Raksha Bandhan Chapter Notes | Mathematics for Class 3 (Maths Mela) PDF Download

Introduction

Understanding Multiplication

Imagine you have a basket full of colorful marbles. You want to know how many marbles are in the basket, right? Let's count them together. As you count, you notice that there are 4 rows of marbles, and each row has 5 marbles. So, you count each row one by one:

1.  5 marbles in the first row,
2. 5 marbles in the second row,
3.  5 marbles in the third row, and
4. 5 marbles in the fourth row.

Now, instead of counting each row separately, you can use multiplication to find the total number of marbles i.e. we can simply say 5 times 4, or you multiply the number of rows (4) by the number of marbles in each row (5). That's 4×5, which equals 20.

So, there are 20 marbles in the basket!

Understanding Division 

Division is a way of sharing things equally among a certain number of people.

• Imagine you have a big box of delicious kaju katlis, and you want to share them equally with your friends. 
• Let's say you have 20 kaju katlis in total and 5 friends to share them with.
  
• Instead of distributing one by one, we can use division to find out how many kaju katlis each friend gets.
• We start with the total number of kaju katlis, which is 20, and then divide it by the number of friends, which is 5 i.e. 20÷5 = 4
• This division process is like repeated subtraction. We subtract 5 kaju katlis at a time until we can't subtract anymore.
  After the first subtraction, we have 15 kaju katlis left: 20−5=15.
  Then, another 5 kaju katlis are subtracted, leaving 10 kaju katlis: 15−5=10.
  
• This process continues until we subtract the last 5 kaju katlis, leaving 0 kaju katlis as shown in the picture below:-
  
• Each time we subtract 5 kaju katlis, we add one count to represent one person's share. So, in total,  20 equally shared by 5 is 4 each. Each friend gets 4 kaju katlis.

This is how division helps us distribute items fairly and equally among a certain number of people, ensuring everyone gets their fair share.

Learning with Story:

Once upon a time, in a cozy little house, there lived a girl named Sara. Sara loved her four cousins: Alex, Ben, Clara, and David. One sunny afternoon, their grandma gave Sara a bag of 12 toffees to share equally with her cousins. Sara wanted to make sure each cousin got the same number of toffees, so she needed to figure out how to do this.

Sara decided to use a method she learned in school called "division." Division helps us find out how to split something into equal parts. Here's how Sara did it:

1. Count the Total Number of Toffees: Sara counted the toffees in the bag and found there were 12 toffees.
2. Count the Number of Cousins: Sara counted her cousins: Alex, Ben, Clara, and David. There were 4 cousins.

Sara realized she needed to divide the total number of toffees (12) by the number of cousins (4). She remembered the division symbol (÷) and set up her problem:

$12÷4=?$

To figure this out, Sara thought about it like this: if she gives 1 toffee to each cousin, she would have given out 4 toffees in total (because there are 4 cousins). She kept giving each cousin 1 toffee until all the toffees were gone.

Here's how she did it step-by-step:

1. She gave 1 toffee to each cousin, so 4 toffees were given out (12 - 4 = 8).
2. She gave another 1 toffee to each cousin, so another 4 toffees were given out (8 - 4 = 4).
3. She gave 1 more toffee to each cousin, giving out the remaining 4 toffees (4 - 4 = 0).

Sara saw that each cousin received 3 toffees. She checked her work: 3 toffees per cousin times 4 cousins equals 12 toffees.

So, the division was correct:

$12÷4=312\; \backslash div\; 4\; =\; 3$

Sara was happy that each of her cousins got an equal share of toffees, and they all enjoyed their sweet treat together. By using division, Sara ensured that everyone was treated fairly and equally. 

Ways of Grouping

Let's talk about a fun way to count things! Imagine you have a bunch of your favorite candies. How would you count them? There are many ways, and we'll explore some exciting methods together!

• Think about your candies . You can put them in groups to count them easily.
  For example, let's say you have 12 toys. You can make 3 groups with 4 candies in each group. So, you have 3 groups of 4 candies each. That's one way to count them!
  
• Now, let's try another way. Instead of 3 groups, let's make 4 groups, each with 3 candies. So, now you have 4 groups of 3 candies each. That's another way to count them!
  
• Whether you make 3 groups of 4 candies or 4 groups of 3 candies, you still have the same total number of candies, which is 12.

This shows us that we can count things by grouping them in different ways, but the total remains the same! It makes counting even more fun!

 Number Line Hopscotch

Once upon a time,  Maya, and their mother found a cool game called "Number Line Hopscotch." Maya jumped 3 steps each time on a curved number track. 

As they played, they noticed something amazing! Maya's jumps went 0, 3, 6, 9.

They realized that by adding the same number, they could guess the next jump. Let's consider Maya's jumps
1     jump     →     3      
2     jumps     →     3 + 3 = 6 = 2 x 3      
3     jumps     →     3 + 3 + 3 = 9 = 3 x 3
4     jumps     →     3 + 3 + 3 + 3 = 12 = 4 x 3, and so on.

Now, they learned that math is like an exciting adventure with hidden patterns. Each jump was like solving a fun puzzle! So, they hopped and laughed, discovering the wonders of numbers. Math wasn't just numbers; it was a fantastic journey of discovery!

Writing Tables

In the Fun Way of Writing Tables game, a little boy Aryan and his friends found a cool way to learn their times tables using sticks. They made a grid with sticks and counted where they crossed to figure out the answers.

Here's how they did it:

• Aryan lined up sticks in rows and columns to make a big square grid.
  
• Then, he counted where the sticks crossed to find the answer to different multiplication questions.
  For example, to find out what 5 times 3 is, she counted where the row labeled "3" and the column labeled "5" crossed.
  
• He noticed a pattern in the answers, like how the last numbers repeated in some of them. This helped her understand how numbers work together.
• Following the same pattern, they discovered some other tables as well,which are shown below:
  
• Aryan and his friends also saw something cool when they looked at the tables for 2, 3, and 5. They noticed that some numbers had a special connection with others. This made them curious, and they wanted to explore more!
• As you can see, when we multiply 1 with 2, we get 2; when we multiply 1 with 3, we get 3 and when we multiply 1 with 5, we get 5.
• So, we can say that any number multiplied to 1 results in the same number.

By playing this game, Aryan and his friends had fun while learning about multiplication tables and discovering new patterns in numbers. Math became an exciting adventure for them!

Word Problems 

1. There are 5 fruits in each basket. If there are 9 baskets filled with fruits, how many fruits are there in total?Sol: No. of fruits in one basket = 5
No. of baskets = 9
Total fruits = Fruits per basket × Number of baskets
= 5 × 9
= 45
Hence, there are 45 fruits in total.

2. Donald , the duck can see 60 Legs in a cow shed , How many cows are there in the shed ?

Sol: Total No. of Legs = 60

No of legs one cow has = 4

Total Number of Cows in the shed = 60 / 4 

=15

Hence, there are 12 cows in the shed .  

This way you can try more such examples , where you can  get familiar with Division and Multiplication.