NEETClass 11thClass 12thClass 12th PlusJEEClass 11thClass 12thClass 12th PlusClass 6-10Class 6thClass 7thClass 8thClass 9thClass 10thOnline CoursesDistance LearningInternational OlympiadNEETClass 11thClass 12thClass 12th PlusJEE (Main+Advanced)Class 11thClass 12thClass 12th PlusJEE MainClass 11thClass 12thClass 12th PlusClass 6-10Class 6thClass 7thClass 8thClass 9thClass 10thKCET/MHT-CETKCETMHT-CETNEET20262025202420232022JEE20262025202420232022Class 6-1020262025JEE MainPrevious Year PapersSample PapersMock TestResultAnalysisSyllabusExam DatePercentile PredictorAnswer KeyCounsellingEligibilityExam PatternJEE MathsJEE ChemistryJEE PhysicsJEE AdvancedPrevious Year PapersSample PapersMock TestResultAnalysisSyllabusExam DateAnswer KeyEligibilityExam PatternRank PredictorNEETPrevious Year PapersSample PapersMock TestResultAnalysisSyllabusExam DateCollege PredictorAnswer KeyRank PredictorCounsellingEligibilityExam PatternBiologyNCERT SolutionsClass 6Class 7Class 8Class 9Class 10Class 11Class 12TextbooksCBSEClass 12Class 11Class 10Class 9Class 8Class 7Class 6SubjectsSyllabusNotesSample PapersQuestion PapersICSEClass 10Class 9Class 8Class 7Class 6State BoardBiharKarnatakaMadhya PradeshMaharashtraTamilnaduWest BengalUttar PradeshOlympiadMathsScienceEnglishSocial ScienceNSOIMONMTCTALLENTEXASATInstant Online ScholarshipAIOT(NEET)ALLEN for SchoolsAbout ALLENBlogsNewsCareersRequest a call backBook a demo
CBSE Notes Class 6 Maths Chapter 3 - Number Play
Number Play is a fun way to explore and understand numbers. It involves discovering patterns, solving puzzles, and using numbers creatively. Through games and activities, students learn to compare, order, and estimate numbers. Number Play helps improve problem-solving skills, mental math, and logical thinking, making math both enjoyable and practical in real-life situations.The PDF provided can be used for quick revision and to revisit the concepts covered in the chapter.
1.0Number Play Class 6 Maths Chapter 3 - Revision Notes
Numbers Can Tell Us Things
Numbers are everywhere, and they help us understand the world around us. For example:
- Your age tells the story of how many birthdays you’ve celebrated.
- The time on the clock tells us when it’s time to eat, play, or study.
Numbers give us information and make life easier to manage!
Supercells
The concept of a supercell can be understood as a cell that is larger than all its adjacent cells.
In the table:
- The supercell would be the number 62, as it is larger than both of its adjacent cells (45 and 55).
- Another example is 511, which is larger than its only adjacent cell, 453.
Playing with Digits
Every number tells a story through its digits. Rearranging, adding, or subtracting digits can create interesting results. Try this: take any 3-digit number, reverse its digits, subtract the smaller from the larger, and reverse the digits again. Add the two numbers—voilà! The result is always 1089.
Pretty Palindromic Patterns
Palindromes are numbers that read the same forward and backward, like 121, 3443, or 78987. They’re not just pretty—they have unique properties. For instance, adding two palindromic numbers often results in another palindrome.
The Magic Number of Kaprekar
Kaprekar's constant (6174) is a magical number. Pick any 4-digit number, rearrange its digits to form the largest and smallest numbers possible, then subtract the smaller from the larger. Repeat this process, and you’ll always land on 6174 in a few steps. Try it—it's mesmerizing!
Clock and Calendar Numbers
Time and dates hide many numerical secrets. For instance:
- The sum of the opposite faces of a clock is always 12.
- Magic squares in calendars reveal constant sums.
Playing with these numbers sharpens mental math skills and offers fun puzzles to solve.
Mental Math: Fast and Fun Calculations
Why use calculators when you can impress friends with mental math? Tricks like multiplying by 11 or squaring numbers ending in 5 are quick and easy. For example:
- To multiply any number by 11, just add the digits and place the sum in between. (e.g., = 572)
Playing with Number Patterns
Numbers reveal endless patterns:
- Odd numbers summed sequentially always form a perfect square.
- Multiplying any number by 9 and summing its digits gives 9.
These patterns make numbers fun to explore.
An Unsolved Mystery — The Collatz Conjecture!
The Collatz Conjecture is a simple yet unsolved problem in mathematics. Take any positive number:
- If it’s even, divide by 2.
- If it’s odd, multiply by 3 and add 1.
Repeat the process, and you’ll eventually reach 1. But no one knows why this always works. Try it with your favourite numbers!
Simple Estimation
Estimation is an essential skill for solving problems quickly. For example, rounding numbers to the nearest 10, 100, or 1000 helps estimate sums, products, or differences without exact calculations.
Games and Winning Strategies
Math games like Sudoku, KenKen, or Nim challenge your logic and sharpen your skills. Strategies often involve recognising patterns or using arithmetic cleverly to win.
Key Concepts to Remember
- Natural Numbers: The set of positive counting numbers starting from 1, 2, 3, 4, and extending endlessly to infinity.
- Whole Numbers: The complete set of natural counting numbers combined with zero, represented as 0, 1, 2, 3, 4, and continuing infinitely.
- Supercell: A specific cell inside a number grid whose value is strictly greater than all of its immediately adjacent neighboring cells (top, bottom, left, and right).
- Digit Sum: The single or multi-digit total obtained by adding all the individual digits of a given number, used to verify arithmetic operations.
- Palindromic Number: A symmetrical number that remains completely unchanged when its digits are written in reverse order, such as 121, 313, 8778, or 16461.
- Kaprekar Routine: An iterative subtraction process applied to four-digit numbers with at least two distinct digits, which consistently reduces to the constant 6174.
- Collatz Conjecture: An unsolved mathematical sequence rule stating that repeatedly taking half of an even number or calculating 3n + 1 for an odd number always leads to 1.
- Simple Estimation: The practice of calculating a reasonable approximate quantity when an exact numeric figure is unnecessary or unavailable.
2.0Important Formulas: Number Play
Counting and Quantity Formulas
- Total Whole Numbers in a Range (from a to b): For any two whole numbers where b>a, the total count of inclusive numbers equals b-a+1. For example, the total count of two-digit numbers from 10 to 99 equals 99-10+1=90.
- Whole Numbers Between Two Values: The total count of whole numbers lying strictly between a and b equals b-a-1. For example, the number of whole numbers strictly between 10 and 20 equals 20-10-1=9.
Digit Sum Verification Rule
- Addition Check using Digit Sums: The digit sum of the addends equals the digit sum of the final sum. For example, in 89+43=132, the digit sum of 89 is 8+9=171+7=8 (or digit sum total 17+7=242+4=6), and the digit sum of 132 is 1+3+2=6.
The Kaprekar Constant Routine
- Kaprekar Subtraction Rule: Take any four-digit number (not all digits identical), arrange the digits in descending order to form A, arrange the digits in ascending order to form B, and compute C=A-B. Repeat the routine with C (using a leading zero if C has fewer than 4 digits) to reach the fixed Kaprekar constant 6174.
The Collatz Sequence Rules
- Even Number Rule: If n is even, the next number in the sequence is n2.
- Odd Number Rule: If n is odd, the next number in the sequence is 3n+1.
3.0Learning Guide for Class 6 Maths Number Play – Chapter 3
- Identifying Supercells in a Number Grid: Examine numbers in adjacent grid cells; if a cell value is strictly greater than its surrounding left, right, top, and bottom neighbors, mark it as a supercell. For example, in the row segment 205, 852, 369, the number 852 is a supercell because 852>205 and 852>369.
- Executing the Reverse-and-Add Palindrome Method: Take any two-digit starting number, reverse its digits, and add the two numbers together. If the sum is not a palindrome, repeat the reverse-and-add steps until a palindromic sum is obtained. For example, starting with 58: step 1 gives 58+85=143; step 2 gives 143+341=484, reaching a palindrome in 2 steps.
- Calculating Digit Occurrences: Count how many times a specific digit appears within a numerical range. For instance, between 1 and 100, the digit '8' appears 20 times across numbers like 8, 18, 28, 80, 81, ..., 88 (counted twice), 89, and 98.
- Tracing the Kaprekar Routine Step-by-Step: Starting with 1234: descending order gives 4321, ascending gives 1234; 4321-1234=3087. Repeating with 3087: 8730-0378=8352. Repeating with 8352: 8532-2358=6174, reaching the Kaprekar constant in 3 iterations.
- Testing the Collatz Sequence: Starting with 12: since 12 is even, take half to get 6; half of 6 is 3; since 3 is odd, compute 3(3)+1=10; then 105168421.
- Recognizing Symmetrical Clock Times: Identify symmetrical or palindromic time readings on 12-hour digital displays where minute digits mirror hour digits, such as 05:55 or 10:01.
- Applying Estimation in Real Life: Use rounded estimates when precise counts are unnecessary, such as estimating party sandwich quantities or determining bookshelf storage capacities.
- Revision Tip on Collatz Chains: Remember that Collatz sequences may rise and fall unpredictably, but every tested whole number eventually lands on the repeating 4-2-1 loop.
4.0Explore Chapter-wise Class 6 Maths Notes
5.0Additional Study Materials for Class 6 Maths
6.0Find the Right Study Resources for Class 6
7.0Benefits of CBSE Notes for Class 6 Maths Chapter 3 - Number Play
- Time-Saving: Instead of going through the entire NCERT Solutions textbook, notes offer a condensed version, saving you valuable study time.
- Better Retention: Organised CBSE notes can aid in better memory and retention of the concepts and methods learned in the chapter.
- Self-Assessment: Some notes might include quick quizzes or practice questions, allowing you to assess your understanding.
- Foundation for Higher Classes: A strong understanding of number play concepts forms a crucial foundation for more advanced topics in higher classes.
- Easy Accessibility: Digital notes can be accessed anytime and anywhere, making learning more convenient.
- Reduced Exam Stress: Having well-prepared notes can boost your confidence and reduce anxiety during exams.