# How Big? How Heavy?

## Overview

This chapter introduces the concepts of **volume** and **weight** through playful, activity-based learning. Children explore how to measure volume using marbles and coins and learn to estimate and calculate weight using real-life examples such as sacks of coins, matchboxes, and everyday objects. It builds foundational understanding of **units of volume (cm³, mL, L)** and **weight (g, kg)** through hands-on comparison, guesswork, and simple math.

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## Key Topics Covered

### 1. Understanding Volume Through Displacement

* Children learn that objects take up space by displacing water in a measuring glass.
* A marble dropped in water raises the level — this rise helps measure the object's volume.
* Informal units such as “marbles” are used to estimate volume.

**Activity:** Drop marbles into a glass, mark levels (e.g., 5 marbles, 10 marbles, etc.), and estimate the volume of small objects in terms of marbles.

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### 2. Making a Measuring Bottle

* Use marbles, coins, or syringes to create a measuring bottle.
* Mark levels at intervals (like 10 mL, 20 mL, up to 60 mL).
* Practice estimating and comparing volume in millilitres.

**Example:**

* 9 five-rupee coins = 10 mL
* 6 marbles = ? mL
* 16 one-rupee coins = ? mL

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### 3. Volume in Centimetre Cubes (cm³)

* A **centimetre cube** (1 cm × 1 cm × 1 cm) is used to estimate and measure volume.
* Children guess and then count how many such cubes will fit in books, matchboxes, or other objects.
* A matchbox volume is roughly **10 cm³**.

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### 4. Building with Matchboxes

* Students construct platforms using matchboxes and calculate volume in terms of number of matchboxes.
* Encourages spatial thinking and estimating capacity in standard units (cm³).

**Example:**

* 14 matchboxes in a layer × 4 layers = 56 matchboxes
* Volume = 56 matchboxes × 10 cm³ = 560 cm³

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### 5. Making and Measuring a Paper Cube

* Children fold 6 squares of paper to make a cube.
* Side of each square = 7 cm → Volume of cube = 7 × 7 × 7 = **343 cm³**
* Compares volume with other structures made of cm cubes or matchboxes.

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### 6. Comparing Volumes of Different Shapes

* Use old postcards folded into pipes of different shapes (triangular, square, etc.)
* Fill each pipe with sand to compare volumes.
* Encourages discovery of which shape can hold more with the same surface area.

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### 7. Understanding Weight and Units (g, kg)

* Introduces units of weight (grams, kilograms) using familiar objects like coins and food.
* 1 five-rupee coin = 9 g
* Bag weighing 9 kg contains 9000 ÷ 9 = **1000 coins**

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### 8. Estimating and Calculating Weight

* Children solve problems like:

* How many coins in a sack weighing 54 kg?
* How much do 3000 two-rupee coins weigh?

**Real-world Connection:** Trekking students reduce weight by drying vegetables.
E.g., 1 kg onions → 100 g when dried.

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### 9. Detecting Fake Notes by Weight

* Story of Shahid, a visually impaired bank employee, who senses a fake note bundle due to different weight.
* Introduces concept of tactile recognition and small differences in weight.

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## New Terms and Definitions

| Term | Definition |
| ---------------- | -------------------------------------------------------------------------- |
| Volume | The amount of space an object takes up |
| Displacement | Pushing water up when an object is put into it |
| Measuring bottle | A container used to measure liquid or object volume using known references |
| Centimetre cube | A small cube with all sides of 1 cm; used to measure volume (cm³) |
| Weight | How heavy something is; measured in grams (g) or kilograms (kg) |
| Kilogram (kg) | A unit of weight equal to 1000 grams |
| Gram (g) | A small unit of weight |
| Estimate | An educated guess or approximation |

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## Practice Questions

### 🟢 Easy (3 Questions)

**1.** If 9 five-rupee coins push up 10 mL of water, how much water will 18 coins push up?

**Answer:** 20 mL
**Explanation:** 9 coins = 10 mL → 18 coins = 2 × 10 = 20 mL

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**2.** A marble pushes up 2 mL of water. What is the volume of 5 marbles?

**Answer:** 10 mL
**Explanation:** 1 marble = 2 mL → 5 marbles = 5 × 2 = 10 mL

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**3.** If one 5-rupee coin weighs 9 g, what is the weight of 3 such coins?

**Answer:** 27 g
**Explanation:** 9 g × 3 = 27 g

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### 🟡 Medium (2 Questions)

**4.** A cube has a side of 5 cm. What is its volume?

**Answer:** 125 cm³
**Explanation:** Volume of a cube = side × side × side = 5 × 5 × 5 = 125 cm³

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**5.** You made a platform using 28 matchboxes. Each matchbox is 10 cm³. What is the total volume?

**Answer:** 280 cm³
**Explanation:** 28 × 10 = 280 cm³

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### 🔴 Difficult (3 Questions)

**6.** A bag of coins weighs 2 kg and 250 g. How many 5-rupee coins are there in the bag?

**Answer:** 250 coins
**Explanation:**
Convert weight to grams → 2 kg 250 g = 2250 g
Each coin = 9 g → 2250 ÷ 9 = 250

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**7.** A paper cube has volume 343 cm³. Another cube has twice the side length. What is the volume of the larger cube?

**Answer:** 2744 cm³
**Explanation:**
Side of larger cube = 2 × 7 = 14 cm
Volume = 14 × 14 × 14 = 2744 cm³

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**8.** You want to fill a box that can hold 1200 cm³ using cubes of 8 cm³ each. How many cubes do you need?

**Answer:** 150 cubes
**Explanation:** 1200 ÷ 8 = 150

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### 🔵 Very Difficult (2 Questions)

**9.** If 100 one-rupee coins weigh 485 g, how much will 10000 coins weigh?

**Answer:** 48 kg 500 g
**Explanation:**
100 coins = 485 g
10000 coins = (100×100) = 100 times heavier = 485 × 100 = 48,500 g = 48 kg 500 g

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**10.** A stage is built using 56 matchboxes. If 4 layers are used, how many matchboxes are in one layer? What are the possible dimensions (length × width) if one layer uses rectangular arrangement?

**Answer:** 14 matchboxes in each layer
**Explanation:** 56 ÷ 4 = 14.
Possible dimensions = 2 × 7 or 1 × 14, depending on arrangement.

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