Class 6 Maths Chapter 1 Patterns in Mathematics Notes
Class 6 Maths Chapter 1 Notes – Class 6 Patterns in Mathematics Notes
Introduction-What is Mathematics?
Mathematics is an exciting journey into the world of patterns and the reasons behind them. These patterns are everywhere-from the spirals in a sunflower to our daily routines and the movement of the stars. Whether we are shopping, cooking, playing or using technology, patterns shape our experiences.
Exploring these patterns is a fun and creative adventure. This year, we want you to see math as both an art and a science, discovering the beauty in its structures and the creativity in its solutions.
Mathematics not only finds what patterns exist but also explains why they exist, leading to new discoveries. For example, understanding the movements of stars and planets led to the theory of gravitation, which helped us explore space. Similarly, studying genetic patterns has changed medical science. This chapter will explore these interesting patterns and their importance in our world.
Patterns in Numbers
One of the basic parts of mathematics is studying patterns in whole numbers: 0,1,2,3,4 and so on. This study is called number theory, which looks at these number patterns to understand them better. Number sequences are some of the simplest and most interesting patterns that mathematicians study. They help us understand the most complex math ideas.
Table-1-shows some key number sequences that are important in mathematics, showing how varied and rich these number patterns can be.
Table 1: Examples of Number Sequences
Visualising Number Sequence’s
Many number sequences can be visualised using pictures. Seeing mathematical patterns through pictures or diagrams can help us understand them better
Let’s represent the first seven sequences in Table 1 using the following pictures.
Table 2: Pictorial representation of some number sequences
Relationship among Number Sequences
Sometimes, number sequences can be connected in surprising ways.
For example: Do you know what happens when we add odd numbers?
Now, some questions arise in our minds: why does this happen, and will it always happen? The answer is yes; it will always happen. But why?
A picture can help explain it. Remember that square numbers are made by counting the dots in a square grid.
This picture shows that 1 + 3 + 5 + 7 + 9 + 11 = 36. Since you can create a similar picture for any square, this explains why adding odd numbers gives square numbers. Another example of related sequences is adding up and down:
This pattern shows another way of getting square numbers by adding numbers up and then down!
Example-1
We can form the pattern according to the given rule.
If the given rule is, start at 5 and add 6 each time by multiplying 2 to the previous number.
Solution: The sequence of number formed is:
5,5 × 2 + 6,5 × 3 + 6,5 × 4 + 6……
i.e., the sequence is 5,16,21,26, …….
Patterns in Shapes
We know that the branch of mathematics that deals with patterns in shapes is called geometry. These patterns that occur in mathematics are called patterins of shapes.
One of the important types of shape patterns studied by mathematicians are shape sequences.
In Table 3, we can see various examples of shape sequences that are followed in geometry.
Keywords
- Iterations: An iteration is a single execution or repetition of a process.
- Koch snowflake: The Koch snowflake is a shape that starts with a triangle and keeps adding tiny triangles to each side over and over, making it look like a super detailed snowflake that goes on forever.
Table 3: Shape sequences
Relationship to Number Sequences
The number sequences are related to the shape sequences in surprising ways.
It is evident by the fact that the number of sides in shape sequences of regular polygons are given by counting numbers, i.e., 3,4,5,6 ….. are called triangle, quadrilateral, pentagon, hexagon etc.
Here, the word ‘regular’ refers to the fact that these shapes have equal-length sides.
Similar observations can be seen in different shapes presented in Table 3.
Example-2
Look at the sequence of numbers given below :
243,81,27,9 ……
Find the next two terms of the sequence by identifying the pattern.
Solution: If we see the given pattern carefully we find that for getting each next term the number is divided by 3.
So, the next two terms are : 3 and 1.