Chapter 5 — Far and Near

Chapter 5 of the Class 5 Mathematics NCERT textbook (Maths Mela), "Far and Near", covers measurement of length across all scales — from millimetres for tiny objects like sprouts and screws to kilometres for long-distance travel — download the PDF to practise unit conversions, addition and subtraction of lengths, and real-world problems drawn from train routes, cable cars, and weaving centres.

• Units of Length and Their Relationships — The chapter introduces four standard units — millimetre (mm), centimetre (cm), metre (m), and kilometre (km) — and establishes the relationships: 10 mm = 1 cm, 100 cm = 1 m, and 1,000 m = 1 km. Students practise converting between units using double number lines.
• Measuring Long Distances in Kilometres — When a distance reaches 1,000 m, it is expressed as 1 km (kilo means thousand). The chapter uses real contexts such as a 3-km race with water stations every 500 m and the Vivek Express train route from Dibrugarh to Kanniyakumari (4,187 km) to build understanding of large-scale measurement.
• Measuring Small Lengths in Millimetres — One centimetre is divided into ten equal parts on a ruler, each called 1 millimetre. Students measure small objects like sprouts, nails, and screws in mm, and draw lines given in combined units such as 5 cm 5 mm or 36 mm, building precision in measurement.
• Adding and Subtracting Lengths — Lengths given in mixed units can be added or subtracted by either working with like units separately and converting (e.g., 3 km 450 m + 4 km 650 m = 8 km 100 m) or converting everything to a single unit first. Both column and mental strategies are encouraged.
• Multiplying and Dividing Lengths — Lengths in mixed units can be multiplied or divided by breaking them into their component units. For example, 20 shirts each needing 1 m 80 cm of cloth require 36 m in total. Division is used to find the daily progress when a 12 km 600 m road is built equally over 6 days.

1. 01The four standard length units in this chapter are mm, cm, m, and km, with the chain 10 mm = 1 cm, 100 cm = 1 m, and 1,000 m = 1 km.
2. 02Kilo means thousand, so 1 kilometre equals 1,000 metres — a useful landmark for measuring distances between towns or long race routes.
3. 03One centimetre on a ruler is divided into 10 millimetre marks; using mm improves precision when measuring small objects like a sprout or a small screw.
4. 04The chapter includes a real Vivek Express train-route exercise with distances up to 4,187 km between Dibrugarh (Assam) and Kanniyakumari (Tamil Nadu).
5. 05Heights of famous world statues — including the Statue of Unity (182 m) and the Statue of Liberty (38 m) — are used to practise comparing and finding differences in metres.
6. 06Non-metric units are also introduced: 1 inch = 2 cm 5 mm and 1 foot = 12 inches or 30 cm, which are used to measure height in everyday life.
7. 07The Gulmarg Gondola cable car in Kashmir, with two sections of 2 km 300 m and 2 km 650 m, is used as a real-world addition-of-lengths problem.