NCERT Class 4 Mathematics Maths Mela Chapter 10 Elephants Tigers and Leopards PDF Download

Chapter 10: Elephants, Tigers, and Leopards

NIM Game (2 Player Game)

You have played a version of this game in the chapter 'Vacation with my Nani Maa' in Grade 3. We will add either 1 or 2 each time to reach the target number 10.

How to play?

1. Player 1 starts by choosing either 1 or 2.
2. Player 2 can also choose either 1 or 2 and add it to the number chosen by Player 1.
3. The two players continue playing by choosing either 1 or 2 and adding it to the previous total.
4. The player who reaches 10 first is the winner.
5. Play it for a few rounds.

Can you win the game if

1. the other player has reached the total of 6 and it is your turn?
2. the other player has reached the total of 7 and it is your turn?
3. the other player has reached the total of 8 and it is your turn? Who wins in each of these cases?

Note for Teachers

Encourage learners to play this game with various target numbers. You could also help note down the sums and the results for learners to analyse.

Teacher's Note

In this game, look for a winning position - a number where you can control the outcome. If your opponent reaches 8, you can add 1 or 2 to make either 9 or 10. If you make 9, your opponent makes 10 and wins; if you make 10, you win. So reaching 8 is a losing position for the player whose turn it is. Work backwards: what positions let you guarantee a win?

Play the game to reach other target numbers (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?

Addition Chart

Look at the table given below and discuss how the table is made.

1. Identify some patterns in the table.
2. Observe the cells where the number 9 appears in the table. How many times do you see number 9? What about other numbers?
3. Are there any rows or columns that contain only even numbers or only odd numbers? Explain your observation.
4. Look at the window frame highlighted in red colour in the table.
   1. Find the sum of the two numbers in each row.
   2. Find the sum of the two numbers in each column. What do you notice?
   3. Now, find the sum of the numbers in each of the two diagonals marked by arrows. What do you notice?
   4. Now, put the red window frame in other places and find the sums as above. What do you notice?
5. Identify some patterns and relationships among the numbers in the blue window frame.

Reverse and Add

1. Take a 2-digit number say, 27. Reverse its digits (72). Add them (99). Repeat for different 2-digit numbers.
2. What sums can we get when we add a 2-digit number with its reverse?
3. List down all numbers which when added to their reverse give
   1. 55
   2. 88
4. Can we get a 3-digit sum? What is the smallest 3-digit sum that we can get?

Fill in the blanks with appropriate numbers.

a)

2540 2540 2540 2590

b)

354 1354

c)

7645 7670 7745

How Many Animals?

India is rich in biodiversity. It is home to some of the endangered wildlife, like elephants, tigers and leopards.

\( \frac{3}{4} \) of the world's tiger population and \( \frac{3}{5} \) of the Asiatic elephant population is in India.

1. The population of elephants in Karnataka is 6049 and in Kerala is 3054. How many total elephants are there in these two states? Estimate the answer. ________

6049 + 3054

[Figure: Breakdown of 6049 and 3054 showing place value decomposition with thousands, hundreds, tens and ones, with carrying shown in the addition process, resulting in 9103, See in your textbook]

There are 9103 elephants in Karnataka and Kerala.

Teacher's Note

When you carry in addition, write the carried amount clearly above the next column. In the ones column, 9 + 4 = 13, which is 1 ten and 3 ones. The 1 ten moves to the tens column, leaving 3 in the ones place. Follow this step-by-step, column by column, and you will avoid mistakes.

2. The highest number of leopards are found in three states. Gujarat has 1355, Karnataka has 1131 and Madhya Pradesh has 1817. How many total leopards are there in these states? Estimate the answer. ________

1355 + 1131 + 1817

[Figure: Breakdown of 1355, 1131 and 1817 showing place value decomposition with thousands, hundreds, tens and ones, with carrying shown in the addition process, resulting in 4303, See in your textbook]

There are 4303 leopards in these three states.

Key Points

• In the NIM game, you win by finding positions where your opponent cannot stop you from reaching the target number. Work backwards from the target to find which numbers are winning and which are losing positions.
• In an addition chart, every number appears in a diagonal line, and rows and columns show how addition patterns repeat in organized ways.
• When adding 2-digit numbers to their reverses, you always get a sum with the same digit repeated (like 99, 121, 33). The middle digit is always 0 for certain sums.
• When adding numbers in columns, carry over to the next place value whenever a column adds up to 10 or more. Always write the carried amount above the column so you do not forget it.

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