represented differently, and play different roles, depending on the context. Try representing some other numbers pictorially in different ways!

Sol.

Some other same numbers that can be represented differently and play different roles that is 1225 . ( $35\times 35$ ). As it is both triangular as well as square number.

4. What would you call the following sequence of numbers?

That's right, they are called hexagonal numbers, Draw these in your notebook. What is the next number in the sequence? Sol.

$1^{\text{st }}$ number $=1$ $2^{\text{nd }}$ number $=1+6=7(2^{\text{nd }}$ number $=1^{\text{st }}$ number $+6\times 1)$ $3^{\text{rd }}$ number $=7+12=19(3^{\text{rd }}$ number $=2^{\text{nd }}$ number $+6\times 2)$ $4^{\text{th }}$ number $=19+18=37(4^{\text{th }}$ number $=3^{\text{rd }}$ number $+6\times 3)$ $5^{\text{th }}$ number $=37+24=61(5^{\text{th }}$ number $=4^{\text{th }}$ number $+6\times 4)$ Hence, the next number in the sequence is 61.

5. Can you think of pictorial ways to visualise the sequence of Powers of 2? Powers of 3?

Here is one possible way of thinking about Powers of 2:

Sol.

4.0Key Features and Benefits Class 6 Maths Chapter 1 Patterns in Mathematics: Exercise 1.3

• Problem-solving proficiency: Provides students with the capability to complete complex and multi-faceted geometry problems. 
• Conceptual interconnectedness: Encourages students to understand how certain geometric concepts and theorems are interconnected. 
• Exam preparation: Important for preparation for exams, as this task typically has questions that assess comprehensive knowledge of triangle congruence.
• Self-pacing: The detailed solutions give students the opportunity to learn at their own pace, going back to the problems that were difficult until they mastered them.