NCERT Solutions Class 6 Maths Chapter 1 Patterns in Mathematics Exercise 1.6

Exercise 1.6 links geometric patterns with numerical sequences by examining elements like sides, edges, and segments of shapes. Students learn how counting these components leads to number sequences such as triangular and square numbers. This exercise highlights the close relationship between geometry and numerical patterns in mathematics.

Allen's NCERT Solutions for Exercise 1.6 help students clearly understand the connection between geometric patterns and number sequences. The step-by-step explanations guide students in analysing shapes by counting elements such as sides, edges, or segments and relating them to numerical sequences like triangular numbers or square numbers.

1.0Download NCERT Solutions of Class 6 Maths Chapter 1 Patterns in Mathematics Exercise 1.6: Free PDF

Download free PDF for NCERT Solutions Class 6 Maths Chapter 1 Patterns in Mathematics Exercise 1.6 to understand the relationship between shape and number sequences.

Key Concepts of Exercise 1.6

• Connecting Shape Patterns to Number Sequences: The understanding of how numbers can represent the properties of a sequence of shapes.
• Explaining the Relationship: The ability to explain why a particular number sequence arises from a particular sequence of shapes (e.g., the number of sides is equal to the number of corners for a regular polygon).
• Predicting Future Terms: The ability to use the established relationship to predict the number of elements or properties in future terms in a shape or number sequence.
• Observing Different Perspectives: Understanding that the same mathematical idea or number can be illustrated pictorially in different ways (e.g., 36 viewed as both a triangular and a square number).

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

3.0NCERT Class 6 Chapter 1 Patterns in Mathematics Exercise 1.6 : Detailed Solutions

1.6 Relation To Number Sequences

1. Count the number of sides in each shape in the sequence of Regular Polygons. Which number sequence do you get? What about the number of corners in each shape in the sequence of Regular Polygons? Do you get the same number sequence? Can you explain why this happens? Sol. Sides and Corners Sequence: The number of sides and corners in each shape of the regular polygon sequence increases by 1 . Triangle: 3 sides, 3 corners Quadrilateral: 4 sides, 4 corners Pentagon: 5 sides, 5 corners Hexagon: 6 sides, 6 corners Heptagon: 7 sides, 7 corners Number Sequence: 3, 4, 5, 6, 7... The number of sides and corners is the same because each corner corresponds to a side in regular polygons.
2. Count the number of lines in each shape in the sequence of Complete Graphs. Which number sequence do you get? Can you explain why? Sol. Number of Lines in Complete Graphs Sequence : The number of lines in a complete graph (Kn) increases based on how many vertices are connected. K2: 1 line K3: 3 lines K4: 6 lines K5: 10 lines
3. How many little squares are there in each shape of the sequence of Stacked Squares? Which number sequence does this give? Can you explain why? Sol. Number of Squares Sequence : As squares are stacked, the number of little squares increases: $1^{\text{st }}$ shape: 1 square $2^{\text{nd }}$ shape: 4 squares $3^{\text{rd }}$ shape: 9 squares $4^{\text{th }}$ shape: 16 squares Number Sequence: 1, 4, 9, 16... The number of squares follows the sequence of square numbers, as each shape forms a perfect square grid.
4. How many little triangles are there in each shape of the sequence of Stacked Triangles? Which number sequence does this give? Can you explain why? (Hint: In each shape in the sequence, how many triangles are there in each row?) Sol. Number of little triangles sequence of Stacked Triangles $=1,4,9,16,25$
5. To get from one shape to the next shape in the Koch Snowflake sequence, one replaces each line segment '-'by a 'speed bump'. As one does this more and more times, the changes become tinier and tinier with very very small line segments. How many total line segments are there in each shape of the Koch Snowflake? What is the corresponding number sequence? (The answer is $3,12,48,\dots$, i.e. 3 times Powers of 4). Sol. Koch Snowflake Line Segments Sequence: $1^{\text{st }}$ shape: 3 line segments $2^{\text{nd }}$ shape: 12 line segments $3^{\text{rd }}$ shape: 48 line segments Number Sequence: 3, 12, 48, ... The number of line segments increases by multiplying the previous number by 4 , forming a sequence of 3 times powers of 4.

4.0Key Features and Benefits Class 6 Maths Chapter 1 Patterns in Mathematics: Exercise 1.6

• Visual-Conceptual Link: Supports students in connecting visual patterns (shapes) with abstract numerical patterns which deepens students' conceptual understanding.
• Logical Reasoning Development: It allows students to find rules and relationships, and to develop critical thinking and logical reasoning skills.
• Problem Solving Application: The tasks provide a context for harnessing pattern recognition part of the math curriculum while moving beyond a simple sequence of numbers. 
• Enhanced Spatial Reasoning: Working on shape sequences, for example, improve students' spatial reasoning skills and enhance visualization.
• Extensive Coverage: The solutions provided align with the textbook objectives of help students make connections between different mathematical ideas.
• Self-Paced Learning: The responses to the tasks have numerous steps and provide the opportunity for students to understand complicated ideas at their own pace.  Supports learning through practice!
• Foundation for Further Topics: Provides students with a strong understanding for more complex topics associated with patterns, sequences and geometric reasoning.