We the Travellers — I – Class 5 Maths Chapter 1 Notes & NCERT PDF

Class 5MathematicsChapter 1NCERT book: Maths Mela - Mathematics Class 5

Notes and a simple summary of Chapter 1 of the NCERT Class 5 Mathematics book, with the official chapter PDF, flashcards, an MCQ quiz and an AI tutor for your doubts.

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Chapter 1: We the Travellers — I

Introduction

The chapter opens with a question: when did you last go on a long trip, how did you travel, and how far did you go? It reminds us that people once travelled on foot, on animals and in boats (boats were probably the first transport humans invented — even before bullock carts!). Today we use cycles, buses, trains, ships, aeroplanes and even spacecraft. Distances and counts like these quickly become large numbers, so this chapter teaches us to read, write, compare and round numbers up to 99,999.

Key Ideas

1. Ten thousand and the TTh column

Count on in thousands: 1,000, 2,000 … 9,000. One more thousand gives ten thousand = 10,000. We add a new column, TTh (Ten Thousands), to the place value chart.

10 Ones = 1 Ten, 10 Tens = 1 Hundred, 10 Hundreds = 1 Thousand, 10 Thousands = 1 Ten Thousand

We place a comma to read large numbers easily: 45,867 is read as forty-five thousand eight hundred sixty-seven.

2. Place value and expanded form

1,380 = 1 Thousand + 3 Hundreds + 8 Tens + 0 Ones

70,405 = 70,000 + 400 + 5

The same number can be broken in many ways: 983 = 90 Tens + 83 Ones; 37,608 = 2 Ten Thousands + 17 Thousands + 6 Hundreds + 8 Ones.

3. Comparing and ordering

A student said 9,990 is greater than 49,014 "because 9 is greater than 4". Wrong! 9,990 has only 4 digits, 49,014 has 5. Always compare the number of digits first, then compare digits from the left.

4. Nearest ten, hundred and thousand (rounding)

The hungry rabbit sits at 2,346:

nearest ten is 2,350 (4 jumps)

nearest hundred is 2,300 (46 jumps)

nearest thousand is 2,000 (346 jumps)

5. Travelling now and then

In one hour a person can travel about 3–5 km on foot, 12–20 km by cycle, 40–160 km by train and 750–920 km by aircraft. A cyclist at 15 km an hour covers 60 km in 4 hours.

6. Pastime mathematics

River crossing: the boatman must never leave the sheep alone with the grass or with the lion.

Pile of pebbles: two piles of 7; whoever picks the last pebble wins. Keep both piles equal after your turn!

Mira's 9 puzzle: reverse two digits and subtract again and again (73 − 37 = 36, 63 − 36 = 27, 72 − 27 = 45, 54 − 45 = 9). Every difference is a multiple of 9: difference = 9 × (difference of the two digits).

King's horses: the caretaker counted horses in the corners twice, so fewer than 20 horses could still show 5 on every side.

Worked Examples

Nearest values of 5,789 → ten: 5,790; hundred: 5,800; thousand: 6,000.

Vehicles for a trip: 461 girls + 439 boys = 900 students. Cars carry 4 → 900 ÷ 4 = 225 cars; aeroplanes carry 180 → 900 ÷ 180 = 5 aeroplanes.

Notes in ₹7,934: ₹10 notes → 793; ₹100 notes → 79; ₹500 notes → 15 (two ₹500 notes make each thousand, 7 × 2 = 14, plus one more from 934).

Ascending order of e-bike prices: ₹39,999 < ₹49,900 < ₹89,999 < ₹90,000 < ₹93,743 < ₹94,983.

Mira's rule: digits 1 and 4 differ by 3, so 41 − 14 = 9 × 3 = 27.

Maths Words

Ten thousand (दस हज़ार)

Place value (स्थानीय मान)

Expanded form (विस्तारित रूप)

Number name (संख्या का नाम)

Ascending order (आरोही क्रम)

Descending order (अवरोही क्रम)

Nearest ten / hundred / thousand (निकटतम दहाई / सैकड़ा / हज़ार)

Estimate (अनुमान)

Pattern (पैटर्न / क्रम)

Maths in Daily Life

Car odometers (Ravi's car has run 56,987 km), town populations, prices of bikes and phones, and the number of words in a book (about 200 pages × 50 words ≈ 10,000 words) are all 4- and 5-digit numbers.

Common Mistakes

Comparing only the first digit (9,990 vs 49,014).

Writing ten thousand ten as 1,010 instead of 10,010.

Forgetting zeros: fifty thousand five is 50,005.

Rounding 2,346 to the nearest hundred as 2,400 — look at the tens digit (4 < 5, so go down to 2,300).

Practice Tips

Use the place value chart and the tokens at the back of the book.

For rounding, draw the rabbit's number line and count jumps both ways.

In sequence questions (10,794, 10,796, 10,798 …) first find the jump size.

💡 Key Learning Points

✓Read and write numbers up to 99,999 using the TTh column and commas
✓Write numbers in expanded form and regroup them (983 = 90 Tens + 83 Ones)
✓Compare and order 4- and 5-digit numbers by counting digits first
✓Find the nearest ten, hundred and thousand of a number
✓Use logical thinking in puzzles like river crossing, pebble piles and Mira's 9 trick

👨‍🏫 Teaching Tips

→Use the tokens (1, 10, 100, 1,000, 10,000) from the end of the book to build 13,520 and 45,867 on desks
→Draw a big number line on the floor and let a child act as the hungry rabbit at 2,346 hopping to the nearest ten, hundred and thousand
→Ask children to collect real 4- and 5-digit numbers: school fees, odometer readings, town populations
→Act out the river crossing puzzle with three children as lion, sheep and grass
→Play the pile of pebbles game in pairs and ask winners to explain their strategy
→Let groups test Mira's 9 puzzle with different digit pairs and fill in her table
→Arrange 20 counters around a square for the King's Horses story and remove them one by one

📋 Assessment Questions

Can the child write 'fifty-six thousand four hundred ninety-one' as 56,491?
Can the child explain why 49,014 is greater than 9,990?
Can the child round 4,017 to the nearest ten, hundred and thousand?
Can the child arrange populations of six towns in descending order?
Can the child find how many ₹100 notes are in ₹65,342?

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