Give and Take Chapter Notes | Mathematics for Class 3 (Maths Mela) PDF Download

Understanding Word Problems

Word problems are mathematical questions presented in words rather than just numbers. They often involve real-life situations and require you to use math to solve them. Let's take an example and see how to solve word problems?

Example Problem: Kishan has 456 saplings in August. He distributed 63 saplings. How many saplings are left with him?

Solution:

1. Identify Given Information:

   • Total saplings Kishan has = 456
   • Saplings distributed = 63

2. Set Up the Equation: To find out how many saplings are left, we subtract the distributed saplings from the total saplings:

   $Total\; saplingsSaplings\; left\backslash text\{Total\; saplings\}\; -\; \backslash text\{Distributed\; saplings\}\; =\; \backslash text\{Saplings\; left\}$Total saplings−Distributed saplings=Saplings left $456-63=?456\; -\; 63\; =\; \backslash text\{?\}$?

3. Solve the Equation: Starting from the right side, we do the subtraction:

   • Ones place: $6-3=36\; -\; 3\; =\; 3$
   • Tens place: $5-65\; -\; 6$. Since 5 is smaller than 6, we borrow 1 from the hundreds place, making it 4, and add 10 to 5, making it 15. Now, $15-6=915\; -\; 6\; =\; 9$
   • Hundreds place: $4-0=44\; -\; 0\; =\; 4$

4. Putting it all together: $456-63=393456\; -\; 63\; =\; 393$

5. Conclusion: Kishan has 393 saplings left with him after distributing 63 saplings.

In summary, when solving word problems, it's crucial to identify the given information, set up the equation based on what you're asked to find, solve the equation step by step, and then conclude with the answer and what it means in the context of the problem.

Estimating Values

Estimating values is important because it helps us quickly understand and make decisions about quantities without needing exact numbers, making math and real-life situations easier to handle.
Let's take a number : 156 + 34

Steps:

1. Identify the Numbers:

   • $156156$ is the first number in the problem.
   • $3434$ is the second number in the problem.

2. Locate the Hundreds Place:

   • In $156156$, the hundreds place digit is $1$1.
   • In 34, there is no hundreds place digit because the number is in the tens place.

3. Round to the Nearest Hundred:

   • Since $156156$ is closer to $200200$ than $100100$ (as it's more than halfway between $100100$ and 200), round $156156$up to $200$.
   • $3434$ remains unchanged because there's no hundreds place to round.

4. Add the Rounded Numbers:

   • Add the rounded numbers: $200+34$

5. Calculate the Estimate:

   • $200+34=234200\; +\; 34\; =\; 234$

Understanding Different Combinations

A number can be made using different combinations. let's see an example:

Example 1: Making 42 Rupees

• 4 x 10 Rupee Notes
• 1 x 2 Rupee Coin

Example 2: Making 42 Rupees (Alternative)

• 8 x 5 Rupee Coins
• 2 x 1 Rupee Coins

Explanation: When we need to make a specific amount of money, we can use different combinations of notes and coins to reach that total. Let's break down the examples:

1. Example 1:

   • We start with 4 ten-rupee notes, each worth 10 rupees.
   • Additionally, we add 1 two-rupee coin, which is 2 rupees.
   • When we combine these, 4 x 10 rupees + 1 x 2 rupees = 40 rupees + 2 rupees = 42 rupees, which is our target amount.

2. Example 2:

   • Here, we use 8 five-rupee coins, each worth 5 rupees.
   • We also include 2 one-rupee coins, each worth 1 rupee.
   • Adding these together, 8 x 5 rupees + 2 x 1 rupee = 40 rupees + 2 rupees = 42 rupees, matching our required amount.

Word Problems Related to Money

Solving money-related word problems involves understanding the problem, identifying the given information, performing calculations, and reaching the solution. Let's go through the steps and then use an example:

Solving Money Word Problems: Step-by-Step

Step 1: Understand the Problem

• Read the problem carefully to understand what information is given and what needs to be found.
• Identify keywords like "earned," "spent," "total," "more," "less," etc., which indicate operations to be performed.

Step 2: Identify Given Information

• Note down the amounts of money mentioned in the problem.
• Pay attention to any additional information provided, such as increases, decreases, or totals.

Step 3: Perform Calculations

• Use addition, subtraction, multiplication, or division as required based on the problem's context.
• Apply the operations to the given amounts to find the solution.

Step 4: Check and Interpret the Answer

• Verify your calculations to ensure accuracy.
• Interpret the answer in the context of the problem to make sure it makes sense.

Example: Problem:
Anu has ₹500. She spends ₹150 on books and then earns ₹200 from selling old toys. How much money does she have now?

Step 1: Understand the Problem

• Anu starts with ₹500.
• She spends ₹150 on books.
• She earns ₹200 from selling old toys.
• We need to find out how much money she has after these transactions.

Step 2: Identify Given Information

• Anu starts with ₹500.
• She spends ₹150.
• She earns ₹200.

Step 3: Perform Calculations

• Start with ₹500.
• Subtract ₹150 (spent on books): ₹500 - ₹150 = ₹350.
• Add ₹200 (earned from selling toys): ₹350 + ₹200 = ₹550.

Step 4: Check and Interpret the Answer

• The calculation shows that Anu has ₹550 after the transactions.

Let's Practice 

1. Look at the given picture and do as directed.

Sol:

2. Tick mark the pairs that are equal.

Sol: