NCERT Solutions for Class 4 Maths Mela Chapter 10 Elephants Tigers and Leopards

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Question. Can you win the game if a) The other player has reached the total of 6 and it is your turn?
Answer: If you add 1, the total becomes 7. If you add 2, the total becomes 8. Both choices put you in a losing position. Therefore, you cannot win when the other player reaches 6.
In simple words: When your opponent gets to 6, any move you make (adding 1 or 2) gives them a winning chance next turn.

Exam Tip: Identify the losing positions first - these are positions where every move leads to a winning position for the opponent.

Question. b) The other player has reached the total of 7 and it is your turn?
Answer: If you add 1, the total becomes 8. If you add 2, the total becomes 9. If you make it 9, your opponent can only add 1 to reach 10 and win. So you should add 1 to make it 8. Then: If your opponent adds 1, the total is 9, and you can add 1 to reach 10 and win. If your opponent adds 2, the total is 10, and your opponent wins. By playing carefully, you can win.
In simple words: Add 1 to make it 8. Then you have a winning path if your opponent adds 1 next.

Exam Tip: Always calculate two moves ahead - your move plus the opponent's best response - to determine if you are in a winning position.

Question. c) The other player has reached the total of 8 and it is your turn?
Answer: If you add 1, the total becomes 9. If you add 2, the total becomes 10 and you win immediately. Therefore, you can win by adding 2.
In simple words: When the opponent reaches 8, you can finish the game right away by adding 2.

Exam Tip: Look for direct winning moves first before considering longer strategies.

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Question. Play the game to reach other target number (like 10, 11, or 12) by adding 1 or 2 each time. Can you find a number in each case when you are sure that you can win?
Answer: For target numbers 10, 11, or 12, the winning strategy is to reach certain key positions. For target 10, the key positions are 7, 4, and 1. For target 11, the key positions are 8, 5, and 2. For target 12, the key positions are 9, 6, and 3. If you can force your opponent to be at a position where they are not at these key positions, you can win.
In simple words: Every target number has special winning numbers. If you reach those numbers before your opponent does, you will win the game.

Exam Tip: Work backwards from the target number - subtract 3 each time to find all the winning positions, since adding 1 or 2 leaves gaps of 3.

Question. Addition Chart - Look at the given table below and discuss how the table is made.
Answer: The top row shows numbers from 0 to 12. The left column also shows numbers from 0 to 12. The plus sign in the top-left corner tells us that this is an addition table. Each cell (box) in the table shows the sum of the number from the row and the number from the column.
In simple words: To read this table, pick a number from the top row and a number from the left column. Where they meet is their sum.

Exam Tip: Addition tables are symmetric - the entry at row 3, column 5 equals the entry at row 5, column 3, because addition is commutative.

Question 1. Identify some patterns in the table.
Answer: The numbers increase by 1 as you move from left to right in any row. The numbers also increase by 1 as you move from top to bottom in any column. Each number in the table is formed by adding the row number and the column number. Numbers on the diagonal (from top-left to bottom-right) increase by 2 each time: 0, 2, 4, 6, 8, and so on.
In simple words: Moving right adds one. Moving down adds one. The diagonal line shows numbers that skip by 2s.

Exam Tip: The diagonal pattern reveals that diagonal entries follow a sequence - this helps predict values without calculating.

Question 2. Observe the cell where the number 9 appears in the table. How many times do you see number 9? What about other numbers?
Answer: The number 9 appears once in the left column and once in the top row. Within the main table, 9 shows up 10 times. It appears wherever the row number plus the column number equals 9. Examples: (0 + 9), (1 + 8), (2 + 7), (3 + 6), (4 + 5), (5 + 4), (6 + 3), (7 + 2), (8 + 1), (9 + 0). So, 9 appears a total of 12 times. For other numbers: Each number appears a fixed number of times. Numbers near the middle (like 9, 10, 11) appear more often. Smaller numbers (like 0 or 1) and larger numbers (like 24) appear fewer times.
In simple words: A number appears in the table at all the different ways you can add two numbers to make it. Middle numbers have more ways than edge numbers.

Exam Tip: Count the appearances by finding all pairs (a, b) where a + b equals your target - this is systematic and avoids missing pairs.

Question 3. Are there any rows or columns that contain only even numbers or only odd numbers? Explain your observation.
Answer: Yes. The row starting with 0 (row 0) has: 0, 2, 4, 6, 8, 10, 12, and so on - all even numbers. The column starting with 0 also has only even numbers. No row or column contains only odd numbers. This is because when you add an even number and an odd number, you get an odd result. When you add an odd number and an odd number, you get an even result. Therefore, odd and even numbers become mixed in most rows and columns.
In simple words: The row of 0 has all even sums. But mixing odd and even numbers always creates a mix of odd and even results.

Exam Tip: Remember: even + even = even, even + odd = odd, odd + odd = even. This rule explains why the table mixes odd and even entries.

Question 4. Look at the window frame highlighted in red colour in the table. a) Find the sum of the two numbers in each row.
Answer: Sum of the two numbers in each row: 10 + 11 = 21 and 11 + 12 = 23.
In simple words: Add the two numbers sitting side by side in each row of the red box.

Exam Tip: Notice that consecutive rows have sums that differ by 2 - this pattern holds whenever you sum two consecutive numbers in consecutive rows.

Question 4. b) Find the sum of the two numbers in each column. What do you notice?
Answer: Sum of the two numbers in each column: 10 + 11 = 21 and 11 + 12 = 23. The result is the same as for the rows.
In simple words: Adding down the column gives the same answer as adding across the row.

Exam Tip: This symmetry happens because the table is symmetric - swapping rows and columns gives the same entries.

Question 4. c) Now, find the sum of the numbers in each of two diagonals marked by arrows. What do you notice?
Answer: Sum of the two numbers in each diagonal: 10 + 12 = 22 and 11 + 11 = 22. The sums of the two diagonals are the same.
In simple words: Both diagonal lines add to the same total.

Exam Tip: In a 2 × 2 square, opposite corner pairs always sum to the same value - this is a key magic square property.

Question 4. d) Now, put the red window frame in other places and find the sums as above. What do you notice?
Answer: When the frame is placed at another location: Sum of rows: 4 + 5 = 9 and 5 + 6 = 11. Sum of columns: 4 + 5 = 9 and 5 + 6 = 11. Sum of diagonals: 4 + 6 = 10 and 5 + 5 = 10. The row and column sums stay consistent, and the diagonal sums remain equal to each other.
In simple words: No matter where you place the frame, the rows and columns give one set of sums, and the two diagonals always equal each other.

Exam Tip: This property holds for any 2 × 2 region of an addition table - it reveals the underlying structure of how addition works.

Question 5. Now, put the red patterns and relationships among the numbers in the blue window frame.
Answer: When using a larger blue window frame: Sum of rows: 7 + 8 + 9 = 24, 8 + 9 + 10 = 27, and 9 + 10 + 11 = 30. Sum of columns: 7 + 8 + 9 = 24, 8 + 9 + 10 = 27, and 9 + 10 + 11 = 30. Sum of diagonals: 7 + 9 + 11 = 27 and 9 + 9 + 9 = 27. The rows and columns show increasing totals (each row/column sum grows by 3), and both diagonals sum to 27.
In simple words: With a 3 × 3 frame, rows go up by 3 each time, columns do the same, and both diagonal lines equal each other.

Exam Tip: Larger frames show that diagonal sums in an addition table equal the center entry times the frame size - here, 9 × 3 = 27.

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Question. Reverse and Add - a) Take a 2 digit number say, 27. Reverse its digits (72). Add them (99). Repeat for different 2-digit numbers.
Answer: Take the number 45; its reverse is 54, and their sum is 99. Take the number 36; its reverse is 63, and their sum is 99.
In simple words: When you flip a two-digit number and add it to the original, you often get 99.

Exam Tip: For a two-digit number with digits a and b, (10a + b) + (10b + a) = 11(a + b), which is always a multiple of 11.

Question. b) What sums can we get when we add a 2 digit number with its reverse?
Answer: When adding a two-digit number with its reverse: If the sum of digits equals or exceeds 10, you get a three-digit sum. If not, you get a two-digit sum. All sums will be multiples of 11.
In simple words: Every answer is a multiple of 11. Some answers are two digits, others are three digits, depending on whether the original digits add to 10 or more.

Exam Tip: The smallest two-digit sum is 11 (from 10); the largest three-digit sum is 198 (from 99) - knowing these bounds helps verify your work.

Question. c) List down all numbers which when added to their reverse give i) 55 ii) 88
Answer: i) Numbers that sum to 55 when added to their reverse: The digits must add to 5. The two-digit numbers are 05, 14, 23, 32, 41, and 50. ii) Numbers that sum to 88 when added to their reverse: The digits must add to 8. The two-digit numbers are 08, 17, 26, 35, 44, 53, 62, 71, and 80.
In simple words: To get a specific sum, look at what the digits need to add to. If they add to 5, the answer is 55. If they add to 8, the answer is 88.

Exam Tip: For a target sum S that is a multiple of 11, find all pairs of digits (a, b) where 11(a + b) = S, then list all numbers with those digit combinations.

Question. d) Can we get a 3 digit sum? What is the smallest 3 digit sum that we can get?
Answer: Yes, we can get a three-digit sum. The smallest three-digit sum is found by checking: 45 + 54 = 99 (not three digits), but 46 + 64 = 110 (three digits). Therefore, the smallest three-digit sum is 110.
In simple words: Start from smaller two-digit numbers and add them to their reverse until you get to 110, which is the smallest three-digit multiple of 11 reachable this way.

Exam Tip: The first three-digit sum happens when the digit sum is 10, giving 11 × 10 = 110 - any pair of single digits adding to 10 works (e.g., 46, 55, 64, 73, 82, 91).

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Question. Fill in the blanks with appropriate numbers. a) [Trees with counts]
Answer: Based on the arithmetic patterns shown: 2540, 2590, 2640, 2690, 2740, 2790.
In simple words: Each tree count increases by 50 from the one before it.

Exam Tip: Look for the pattern (difference or ratio) between known numbers, then apply it to fill the blanks consistently.

Question. b) [Mailbox counts]
Answer: Based on the arithmetic patterns shown: 354, 1354, 2354, 3354, 4354, 5354, 6354.
In simple words: Each mailbox count increases by 1000 from the one before it.

Exam Tip: When numbers increase by a constant amount, that amount is the common difference - use it to predict missing values.

Question. c) [Number line with animals]
Answer: Based on the arithmetic patterns shown: 7645, 7670, 7695, 7720, 7745, 7770, 7795, 7820.
In simple words: Each number on the line increases by 25 from the previous one.

Exam Tip: On a number line, find the interval (distance between marked numbers) and add it repeatedly to fill in missing values.

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Question 1. The population of elephants in Karnataka is 6049 and in Kerala is 3045. How many total elephants are there in these two states?
Answer: Elephants in Karnataka total 6049. Elephants in Kerala total 3045. Adding these together: 6049 + 3045 = 9103. Therefore, 9103 elephants live in these two states combined.
In simple words: When you put the elephants from both states together, you get 9103.

Exam Tip: Always line up the numbers by place value (ones, tens, hundreds, thousands) before adding to avoid mistakes.

Question 2. The highest number of leopards found in three states. Gujarat has 1355, Karnataka has 1131 and Madhya Pradesh has 1817. How many total leopards are there in these states?
Answer: The number of leopards in Gujarat is 1355. The number of leopards in Karnataka is 1131. The number of leopards in Madhya Pradesh is 1817. Using rounded values to estimate: 1400 + 1100 + 1800 = 4300. Therefore, the total number of leopards is approximately 4300.
In simple words: Round each number, then add the rounded numbers to get an estimate of the total.

Exam Tip: When asked for the total of multiple values, use rounding to the nearest hundred for a quick estimate, then verify with exact addition if needed.

Question 3. Maharashtra has 444 tigers. Madhya Pradesh has 341 more tigers than Maharashtra. Uttarakhand has 116 tigers more than Maharashtra. a) How many tigers does Madhya Pradesh have?
Answer: Maharashtra has 444 tigers. Madhya Pradesh has 341 more tigers than Maharashtra, so: 444 + 341 = 785 tigers in Madhya Pradesh.
In simple words: Start with Maharashtra's count and add 341 to find Madhya Pradesh's count.

Exam Tip: When a problem says "X more than Y," add X to Y's value - never subtract.

Question 3. b) How many tigers does Uttarakhand have?
Answer: Uttarakhand has 116 more tigers than Maharashtra, so: 444 + 116 = 560 tigers in Uttarakhand.
In simple words: Take Maharashtra's number and add 116 to get Uttarakhand's number.

Exam Tip: Keep track of which state is your reference (base) before adding the difference.

Question 3. c) How many tigers does Madhya Pradesh and Uttarakhand have together?
Answer: Madhya Pradesh has 785 tigers and Uttarakhand has 560 tigers. Adding them together: 785 + 560 = 1345 tigers for both states combined.
In simple words: Add the two state counts to find the total for both.

Exam Tip: For multi-part problems, use the answers from previous parts (if correct) to answer later parts - this saves calculation time.

Question 3. d) How many tigers are there in total across the three states?
Answer: Maharashtra has 444 tigers, Madhya Pradesh has 785 tigers, and Uttarakhand has 560 tigers. The total across all three states is: 444 + 785 + 560 = 1789 tigers.
In simple words: Add all three state counts together to get the grand total.

Exam Tip: You can also add your answer from part (c) to Maharashtra's count: 1345 + 444 = 1789, which is a good verification method.

Question. More or Less? 1. Assam has 5719 elephants. It has 3965 more elephants than Meghalaya. How many elephants are there in Meghalaya?
Answer: Assam has 5719 elephants total. Assam has 3965 more elephants than Meghalaya. Using approximation for calculation: Assam ≈ 5700 and the difference ≈ 4000, so Meghalaya ≈ 5700 - 4000 = 1700 elephants. For exact calculation: Meghalaya = 5719 - 3965 = 1754 elephants.
In simple words: If one place has more, subtract that difference to find the other place's count.

Exam Tip: When told "A has X more than B," use the formula: B = A - X. Note the difference between the rough estimate (1700) and exact answer (1754).

Question 2. The population of leopards as per the 2022 census was 8820 in the Central India and the Eastern Ghats. It had increased by 749 in comparison to the number of leopards in 2018 in the same region. How many leopards were there in 2018?
Answer: The leopard population in 2022 was 8820. The population grew by 749 from 2018 to 2022. To find the 2018 population, subtract the increase: 8820 - 749 = 8071. Therefore, 8071 leopards lived in the region in 2018.
In simple words: If the count went up by 749, then the old count was 749 less than the new count.

Exam Tip: When a quantity "increased by X," the earlier value is always smaller - subtract X from the later value to find it.

Question 3. Write the number of animals on this map based on the data from the problems in the previous pages.
Answer: Using data from earlier problems: Karnataka elephants: 6049. Assam elephants: 5719 (rounded for some estimates in previous work, actual used here). Kerala elephants: 3045 (or 3054 as used in the map). Uttarakhand tigers: 560. Madhya Pradesh tigers: 785. Assam and other regions: 1229 (total tigers across mentioned states). Gujarat, Karnataka, Madhya Pradesh leopards: 1355, 1131, 1817, totaling approximately 4303 leopards across the three states.
In simple words: Fill in the map boxes with the animal counts calculated from all the word problems solved earlier.

Exam Tip: Keep a running record of all calculated values from each problem - this becomes your data bank for map-based summary questions.

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Question. Let Us Do - 1. The board in the ticket office in the Kaziranga National Park shows the following: a) How many more visitors came in December than in November?
Answer: The number of visitors in December was 8591. The number of visitors in November was 6415. The difference is: 8591 - 6415 = 2176. Therefore, 2176 more visitors came in December than in November.
In simple words: Subtract November's visitor count from December's count to find how many more came in December.

Exam Tip: Always subtract the smaller number from the larger number to get a positive difference representing "how many more."

Question 1. b) The number of visitors in November is 1587 more than October. How many visitors were there in October?
Answer: The number of visitors in November was 6415. November had 1587 more visitors than October. Therefore, the number of visitors in October was: 6415 - 1587 = 4828.
In simple words: If November is 1587 more than October, then October is 1587 less than November.

Exam Tip: Reverse the logic: if "A is X more than B," then "B is A minus X."

Question 2. In a juice making factory, women make different types of juices as given below: a) The number of bottles of guava juice is 759 more than the number of bottles of pineapple juice. Find the number of bottles of guava juice.
Answer: The factory makes 1348 bottles of pineapple juice. Guava juice bottles are 759 more than pineapple: 1348 + 759 = 2107 bottles of guava juice are produced.
In simple words: Add the pineapple count to the extra amount to find the guava count.

Exam Tip: Identify the base quantity (pineapple), then add the difference to find the related quantity (guava).

Question 2. b) The number of bottles of orange juice is 1257 more than the number of bottles of guava juice and 1417 less than the number of bottles of passion fruit juice. How many bottles of orange juice are made in a month?
Answer: Guava juice bottles total 2107. Orange juice is 1257 more: 2107 + 1257 = 3364 bottles. We can verify: orange juice is also 1417 less than passion fruit, which is 4781 bottles. Check: 4781 - 1417 = 3364 bottles. Therefore, 3364 bottles of orange juice are made in a month.
In simple words: Add to the guava count, or subtract from the passion fruit count - both methods give the same orange juice total.

Exam Tip: When two different relationships are given for the same quantity, use both to verify your answer is correct.

Question 2. c) Is the total number of bottles of guava juice and orange juice more or less than the number of bottles of passion fruit juice? How much more or less?
Answer: Guava juice has 2107 bottles and orange juice has 3364 bottles. Together: 2107 + 3364 = 5471 bottles. Passion fruit juice has 4781 bottles. Comparing: 5471 - 4781 = 690. Therefore, the combined guava and orange juice count is 690 more bottles than passion fruit juice.
In simple words: Add guava and orange together, then compare to passion fruit to see which is bigger and by how much.

Exam Tip: For comparison questions, always find the total of the items being compared, then subtract to find the difference.

Question 3. In a small town, the following vehicles were registered in the year 2022. Find the number of vehicles as per the conditions given below. a) The number of buses is 253 more than the number of jeeps. How many busses are there in the town?
Answer: The town has 6304 jeeps. Buses are 253 more: 6304 + 253 = 6557 buses.
In simple words: Add 253 to the jeep count to get the bus count.

Exam Tip: When finding a related quantity that is "more," always add the difference to the base quantity.

Question 3. b) The number of tractors in 5247 less than the number of busses. How much tractors are in the town?
Answer: Buses total 6557. Tractors are 5247 less: 6557 - 5247 = 1310 tractors.
In simple words: Subtract 5247 from the bus count to find the tractor count.

Exam Tip: When a quantity is "less," subtract that amount from the base quantity.

Question 3. c) The number of taxis is 1579 more than the number of tractors? How many taxis are there?
Answer: Tractors total 1310. Taxis are 1579 more: 1310 + 1579 = 2889 taxis.
In simple words: Add 1579 to the tractor count to get the taxi count.

Exam Tip: Follow the same pattern: when told a quantity is "more," add the difference to the reference number.

Question 3. d) Arrange the numbers of each type of vehicle from lowest to highest.
Answer: Arranged from smallest to largest: Tractors (1310), Taxis (2889), Jeeps (6304), Buses (6557).
In simple words: Sort all four vehicle counts from the smallest number to the largest number.

Exam Tip: When arranging numbers in order, compare digits starting from the leftmost (highest place value) to determine rank quickly.

Question. Important Concepts Covered in Chapter 10 Maths Mela - 4. Solve a) 1459 + 476 b) 3863 + 4188 c) 5017 + 899 d) 4285 + 2132 e) 3158 + 1052 f) 7293 - 2819 g) 3105 - 1223 h) 8006 - 5567 i) 5000 - 4124 j) 9018 - 487
Answer: a) 1459 + 476 = 1935 b) 3863 + 4188 = 8051 c) 5017 + 899 = 5916 d) 4285 + 2132 = 6417 e) 3158 + 1052 = 4210 f) 7293 - 2819 = 4474 g) 3105 - 1223 = 1882 h) 8006 - 5567 = 2439 i) 5000 - 4124 = 876 j) 9018 - 487 = 8531
In simple words: For each problem, add or subtract the two numbers by aligning them by place value, then write the result.

Exam Tip: Always line up ones, tens, hundreds, and thousands places before adding or subtracting to avoid errors.

Question 5. The children in a school in Chittoor are planning to organise a Baal Mela in their school. Raju, Rani and Roja decided to raise some money to make arrangements for the mela. The money is available in notes of 500, 100, 50, 10 and coins of 5, 2 and 1. They decide to put the money in the School Panchayat Bank.
Answer: The amounts collected are: Raju: Rs. 2045, Rani: Rs. 3578, Roja: Rs. 1240. These amounts can be broken down into different combinations of notes and coins. For example, Raju's Rs. 2045 can be made from: 4 notes of Rs. 500, 0 notes of Rs. 100, 0 notes of Rs. 50, 4 notes of Rs. 10, 1 coin of Rs. 5, 0 coins of Rs. 2, 0 coins of Rs. 1. Other combinations using different denominations are also possible while keeping the total the same.
In simple words: Each child collected a certain amount of money using different notes and coins. The same total can be made in many different ways by using different combinations.

Exam Tip: When finding combinations of notes and coins, work from the largest denomination downward to minimize the number of pieces used.

Question 5. Help each of the children fill the deposit slip given below. Different combinations of notes can give the same amount. Can you guess a possible combination of notes they might have? Fill in the amounts appropriately.
Answer: For Raju (Rs. 2045): One possible combination is 4 notes of Rs. 500 (Rs. 2000), 0 notes of Rs. 100, 0 notes of Rs. 50, 4 notes of Rs. 10 (Rs. 40), 1 coin of Rs. 5 (Rs. 5), totaling Rs. 2045. Another combination could be 3 notes of Rs. 500, 5 notes of Rs. 100, 0 notes of Rs. 50, 4 notes of Rs. 10, 1 coin of Rs. 5, totaling Rs. 2045. For Rani (Rs. 3578): One possible combination is 7 notes of Rs. 500, 0 notes of Rs. 100, 1 note of Rs. 50, 2 notes of Rs. 10, 1 coin of Rs. 5, 1 coin of Rs. 2, 1 coin of Rs. 1. For Roja (Rs. 1240): One possible combination is 2 notes of Rs. 500, 2 notes of Rs. 100, 0 notes of Rs. 50, 4 notes of Rs. 10, totaling Rs. 1240.
In simple words: For each child's total amount, write one set of notes and coins that adds up to that amount. Many different sets work for the same total.

Exam Tip: To check if your combination is correct, multiply each note/coin by how many you have, add all the products, and verify the sum matches the target amount.

Question 1. Solve.
(a) Add 3695 and 4208
(b) Add 2507 and 6847
(c) Subtract 3521 from 6352
(d) Subtract 2726 from 8803
Answer:
(a) 7903
(b) 9354
(c) 2831
(d) 6077
In simple words: Stack the numbers one on top of the other, lining up the place values. Add or subtract starting from the ones place, moving left to the tens, hundreds, and thousands.

Exam Tip: Always align numbers by place value before adding or subtracting. Check your work by adding the answer back to the number you subtracted - you should get the original number.

Question 2. Arrange the following in columns and solve in your notebook.
(a) 3683 - 971
(b) 8432 - 46
(c) 4011 - 3666
(d) 5203 - 2745
(e) 1465 + 632
(f) 3567 + 77
(g) 8263 + 3737
(h) 5429 + 3287
Answer:
(a) 2712
(b) 8386
(c) 345
(d) 2458
(e) 2097
(f) 3644
(g) 12000
(h) 8716
In simple words: Write each number in its place. For subtraction, start from the right and take away. For addition, put the numbers in columns and add each column from right to left.

Exam Tip: When subtracting, if the bottom number is bigger than the top number in any column, borrow from the next column on the left.

Question 1. Find easy ways to solve the following problems. Write the answers in the given space. Share your thinking with the grade.
(a) 8787 - 99 = __________
(b) 4596 + 104 = __________
(c) 3459 + 21 = __________
(d) 5010 + 95 = __________
(e) 4990 + 310 = __________
(f) 7844 - 15 = __________
(g) 260 + 240 = __________
(h) 1575 - 125 = __________
(i) 3999 + 290 = __________
Answer:
(a) 8787 - 99 = 8787 - 100 + 1 = 8688
(b) 4596 + 104 = 4596 + 100 + 4 = 4700
(c) 3459 + 21 = 3459 + 20 + 1 = 3480
(d) 5010 + 95 = 5010 + 100 - 5 = 5105
(e) 4990 + 310 = 4990 + 10 + 300 = 5300
(f) 7844 - 15 = 7844 - 10 - 5 = 7829
(g) 260 + 240 = 200 + 200 + 60 + 40 = 500
(h) 1575 - 125 = 1450 - 100 - 25 = 1325
(i) 3999 + 290 = 3999 + 1 + 289 = 4000 + 289 = 4289
In simple words: Look for numbers that are close to 100 or multiples of 10. Break them into easier pieces to make the math simpler in your head.

Exam Tip: Show your method clearly. Breaking numbers into convenient parts (like splitting 99 into 100 - 1) is a valid strategy and shows your thinking.

Question 2. Use the signs <, =, > as appropriate to compare the following without actually calculating. Try to reason them out and share in grade.
(a) 54 + 97 _____ 54 + 90
(b) 84 - 68 _____ 90 - 68
(c) 76 + 85 _____ 80 + 86
(d) 73 - 54 _____ 73 - 56
Answer:
(a) 54 + 97 > 54 + 90 (When you add a bigger number, the result becomes larger. Since 97 is bigger than 90, the left side is bigger.)
(b) 84 - 68 < 90 - 68 (When you take away the same amount from different numbers, the starting bigger number leaves more. Since 84 is smaller than 90, the left side is smaller.)
(c) 76 + 85 < 80 + 86 (The right side has a bigger first number and a bigger second number, so the right side is larger.)
(d) 73 - 54 > 73 - 56 (When you subtract a smaller number, you are left with more. Since 54 is smaller than 56, the left side is bigger.)
In simple words: You do not have to calculate. Think about which side has bigger numbers being added or smaller numbers being taken away.

Exam Tip: Always explain your reasoning by comparing the numbers or the amounts being added or subtracted. This shows you understand, not just that you guessed.

Question 3. Use the given information to find the values. Share your reasoning with the grade.
(a) 139 + 175 = 314; find 314 - 175 = __________
(b) 845 - 394 = 451; find 845 - 395 = __________
(c) 354 + 167 = 521; find 354 + 168 = __________
(d) 456 + 209 = 665; find 446 + 219 = __________
Answer:
(a) 314 - 175 = 139 (Adding and subtracting are opposite actions. If you add 175 to 139 to get 314, then taking away 175 from 314 brings you back to 139.)
(b) 845 - 395 = 450 (You are subtracting 1 more than before. When you subtract a bigger amount, your answer gets 1 smaller. Before you got 451, now you get 450.)
(c) 354 + 168 = 522 (You are adding 1 more than before. When you add a bigger amount, your answer gets 1 bigger. Before you got 521, now you get 522.)
(d) 446 + 219 = 665 (The first number went down by 10, but the second number went up by 10. These changes cancel each other out, so the sum stays the same at 665.)
In simple words: When you change one number by a small amount, the answer changes too. If you subtract more, the result gets smaller. If you add more, the result gets bigger. But if one goes up and one goes down by the same amount, the total stays the same.

Exam Tip: Use earlier results to find new answers quickly. Explain how a small change in the numbers affects the final result - this shows deep understanding.

Question 1. Add.
(a) 2783 + 378
(b) 8948 + 97
(c) 7006 + 367
(d) 8009 + 485
(e) 6062 + 3809
(f) 3792 + 2688
(g) 4999 + 3888
(h) 5005 + 4895
(i) 5768 + 4053
(j) 3480 + 479
Answer:
(a) 3161
(b) 9045
(c) 7373
(d) 8494
(e) 9871
(f) 6480
(g) 8887
(h) 9900
(i) 9821
(j) 3959
In simple words: Place one number above the other so the ones, tens, hundreds, and thousands line up. Add each column starting from the right. If a column makes 10 or more, carry the extra to the next column.

Exam Tip: Write out the numbers in columns clearly. Double-check by adding the two numbers in a different order - addition works both ways and you should get the same answer.

Question 2. Subtract.
(a) 4456 - 2768
(b) 5300 - 467
(c) 8067 - 4546
(d) 5302 - 1034
(e) 8004 - 3107
(f) 3400 - 897
(g) 9382 - 4857
(h) 7561 - 2933
(i) 6478 - 5986
(j) 3444 - 2555
Answer:
(a) 1688
(b) 4833
(c) 3521
(d) 4268
(e) 4897
(f) 2503
(g) 4525
(h) 4628
(i) 492
(j) 889
In simple words: Line up the bigger number on top and the smaller number below, matching up the place values. Subtract each column starting from the right. If the bottom digit is bigger, borrow 1 from the column to the left.

Exam Tip: After you subtract, add your answer to the bottom number. You should get the top number back - this is a quick way to check if you are right.

Question 3. Fill the squares with the numbers 1-9. The difference between any two neighbouring squares (connected by a line) must be odd. Can you find other ways to fill the squares? Can you do the same thing such that the difference between any two neighbouring squares is even?
Answer: One solution (where the difference must be odd):

3 - 2 - 1 - 1 - 8 - 7
| | | | | |
4 - 5 - 8 1 - 9 - 6
| | | | | |
7 - 6 - 9 - 3 - 4 - 5

OR

1 - 8 - 7
| | |
2 - 9 - 6
| | |
3 - 4 - 5

For odd differences: Place odd numbers next to even numbers (e.g., 1 next to 2, 8 next to 7). Odd minus even always gives an odd answer.

For even differences, it is not possible to fill a connected grid with all nine different numbers (1-9) such that every pair of neighbours has an even difference. This is because you cannot alternate between odd and even numbers in a connected way that uses all nine digits without repeating.
In simple words: For odd differences, put odd numbers next to even numbers. An odd number minus an even number is always odd. For even differences, you would need to put numbers that are close to each other (like 2 and 4, or 6 and 8), but you only have nine numbers and many connections, so it is very hard or impossible.

Exam Tip: Understand why the pattern works: odd - even = odd, and even - even = even. Test different arrangements and explain why some work and others do not based on this rule.