Class 6 : Maths ( English ) – Lesson 3. Number Play

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On December 12, 2025

EXPLANATION AND ANALYSIS

🌿 1. Introduction: Playing with Numbers

Numbers are not just symbols written in notebooks; they are ideas that help us count, compare, arrange, and understand the world around us. From counting steps while walking, arranging students in a line, checking house numbers, to playing board games and puzzles, numbers are everywhere. Number Play means exploring numbers in a creative and logical way to understand their properties, patterns, and behaviour.

🔵 This chapter encourages curiosity about numbers
🟢 It shows that mathematics can be playful and logical at the same time
🟡 Students learn to think, experiment, and reason with numbers
🔴 The focus is on understanding, not memorising

🧠 2. Counting Numbers and Their Uses

Counting numbers are the first numbers we learn.

🔹 Counting numbers start from 1 and go on endlessly: 1, 2, 3, 4, …
🔹 They help us count objects like books, students, or steps
🔹 They are used to show quantity, order, and position

💡 Concept:
Counting numbers are used to answer the question “how many?”

✏️ Note:
Zero is not a counting number, but it plays an important role in mathematics.

🌱 3. Whole Numbers

When zero is included with counting numbers, we get whole numbers.

🔵 Whole numbers = 0, 1, 2, 3, 4, …
🟢 Zero represents nothing or absence of quantity
🟡 Whole numbers help in situations where nothing is counted

🔹 Example:
Number of apples in an empty basket = 0

💡 Concept:
Whole numbers are counting numbers plus zero.

🧠 4. Even and Odd Numbers

Numbers can be classified based on divisibility by 2.

🔵 Even numbers
🔹 Numbers that can be divided exactly by 2
🔹 Example: 2, 4, 6, 8, 10

🟢 Odd numbers
🔹 Numbers that cannot be divided exactly by 2
🔹 Example: 1, 3, 5, 7, 9

✏️ Note:
An even number always ends with 0, 2, 4, 6, or 8.

💡 Concept:
Every whole number is either even or odd.

🌿 5. Place Value and Face Value

Every digit in a number has a value based on its position.

🔵 Face value is the digit itself
🟢 Place value depends on the position of the digit in the number

🔹 Example: In the number 345
🔹 Face value of 4 = 4
🔹 Place value of 4 = 40

💡 Concept:
Place value = digit × value of its position

🧠 6. Expanded Form of Numbers

Numbers can be written as the sum of their place values.

🔵 Example: 582
🔹 500 + 80 + 2

🟢 Expanded form helps us understand the structure of numbers
🟡 It makes addition and subtraction easier

✏️ Note:
Expanded form clearly shows the contribution of each digit.

🌱 7. Comparing Numbers

Numbers can be compared to find which is greater or smaller.

🔵 Larger number means greater quantity
🟢 Smaller number means lesser quantity
🟡 Comparison symbols are used: >, <, =

🔹 Example:
456 > 432

💡 Concept:
Compare numbers starting from the highest place value.

🧠 8. Ascending and Descending Order

Numbers can be arranged in order.

🔵 Ascending order: smallest to greatest
🟢 Descending order: greatest to smallest

🔹 Example:
Ascending: 3, 7, 12, 25
Descending: 25, 12, 7, 3

✏️ Note:
Ordering numbers helps in data organisation and problem solving.

🌿 9. Properties of Numbers (Simple Observations)

Playing with numbers helps us notice simple properties.

🔵 Adding zero to a number does not change it
🟢 Multiplying a number by 1 gives the same number
🟡 Multiplying a number by zero gives zero

💡 Concept:
Numbers follow fixed rules called properties.

🧠 10. Fun with Number Patterns

Number play often involves observing patterns.

🔵 Example: 2, 4, 6, 8
🟢 Example: 1, 3, 6, 10

🔹 Patterns help us predict the next number
🔹 They train logical and analytical thinking

✏️ Note:
Finding the rule is more important than finding the answer.

🌍 11. Numbers in Daily Life

Numbers help us in many daily situations.

🔵 House numbers and vehicle numbers
🟢 Phone numbers and PIN codes
🟡 Scores in games and marks in exams
🔴 Calendar dates and time

💡 Concept:
Without numbers, daily life would be disorganised.

🧠 12. Importance of Number Play

Number play builds confidence in mathematics.

🔹 It improves number sense
🔹 It develops logical reasoning
🔹 It prepares students for algebra and higher maths

💡 Concept:
Strong understanding of numbers is the foundation of all mathematics.

📘 Summary

The chapter Number Play helps students understand numbers in a meaningful and enjoyable way. It begins with counting numbers and whole numbers, explaining their uses in everyday life. Students learn about even and odd numbers, place value, face value, and expanded form, which help them understand the structure of numbers. Comparing numbers and arranging them in ascending or descending order strengthens logical thinking.

The chapter also introduces simple number properties and number patterns, showing that numbers follow clear rules. By relating numbers to daily-life situations, the lesson makes mathematics practical and relatable. Overall, Number Play builds strong number sense and prepares students for advanced topics in mathematics.

📝 Quick Recap

🟢 Counting numbers start from 1
🟡 Whole numbers include zero
🔵 Every number is either even or odd
🔴 Place value depends on position
⚡ Numbers can be compared and ordered
🧠 Number play builds logical thinking

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TEXTBOOK QUESTIONS

🔒 ❓ Question 1
There is only one supercell (number greater than all its neighbours) in this grid. If you exchange two digits of one of the numbers, there will be 4 supercells. Figure out which digits to swap.

📌 ✅ Answer
🔹 A supercell is a number that is greater than all numbers touching it.
🔹 By observing the grid carefully, 62,871 is the only number greater than all its neighbours.
🔹 To create more supercells, this dominating number must be reduced.
🔹 Swap two digits within 62,871.
🔹 Swapping 6 and 1 gives 12,876.
🔹 This allows nearby numbers to become greater than their neighbours, creating 4 supercells.
✔️ Final: Swap digits 6 and 1 in 62,871.
✏️ Note: This is an exploratory question. Any valid swap that creates 4 supercells is acceptable.

🔒 ❓ Question 2
How many rounds does your year of birth take to reach the Kaprekar constant?

📌 ✅ Answer
🔹 The Kaprekar constant for 4-digit numbers is 6174.
🔹 Write your year of birth as a 4-digit number.
🔹 Arrange the digits in descending order to form the largest number.
🔹 Arrange the digits in ascending order to form the smallest number.
🔹 Subtract the smaller number from the larger number.
🔹 Repeat the steps until 6174 is obtained.
✔️ Final: The number of repetitions needed is the required number of rounds.

🔒 ❓ Question 3
We are the group of 5-digit numbers between 35,000 and 75,000 such that all of our digits are odd. Who is the largest number? Who is the smallest number? Who is the closest to 50,000?

📌 ✅ Answer
🔹 Allowed odd digits are 1, 3, 5, 7 and 9.

🔹 Smallest number
🔸 Starting from 35,000, replace even digits with the smallest odd digits.
✔️ Final: 35,111

🔹 Largest number
🔸 The number must be less than 75,000 and all digits must be odd.
✔️ Final: 73,999

🔹 Closest to 50,000
🔸 The nearest valid odd-digit number above 50,000 is 51,111.
✔️ Final: 51,111

🔒 ❓ Question 4
Estimate the number of holidays you get in a year including weekends, festivals and vacation. Then try to get an exact number.

📌 ✅ Answer
🔹 Weekends ≈ 52 × 2 = 104 days.
🔹 Festivals ≈ 15 days.
🔹 Vacations ≈ 50 days.
🔹 Estimated total ≈ 169 days.
🔹 The exact number can be found by checking the school calendar and removing overlaps.
✔️ Final: Exact value depends on the calendar used.

🔒 ❓ Question 5
Estimate the number of liters a mug, a bucket and an overhead tank can hold.

📌 ✅ Answer
🔹 Mug ≈ 0.25 to 0.5 L.
🔹 Bucket ≈ 10 to 20 L.
🔹 Overhead tank ≈ 500 to 2000 L.

🔒 ❓ Question 6
Write one 5-digit number and two 3-digit numbers such that their sum is 18,670.

📌 ✅ Answer
🔵 Step 1: Choose a 5-digit number = 17,000.
🔵 Step 2: Choose two 3-digit numbers = 800 and 870.
🔵 Step 3: 17,000 + 800 = 17,800.
🔵 Step 4: 17,800 + 870 = 18,670.
✔️ Final: 17,000 + 800 + 870 = 18,670.

🔒 ❓ Question 7
Choose a number between 210 and 390. Create a number pattern that will sum to this number.

📌 ✅ Answer
🔹 Choose the number 300.
🔵 Step 1: Use the pattern 1 + 2 + 3 + … + 24.
🔵 Step 2: Sum = 24 × 25 / 2.
✔️ Final: 1 + 2 + 3 + … + 24 = 300.

🔒 ❓ Question 8
Why is the Collatz conjecture correct for all powers of 2?

📌 ✅ Answer
🔹 All powers of 2 are even numbers.
🔹 Even numbers are divided by 2 in the Collatz rule.
🔹 This process continues until the number becomes 1.
✔️ Final: The Collatz conjecture holds for all powers of 2.

🔒 ❓ Question 9
Check if the Collatz conjecture holds for the starting number 100.

📌 ✅ Answer
🔵 100/2 = 50
🔵 50/2 = 25
🔵 325 + 1 = 76
🔵 76/2 = 38
🔵 38/2 = 19
🔵 319 + 1 = 58
🔵 58/2 = 29
🔵 329 + 1 = 88
🔵 88/2 = 44
🔵 44/2 = 22
🔵 22/2 = 11
🔵 311 + 1 = 34
🔵 34/2 = 17
🔵 317 + 1 = 52
🔵 52/2 = 26
🔵 26/2 = 13
🔵 313 + 1 = 40
🔵 40/2 = 20
🔵 20/2 = 10
🔵 10/2 = 5
🔵 3*5 + 1 = 16
🔵 16/2 = 8
🔵 8/2 = 4
🔵 4/2 = 2
🔵 2/2 = 1
✔️ Final: The conjecture holds for 100.

🔒 ❓ Question 10
Starting with 0, players alternate adding numbers between 1 and 3. The first person to reach 22 wins. What is the winning strategy?

📌 ✅ Answer
🔹 Winning numbers follow a pattern of adding 4.
🔹 Target numbers are 2, 6, 10, 14, 18 and 22.
🔹 The first player starts by adding 2.
🔹 After each opponent’s move, add the number needed to make the total increase by 4.
✔️ Final: The first player has a guaranteed winning strategy.

(CBSE MODEL QUESTION PAPER)

ESPECIALLY MADE FROM THIS CHAPTER ONLY

🔵 Section A — Very Short Answer (1 mark each)

🔒 ❓ Question 1
What are counting numbers?
📌 ✅ Answer:
🔹 Counting numbers are numbers used for counting objects
🔸 They start from 1 and go on endlessly

🔒 ❓ Question 2
Write the smallest whole number.
📌 ✅ Answer:
🔹 The smallest whole number is 0

🔒 ❓ Question 3
Is 15 an even or an odd number?
📌 ✅ Answer:
🔹 15 is not divisible by 2
🔸 Therefore, it is an odd number

🔒 ❓ Question 4
Write the face value of digit 7 in the number 478.
📌 ✅ Answer:
🔹 The face value of a digit is the digit itself
🔸 Face value of 7 is 7

🔒 ❓ Question 5
What is the place value of 6 in the number 362?
📌 ✅ Answer:
🔹 The digit 6 is in the tens place
🔸 Place value of 6 = 60

🔒 ❓ Question 6
True or False:
Zero is a counting number.
📌 ✅ Answer:
🔹 Zero is not used for counting objects
✔️ Final: False

🟢 Section B — Short Answer I (2 marks each)

🔒 ❓ Question 7
Define whole numbers.
📌 ✅ Answer:
🔹 Whole numbers include zero and all counting numbers
🔸 They are written as 0, 1, 2, 3, …

🔒 ❓ Question 8
Write any two even numbers and two odd numbers.
📌 ✅ Answer:
🔹 Even numbers: 4, 8
🔸 Odd numbers: 5, 9

🔒 ❓ Question 9
Write the expanded form of 405.
📌 ✅ Answer:
🔹 405 = 400 + 0 + 5

🔒 ❓ Question 10
Compare the numbers using >, < or = :
(i) 568 ___ 586
(ii) 720 ___ 702
📌 ✅ Answer:
🔹 568 < 586
🔸 720 > 702

🔒 ❓ Question 11
Arrange the numbers 34, 12, 45, 28 in ascending order.
📌 ✅ Answer:
🔹 Ascending order means smallest to greatest
🔸 Order: 12, 28, 34, 45

🔒 ❓ Question 12
Write one use of numbers in daily life.
📌 ✅ Answer:
🔹 Numbers are used to tell time and dates

🟡 Section C — Short Answer II (3 marks each)

🔒 ❓ Question 13
Explain the difference between counting numbers and whole numbers.

📌 ✅ Answer:
🔹 Counting numbers start from 1 and go on endlessly
🔹 Whole numbers include 0 along with all counting numbers
🔸 Therefore, whole numbers = counting numbers + 0

🔒 ❓ Question 14
State whether the following numbers are even or odd and give reason:
(i) 48
(ii) 73

📌 ✅ Answer:
🔹 48 is divisible by 2, so it is an even number
🔸 73 is not divisible by 2, so it is an odd number

🔒 ❓ Question 15
Write the place value of each digit in the number 506.

📌 ✅ Answer:
🔹 Place value of 5 = 500
🔹 Place value of 0 = 0
🔸 Place value of 6 = 6

🔒 ❓ Question 16
Write the expanded form of 7,204 and explain it.

📌 ✅ Answer:
🔹 7,204 = 7,000 + 200 + 0 + 4
🔸 Expanded form shows the value of each digit according to its place

🔒 ❓ Question 17
Compare the numbers and write the greater one:
(i) 3,456 and 3,465
(ii) 8,109 and 8,091

📌 ✅ Answer:
🔹 In (i), 3,465 > 3,456
🔸 In (ii), 8,109 > 8,091

🔒 ❓ Question 18
Arrange the numbers 615, 165, 651, 516 in descending order.

📌 ✅ Answer:
🔹 Descending order means greatest to smallest
🔸 Order: 651, 615, 516, 165

🔒 ❓ Question 19
Write two properties of whole numbers.

📌 ✅ Answer:
🔹 Adding 0 to a whole number does not change the number
🔸 Multiplying a whole number by 1 gives the same number

🔒 ❓ Question 20
Give two examples where zero is useful in daily life.

📌 ✅ Answer:
🔹 Zero shows no balance in a bank account
🔸 Zero shows no score in a game

🔒 ❓ Question 21
Write the next two numbers in the pattern and state the rule:
2, 5, 8, 11, ___, ___

📌 ✅ Answer:
🔹 The pattern increases by adding 3 each time
🔸 Next numbers: 14, 17

🔒 ❓ Question 22
Why is place value important in numbers?

📌 ✅ Answer:
🔹 Place value tells the actual value of a digit in a number
🔹 It helps in reading, writing, and comparing numbers
🔸 It makes calculations easier and meaningful

🔴 Section D — Long Answer (4 marks each)

🔒 ❓ Question 23
Explain the difference between face value and place value with an example.

📌 ✅ Answer:
🔹 Face value of a digit is the digit itself, regardless of its position
🔹 Place value of a digit depends on its position in the number
🔹 Example: In the number 638
🔸 Face value of 3 is 3
🔸 Place value of 3 is 30
✔️ Final: Face value shows the digit, place value shows its actual worth

🔒 ❓ Question 24
Write a number using digits 5, 0, 3, and 8 only once each. Then find its expanded form.

📌 ✅ Answer:
🔹 One possible number formed is 5,038
🔹 Expanded form is written using place values
🔸 5,038 = 5,000 + 0 + 30 + 8
✔️ Final: Expanded form correctly shows the value of each digit

🔒 ❓ Question 25
How can you check whether a number is even or odd? Explain with examples.

📌 ✅ Answer:
🔹 A number is even if it is divisible by 2
🔹 A number is odd if it is not divisible by 2
🔹 Example: 24 ÷ 2 = 12, so 24 is even
🔸 Example: 35 ÷ 2 does not give a whole number, so 35 is odd
✔️ Final: Divisibility by 2 decides even or odd

🔒 ❓ Question 26
Arrange the numbers 4,305; 4,530; 4,053; 4,350 in ascending order and explain the method.

📌 ✅ Answer:
🔹 Ascending order means smallest to greatest
🔹 Compare numbers starting from the highest place value
🔹 All numbers have 4 in the thousands place
🔹 Compare hundreds place next
🔸 Order: 4,053 < 4,305 < 4,350 < 4,530
✔️ Final: Ascending order is 4,053, 4,305, 4,350, 4,530

🔒 ❓ Question 27
OR
Explain why zero is important in mathematics with examples.

📌 ✅ Answer:
🔹 Zero represents no quantity
🔹 It helps in writing large numbers like 10, 100, 1,000
🔹 Adding zero to a number does not change the number
🔸 Example: 25 + 0 = 25
✔️ Final: Zero plays a key role in number system and calculations

🔒 ❓ Question 28
Write any two properties of whole numbers and explain them.

📌 ✅ Answer:
🔹 Property 1: Addition property of zero
🔹 Adding zero to any whole number gives the same number
🔹 Property 2: Multiplication property of one
🔸 Multiplying any whole number by 1 gives the same number
✔️ Final: Whole numbers follow fixed and useful properties

🔒 ❓ Question 29
A student says that 405 and 45 are almost the same numbers because they contain the same digits. Do you agree? Give reasons.

📌 ✅ Answer:
🔹 The statement is incorrect
🔹 The position of digits changes the value of the number
🔹 In 405, digit 4 has place value 400
🔸 In 45, digit 4 has place value 40
✔️ Final: Same digits can give different numbers due to place value

🔒 ❓ Question 30
OR
Explain how numbers are useful in daily life with suitable examples.

📌 ✅ Answer:
🔹 Numbers are used to count objects like books and students
🔹 They help in telling time and dates
🔹 Numbers are used in money transactions and shopping
🔸 They help in measuring distance, weight, and temperature
✔️ Final: Numbers make daily life organised and manageable