Knowing our numbers- An overview
Knowing our Numbers is the first chapter in NCERT for the 6th class. It is very important to go through this chapter thoroughly as it would create a foundation for students for the further chapters in the book. The topics that are discussed in this chapter are listed below-
Introduction
Comparing Numbers
Large Numbers in practice
Estimation
Using brackets
Roman Numerals
Introduction
The first section is the introduction which introduces the importance of numbers that help us to count or arrange the objects and are used in many different contexts. These are arithmetic values that help us to convey the magnitude of all the objects that are present around us.
Comparing Numbers
In order to understand mathematical concepts such as greater than or equal to, the comparison of numbers is important. The subtopics of comparing numbers are:
How many numbers can you make?
In this part, students will learn how they can make numbers from given digits. Numbers will be formed in such a way that no digit is repeated in a single number and there cannot be two exact numbers. Students will also learn about the different orders of numbers which are ascending (smallest to greatest) and descending (greatest to smallest).
Shifting digits
In this part, students will learn how a small shift in the digits of the numbers can make a difference in the value of the number.
Introducing 10,000
In this part, students learn about the greatest 3-digit number which is 999, and what happens when we add a 1 to 999.
Revisiting place value
In this part, students will learn about the expansion of 2-digit, 3-digit, and 4-digit numbers and the place value for each digit.
Introducing 1,00,000
In this part, students will learn about the greatest 5-digit number which is 99999, and what happens when 1 is added to 99999.
Larger Numbers
In this section, students will learn about the greatest and smallest 6-digit, 7-digit, and 8-digit numbers which include numbers like 10 lakh and one crore.
An aid in reading and writing large numbers
This section will explain to the students how to read and write large numbers by identifying the digits in one place, tens place, hundreds place, and so on.
Use of commas
This chapter will also help the students to learn the use and importance of commas in the number system.
Large Numbers in practice
Students will learn about large numbers and how they can be written in shorter forms by using units such as centimeters and meters, grams and kilograms, meters and kilometers, etc.
Estimation
This section will help the students to learn about the approximate or near values of certain numbers. Let us have a look at the subsections.
Estimating the nearest tens by rounding off
In this section, students will learn how to round off numbers to the nearest tens. Suppose 13 is a number that lies between 10 and 20, but since it is closer to 10, therefore it would be rounded off to the nearest tens which are 10.
Estimating the nearest hundreds by rounding off
Here students will learn how to round off numbers to the nearest hundreds, for example, 310 lies between 300 and 400 but are closer to 300, therefore it will be rounded off to 300.
Estimating the nearest thousands by rounding off
Just like nearest tens and hundreds, students will also learn about how to round off numbers to the nearest thousand. For example, 8600 is a number that lies between 8000 and 9000 but since it is closer to 9000, it would be rounded off to the nearest thousand which is 9000.
Estimating outcomes of number situations
Students will learn about the situations where we need to answer quickly for how to add numbers quickly by keeping the digits of the numbers being added in the same place and rounding them off to the nearest values.
To estimate sum or difference
It is not always necessary that you need to round off, therefore in this section students will learn why and when we need to round off.
To estimate products
Here the students will learn about the general rule which states that estimating while multiplying can be done by rounding off each factor to its greatest place and then multiplying those factors.
Using brackets
Students will learn about the use of brackets and how they are used in order to avoid confusion while doing mathematical calculations. In expanding brackets the students will learn the systematic procedure for the removal of brackets.
Roman Numerals
Students will study one of the earliest systems which are roman numerals and are still used in many places
FAQs on Knowing our Numbers
1. What is the primary learning objective of the CBSE Class 6 chapter 'Knowing Our Numbers'?
The main goal of 'Knowing Our Numbers' is to build a strong foundation for all future mathematical concepts. This chapter teaches students essential skills such as comparing large numbers, understanding place value, using commas correctly, and working with different numeration systems. It ensures students can confidently read, write, estimate, and perform basic operations with large numbers, which is crucial for solving more complex problems later.
2. How can we compare two large numbers easily?
To compare large numbers, you can follow a simple two-step method as per the NCERT syllabus:
- Step 1: Count the digits. The number with more digits is always greater. For example, 10,000 (5 digits) is greater than 9,999 (4 digits).
- Step 2: If the digit count is the same, start comparing the digits from the leftmost position. The number with the larger digit in the first differing position is the greater number. For example, in 45,678 and 45,789, the first two digits are the same. We then compare the third digit (6 and 7), and since 7 > 6, the number 45,789 is greater.
3. What is the difference between the Indian and International Systems of Numeration?
The main difference lies in how digits are grouped using commas and the names given to these groups.
- The Indian System of Numeration uses periods of Lakhs and Crores. Commas are placed after the hundreds place (3 digits from the right), then after every two digits. For example, 5,08,01,592 is read as 'Five crore eight lakh one thousand five hundred ninety-two'.
- The International System of Numeration uses periods of Millions and Billions. Commas are placed after every three digits from the right. The same number, 50,801,592, is read as 'Fifty million eight hundred one thousand five hundred ninety-two'.
4. Why is estimation important in mathematics and daily life?
Estimation is the skill of finding an approximate value rather than an exact one. Its importance is twofold:
- In Mathematics: It helps in quickly checking the reasonableness of an answer. For example, if you multiply 48 by 52, you can estimate it as 50 x 50 = 2500. If your calculated answer is 24,960, you know there's a mistake.
- In Daily Life: It is used for practical purposes where exact numbers are not necessary, like estimating the cost of groceries, the time a journey will take, or the number of people at an event. It makes calculations faster and more manageable.
5. How does using brackets change the answer in a mathematical problem?
Brackets are used to group numbers and operations that must be performed first, following the BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) rule. Changing the placement of brackets can completely change the result. For example:
- With brackets: (8 - 3) × 2 = 5 × 2 = 10. (Subtraction is done first).
- Without brackets: 8 - 3 × 2 = 8 - 6 = 2. (Multiplication is done first).
6. What is the smallest 6-digit number and how is it formed?
The smallest 6-digit number is 1,00,000 (one lakh). It is formed by adding 1 to the largest 5-digit number, which is 99,999. The pattern is that the smallest number of 'n' digits is always obtained by adding 1 to the greatest number of 'n-1' digits.
7. Why do we still learn about Roman numerals when we have the Indian and International systems?
Learning Roman numerals is important for several reasons, even in the modern era:
- Historical Context: It helps us understand a different, non-place value system of counting used in ancient times.
- Practical Applications: They are still used on clock faces, for numbering book chapters or series volumes, and to denote monarchs or popes (e.g., Queen Elizabeth II).
- Cognitive Skills: It encourages flexible thinking about how numbers can be represented and enhances logical reasoning.
