Calendar Magic Aur Algebra Grids | Class 8 Maths Book 2 Ch 6

📘 Class 8 · Ganita Prakash Book 2Ch 6 · Algebra PlayPost 4 / 7⏱ 25–30 min

Calendar Magic Aur Algebra Grids 📅

IS POST MEIN

Pehle Yeh Aata Hai?Kahani Concept Deep Concept Examples Real Life Galti 10 MCQs FAQs Practice HOTS Olympiad Recap

✅ Pehle Yeh Aata Hai?

Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:

Calendar mein ek din ke neeche wala din kitna bada?
4a + 16 = 40 → a?
2 × 2 dabbe mein kitne numbers?

Answers dekho

Teeno sahi? Badhiya! Pyramid wala algebra yaad karo: Post 3.

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🎬 Kahani: Calendar Ka 2 × 2 Dabba

Priya ne deewar ke calendar pe Rohan se kaha: “Koi bhi 2 × 2 dabba (4 tareekhein) chuno, bas unka jod batao.”

Rohan: “40.” Priya: “Tumhare dabbe mein 6, 7, 13, 14 hain!” 📅

Rohan dang. Priya ne 2 second mein kaise bataaya? Algebra se!

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📖 Concept: Ek Letter Se Poora Dabba

Step 1: Dabba letter-number mein

Upar-baayein = a. Daayein = a + 1. Neeche (agla hafta) = a + 7, aur a + 8.

a	a + 1
a + 7	a + 8

Jod = 4a + 16.

Step 2: Jod se a

Jod 40: 4a + 16 = 40 → a = 6 → 6, 7, 13, 14 ✅. Jod 36: 4a = 20 → a = 5 → 5, 6, 12, 13.

WHY? Ek letter ne chaaron numbers ko jod diya; ek equation, ek jawab.

Step 3: Shortcut

Jod ÷ 4 − 4 = a. 40 ÷ 4 − 4 = 6 ✅

Step 4: Apni calendar trick

3 × 3 dabba: beech wala m, jod = 9m (har number m se jitna kam, uske saamne utna zyada). Jod 117 → m = 13. Ek line ke 3 din: 3a + 3. Ek column ke 3: 3a + 21.

Step 5: Algebra grids (shapes = numbers)

Chhote puzzle: har row mein shapes ke number jodo = aakhri number.

🔺	🔺	🔺	= 15
🔺	⭐	⭐	= 21
⭐	🔵	🔵	= 18

🔺 = 5. Phir 5 + 2⭐ = 21 → ⭐ = 8. Phir 8 + 2🔵 = 18 → 🔵 = 5. Ek-ek karke sab khula!

WHY yeh algebra? Shapes = letter-numbers; har row = ek equation.

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🔐 Deep Concept: Jod Hamesha 4 Ka Multiple Kyun?

4a + 16 = 4(a + 4), hamesha 4 se divide! To agar koi 2 × 2 dabbe ka jod 42 bataaye, aap turant keh sakte ho: “Jhooth!” 😄

Aur a + 4 = jod ÷ 4 = chaaron ka average, jo dabbe ke beech (a aur a + 8 ke beech) hai. Average yahan bhi santulan bindu (Ch 5)! 🔐

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✏️ Solved Examples

Example 1 (Easy): Jod 56. Dabba?

56 ÷ 4 − 4 = 10 → 10, 11, 17, 18.

WHY sahi hai? 10 + 11 + 17 + 18 = 56 ✅

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Example 2 (Medium): 3 × 3 dabba ka jod 135. Beech?

135 ÷ 9 = 15.

WHY sahi hai? 7, 8, 9, 14, 15, 16, 21, 22, 23 → 135 ✅

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Example 3 (NCERT style): Jod 36 ka 2 × 2 dabba?

4a + 16 = 36 → a = 5 → 5, 6, 12, 13.

WHY sahi hai? 36 ✅

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Priya ka mantra: “Jod ÷ 4, minus 4, aur dabba haazir!” 🎉

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🏠 Real Life Mein

📅 Calendar trick family ke saath.
🧩 Sudoku jaise number puzzles.
📊 Spreadsheet mein rows-columns ke jod.
🔢 Patterns pehchaanna (7 ka farak).

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🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
2 × 2 dabba	✅ 4a + 16	a = (jod − 16) ÷ 4
3 × 3 dabba	✅ 9m	m = beech
Jod 4 ka multiple nahi	❌ Galat jod	2 × 2 ke liye
Shapes puzzle	✅ Jis row mein ek hi shape, wahan se shuru	Ek-ek kholo

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❌→✅ Worked Mistake

Sawaal: 2 × 2 jod 48. Dabba?

❌ Galat: “48 ÷ 4 = 12, to 12, 13, 19, 20.”

Galti kya hai? 12 average hai, a nahi ❌

✅ Sahi: a = 12 − 4 = 8 → 8, 9, 15, 16 (jod 48 ✅).

Yaad rakho: a = jod ÷ 4 − 4.

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📝 10 MCQs

Q1. 2 × 2 jod formula?

(a) 4a + 16

(b) 4a

(c) 4a + 8

(d) a + 16

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q2. Jod 40 ka a?

(a) 6

(b) 10

(c) 4

(d) 8

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Average.
(c) galat: Nahi.
(d) galat: Nahi.

Q3. Jod 36?

(a) 5, 6, 12, 13

(b) 9, 10, 16, 17

(c) 4, 5, 11, 12

(d) 6, 7, 13, 14

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Nahi.
(c) galat: 32.
(d) galat: 40.

Q4. Kaun 2 × 2 jod mumkin nahi?

(a) 42

(b) 40

(c) 44

(d) 48

Solution dekho

Sahi jawab: (a)

(a) sahi: 4 ka multiple nahi ✅
(b) galat: Haan.
(c) galat: Haan.
(d) galat: Haan.

Q5. 3 × 3 jod 117, beech?

(a) 13

(b) 9

(c) 117

(d) 12

Solution dekho

Sahi jawab: (a)

(a) sahi: 117 ÷ 9 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q6. Calendar mein neeche wala?

(a) + 7

(b) + 1

(c) + 8

(d) + 6

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Daayein.
(c) galat: Tircha.
(d) galat: Nahi.

Q7. Shapes: 🔺🔺🔺 = 15?

(a) 5

(b) 15

(c) 3

(d) 45

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q8. 🔺 = 5, 🔺⭐⭐ = 21: ⭐?

(a) 8

(b) 16

(c) 21

(d) 5

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q9. Jod 56 ka dabba?

(a) 10, 11, 17, 18

(b) 14, 15, 21, 22

(c) 12, 13, 19, 20

(d) 9, 10, 16, 17

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Nahi.
(c) galat: 64.
(d) galat: 52.

Q10. Average (2 × 2)?

(a) a + 4

(b) a

(c) a + 8

(d) a + 16

Solution dekho

Sahi jawab: (a)

(a) sahi: (4a + 16) ÷ 4 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

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❓ FAQs (Bachchon Ke Asli Sawaal)

1. Kya mahine ke aakhir mein dabba chalega?

Haan, agar chaaron tareekhein usi mahine mein hon.

2. 3 × 3 mein 9m kyun?

Beech se har taraf barabar upar-neeche, cancel.

3. Tircha dabba?

Apna formula banao: a, a + 8, … algebra se.

4. Shapes puzzle kahan se shuru?

Jis row mein ek hi tarah ki shape ho.

5. Kya negative aa sakta?

Calendar mein nahi; galat jod ka sanket.

6. Algebra grid aur equations?

Ek hi cheez, alag roop.

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🏋️ Practice Zone (12 Sawaal)

Q1. Easy Jod 32: dabba?

Solution dekho

4, 5, 11, 12.

Q2. Easy Jod 60?

Solution dekho

11, 12, 18, 19.

Q3. Easy 3 × 3, beech 10: jod?

Solution dekho

90.

Q4. Easy Ek line ke 3 din (a, a+1, a+2) jod?

Solution dekho

3a + 3.

Q5. Medium Ek column ke 3 din jod 45. Upar wala?

Solution dekho

3a + 21 = 45 → 8.

Q6. Medium Line ke 3 din jod 48?

Solution dekho

3a + 3 = 48 → 15, 16, 17.

Q7. Medium Jod 50 (2 × 2) mumkin?

Solution dekho

50 ÷ 4 nahi poora → nahi.

Q8. NCERT style Apni calendar trick banao (koi shape).

Solution dekho

Jaise L-shape: a, a+7, a+14, a+15 → 4a + 36.

Q9. NCERT style Shapes: ⭐⭐ = 16, ⭐🔵 = 11. 🔵?

Solution dekho

⭐ = 8 → 🔵 = 3.

Q10. Medium 3 × 3 jod 162?

Solution dekho

m = 18.

Q11. Medium 2 × 2 ke tirchhe kone (a, a+8) ka jod vs (a+1, a+7)?

Solution dekho

Dono 2a + 8, barabar!

Q12. NCERT style Algebra grid ka ek apna banao.

Solution dekho

Khud karo!

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🧠 HOTS (Sochne Wale Sawaal)

Q1. 2 × 2 mein tirchhe kono ka guna: a(a+8) vs (a+1)(a+7)?

Solution dekho

a² + 8a vs a² + 8a + 7: farak hamesha 7!

Q2. Kya 3 × 3 ka jod 9 ka multiple hamesha?

Solution dekho

Haan, 9m.

Q3. Jod se 2 × 2 dabba, par calendar mein a + 1 agle hafte (Saturday) to?

Solution dekho

Trick tootegi; dabba hafte ke andar hona chahiye.

Q4. 4 × 4 dabba (upar-baayein a) ka jod?

Solution dekho

16a + 4 × (0+1+2+3) + 4 × (0+7+14+21) = 16a + 192.

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🏆 Olympiad Corner

Q1. 4 × 4 dabba jod 368: a?

Solution dekho

16a + 192 = 368 → a = 11.

Q2. 3 × 3 dabba mein kone ka jod?

Solution dekho

m−8, m−6, m+6, m+8 → 4m.

Q3. 2 × 2 ka guna-farak (tirchha) kyun 7?

Solution dekho

(a+1)(a+7) − a(a+8) = 7.

Q4. 3 × 3 dabba mein beech 15. Chaaron kone?

Solution dekho

m − 8, m − 6, m + 6, m + 8 → 7, 9, 21, 23.

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💗 CharuMam Motivation

Priya ne ek letter (a) se poore dabbe ka raaz khol diya. 📅

Ek chhoti si chaabi (key idea) kai taale kholti hai. Har chapter ki “chaabi” dhoondho, baaki aasaan! 🔑

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🟢 Master Recap

2 × 2: a, a + 1, a + 7, a + 8 → jod 4a + 16.
a = jod ÷ 4 − 4; jod hamesha 4 ka multiple.
3 × 3: jod = 9 × beech.
Algebra grids: shapes = letters, rows = equations.
Ek-ek karke kholo: jahan ek hi shape ho, wahan se.

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👉 Aage Kya?

Teen digits 2, 3, 5: kaise lagaayein ki guna sabse bada aaye? Agle post mein! ✖️

← Pichla: Post 3 — Number Pyramids 📚 Chapter 6 ke saare posts Agla: Post 5 — Sabse Bada Guna →

Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬

✅ Pehle Yeh Aata Hai?

🎬 Kahani: Calendar Ka 2 × 2 Dabba

📖 Concept: Ek Letter Se Poora Dabba

Step 1: Dabba letter-number mein

Step 2: Jod se a

Step 3: Shortcut

Step 4: Apni calendar trick

Step 5: Algebra grids (shapes = numbers)

🔐 Deep Concept: Jod Hamesha 4 Ka Multiple Kyun?

✏️ Solved Examples

🏠 Real Life Mein

🧭 Kab Use Karein, Kab Nahi

❌→✅ Worked Mistake

📝 10 MCQs

❓ FAQs (Bachchon Ke Asli Sawaal)

🏋️ Practice Zone (12 Sawaal)

🧠 HOTS (Sochne Wale Sawaal)

🏆 Olympiad Corner

💗 CharuMam Motivation

🟢 Master Recap

👉 Aage Kya?

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