Mathematics: Class 4 — Chapter 8: Weigh It, Pour It

8.1 Introduction to Weight

In Grade 3, we learnt about measuring weight and capacity. Let us explore more about measuring weight and capacity using standard units like kilograms (kg) and grams (g).

8.1.1 Fun at Vegetable Market!

Rita and Shabnam went to the market to buy some fruits and vegetables. They observed the vegetable seller weighing vegetables using a pan balance.

  • How do we compare the weights of different animals or objects?
  • What will be the weight of a half pumpkin if a whole pumpkin is balanced with certain weights?

8.1.2 Estimating and Verifying Weights

We can estimate whether the weight of common fruits and vegetables is less than or more than $1\text{ kg}$, and then verify using a weighing balance:

  • 6 Bananas
  • 5 Potatoes
  • 10 Tomatoes
  • 15 Onions

8.1.3 Grams and Kilograms

We often write kg for kilogram and g for gram.

  • $1\text{ kg} = 1000\text{ g}$
  • $2\text{ packets of } 500\text{ g} = 1000\text{ g} = 1\text{ kg}$
  • So, $1\text{ packet of } 500\text{ g} = \frac{1}{2}\text{ kg}$
  • $4\text{ packets of } 250\text{ g} = 1000\text{ g} = 1\text{ kg}$
  • So, $1\text{ packet of } 250\text{ g} = \frac{1}{4}\text{ kg}$
  • $10\text{ packets of } 100\text{ g} = 1000\text{ g} = 1\text{ kg}$

8.1.4 Balancing Weights

Understanding relationships between different weights:

  • How many $250\text{ g}$ packets will balance one $500\text{ g}$ packet?
    Answer: $2$ packets, because $250\text{ g} = \frac{1}{2} \text{ of } 500\text{ g}$.
  • Pan Balance Tilt: A pan balance tilts towards the heavier side. If one side has $1\text{ kg}$ and the other has $4$ packets of $200\text{ g}$ ($800\text{ g}$), the balance tilts towards the $1\text{ kg}$ side.
8.2 Weighing in Everyday Life

8.2.1 Choosing the Right Unit

Depending on the weight of an object, we choose an appropriate unit of measurement:

  • Kilograms (kg): Used for heavier objects like a newborn baby, a table, a refrigerator, or a sack of wheat.
  • Grams (g): Used for lighter objects like a pen, a leaf, a sharpener, a geometry box, or a wristwatch.

8.2.2 Sweet Boxes Problem

Mr. Shrinathan, a sweet shop owner, has orders for $1\text{ kg}$ of Kaju-katli. Let's calculate the number of boxes needed for different box capacities:

  • For boxes of $500\text{ g}$ each: $\frac{1000\text{ g}}{500\text{ g}} = 2\text{ boxes}$
  • For boxes of $250\text{ g}$ each: $\frac{1000\text{ g}}{250\text{ g}} = 4\text{ boxes}$
  • For boxes of $100\text{ g}$ each: $\frac{1000\text{ g}}{100\text{ g}} = 10\text{ boxes}$
  • For boxes of $50\text{ g}$ each: $\frac{1000\text{ g}}{50\text{ g}} = 20\text{ boxes}$

8.2.3 Weighing Machines and Estimation

Different types of weighing machines are used for different purposes (e.g., spring balance, platform balance, digital weighing scale, baby weighing scale).

Let's match some common objects with their estimated weights:

  • A cat: $3\text{ kg to } 5\text{ kg}$
  • An elephant: $\text{More than } 1000\text{ kg}$
  • A 1-litre filled bottle: $800\text{ g to } 1000\text{ g}$ (approx. $1\text{ kg}$)
  • A tiger: $150\text{ kg to } 300\text{ kg}$
  • An empty gas cylinder: $15\text{ kg}$
  • A pen: $10\text{ g to } 15\text{ g}$
  • A leaf: $1\text{ g to } 5\text{ g}$
  • A wooden chair: $6\text{ kg to } 10\text{ kg}$

8.2.4 Do You Know?

Mirabai Chanu is an Indian weightlifter. She won the silver medal at the 2020 Tokyo Olympics in the Women's $49\text{ kg}$ event. She lifted a total of $202\text{ kg}$.

8.3 Measuring Capacity

Capacity is the amount of liquid a container can hold. The standard units of capacity are litres (l) and millilitres (ml).

8.3.1 Litres and Millilitres

We often write l for litre and ml for millilitre.

  • $1\text{ l} = 1000\text{ ml}$
  • $2\text{ bottles of } 500\text{ ml} = 1000\text{ ml} = 1\text{ l}$
  • $4\text{ bottles of } 250\text{ ml} = 1000\text{ ml} = 1\text{ l}$
  • $10\text{ bottles of } 100\text{ ml} = 1000\text{ ml} = 1\text{ l}$

8.3.2 Fractional Capacities

  • $250\text{ ml in } \frac{1}{2}\text{ l} = 2\text{ times}$ (since $\frac{1}{2}\text{ l} = 500\text{ ml}$)
  • $250\text{ ml in } 750\text{ ml} = 3\text{ times}$
  • $100\text{ ml in } \frac{1}{2}\text{ l} = 5\text{ times}$
  • $100\text{ ml in } 800\text{ ml} = 8\text{ times}$

8.3.3 Small Capacities (Droppers and Dosing Cups)

For very small quantities of liquids, we use smaller units and tools:

  • A dosing cup of $10\text{ ml}$ will take $10$ times to fill a $100\text{ ml}$ bottle.
  • How many $10\text{ ml}$ dosing cups will fill:
    • A $250\text{ ml}$ glass? Answer: $25$ cups
    • A $500\text{ ml}$ vessel? Answer: $50$ cups
    • A $1\text{ l}$ bottle? Answer: $100$ cups
  • Using a $1\text{ ml}$ dropper:
    • It takes $10$ droppers of $1\text{ ml}$ to fill a $10\text{ ml}$ dosing cup.

8.3.4 Liquids Used in Small Quantities

Some liquids are used in very small quantities at a time:

  • Eye drops: Less than $1\text{ ml}$ at a time.
  • Honey / Cough Syrup: Around $5\text{ ml}$ to $10\text{ ml}$ (one or two teaspoons).
  • Cooking Oil: Around $10\text{ ml}$ to $15\text{ ml}$ per dish.

8.3.5 Measuring Cans

Commonly used measuring cans for milk and other liquids come in sizes of:

  • $50\text{ ml}$
  • $100\text{ ml}$
  • $200\text{ ml}$
  • $500\text{ ml}$
  • $1000\text{ ml}$ ($1\text{ l}$)
8.4 Water Conservation

8.4.1 Water Conservation in Everyday Life

Every drop of water is precious. A small slow drip from a leaking tap or water purifier can waste a significant amount of water over time:

  • If a leaking tap wastes about $1\text{ cup}$ of water in an hour, it can waste several litres in a single day!
  • Activity: Place a container under a leaking tap for one hour to measure the wasted water and calculate the daily and weekly loss.