NCERT Class 4 Maths · Chapter 10
Elephants, Tigers, and Leopards
Adding and subtracting 4-digit numbers with regrouping, number games, patterns in the addition chart, and smart mental tricks.
📌 What you’ll learn in this chapter
- A winning strategy for the NIM game
- Patterns in an addition chart
- Adding and subtracting 4-digit numbers (regrouping in Th, H, T, O)
- Word problems with “more than” and “less than”
- Quick mental tricks, like “subtract 100, then add 1”
🐘 Let’s Begin: Counting Wild Animals
Forest officers count the elephants in two forests. Forest A has 2,786, and Forest B has 1,538. How many are there in all?
These are big numbers, but we add them the same way as small ones: place by place, starting from the Ones.
🎮 Part 1: The NIM Game (Add 1 or 2 to Reach 10)
Players take turns adding 1 or 2. Whoever reaches 10 wins.
💡 Secret strategy
Try to land on 1, 4, 7 (and then 10). These are 3 apart. Whatever your friend adds (1 or 2), you add enough to make 3 in that round.
For a target of 11, land on 2, 5, 8. For 12, land on 3, 6, 9.
For a target of 11, land on 2, 5, 8. For 12, land on 3, 6, 9.
➕ Part 2: Adding 4-Digit Numbers
2,786 + 1,538
| Th | H | T | O | |
|---|---|---|---|---|
| Regroup | 1 | 1 | 1 | |
| 2 | 7 | 8 | 6 | |
| + | 1 | 5 | 3 | 8 |
| = | 4 | 3 | 2 | 4 |
O: 6 + 8 = 14 (write 4, 1 ten over) · T: 8 + 3 + 1 = 12 (write 2, 1 hundred over) · H: 7 + 5 + 1 = 13 (write 3, 1 thousand over) · Th: 2 + 1 + 1 = 4 → 4,324 elephants
➖ Part 3: Subtracting 4-Digit Numbers
6,003 − 2,478 (There are lots of zeros, so regroup carefully!)
Ones: 3 − 8? The tens and hundreds are 0, so break 1 thousand: 6 Th → 5 Th + 10 H. Then 10 H → 9 H + 10 T. Then 10 T → 9 T + 10 O. Now the ones = 13.
13 − 8 = 5 · 9 − 7 = 2 · 9 − 4 = 5 · 5 − 2 = 3 → 3,525
Check: 3,525 + 2,478 = 6,003 ✅
⚠️ Common mistake
Forgetting to reduce a digit after borrowing from it. Always cross it out and write the new number above.
🤔 Part 4: “More Than” and “Less Than” Problems
- “B has 340 more than A” → B = A + 340
- “A has 340 more than B” → B = A − 340 (B is the smaller one!)
💡 Draw a bar
Draw two bars: a long one for the bigger number and a short one for the smaller number. The gap is the “more/less” part. This shows whether to add or subtract.
⚡ Part 5: Mental Tricks
- 4,568 − 99 → subtract 100 = 4,468, then add 1 = 4,469
- 2,396 + 104 → 2,396 + 4 = 2,400, then + 100 = 2,500
- If 245 + 130 = 375, then 245 + 131 = 376 (one more)
- If 600 − 250 = 350, then 600 − 251 = 349 (taking away more leaves less)
✏️ Practice Time
Try these on your own first, then check your answer below each question.
Q1. 3,678 + 2,459 = ?
✅ Answer6,137
Q2. 8,000 − 3,652 = ?
✅ Answer4,348
Q3. A park had 4,215 visitors on Saturday and 1,380 more on Sunday. How many came on Sunday?
✅ Answer4,215 + 1,380 = 5,595
Q4. 6,250 − 199 = ? (quick way)
✅ Answer6,250 − 200 + 1 = 6,051
Q5. Add 34 and its reverse, 43. What do you get?
✅ Answer77 (a multiple of 11)
📘 NCERT Textbook Activity Help
Hints and answers for the activities in the textbook, page by page. Try each one yourself before looking at the answer!
Pages 149–150 · NIM GameCan you win?
✅ Answer(a) At 6: yes. Add 1 to make 7, and you will win. (b) At 7: no, if your friend plays well. Whatever you add, they can reach 10. (c) At 8: yes. Add 2 to reach 10.
Safe numbers: target 10 → 1, 4, 7 · target 11 → 2, 5, 8 · target 12 → 3, 6, 9
Pages 150–151 · Addition ChartSafe numbers: target 10 → 1, 4, 7 · target 11 → 2, 5, 8 · target 12 → 3, 6, 9
Patterns
✅ Answer1. Each number is 1 more than the one on its left and the one above it. Numbers on each slanting line (from top right to bottom left) are the same.
2. 9 appears 10 times (0 + 9, 1 + 8 … 9 + 0). A number n up to 12 appears n + 1 times.
3. No row or column has only even or only odd numbers. They go odd, even, odd…
4. Red window (10, 11 / 11, 12): row sums 21 and 23, column sums 21 and 23 (the same). Diagonals: 10 + 12 = 22 and 11 + 11 = 22 (equal!). This works wherever you put the window.
5. Blue window (7 8 9 / 8 9 10 / 9 10 11): the middle number is 9. Opposite numbers around it add up to 18 (= 2 × 9), and the diagonals are the same.
Page 151 · Reverse and Add2. 9 appears 10 times (0 + 9, 1 + 8 … 9 + 0). A number n up to 12 appears n + 1 times.
3. No row or column has only even or only odd numbers. They go odd, even, odd…
4. Red window (10, 11 / 11, 12): row sums 21 and 23, column sums 21 and 23 (the same). Diagonals: 10 + 12 = 22 and 11 + 11 = 22 (equal!). This works wherever you put the window.
5. Blue window (7 8 9 / 8 9 10 / 9 10 11): the middle number is 9. Opposite numbers around it add up to 18 (= 2 × 9), and the diagonals are the same.
Sums with reverses
✅ Answer(a) 27 + 72 = 99, 34 + 43 = 77… (b) The sum is always a multiple of 11 (11 × the digit sum). (c) i) 55: 14, 23, 32, 41, 50 (digits add to 5) ii) 88: 17, 26, 35, 44, 53, 62, 71, 80 (d) Yes. The smallest 3-digit sum is 110 (e.g. 19 + 91, 28 + 82).
Fill the blanks: (a) Jumps of +10 (b) Jumps of +100 (c) Jumps of +25. Find the jump first, then continue the pattern.
Pages 152–154 · How Many Animals?Fill the blanks: (a) Jumps of +10 (b) Jumps of +100 (c) Jumps of +25. Find the jump first, then continue the pattern.
Elephants, leopards, and tigers
✅ AnswerElephants: 9,103 · Leopards: 4,303
Tigers: (a) Madhya Pradesh 444 + 341 = 785 (b) Uttarakhand 444 + 116 = 560 (c) 785 + 560 = 1,345 (d) 444 + 785 + 560 = 1,789
Pages 155–156 · More or Less?Tigers: (a) Madhya Pradesh 444 + 341 = 785 (b) Uttarakhand 444 + 116 = 560 (c) 785 + 560 = 1,345 (d) 444 + 785 + 560 = 1,789
Meghalaya and the leopards of 2018
✅ AnswerMeghalaya: 5,719 − 3,965 = 1,754 · Leopards in 2018: 8,820 − 749 = 8,071
Map: fill in the numbers from these problems (e.g. Karnataka elephants 6,049, Kerala 3,054, Assam 5,719, Meghalaya 1,754, and the tiger counts from above).
Pages 157–158 · Let Us DoMap: fill in the numbers from these problems (e.g. Karnataka elephants 6,049, Kerala 3,054, Assam 5,719, Meghalaya 1,754, and the tiger counts from above).
Visitors, juice, and vehicles
✅ Answer
1. (a) 8,591 − 6,415 = 2,176 (b) October = 6,415 − 1,587 = 4,828
2. (a) Guava = 1,348 + 759 = 2,107 (b) Orange = 2,107 + 1,257 = 3,364 (check: 3,364 + 1,417 = 4,781 ✅) (c) Guava + orange = 5,471, which is 690 more than passion fruit.
3. (a) Buses = 6,304 + 253 = 6,557 (b) Tractors = 6,557 − 5,247 = 1,310 (c) Taxis = 1,310 + 1,579 = 2,889 (d) Tractors < Taxis < Jeeps < Buses
4. (a) 1,935 (b) 8,051 (c) 5,916 (d) 6,417 (e) 4,210 (f) 4,474 (g) 1,882 (h) 2,439 (i) 876 (j) 8,531
Pages 159–160 · Deposit slips2. (a) Guava = 1,348 + 759 = 2,107 (b) Orange = 2,107 + 1,257 = 3,364 (check: 3,364 + 1,417 = 4,781 ✅) (c) Guava + orange = 5,471, which is 690 more than passion fruit.
3. (a) Buses = 6,304 + 253 = 6,557 (b) Tractors = 6,557 − 5,247 = 1,310 (c) Taxis = 1,310 + 1,579 = 2,889 (d) Tractors < Taxis < Jeeps < Buses
4. (a) 1,935 (b) 8,051 (c) 5,916 (d) 6,417 (e) 4,210 (f) 4,474 (g) 1,882 (h) 2,439 (i) 876 (j) 8,531
Raju, Rani, and Roja
✅ AnswerRaju: 50 × 2 = ₹100 · 10 × 14 = ₹140 · 5 × 1 = ₹5 · 2 × 0 = 0 · 1 × 0 = 0 · Total ₹1,500 + ₹300 + ₹100 + ₹140 + ₹5 = ₹2,045 (two thousand forty-five)
Rani ₹3,578 (one possible way): 500 × 7 = 3,500 · 50 × 1 = 50 · 10 × 2 = 20 · 5 × 1 = 5 · 2 × 1 = 2 · 1 × 1 = 1 → three thousand five hundred seventy-eight
Roja ₹1,240 (one possible way): 500 × 2 = 1,000 · 100 × 2 = 200 · 10 × 4 = 40 → one thousand two hundred forty
Pages 161–162 · Let Us SolveRani ₹3,578 (one possible way): 500 × 7 = 3,500 · 50 × 1 = 50 · 10 × 2 = 20 · 5 × 1 = 5 · 2 × 1 = 2 · 1 × 1 = 1 → three thousand five hundred seventy-eight
Roja ₹1,240 (one possible way): 500 × 2 = 1,000 · 100 × 2 = 200 · 10 × 4 = 40 → one thousand two hundred forty
Columns and easy ways
✅ Answer
1. (a) 7,903 (b) 9,354 (c) 2,831 (d) 3,077
2. (a) 2,712 (b) 8,386 (c) 345 (d) 2,458 (e) 2,097 (f) 3,644 (g) 12,000 (h) 8,716
Easy ways: (a) 8,688 (b) 4,700 (c) 3,480 (d) 5,105 (e) 5,300 (f) 7,829 (g) 500 (h) 1,450 (i) 4,289
Compare: 54 + 97 > 54 + 90 · 84 − 68 < 90 − 68 · 76 + 85 < 80 + 86 · 73 − 54 > 73 − 56
Use the given facts: 314 − 175 = 139 · 845 − 395 = 450 · 354 + 168 = 522 · 446 + 219 = 665 (10 less + 10 more = the same)
Page 163 · Practice2. (a) 2,712 (b) 8,386 (c) 345 (d) 2,458 (e) 2,097 (f) 3,644 (g) 12,000 (h) 8,716
Easy ways: (a) 8,688 (b) 4,700 (c) 3,480 (d) 5,105 (e) 5,300 (f) 7,829 (g) 500 (h) 1,450 (i) 4,289
Compare: 54 + 97 > 54 + 90 · 84 − 68 < 90 − 68 · 76 + 85 < 80 + 86 · 73 − 54 > 73 − 56
Use the given facts: 314 − 175 = 139 · 845 − 395 = 450 · 354 + 168 = 522 · 446 + 219 = 665 (10 less + 10 more = the same)
Add, subtract, and the number grid
✅ Answer
Add: (a) 3,161 (b) 9,045 (c) 7,373 (d) 8,494 (e) 9,871 (f) 6,480 (g) 8,887 (h) 9,900 (i) 9,821 (j) 3,959
Subtract: (a) 1,688 (b) 4,833 (c) 3,521 (d) 4,268 (e) 4,897 (f) 2,503 (g) 4,525 (h) 4,628 (i) 492 (j) 889
Grid (odd differences): odd numbers in the corners and centre, and even numbers in between:
1 2 3 / 4 5 6 / 7 8 9 works! (Neighbours differ by 1 or 3.) Other ways: swap odd numbers among the odd places, and even numbers among the even places.
Even differences: not possible. All the squares would need the same kind of number (all odd or all even), but 1–9 has 5 odd and 4 even numbers.
Subtract: (a) 1,688 (b) 4,833 (c) 3,521 (d) 4,268 (e) 4,897 (f) 2,503 (g) 4,525 (h) 4,628 (i) 492 (j) 889
Grid (odd differences): odd numbers in the corners and centre, and even numbers in between:
1 2 3 / 4 5 6 / 7 8 9 works! (Neighbours differ by 1 or 3.) Other ways: swap odd numbers among the odd places, and even numbers among the even places.
Even differences: not possible. All the squares would need the same kind of number (all odd or all even), but 1–9 has 5 odd and 4 even numbers.
👨👩👧 Tips for Parents
- Play NIM at home with different targets. Let your child discover the winning trick.
- Use real numbers from the news (population, distances) for adding and subtracting.
- Practise “subtract 99 or add 101” style mental sums.