We the Travellers — II – Class 5 Maths Chapter 4 Notes & NCERT PDF

Class 5MathematicsChapter 4NCERT book: Maths Mela - Mathematics Class 5

Notes and a simple summary of Chapter 4 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 4: We the Travellers — II

Introduction

The travel theme continues with addition and subtraction of large numbers. We fill fuel in lorries and minibuses, add up the length of India's North–South Corridor, follow a ship from Mumbai to Chennai, plan Mary's train journey and even check certificates at a Math Metric Mela.

Key Ideas

1. Making sums equal

Two groups of numbers have different sums. Swap numbers between the groups to make the sums equal in the fewest moves — think about how much each swap changes each sum.

2. Adding and subtracting with regrouping

A lorry has 28 l of fuel; 75 l more is added → 28 + 75 = 103 l (10 ones = 1 ten).

A minibus shows 18 l, then 65 l after refuelling → 65 − 18 = 47 l filled (1 ten = 10 ones). Check: 18 + 47 = 65.

3. Addition and subtraction are related

If 46 + 21 = 67, then 67 − 21 = 46 and 67 − 46 = 21.

We use this to check every subtraction.

4. Sums of consecutive numbers

Consecutive numbers follow one another (29, 30, 31, 32).

Sum of 2 consecutive numbers is always odd.

Sum of 3 consecutive numbers = 3 × middle number (67 + 68 + 69 = 3 × 68 = 204).

Sum of 5 consecutive numbers = 5 × middle number (48 + 49 + 50 + 51 + 52 = 250).

5. Adding and subtracting large numbers

Keep digits aligned — ones under ones, tens under tens — and add or subtract as with small numbers.

North–South Corridor: 1,855 km + 1,862 km = 3,717 km.

Mumbai to Chennai by sea is 2,700 km; Mumbai to Cochin is 1,083 km, so 1,617 km remain.

Talon–Sagres route (15,150 km) is 4,922 km longer than Cairo–Cape Town (10,228 km).

6. Quick sums and differences

Piku's trick for 1,000: 877 + ? = 1,000 → make each digit up to 9 (877 → 122) and add 1 → 123.

Namita's trick: to subtract 9, subtract 10 and add 1 (67 − 9 = 58); to subtract 99, subtract 100 and add 1 (763 − 99 = 664).

7. Even, odd and palindromes

Even + even = even, odd + odd = even, odd + even = odd. A torch is ON after odd numbers of presses, so after the 23rd press it is ON. Palindromes read the same both ways: 101, 111, … 191.

Worked Examples

Mary's money: 12,540 − 3,275 + 4,900 − 2,645 − 1,275 = ₹10,245 left.

Truck load: 3,675 kg + 2,850 kg = 6,525 kg; 8,250 − 6,525 = 1,725 kg more can be loaded.

Priyanka Mohite: highest peak Everest 8,848 m, lowest Elbrus 5,642 m → difference 3,206 m. She was 20 in 2013, so she was born in 1993.

Math Metric Mela, Jaunpur: 19,043 certificates for 19,265 students → 222 short. Raigad: 20,863 − 19,974 = 889 extra.

Cricket: Virat has 27,599 runs, 6,758 less than Sachin → Sachin = 27,599 + 6,758 = 34,357 runs.

Maths Words

Sum (योग), Difference (अंतर)

Regroup (पुनर्समूहन / हासिल लेना)

Consecutive numbers (क्रमागत संख्याएँ)

Even number (सम संख्या), Odd number (विषम संख्या)

Palindrome (पैलिंड्रोम — आगे-पीछे एक जैसी संख्या)

Estimate (अनुमान)

Maths in Daily Life

Fuel bills, trip budgets, road distances, savings and shop bills all need quick and correct addition and subtraction.

Common Mistakes

Misaligning digits when numbers have different lengths (56 + 56,789).

Forgetting to regroup across a zero (2,700 − 1,083).

Adding when the question needs subtraction — read "how much more / left / short" carefully.

Not checking subtraction by adding back.

Practice Tips

Estimate first (e.g. ₹70,500 vs about ₹40,000 + ₹10,000 + ₹20,000) and then calculate.

Use the addition–subtraction relation to check answers.

For consecutive sums, find the middle number first.

💡 Key Learning Points

✓Add and subtract numbers up to 5 digits with regrouping by aligning place values
✓Use the relation between addition and subtraction to check answers
✓Find sums of consecutive numbers using the middle number
✓Use quick tricks for making 100, 1,000, 10,000 and for subtracting 9 or 99
✓Understand even and odd sums and identify palindrome numbers

👨‍🏫 Teaching Tips

→Write the 'Making Sums Equal' numbers on paper slips so children can physically swap them
→Use a map of India to trace the North–South Corridor and Mumbai–Cochin–Chennai sea route
→Run a class 'fuel station' role-play for adding and subtracting litres
→Ask pairs to invent their own consecutive-number sums and find the middle-number rule
→Use a real torch or switch to explore the ON/OFF odd-even pattern
→Before every word problem, ask children to estimate the answer in round numbers
→Hold a mini 'Math Metric Mela' where teams check whether certificates were enough

📋 Assessment Questions

Can the child subtract 1,083 from 2,700 correctly and check by adding?
Can the child find 67 + 68 + 69 without adding one by one?
Can the child quickly find 4,103 + ? = 10,000?
Can the child solve a multi-step money problem like Mary's journey?
Can the child explain why the sum of two odd numbers is even?

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