Number Play Class 7 Maths Worksheet with Answers Chapter 6

Ganita Prakash Part-I, Grade 7, Textbook of Mathematics – Chapter 6 is titled “Number Play”. This chapter is about spotting patterns in numbers and thinking smartly. It has very little to do with not hard calculations. Children line up by height, cards are added to make a target, grids turn into magic squares, and letters hide behind digits. The worksheet below covers every key idea from the chapter. The main ones are:

• Number sequences from height arrangements
• Parity – odd and even numbers
• Parity of sums, differences and products
• Sums in grids and magic squares
• Virahanka–Fibonacci numbers
• Cryptarithms (digits in disguise)

Keep these important formulas ready before you start:

• nth even number = 2n
• nth odd number = 2n − 1
• even + even = even, odd + odd = even, even + odd = odd
• Magic square with 1–9: magic sum = 15 and the centre number = 5
• Virahanka–Fibonacci rule: next number = sum of the two numbers before it (1, 2, 3, 5, 8, 13, 21, 34, …)

Learn one small trick and many questions become easy. To check if a sum is odd or even, you don’t need to add – just count how many odd numbers are in it. Solve the problems in the order given, from simple to tricky, and you will build confidence. The questions are grouped into four levels – Basic, Standard, Advanced, and HOTS – and a full answer key is given at the end.

Class 7 Maths Worksheet – Chapter 6: Number Play

Basic

1. State whether each number is odd or even:
   • 248
   • 1,357
   • 9,990
   • 4,001
2. Find the parity of each sum without adding the numbers:
   • Even + Even
   • Odd + Odd
   • Even + Odd
   • Odd + Odd + Odd
3. Find the parity of each difference:
   • Even − Even
   • Odd − Odd
   • Even − Odd
   • Odd − Even
4. Find the parity of the number of small squares in each grid:
   • 15 × 21
   • 24 × 37
   • 82 × 14
   • 101 × 99
5. Write the:
   • 15th even number
   • 20th odd number
   • 50th even number
   • 75th odd number
6. Fill in the blanks:
   • The nth even number is ______
   • The nth odd number is ______
   • An expression that always gives an even number is ______
   • An expression that always gives an odd number is ______
7. A light bulb is switched ON. It is toggled:
   • 16 times
   • 37 times
   • 100 times

   State whether the bulb will finally be ON or OFF in each case.

Standard

1. Find the parity of the following products without multiplying:
   • 37 × 45
   • 64 × 19
   • 125 × 204
   • 91 × 73 × 28
2. Decide whether each statement is Always True, Only Sometimes True, or Never True:
   • If a person says “0” in the height arrangement, they are the tallest in the group.
   • If a person is the tallest, they say “0”.
   • The first person in a line always says “0”.
   • A person standing in the middle of a line can never say “0”.
3. Can five odd numbers have an even sum? Can six odd numbers have an even sum?
   Explain using parity.
4. Two siblings were born exactly one year apart. Can the sum of their ages be:
   • 47
   • 68
   • 101

   Give reasons.

5. Complete the magic square using the numbers 1 to 9 exactly once:

   8	1	6
   3	5	?
   ?	?	2

6. Find the magic sum of a 3 × 3 magic square made using the numbers 1 to 9.
   What is the sum of all the row sums?
7. Continue the Virahāṅka sequence and write the next four terms:
   
   1, 2, 3, 5, 8, 13, 21, 34, 55, …

Advance

1. Write the parity of each expression for any whole number n:
   • 2n
   • 2n − 1
   • 4n + 6
   • 5n + 2
2. Find the parity of the sum of:
   • The numbers from 1 to 50
   • The numbers from 1 to 99
   • The first 25 odd numbers
3. A grid has 135 rows and 654 columns. Without finding the total number of squares, state whether the number of small squares is odd or even.
   What condition must a rectangular grid satisfy to have an odd number of small squares?
4. Create a magic square using the nine consecutive numbers from 16 to 24.
   Find its magic sum.
5. In a 3 × 3 magic square, the centre number is 20. Write one possible magic square and state its magic sum.
6. Two consecutive Virahāṅka numbers are 377 and 610.
   Find:
   • The next two terms
   • The previous two terms
7. Angaan can climb one or two steps at a time. How many different ways can he climb a staircase with:
   • 4 steps
   • 5 steps
   • 8 steps

HOTS

1. Lakpa has an odd number of ₹1 coins, an odd number of ₹5 coins and an even number of ₹10 coins.
   Can the total value of his coins be ₹205? Explain using parity.
2. A book has loose sheets, with two page numbers on each sheet. Can the sum of the page numbers on 50 loose sheets be 6000?
   Explain using odd and even numbers.
3. A 3 × 3 magic square has magic sum 15. If 4 is added to every entry, what is the new magic sum?
   If every entry is doubled instead, what is the new magic sum?
4. Make a 3 × 3 magic square with magic sum 0. At least one number must be negative, and all entries cannot be zero.
5. Without calculating the exact values, identify which statements are true:
   • 4m − 1 always gives an odd number.
   • 6j − 4 gives all even numbers.
   • 2p + 1 and 2q − 1 both describe odd numbers.
   • 2f + 3 can give both odd and even numbers.
6. The parity pattern in the Virahāṅka sequence repeats as Odd, Even, Odd.
   What is the parity of:
   • The 20th term
   • The 27th term
   • The 100th term
7. A number is the sum of three consecutive whole numbers.
   Can the sum be:
   • 51
   • 52
   • 99

   Find the three numbers wherever possible.

Answer Key

Basic – Answers

1. • 248: Even
   • 1,357: Odd
   • 9,990: Even
   • 4,001: Odd
2. • Even + Even = Even
   • Odd + Odd = Even
   • Even + Odd = Odd
   • Odd + Odd + Odd = Odd
3. • Even − Even = Even
   • Odd − Odd = Even
   • Even − Odd = Odd
   • Odd − Even = Odd
4. • 15 × 21 = Odd
   • 24 × 37 = Even
   • 82 × 14 = Even
   • 101 × 99 = Odd

   Hint: A product is odd only when every factor is odd.

5. • 15th even number = 30
   • 20th odd number = 39
   • 50th even number = 100
   • 75th odd number = 149
6. • nth even number = 2n
   • nth odd number = 2n − 1
   • Always even = 2n
   • Always odd = 2n + 1
7. • 16 toggles: ON
   • 37 toggles: OFF
   • 100 toggles: ON

   Hint: An even number of toggles returns the bulb to its original state.

Standard – Answers

1. • 37 × 45 = Odd
   • 64 × 19 = Even
   • 125 × 204 = Even
   • 91 × 73 × 28 = Even
2. • If a person says 0, they are tallest: Only Sometimes True
   • If a person is tallest, they say 0: Always True
   • The first person always says 0: Always True
   • A middle person can never say 0: Only Sometimes True
3. Five odd numbers cannot have an even sum.
   Six odd numbers can have an even sum.
   • Hint: An odd number of odd addends gives an odd sum. An even number of odd addends gives an even sum.
4. • 47: Possible, for example 23 and 24.
   • 68: Not possible.
   • 101: Possible, for example 50 and 51.

   Hint: Consecutive numbers consist of one odd and one even number, so their sum is always odd.

5. 8	1	6
   3	5	7
   4	9	2

   Magic sum = 15

6. Magic sum = 15
   Sum of all row sums = 45
   • Hint: 1 + 2 + 3 + … + 9 = 45.
7. 89, 144, 233, 377
   • Hint: Each term is the sum of the previous two terms.

Advance – Answers

1. • 2n = Even
   • 2n − 1 = Odd
   • 4n + 6 = Even
   • 5n + 2 = Odd or even, depending on n
2. • Sum from 1 to 50 = Odd
   • Sum from 1 to 99 = Even
   • Sum of first 25 odd numbers = Odd
3. The number of small squares is even.
   A rectangular grid has an odd number of small squares only when both its dimensions are odd.

4. 23	16	21
   18	20	22
   19	24	17

   Magic sum = 60

5. 23	16	21
   18	20	22
   19	24	17

   Magic sum = 60

6. Next two terms: 987 and 1597
   Previous two terms: 144 and 233
   • Hint: 377 + 610 = 987; 610 + 987 = 1597. Work backwards by subtraction.
7. • 4 steps: 5 ways
   • 5 steps: 8 ways
   • 8 steps: 34 ways

HOTS – Answers

1. No, the total cannot be ₹205.
   • Hint: Odd number of ₹1 coins gives an odd amount. Odd number of ₹5 coins also gives an odd amount. Their sum is even. Even number of ₹10 coins gives an even amount. So the final total must be even.
2. Yes, it is possible.
   • Hint: Each sheet has one odd and one even page number, so the sum on each sheet is odd. The sum of 50 odd numbers is even. Since 6000 is even, it is possible.
3. • Adding 4 to every entry: New magic sum = 15 + (3 × 4) = 27
   • Doubling every entry: New magic sum = 15 × 2 = 30

4. 3	−4	1
   −2	0	2
   −1	4	−3

   Every row, column and diagonal has sum 0.

5. True statements:
   • 4m − 1 always gives an odd number.
   • 2p + 1 and 2q − 1 both describe odd numbers.

   False statements:

   • 6j − 4 does not give all even numbers.
   • 2f + 3 always gives an odd number.
6. • 20th term: Odd
   • 27th term: Odd
   • 100th term: Odd
   • Hint: Terms in positions 2, 5, 8, 11, … are even. These positions leave remainder 2 when divided by 3.
7. • 51: Possible: 16, 17 and 18
   • 52: Not possible
   • 99: Possible: 32, 33 and 34

   Hint: The sum of three consecutive numbers is always divisible by 3.

Other Class 7 Maths worksheet

Ganita Prakash Part-I, Grade 7

• Large Numbers Around Us Class 7 Maths Worksheet
• Arithmetic Expressions Class 7 Maths Worksheet
• A Peek Beyond the Point Class 7 Maths Worksheet
• Number Play Class 7 Maths Worksheet
• Working with Fractions Class 7 Maths Worksheet

Ganita Prakash Part-II, Grade 7

• Operations with Integers Class 7 Maths Worksheet
• Another Peek Beyond the Point Class 7 Maths Worksheet
• Finding the Unknown Class 7 Maths Worksheet

Back to all Class 7 Maths Worksheets