Ch 3 of Ganita Prakash — "Number Play" — takes students on a playful journey through the world of numbers. Through puzzles, games, and explorations, students discover fascinating properties of numbers, including palindromes, digit patterns, and number tricks. This chapter makes mathematics engaging while reinforcing place value and number operations.
Numbers can be explored by looking at their digits. A 2-digit number like 47 can be written as 10 × 4 + 7. When you reverse a 2-digit number and find the difference, interesting patterns emerge. For example: 73 − 37 = 36, 84 − 48 = 36. The difference of a 2-digit number and its reverse is always a multiple of 9.
A palindrome number reads the same forwards and backwards: 121, 1331, 12321 are all palindromes. An interesting activity is the "reverse and add" process: take any number, reverse it, and add the two. Repeat until you get a palindrome. For example: 56 → 56 + 65 = 121 (palindrome in one step!).
The chapter explores several number tricks. Multiplying any number by 9 gives a result whose digits add up to 9 (or a multiple of 9). Magic squares, where every row, column, and diagonal adds to the same sum, are another fascinating puzzle. These activities build number sense and logical thinking.
Understanding place value is essential for number play. Students explore what happens when they rearrange digits: the largest 3-digit number using digits 3, 7, 1 is 731 and the smallest is 137. The difference between the largest and smallest arrangements of the same digits reveals interesting patterns.
Download the official NCERT PDF for Ch 3 "Number Play" from the NCERT website: https://ncert.nic.in/textbook/pdf/fegp103.pdf. You can also download the complete Ganita Prakash textbook: https://ncert.nic.in/textbook/pdf/fegp1ps.zip
A palindrome number is a number that reads the same from left to right as from right to left. Examples include 11, 121, 1331, and 12321.
For most numbers, the reverse-and-add process eventually produces a palindrome, but this has not been proven for every number. The number 196, for instance, has been tested for millions of steps without producing a palindrome.
This is because 9 = 10 − 1. When you multiply by 9, the tens digit increases by 1 and the units digit decreases by 1, keeping the digit sum constant at 9.
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