Class 6 Maths · Original EZT practice
Number Play (Class 6 Maths Chapter 3): games and patterns hiding inside numbers
Numbers follow rules you can play with. Add two odd numbers and something predictable always happens; reverse a two-digit number and a hidden 11 appears. This chapter turns those patterns into games - and every game below comes with the reason it always works. Below: the ideas in plain words, then original EZT practice with worked answers. (Note: this is original practice, not a textbook exercise key.)
10 original worked examples, 10 fresh self-check questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 17 October 2026:
1. Even and odd: the parity rules
Even numbers end in 0, 2, 4, 6 or 8; odd numbers end in 1, 3, 5, 7 or 9. Their sums and products follow fixed rules: even + even = even; odd + odd = even; even + odd = odd. Even x anything = even; odd x odd = odd.
2. Consecutive numbers and quick sums
Consecutive numbers follow each other, like 14 and 15. Their sum is always odd - one is even, the other odd. And the counting numbers add up fast with a trick: 1 + 2 + ... + 10 = 10 x 11 / 2 = 55.
3. Odd numbers and perfect squares
Add the first few odd numbers and a surprise appears: 1 = 1, 1 + 3 = 4, 1 + 3 + 5 = 9, 1 + 3 + 5 + 7 = 16 - the sum of the first n odd numbers is always n squared.
4. Digit reversal tricks
Take a two-digit number like 42, reverse it to 24, and add: 42 + 24 = 66 = 11 x 6 - always 11 times the sum of the digits. Subtract instead: 82 - 28 = 54 = 9 x 6 - always 9 times the difference of the digits. The reason: 42 is 4 tens + 2 ones, so reversing and adding gives 11 of each digit.
5. Palindromes: numbers that read the same backwards
121, 242 and 7337 are palindromes - identical forwards and backwards. Reversal-and-add often makes one: start with 56, reverse and add to get 56 + 65 = 121 - a palindrome in one step.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Predict even plus even
Choose the method: Use the last digit before doing the full addition.
EZT practice question
Without adding fully, is 12 + 8 even or odd?
Show the worked solution
- 12 is even and 8 is even.
- Even + even always gives an even sum.
Answer: Even + even = even (it is 20).
Check: The last digit of 20 is 0, so the sum is even.
Watch for this: Do not add the tens first; the parity rule is quicker and safer.
Now try it yourself
Is 34 + 62 even or odd?
Check your answer
Even.
Both numbers are even, and even + even = even.
Predict odd plus odd
Choose the method: Pair two odd last digits and check the parity rule.
EZT practice question
Is 7 + 9 even or odd?
Show the worked solution
- 7 is odd and 9 is odd.
- Odd + odd always gives an even sum.
Answer: Odd + odd = even (it is 16).
Check: 16 ends in 6, an even digit.
Watch for this: Two odd numbers do not make another odd sum.
Now try it yourself
Is 21 + 35 even or odd?
Check your answer
Even.
Both addends are odd, and odd + odd = even.
Predict odd plus even
Choose the method: Check one even and one odd last digit.
EZT practice question
Is 7 + 8 even or odd?
Show the worked solution
- 7 is odd and 8 is even.
- Odd + even always gives an odd sum.
Answer: Odd + even = odd (it is 15).
Check: 15 ends in 5, an odd digit.
Watch for this: The order does not matter: even + odd is also odd.
Now try it yourself
Is 44 + 17 even or odd?
Check your answer
Odd.
An even number plus an odd number has an odd sum.
Predict even and odd products
Choose the method: Look for an even factor before multiplying.
EZT practice question
Is 4 x 7 even or odd? What about 3 x 5?
Show the worked solution
- 4 is even, so 4 x 7 has an even factor.
- 3 and 5 are both odd, and odd x odd stays odd.
Answer: 4 x 7 = 28 is even (an even factor makes the product even); 3 x 5 = 15 is odd (odd x odd stays odd).
Check: 28 ends in 8 and 15 ends in 5.
Watch for this: An odd product needs every factor to be odd.
Now try it yourself
Is 6 x 9 even or odd?
Check your answer
Even.
The factor 6 is even, so the product is even.
Use parity for consecutive numbers
Choose the method: Notice that neighbours always contain one even and one odd.
EZT practice question
Is the sum of two consecutive numbers ever even?
Show the worked solution
- Consecutive numbers are one even and one odd.
- Even + odd is odd.
Answer: No - one is always even and the other odd, so the sum is always odd (14 + 15 = 29).
Check: Any neighbour pair, such as 20 and 21, gives an odd total.
Watch for this: Do not test only small pairs; the parity pattern covers every pair.
Now try it yourself
What is the parity of 50 + 51?
Check your answer
Odd.
50 is even and 51 is odd.
Use first-last pairs for a quick sum
Choose the method: Pair numbers from opposite ends and count the equal pairs.
EZT practice question
Add 1 + 2 + 3 + ... + 10 quickly.
Show the worked solution
- Pair first and last: 1 + 10 = 11, 2 + 9 = 11, and so on.
- There are five pairs, so 5 x 11 = 55.
Answer: Pair first and last: (1+10) + (2+9) + ... = 11 five times = 55.
Check: The formula gives 10 x 11 / 2 = 55.
Watch for this: There are five pairs, not ten pairs.
Now try it yourself
Use pairing to add 1 + 2 + ... + 12.
Check your answer
78.
Six pairs each make 13, and 6 x 13 = 78.
Connect odd sums with squares
Choose the method: Count how many odd numbers are being added.
EZT practice question
What is 1 + 3 + 5 + 7 + 9?
Show the worked solution
- These are the first five odd numbers.
- The sum of the first n odd numbers is n squared.
Answer: 25 = 5 x 5 - the sum of the first five odd numbers is 5 squared.
Check: 1 + 3 + 5 + 7 + 9 adds to 25 directly.
Watch for this: The square uses the count of odd terms, not the largest term.
Now try it yourself
What is the sum of the first six odd numbers?
Check your answer
36.
The first six odd numbers sum to 6 squared.
Test the two-digit reversal addition trick
Choose the method: Add the number and its reverse, then compare with 11 times the digit sum.
EZT practice question
Check the addition trick on 53.
Show the worked solution
- Reverse 53 to 35 and add: 53 + 35 = 88.
- The digit sum is 5 + 3 = 8, and 11 x 8 = 88.
Answer: 53 + 35 = 88 = 11 x 8, and 8 is 5 + 3 - the trick holds.
Check: In 10a + b and 10b + a, the sum is 11(a + b).
Watch for this: Use the sum of the digits for addition, not the difference.
Now try it yourself
Check the addition trick on 72.
Check your answer
72 + 27 = 99 = 11 x 9.
The digits add to 9.
Test the two-digit reversal subtraction trick
Choose the method: Subtract the smaller number from the larger, then compare with 9 times the digit difference.
EZT practice question
Check the subtraction trick on 61.
Show the worked solution
- Reverse 61 to 16 and subtract: 61 - 16 = 45.
- The digit difference is 6 - 1 = 5, and 9 x 5 = 45.
Answer: 61 - 16 = 45 = 9 x 5, and 5 is 6 - 1 - the trick holds.
Check: The tens and ones contributions leave 9 times the digit difference.
Watch for this: Use the positive difference between the digits.
Now try it yourself
Check the subtraction trick on 83.
Check your answer
83 - 38 = 45 = 9 x 5.
The digit difference is 5.
Check a palindrome and one reverse-add step
Choose the method: Read the digits in both directions before deciding.
EZT practice question
Is 343 a palindrome? What do you get from 68 after one reverse-and-add?
Show the worked solution
- 343 reads the same backwards.
- 68 + 86 = 154, which is not a palindrome yet.
Answer: 343 reads the same backwards, so yes; 68 + 86 = 154 (not yet a palindrome - another step gives 154 + 451 = 605, still not - keep playing!).
Check: 154 reversed is 451, so it is not a palindrome.
Watch for this: A number with repeated digits is not automatically a palindrome; the full order must match backwards.
Now try it yourself
Is 232 a palindrome?
Check your answer
Yes.
It reads the same forwards and backwards.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Even or odd: 99 + 99?
- Sum 1 + 2 + ... + 20 using the pairing trick.
- What is the sum of the first 8 odd numbers?
- Pick any two-digit number and test both reversal tricks.
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Questions about this practice page
- What are the rules for adding even and odd numbers?
- Even + even = even, odd + odd = even, and even + odd = odd - the last digit decides, so you never need the full sum.
- What is the quick way to add 1 to 100?
- Pair first and last - 101 fifty times, so 5050. The same trick gives 1 to n as n x (n+1) / 2.
- Why is a two-digit number plus its reverse always divisible by 11?
- The number is 10a + b and its reverse 10b + a; adding gives 11a + 11b = 11(a + b).
- What is a palindrome number?
- One that reads the same forwards and backwards, like 121 or 7337 - reversing and adding often produces one.
- Are these the NCERT exercise questions for Number Play?
- No. EZT pages are original practice on this chapter - use them to prepare for the textbook exercises, not as a substitute for your book.