NCERT Book Class 6 Maths Patterns in Mathematics PDF Download

Chapter 1: Patterns in Mathematics

1.1 What is Mathematics?

Mathematics is, in large part, the search for patterns, and for the explanations as to why those patterns exist.

Such patterns indeed exist all around us - in nature, in our homes and schools, and in the motion of the sun, moon, and stars. They occur in everything that we do and see, from shopping and cooking, to throwing a ball and playing games, to understanding weather patterns and using technology.

The search for patterns and their explanations can be a fun and creative endeavour. It is for this reason that mathematicians think of mathematics both as an art and as a science. This year, we hope that you will get a chance to see the creativity and artistry involved in discovering and understanding mathematical patterns.

It is important to keep in mind that mathematics aims to not just find out what patterns exist, but also the explanations for why they exist. Such explanations can often then be used in applications well beyond the context in which they were discovered, which can then help to propel humanity forward.

For example, the understanding of patterns in the motion of stars, planets, and their satellites led humankind to develop the theory of gravitation, allowing us to launch our own satellites and send rockets to the Moon and to Mars; similarly, understanding patterns in genomes has helped in diagnosing and curing diseases - among thousands of other such examples.

Figure it Out

1. Can you think of other examples where mathematics helps us in our everyday lives?
2. How has mathematics helped propel humanity forward? (You might think of examples involving: carrying out scientific experiments; running our economy and democracy; building bridges, houses or other complex structures; making TVs, mobile phones, computers, bicycles, trains, cars, planes, calendars, clocks, etc.)

Teacher's Note

Mathematics is not just about calculations or memorizing rules. When you see patterns, you should ask yourself: why does this pattern work this way? For instance, even numbers always end in 0, 2, 4, 6, or 8 - but understanding why will help you remember it far better than just memorizing the definition.

1.2 Patterns in Numbers

Among the most basic patterns that occur in mathematics are patterns of numbers, particularly patterns of whole numbers:

\( 0, 1, 2, 3, 4, \ldots \)

The branch of Mathematics that studies patterns in whole numbers is called number theory.

Number sequences are the most basic and among the most fascinating types of patterns that mathematicians study. Table 1 shows some key number sequences that are studied in Mathematics.

Figure it Out

1. Can you recognise the pattern in each of the sequences in Table 1?
2. Rewrite each sequence of Table 1 in your notebook, along with the next three numbers in each sequence! After each sequence, write in your own words what is the rule for forming the numbers in the sequence.

Teacher's Note

Look at the odd numbers: 1, 3, 5, 7, 9... Notice that each number is 2 more than the one before it. For even numbers: 2, 4, 6, 8... the same rule applies. When you find the rule yourself, write it down in simple language - this is your first step toward understanding why sequences work the way they do.

1.3 Visualising Number Sequences

Many number sequences can be visualised using pictures. Visualising mathematical objects through pictures or diagrams can be a very fruitful way to understand mathematical patterns and concepts. Let us represent the first seven sequences in Table 1 using the following pictures.

Key Points

• Mathematics is about finding patterns and understanding why those patterns exist, not just in textbooks but in nature, technology, and everyday life.
• Number theory is the branch of mathematics that studies patterns in whole numbers, and number sequences are the most basic type of mathematical patterns.
• Common number sequences include counting numbers, odd and even numbers, triangular numbers, squares, cubes, and powers, each following its own rule.
• Drawing pictures or using diagrams to visualize number sequences is a powerful way to understand and remember the patterns.

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