NCERT Revision Notes for Class 5 Maths Chapter 1: We the Travellers — I – Free PDF Download

Chapter 1 of Class 5 Maths (Math-Mela), We the Travellers – I, takes the number work from earlier classes into bigger territory: reading and writing 5-digit and 6-digit numbers, understanding place value in a large number, rounding numbers sensibly, writing numbers in expanded form, and comparing large numbers digit by digit. The chapter is framed around a journey – travellers moving between towns and covering distances – and along the way it also introduces a classic river-crossing logic puzzle that builds sequencing and reasoning skills alongside the number work.

Key Concepts

Place Value in Large Numbers

Every digit in a number has a value that depends on its position. In the number 4,72,915, the digit 4 is in the lakhs place (value 4,00,000), 7 is in the ten-thousands place (70,000), 2 is in the thousands place (2,000), 9 is in the hundreds place (900), 1 is in the tens place (10), and 5 is in the ones place (5). Reading large numbers correctly means grouping digits from the right in twos after the first three (Indian place-value system: ones, tens, hundreds, thousands, ten-thousands, lakhs).

Expanded Form

Expanded form writes a number as the sum of the values of each of its digits. For example, 4,215 = 4000 + 200 + 10 + 5, and 62,708 = 60,000 + 2,000 + 700 + 0 + 8. Writing numbers this way makes the value of each digit explicit and helps when adding or subtracting large numbers mentally.

Rounding Numbers

Rounding gives a simpler, approximate value that is easier to work with. The rule: look at the digit immediately to the right of the place you are rounding to. If that digit is 5 or more, round up; if it is 4 or less, round down (keep the same digit and replace everything to the right with zeros).

• Round 4,367 to the nearest ten: look at the ones digit (7) → round up → 4,370.
• Round 4,367 to the nearest hundred: look at the tens digit (6) → round up → 4,400.
• Round 4,367 to the nearest thousand: look at the hundreds digit (3) → round down → 4,000.

Comparing and Ordering Numbers

To compare two numbers, first compare the number of digits – a number with more digits is always bigger. If the digit count is the same, compare digit by digit from the leftmost (highest) place value until you find a difference. For example, comparing 52,840 and 52,480: both start with 52, but the hundreds digit decides it – 8 > 4, so 52,840 is bigger.

Forming Numbers From Digits

Given a set of digits, the greatest number is formed by arranging digits in descending order, and the smallest by arranging them in ascending order (careful: if 0 is one of the digits, it cannot be placed as the leftmost digit of the smallest number – it goes in the next position instead).

The River-Crossing Puzzle

The chapter also includes a classic logic puzzle where a traveller must carry a wolf, a goat, and a bag of grass across a river using a boat that can only carry one item at a time, without ever leaving the wolf alone with the goat, or the goat alone with the grass. Solving it teaches step-by-step planning and checking every move for safety before going ahead – a reasoning skill distinct from, but complementary to, number work.

Worked Examples

Example 1: Expanded Form to Standard Form

Write the number represented by 3,00,000 + 40,000 + 5,000 + 600 + 20 + 1 in standard form.
Add the place values in order: 3,00,000 + 40,000 + 5,000 + 600 + 20 + 1 = 3,45,621.

Example 2: Rounding a Distance

A bus covers 68,245 metres in a day. Round this distance to the nearest thousand.
Look at the hundreds digit (2) – since 2 is less than 5, round down → 68,000 metres.

Example 3: Greatest and Smallest Number

Using the digits 6, 0, 9, 2 once each, form the greatest and smallest 4-digit numbers.
Greatest: arrange in descending order → 9,620.
Smallest: since 0 cannot lead, place the next smallest digit (2) first, then 0, then the rest in ascending order → 2,069.

Quick Recap

• Place value depends on a digit’s position: ones, tens, hundreds, thousands, ten-thousands, lakhs.
• Expanded form breaks a number into the sum of its place values.
• Rounding rule: check the digit one place to the right of where you are rounding – 5 or more rounds up, 4 or less rounds down.
• To compare numbers, compare digit count first, then compare digit by digit from the left.
• Greatest number from given digits: arrange in descending order; smallest: ascending order, with 0 never leading.
• The river-crossing puzzle builds sequencing logic separate from, but alongside, number skills.

Common Mistakes to Avoid

• Checking the wrong digit when rounding – always look one place to the right of the rounding place, not the last digit of the whole number.
• Forgetting that a 0 cannot be the leading digit when forming the smallest number from a digit set.
• Comparing numbers by only looking at the first digit instead of continuing digit by digit until a difference appears.
• Writing expanded form with the wrong number of zeros for a place, especially when a digit is 0 (it still needs to be accounted for, even as “+0”).
• Rushing the river-crossing puzzle without checking each step for a forbidden combination left alone.

Home Practice Tips

• Pick any 5-digit number from a newspaper, bus number, or product code and identify the place value of each digit aloud.
• Round grocery bill amounts or distances seen on road signs to the nearest ten, hundred, and thousand as a quick daily habit.
• Give a child five digit cards and ask them to build the greatest and smallest possible numbers, then check together.
• Act out the river-crossing puzzle at home with toy figures or drawn cutouts to make the logic visible step by step.
• Practise comparing pairs of large numbers from vehicle number plates or phone numbers digit by digit.

Frequently Asked Questions

Q1. Why is place value so important in large numbers?
Because the same digit means different things depending on where it sits – a 5 in the ones place is worth five, but a 5 in the ten-thousands place is worth fifty thousand, so reading a number correctly depends entirely on recognising each digit’s position.

Q2. What is the difference between rounding down and rounding off?
“Rounding off” is the general process of finding a nearby simpler number; “rounding down” specifically means keeping the digit the same and replacing digits to the right with zero, which happens when the check-digit is 4 or less.

Q3. Why does the smallest number rule treat 0 differently?
A number cannot start with 0 (that would just remove a digit and reduce the number of digits), so when forming the smallest number, 0 is placed as the second digit instead of the first.

Q4. What skill does the river-crossing puzzle build besides number sense?
It builds logical sequencing – deciding the order of moves so that no unsafe combination (like the wolf and goat alone together) is ever left unattended, which is a foundational reasoning skill used later in more formal logic and problem-solving.

Q5. How many times should a number be rounded when solving a word problem?
Only round when the question specifically asks for an approximate or estimated value; for exact word problems, use the full precise number throughout the calculation and round only the final answer if instructed.

Full walkthrough: Chapter 1 Solutions · Extra Questions.

Written by Satish

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