Mathematics: Class 4 — Chapter 6: Measuring Length

6.1 Introduction to Measuring Length

In daily life, terms like tall, wide, short, long, height, width, depth, and breadth all refer to length measurement. These words are used depending on different situations and orientations, but they all denote length.

Metre Ropes and Fractional Parts

Lengths can be measured using ropes of standard lengths. We can define fractional parts of a metre as follows:

  • 1 Metre ($1\text{ m}$): The standard unit of length.
  • Half Metre ($\frac{1}{2}\text{ m}$): Equal to half of a metre.
  • Quarter Metre ($\frac{1}{4}\text{ m}$): Equal to one-fourth of a metre.

These units share the following relationships:

  • $1\text{ m} = \frac{1}{2}\text{ m} + \frac{1}{2}\text{ m}$
  • $1\text{ m} = \frac{1}{4}\text{ m} + \frac{1}{4}\text{ m} + \frac{1}{4}\text{ m} + \frac{1}{4}\text{ m}$
  • $\frac{1}{2}\text{ m} = \frac{1}{4}\text{ m} + \frac{1}{4}\text{ m}$
6.2 Estimating and Guessing Lengths

Developing an estimation of length helps in comparing sizes in our surroundings without immediate measurement tools.

Approximate Lengths of Common Objects

  • Blue Whale: Length is about $30\text{ m}$.
  • Crocodile: Length is about $6\text{ m}$.
  • Ostrich: Height is about $3\text{ m}$.
  • Giraffe: Height is about $4\text{ m}$.
6.3 Measuring Small Things (Centimetres)

To measure small items like an eraser, a pencil, or a seed, we need a unit smaller than a metre. A standard metre scale is divided into 100 equal parts. The length of each part is called a Centimetre (cm).

Metre to Centimetre Conversions

The relationship between metres and centimetres is defined as:

  • $1\text{ m} = 100\text{ cm}$
  • $\frac{1}{2}\text{ m} = 50\text{ cm}$
  • $\frac{1}{4}\text{ m} = 25\text{ cm}$

Measuring with a Broken Scale

If a scale is broken and does not start at $0$, we can still measure the length of an object by finding the difference between the starting mark and the ending mark on the scale.

$$\text{Length} = \text{Ending Reading} - \text{Starting Reading}$$

6.4 Metres and Centimetres

Lengths can be expressed using a combination of metres and centimetres. For example, a height of $120\text{ cm}$ can be written as $1\text{ m } 20\text{ cm}$ because:

$$120\text{ cm} = 100\text{ cm} + 20\text{ cm} = 1\text{ m } 20\text{ cm}$$

Conversion Exercises

  • $2\text{ m} = 200\text{ cm}$
  • $4\text{ m} = 400\text{ cm}$
  • $6\text{ m} = 600\text{ cm}$
  • $8\text{ m} = 800\text{ cm}$
6.5 Fencing, Lacing, and Perimeter

When we measure the boundary of a shape, we are finding its perimeter.

Definition of Perimeter

The length of the boundary of a closed object or shape is called its perimeter.

Measuring Perimeter using a Dot Grid

A dot grid with dots spaced $1\text{ cm}$ apart can be used to find the perimeter of various shapes by counting the number of $1\text{ cm}$ segments along the boundary of the shape.