Class 8 NCERT bridge course Answers Activity W 3.2 Let’s Brainstorm

 Activity W 3.2 Let’s Brainstorm 

 Students may be asked to solve the following puzzles either in groups or individually.

 They may explain their strategy of obtaining the result. 

Let’s Brainstorm 

Puzzle 1: Symbol Grid

1. The grid below has symbols that contain a whole number value less than 10. 

Each symbol has its own value. 

The numbers you see at the end of each row and column are the sums of the figures’ values for that row or column.

Can you find out the value of each symbol ? 

ANSWER:

Let’s name the shapes:

• 🟦 Pentagon = P

• 🔺 Triangle = T

• ⭐ Star = S

• ➕ Plus = C

And solve!

Row equations:1️⃣ 

1. P+T+P+S=15

2. C+S+P+S=23

3.T+C+T+?=16

4. S+T+?+P=14

Column equations:

1. P+C+T+S=20

2. T+S+C+T=24

3. P+P+T+?=7

4. S+S+?+P=17

SOLVE

From Row 3 and Column 3, the missing symbol must be the same in both — let’s call it X for now.

Let’s focus on easy rows:

Row 3:  T+C+T+X=16

Row 4:   S+T+X+P=14

Col 3:  P+P+T+X=7

Let’s assume X = 0 to test:

From Col 3:   𝑃+P+T=7

From Row 3:  T+C+T=16

So  2T+C=16.

From Col 1: P+C+T+S=20.

And from Row 1: 2P+T+S=15.

From Row 3:  2T+C=16

From Col 3:  2P+T=7

From Row 4: S+T+P=14 (since X=0)

Now solving this small system:

From (2)  2P+T=7 → T=7−2P

Substitute into (1):

2(7−2P)+C=16

14−4P+C=16

C=4P+2.

Now substitute into Col 1:

P+C+T+S=20.

Substitute 

C=4P+2 and 

T=7−2P:

P+(4P+2)+(7−2P)+S=20

Simplify:

P+4P+2+7−2P+S=20

3P+9+S=20

S=11−3P.

If  P=1: 

S=11−3(1)=8

T=7−2(1)=5

C=4(1)+2=6

Now check Row 2:

C+S+P+S=23

6+8+1+8=23 

SOLUTION:

• 🟦 Pentagon P=1
• 🔺 Triangle T= 5
• ⭐ Star  S = 8
• ➕ Plus C = 6

Puzzle 2: Symbol Equation

2. Here, you are given two representations, where symbols have been used. 

Each symbol represents a numeric value. Find the value of each symbol.

SOLUTION:

Given the equations:

• • 🟦 Blue Square = S

  • 🔺 Orange Triangle = T

  • 🟡 Yellow Circle = C

  • ⭐ Star = R

EQUATION 1:  S+S+S=15 --> 3S = 15 --> S = 5

EQUATION 2:  T+T+S=13 -->  2T + 5 = 13 --> 2T = 8 --> T = 4

EQUATION 3 : T+C+S=15 --> 4 + C + 5 = 15 --> C = 15 - 9=6

EQUATION 4: C+C+S=?

EQUATION 5: C + T + T = ?

EQUATION 6 : C + T = 8

EQUATION 7: C + T = 4

EQUATION 8 : R + S =12 --> R + 5 = 12 --> R = 12 -5 =7

EQUATION 9 : R + S = S

EQUATION 10 : S + S = R --> 2S = R

SOLUTION:

🟦 Blue Square (S)

= 5

🔺 Orange Triangle (T)

= 4

🟡 Yellow Circle (C) =

6

⭐ Star (R)

= 12 - 5 = 7

🟡 + 🟡 + 🟦 = 6 + 6 + 5 = 17

🟡 + 🔺+ 🔺 = 6 + 4 + 4 = 14

Puzzle 3: Make 5+5+5 = 550 True

3. Make the following equation true by drawing/putting/writing a single line.

SOLUTION : 

 Just draw a slanted line on the first "+" to turn it into 4:

545 + 5 = 550! 

Puzzle 4:Roman Numeral Trick 

What should be added to IX to make six?

Add S in front of IX to form SIX.
So the answer is: Add ‘S’! 

Teachers may try to find some more such puzzles that will engage students in the process of exploration

Puzzle 1: Symbol Sums

Symbol	Meaning
🍎 Apple = ?
🍌 Banana = ?
🍇 Grapes = ?

Equations:

1. 🍎 + 🍎 + 🍎 = 18

2. 🍌 + 🍎 + 🍌 = 16

3. 🍇 + 🍇 + 🍎 = 20

Find the value of each fruit!

Solution:

1. 🍎 + 🍎 + 🍎 = 18 → 🍎 = 6

2. 🍌 + 6 + 🍌 = 16 → 2🍌 = 10 → 🍌 = 5

3. 🍇 + 🍇 + 6 = 20 → 2🍇 = 14 → 🍇 = 7

Final Answer:
🍎 = 6, 🍌 = 5, 🍇 = 7.

Puzzle 2: Number Logic

Symbol	Meaning
🐾 Paw = ?
🐟 Fish = ?
🦴 Bone = ?

Equations:

1. 🐾 + 🐾 + 🐟 = 22

2. 🐟 + 🦴 + 🦴 = 14

3. 🐾 + 🦴 = 13

Find the value of 🐾, 🐟, 🦴.

Solution:

From (3):
🐾 + 🦴 = 13 → 🦴 = 13 - 🐾.

Substitute into (2):
🐟 + 2(13 - 🐾) = 14
Simplify and solve using substitution or trial.
For example:
If 🐾 = 8, 🦴 = 5.

Now check in (1):
8 + 8 + 🐟 = 22 → 🐟 = 6.

 So final values:
🐾 = 8, 🐟 = 6, 🦴 = 5.

Puzzle 3: Matchstick Equation

Make the equation correct by moving 1 matchstick:

6 + 4 = 9  

Solution:
Move one stick from "6" to make it "5":

5 + 4 = 9