Class 8 NCERT bridge course Answers Activity W 4.1 zigzag puzzle

Activities for Week  4 

Activity W 4.1: 

Teacher may ask students to play this puzzle. 

This is a zigzag puzzle with numbers 1, 2, 3 and 4. 

Your objective is to navigate through the grid, starting from the number 1 in the top-left corner. 

You must follow the numbers in sequential order, ensuring that each number is visited exactly once. 

 The path can move in horizontal, vertical, or diagonal directions but cannot cross itself.

let’s tackle this puzzle step by step!

We start at the 1 in the top-left corner (marked "START").

Step 1: Start at 1 (Row 1, Column 1).

Step 2: Find 2

From the start position, the closest 2 is diagonally down-right to (Row 2, Column 2).

Step 3: Find 3

From (2,2), move diagonally down-right again to (3,3), which is a 3.

Step 4: Find 4

From (3,3), move right to (3,4) where you’ll find 4.

Step 5: Find the next 1

From (3,4), move diagonally down-left to (4,3) where there's a 1.

Step 6: Find 2

From (4,3), move left to (4,2) for 2.

Step 7: Find 3

From (4,2), move up to (3,2) for 3.

Step 8: Find 4

From (3,2), move diagonally down-left to (4,1) for 4.

Step 9: Find 1

From (4,1), move down to (5,1) for 1.

Step 10: Find 2

From (5,1), move right to (5,2) for 2.

Step 11: Find 3

From (5,2), move right to (5,3) for 3.

Step 12: Find 4

From (5,3), move right to (5,4) for 4.

Step 13: Find 1

From (5,4), move diagonally down-left to (6,3) for 1.

Step 14: Find 2

From (6,3), move left to (6,2) for 2.

Step 15: Find 3

From (6,2), move down to (7,2) for 3.

Step 16: Find 4

From (7,2), move right to (7,3) for 4.

Step 17: Find 1

From (7,3), move right to (7,4) for 1.

Step 18: Find 2

From (7,4), move down to (8,4) for 2.

Step 19: Find 3

From (8,4), move left to (8,3) for 3.

Step 20: Find 4

From (8,3), move left to (8,2) for 4.

Step 21: Find 1

From (8,2), move down to (9,2) for 1.

Step 22: Find 2

From (9,2), move right to (9,3) for 2.

Step 23: Find 3

From (9,3), move right to (9,4) for 3.

Step 24: Find 4

From (9,4), move right to (9,5) for 4.

Step 25: Find 1 (Final — END!)

From (9,5), move right to (9,6) for the final 1 — marked END!

Puzzle solved!

  Class 8 NCERT bridge course Answers Activity W 3. 6 SOLVE THE GRID

 Students may be motivated to work on this puzzle. This will help them link different mathematical concepts

Fill in the missing numbers: 

1. The missing values are the whole numbers between 1 and 16. 

2. Each number is only used once. 

3. Each row is a math equation. 

4. Each colu6ath equation. 

Remember that multiplication and division are performed before addition and subtraction

• Third row, middle cell = 11.

• Last row result = 38.

• First column result = 9.

• Last row first number = 9.

• Bottom total = 19 for the last column.

• One row equals 98 (that’s high — so likely multiplication-heavy).

Another way

find more ways but follow the rules

Class 8 NCERT bridge course Answers Activity W 3. 5 Fun riddle

 Activity W 3.5 Fun riddle 

Students may be encouraged to solve this riddle and should be asked to explain their strategy to solve it. This can give them an idea about solving linear equations. If the following equations are true: Then solve these

1️⃣ 🌱 + 🌸 = 🦋
2️⃣ 🦋 - 🌱 = 🌸
3️⃣ 🦋 - 🌸  = 🌱

4️⃣ 🌸+ 🌱  - 🌸 =🌱

Let’s assign:

• 🌱 = p

• 🌸 = f

• 🦋 = b

Step 1: Solve the first two equations.

From Equation 1: p + f = b

From Equation 2: b - p = f

Step 2: Substitute Equation 1 into Equation 2.

Substitute b = p + f into Equation 2:

(p + f) - p = f
f = f

 This is always true, so the values depend on the third equation.

Step 3: Use the third equation.

From Equation 3:
b + f - p = p

Substitute b = p + f:

(p + f) + f - p = p
p + f + f - p = p
2f = p

Now substitute back:

If p = 2f,
then from Equation 1:

2f + f = b
so, b = 3f

So the values are:

• 🌱 (p) = 2f

• 🌸 (f) = f

• 🦋 (b) = 3f

Now solve the bottom part!

1️⃣ 🌱 + 🌱 + 🌸 = ?
= 2p + f
= 2(2f) + f = 4f + f = 5f

2️⃣ 🌱 - 🌸 = ?
= p - f = 2f - f = f

3️⃣ 🌱 + 🌸 - 🦋 = ?
= p + f - b
= 2f + f - 3f = 0

4️⃣ 🦋 - 🌱 = ?
= b - p = 3f - 2f = f

5️⃣ 🌸 + 🌱 - 🌱 = ?
= f + p - p = f

Final Answers:

1. 🌱 + 🌱 + 🌸 = 🦋 5f (depends on f)

2. 🌱 - 🌸 = 🌸 f

3. 🌱 + 🌸 - 🦋 = 0

4. 🦋 - 🌱 = 🌸

5. 🌸 + 🌱 - 🌱 = 🌸 f

We can also solve by assume values, like if 🌸 = 1, then:
🌱 = 2, 🦋 = 3 — and substitute!

TRY THIS!

🧠 Puzzle 1: Fruit Equation

🍎 + 🍎 + 🍌 = 12
🍌 + 🍇 = 8
🍎 + 🍇 = 10

Questions:
a) What is the value of each fruit?
b) 🍇 + 🍎 - 🍌 = ?

🧠 Puzzle 2: Animal Equation

🐶 + 🐱 = 14
🐱 + 🐰 = 10
🐶 - 🐰 = 6

Questions:
a) What is the value of 🐶, 🐱, and 🐰?
b) 🐶 + 🐱 + 🐰 = ?

🧠 Puzzle 3: Shape Equation

🔺 + 🔵 = 15
🔵 + 🟪 = 20
🔺 + 🟪 = 25

Questions:
a) What is the value of each shape?
b) 🔺 + 🔵 + 🟪 = ?

SOLUTIONS

🍎 Puzzle 1: Fruit Equation

Given:
1️⃣ 🍎 + 🍎 + 🍌 = 12
2️⃣ 🍌 + 🍇 = 8
3️⃣ 🍎 + 🍇 = 10

Solution:

From equation 1️⃣:
2🍎 + 🍌 = 12
So, 🍌 = 12 − 2🍎

Substitute into 2️⃣:
(12 − 2🍎) + 🍇 = 8
🍇 = 8 − (12 − 2🍎)
🍇 = 2🍎 − 4

Now substitute into 3️⃣:
🍎 + (2🍎 − 4) = 10
3🍎 = 14
🍎 = 14 ÷ 3 ≈ 4.67

But since the puzzle suggests whole numbers, let's double-check.
Actually, this puzzle seems set up for decimals or might have a typo — usually these are whole numbers.

👉 If you want, I can adjust the numbers slightly so they fit perfectly.

🐶 Puzzle 2: Animal Equation

Given:
1️⃣ 🐶 + 🐱 = 14
2️⃣ 🐱 + 🐰 = 10
3️⃣ 🐶 − 🐰 = 6

Solution:

From 1️⃣: 🐶 = 14 − 🐱
From 2️⃣: 🐰 = 10 − 🐱

Substitute into 3️⃣:
(14 − 🐱) − (10 − 🐱) = 6
14 − 🐱 − 10 + 🐱 = 6
4 = 6 — ❌ this is impossible!

So this puzzle needs correction — the values don't balance.

🔺 Puzzle 3: Shape Equation

Given:
1️⃣ 🔺 + 🔵 = 15
2️⃣ 🔵 + 🟪 = 20
3️⃣ 🔺 + 🟪 = 25

Solution:

From 1️⃣: 🔺 = 15 − 🔵
Substitute into 3️⃣:
(15 − 🔵) + 🟪 = 25
🟪 = 10 + 🔵

Now substitute 🟪 into 2️⃣:
🔵 + (10 + 🔵) = 20
2🔵 = 10
🔵 = 5

Now substitute 🔵 = 5 into:
🔺 = 15 − 5 = 10
🟪 = 10 + 5 = 15

✅ Final values:
🔺 = 10
🔵 = 5
🟪 = 15

Extra Question: 🔺 + 🔵 + 🟪 = 10 + 5 + 15 = 30

Class 8 NCERT bridge course Answers Activity W 3. 4: Packing a Suitcase

Activity W 3.4: Packing a Suitcase

 In this activity, students may be made to explore the concept of volume by packing objects into a given space, helping them understand how shape, size and arrangement affect capacity. 

Material Required 

 A box (representing a suitcase) 

Various small objects (for example, cubes, balls, books, folded paper, toy blocks, foam, pieces) 

 Paper and pencils for recording observations.

 Step 1: Observation & Thinking

 Show students the box (supposed to be a suitcase) and the small objects. 

Ask: 

Q: What do you think will happen if we try to fit all these objects into the box?

ANSWER: 

Some objects will fit, but not all of them, because the box has limited space.

 Q: Will all the objects fit? Why or why not?

A: No, all the objects may not fit because each object takes up space and the box has a fixed volume.

 Q: What do we need to consider while packing a suitcase in real life?

A: We need to consider the size, shape, and arrangement of objects so that they fit well and make full use of the space.

Step 2: Exploration During Packing

 Divide the students into small groups and give each group a box and a set of objects. 

 Ask them to try different ways of packing the objects inside the box. 

Encourage them to think critically by asking them: 

 Q: Which objects fit easily and why?

A: Small or regularly shaped objects (like cubes or folded paper) fit easily because they can be arranged neatly without leaving gaps.

Q: Which objects take up the most space?

A: Large or round objects (like balls) take up more space because their shape leaves gaps around them when packed.

 Q: Does the order or arrangement of the objects affect how much fits?

A: Yes! If objects are arranged properly, more items can fit. Poor arrangement wastes space.

 Step 3: Counting and Understanding Volume 

 Let the students count the objects they successfully fit into the box.

 Ask them to remove the objects and estimate which object has more space and which has less. 

 Introduce the idea of volume as the total space an object occupies. 

 Explain how different shapes and arrangements affect and how space/volume of the box/suitcase is used. 

How Different Shapes and Arrangements Affect Space and Volume in a Box or Suitcase

The shape of an object and the way it is arranged inside a box or suitcase decides how much space is used and how many objects can fit.

• Shapes:
  Objects that have flat sides, like cubes or books, fit together tightly with less empty space in between.
  Objects with curved or round shapes, like balls, leave gaps around them when packed — so even though the object itself is small, it can waste space because of the gaps.

• Arrangements:
  If objects are arranged neatly, like placing big or flat items first and filling the gaps with smaller ones, the space is used more wisely and more things can fit.
  But if objects are placed randomly or carelessly, a lot of empty space gets wasted, even though the total volume of the box stays the same.

In short:
The volume of the box doesn’t change, but the way we choose the shape of objects and the way we arrange them makes a big difference in how much we can pack into the box.

This is the same reason why, in real life, packing a suitcase properly, arranging groceries, or designing storage shelves always needs smart use of space!

Ask: 

Q: If two objects have the same height and width but different shapes, do they take up the same amount of space?

A: Not always. Shape affects how much space is used. Some shapes leave gaps even if their height and width are the same. 

Q: If we had a bigger box, would we be able to fit double the objects? Why or why not?

A: Not always. It depends on how the objects are arranged. Even in a bigger box, bad arrangement can waste space.

Step 4: Real-Life Connection 

 Discuss how this applies to real-life situations, such as: 

 Packing a suitcase efficiently for travel 

 Fitting groceries into a bag or fridge 

Storing books in a bookshelf 

Real-Life Applications of Shape, Arrangement, and Volume

Understanding how shapes and arrangements affect the use of space is very useful in daily life! Here are some examples:

🧳 Packing a Suitcase for Travel
When you pack for a trip, you can’t just throw clothes and things into a suitcase randomly.
If you fold clothes neatly and place flat or large items first, then fill small gaps with socks, belts, or chargers, you can fit more items.
Arranging items properly saves space and prevents the suitcase from overflowing!

🛒 Fitting Groceries into a Bag or Fridge
When placing groceries into a shopping bag or fridge, the shape of the items matters.

• Boxes and cartons stack easily because of their flat sides.

• Round fruits or bottles leave gaps, so you must arrange them smartly to use the space fully.
  Using the right order and arrangement helps fit more groceries into the same bag or fridge.

📚 Storing Books in a Bookshelf
Books are usually rectangular, so they fit neatly side by side on a shelf.
If books are placed upright, one after another, the shelf holds more books. But if books are placed lying flat or randomly, there’s wasted space, and fewer books will fit.
So, the shape of books and arrangement help use the full space of the shelf.

Summary:

In real life, understanding volume and arrangement helps us organize things better, save space, and carry more without wasting room — whether it’s in bags, suitcases, shelves, or storage rooms!

 Ask: 

 Q: Why is understanding volume important in everyday life?

A: Understanding volume helps us pack, store, and arrange things efficiently — like when packing luggage, filling a fridge, or stacking boxes. 

Q: How do packers or architects use the idea of volume to maximize space?

A: Packers arrange items to fit as many as possible, using the least space. Architects design rooms, shelves, and storage to hold more things comfortably by calculating the volume.

 Reflections 

Summarise that volume is the amount of space an object takes up. 

Reflection Summary

Volume means the total space an object occupies.
Different shapes and arrangements affect how well things fit in a given space.
This helps in real-life situations like:

• Packing for a trip

• Stacking books or boxes

• Designing shelves, rooms, and storage spaces.

Also, different shapes and arrangements can affect how things fit together in a given box. 

 Encourage students to think about other real-life situations, where understanding volume is useful 

(for example, arranging furniture, stacking boxes, designing storage spaces). 

 In each of the above steps, teachers may frame more questions that would not only lead to the concept of volume but also allow students to play with this idea joyfully. 

 Students may also be allowed to frame questions and ask other groups or students

Fun & Curious Questions for Exploring Volume

While Packing a Suitcase:

1️⃣ If you fold clothes smaller, can you fit more in the suitcase? Why?
✅ Answer: Yes! Folding clothes reduces their shape size, allowing them to fit more neatly and take up less space — so more clothes fit.

2️⃣ If two objects are the same weight, do they always take up the same space?
✅ Answer: No. Weight and volume are different. A heavy metal ball and a pile of feathers could weigh the same but take up very different amounts of space.

3️⃣ Can you fit more soft things like clothes or hard things like toys into the suitcase? Why?
✅ Answer: Soft things like clothes can be squeezed and folded, so usually more soft things can fit compared to hard, rigid toys.

4️⃣ Does changing the order of packing make more space or less space?
✅ Answer: Changing the order can create more space. Packing flat items first and placing smaller ones in gaps uses space more efficiently.

5️⃣ If the suitcase was twice as tall, would it hold twice as many things?
✅ Answer: Yes, if the base area stays the same, doubling the height would double the volume, so it could hold twice as many items.

🛒 While Fitting Groceries in a Bag:

1️⃣ Which type of items take more space — round fruits or flat boxes?
✅ Answer: Round fruits usually waste space between them, while flat boxes stack better and use space more efficiently.

2️⃣ Can you fit more if you remove the packaging from items? Why or why not?
✅ Answer: Yes, packaging often adds extra space around items. Removing it can make the items fit better.

3️⃣ Why do shopkeepers arrange items neatly on shelves?
✅ Answer: Neat arrangement saves space and makes it easier to find and display more products.

4️⃣ If all the items were packed in cube shapes, would you save more space?
✅ Answer: Yes, cubes fit together perfectly without gaps, so space is used most efficiently.

5️⃣ Why do we sometimes use big bags even when the items are few?
✅ Answer: Sometimes the shape of the items is odd, or they are fragile and need space, even if they are few.

📚 While Storing Books in a Bookshelf:

1️⃣ Which way do books take less space — standing or lying flat? Why?
✅ Answer: Standing books side by side usually uses less space because there are fewer gaps compared to stacking them flat.

2️⃣ If the shelf was made deeper, would you be able to store double the books?
✅ Answer: If the books fit perfectly, yes! A deeper shelf could hold more rows of books, depending on their size.

3️⃣ Can a shelf with less height hold more books if the books are smaller?
✅ Answer: Yes! If books are shorter in height, even a low shelf can hold more books in total.

4️⃣ Do all books with the same height and width take up the same volume? Why not?
✅ Answer: No. Thickness also matters — two books of the same height and width could have different thickness, so their volumes would differ.

5️⃣ How do libraries save space when arranging thousands of books?
✅ Answer: By arranging books upright, using adjustable shelves, and grouping similar-sized books together to reduce gaps.

Summary:

Understanding the relationship between shape, size, arrangement, and volume helps us use space wisely — whether packing for travel, storing groceries, arranging books, or designing storage spaces!

Participation of Special Children 

 Use lightweight objects, like foam blocks or paper cubes that are easy to grasp. 

 Ensure that materials are placed at an accessible the height for students using wheelchairs. 

 Allow students to work in pairs or small groups, so tasks can be shared based on ability and comfort. 

 Encourage discussions, where all students share their ideas

Student Challenge Questions:

1. Can you create your own object-packing puzzle for another group?

2. What’s the smallest object in the room that takes up the most space compared to its weight?

3. Can you think of a place where volume matters more than area? (e.g. water tank, swimming pool)

4. If two containers have the same shape but different sizes, how does their volume compare?

5. Why is it important for architects and designers to understand volume when building houses or rooms?

1️⃣ Can you create your own object-packing puzzle for another group?
✅ Answer: Yes! You can collect different-shaped classroom items like erasers, pencils, chalk boxes, and toy blocks. Give them to another group and challenge them to fit all the items into a box, bag, or container using the least amount of space. The puzzle can include rules, like "no stacking" or "must fit in 2 minutes."

2️⃣ What’s the smallest object in the room that takes up the most space compared to its weight?
✅ Answer: A balloon or a foam ball!
A balloon is very light but takes up a lot of space because it’s full of air. Foam blocks are also light but big in size.

3️⃣ Can you think of a place where volume matters more than area? (e.g., water tank, swimming pool)
✅ Answer:

• Water tanks — the more volume, the more water can be stored.

• Swimming pools — the depth adds volume so people can swim.

• Shipping containers — need enough volume to store lots of goods.

• Fridge or cupboard — the inside space (volume) matters more than the outside area.

4️⃣ If two containers have the same shape but different sizes, how does their volume compare?
✅ Answer: The bigger container will have more volume even if the shape is the same.
If one is a scaled-up version of the other, the volume increases much faster than the size — it grows in all three dimensions (length, width, and height).

5️⃣ Why is it important for architects and designers to understand volume when building houses or rooms?
✅ Answer:

• They need to calculate the space for people, furniture, and air circulation.

• Knowing volume helps design rooms that are comfortable, safe, and useful.

• It also helps with heating, cooling, and lighting — a room that looks big in area might feel small if the volume is low (for example, low ceiling).

• Storage spaces like cupboards, shelves, and attics are designed by understanding volume.