Number Play Sums for Class 6 — Free CBSE Worksheet PDF with Answers

Number Play is one of the most exciting chapters in the new NCERT Ganita Prakash textbook for Class 6 CBSE. Instead of just doing calculations, you explore surprising properties of numbers — palindromes that read the same backwards, digit sums that reveal hidden patterns, and the magical Kaprekar routine that always leads to 6174 for any 4-digit number (whose digits are not all the same).

This chapter builds number sense and mathematical thinking. It teaches you that maths is not only about getting the right answer — it is about asking interesting questions and noticing patterns. These skills are exactly what Olympiad and competitive exam questions test.

The worksheet has 60 questions across three levels. Level 1 covers identifying palindromes, computing digit sums, and recognising basic patterns. Level 2 works through reverse-and-add, Kaprekar steps, and divisibility checks. Level 3 has multi-step puzzles, magic squares, and pattern discovery.

A palindrome reads the same forwards and backwards. $121$, $1331$, $14541$, and $1001$ are all palindromes. Single-digit numbers are also palindromes by convention. Many 2-digit and 3-digit numbers can be turned into palindromes by repeatedly reversing the digits and adding.

Try $57$: reverse to $75$, add — $57 + 75 = 132$. Reverse $132$ to $231$, add — $132 + 231 = 363$, which is a palindrome. Some numbers reach a palindrome in one step, others in many. Class 6 students enjoy this process because it feels like a magic trick that works.

Pick any 4-digit number where not all digits are the same (e.g., $3087$). Arrange the digits in descending order ($8730$) and ascending order ($0378$). Subtract: $8730 - 0378 = 8352$. Repeat with the result. After at most 7 steps, you will reach $6174$, called Kaprekar's constant. From $6174$, the routine gives $6174$ again, so it sticks.

This works for any 4-digit starting number with at least two different digits. The reason is a beautiful piece of mathematics, and Class 6 students should try the routine on a few different starting numbers to see it in action. The chapter exercise asks students to perform the steps for given numbers and report the result.

The digit sum of a number is found by adding all its digits. The digit sum of $9876$ is $9 + 8 + 7 + 6 = 30$. Adding again, $3 + 0 = 3$, giving the digital root.

If the digit sum of a number is divisible by $3$, the number itself is divisible by $3$. If the digit sum is divisible by $9$, the number is divisible by $9$. So $729$ has digit sum $7 + 2 + 9 = 18$, and $18$ is divisible by $9$, so $729$ is divisible by $9$. This trick is faster than long division and is a CBSE favourite.