House of Hundreds - I Chapter Notes | Mathematics for Class 3 (Maths Mela) PDF Download

Introduction

Let's Understand with Story

Once upon a sunny day, at the lively carnival grounds, Ajit, Tom, and Joy found themselves at a colorful stall filled with delicious toffees. Joy's eager hands quickly grabbed two toffees, sparking a guessing game among the friends. Curious and excited, they wondered about the total number of toffees hidden within the boxes, starting a sweet adventure of counting and discovery.

Guessing and Counting Toffees

• Starting with the two toffees that Joy eagerly grabbed, they carefully counted the toffees in each box, one by one.
• Working together, they combined their counts and found that there were 298 toffees in total.
• Joy, with a playful smile, decided to add one more to make it a nice, even number, bringing the count to 299.
• Feeling the excitement rising, they couldn't resist adding one more toffee, reaching the magical milestone of 300.
• Their faces lit up with joy as they celebrated their achievement, laughing and cheering together.

Let's Practice -1 

1. Joy is hopping on the tiles at the fair. Can you guess the missing numbers below:

Have you tried guessing the numbers yet? If not, that's okay! The missing numbers have been given below for you:

2. Imagine there are some ants on the ground that found some food. Can you guess how many ants there might be? After making a guess, let's count them together to see if our guess was correct.

Hint:

Well done! You've guessed the right number. So, the total number of ants are 127.

Writing Number Sentences

Imagine you have big bundles of matchsticks as shown in the picture below. Each big bundle has 10 smaller bundles inside. Each of these smaller bundles has 10 matchsticks.

So, to find out how many matchsticks are in one big bundle, we multiply: 10 (small bundles) x 10 (matchsticks in each small bundle) = 100 matchsticks in one big bundle.
But wait! We have two big bundles, so we multiply 100 (matchsticks in one big bundle) x 2 (big bundles) = 200 matchsticks in total from the big bundles.

Now, we have 3 small bundles left over along with 5 matchsticks extra.
Each of these small bundles has 10 matchsticks, so we multiply: 3 (extra small bundles) x 10 (matchsticks in each small bundle)
= 30 matchsticks in total from the extra small bundles + 5 matchsticks extra
= 35 matchsticks  So, all together, we have 200 matchsticks from the big bundles and 35 matchsticks from the small bundles and extra matchsticks , making a total of 235 matchsticks.

Number Sentence for number 235 can be written in the following ways:-

• 200 and 35 more (200+35), or
• 15 less than 250 (250 - 15).

Number Fun: Up and Down We Go!

Once upon a time, there were five friends named Jack, Lily, Ben, Mia, and Sam. They were all going on a camping trip together.

• Jack brought 5 apples with him for everyone to share. He decided to give one more apple to share with Lily. So, now they had 6 apples in total. Adding 1 made the number of apples bigger.
  
• Meanwhile, Ben had 10 marshmallows to roast over the campfire. But Sam accidentally dropped 2 of them into the fire. Now, they only had 8 marshmallows left. Taking away 2 made the number of marshmallows smaller.

So, by adding more or taking away some, the number of things they had changed during their camping adventure!
Now, Let's play with numbers! We'll learn how to increase or decrease them.
(i) 285 – increase the number by one
Sol: Here, we've to make the number bigger by adding one i.e. 285+1. We'll get 286.

(ii) 147 – increase the number by ten 
Sol: Here, we've to make the number bigger by adding ten i.e. 147+10. We'll get 148.

(iii) 367 – decrease the number by 2
Sol: Here, we've to make the number a bit smaller by taking away 2. which means 367-2. We'll get 365.

(iv) 289 – decrease the number by 10
Sol: Here, we've to make the number a bit smaller by taking away 10. which means 289-10. We'll get 279.

(v) 290 – increase the number by 20
Sol: Here, we've to make the number bigger by adding 20 i.e. 290+20. We'll get 310.

Yay! You've learnt how to make numbers bigger and smaller. Well done.

Counting the Number of letter in Number Names 

Counting the number of letters in the names of numbers is a fun way to learn about both counting and numbers themselves. Here's how you can do it:

• Write Down the Number: Start by writing down the number whose name you want to count the letters for. For example, let's take the number "Eleven."
• Spell Out the Number: Write the number in words. "Eleven" is spelled as E-L-E-V-E-N.
• Count the Letters: Count each letter in the word. "Eleven" has five letters: E-L-E-V-E-N.
  
• Repeat for Other Numbers: You can repeat this process for other numbers as well. For instance, "three" has five letters (T-H-R-E-E), "seven" has five letters (S-E-V-E-N), and "twenty" has six letters (T-W-E-N-T-Y)

Writing Numbers in Sentences

• When we count or talk about numbers, we use special words called number names. 
• These help us say numbers in words instead of just using digits. Let's learn how to write number names for three-digit numbers.
• Three-digit numbers are numbers that have three digits in them.
  We read them from left to right, just like we read words in a book.
  
• The number 123 has three digits: 1, 2, and 3.
  Each digit has its own place: hundreds, tens, and ones.
• To write three-digit numbers in words, we start by saying how many hundreds, then how many tens, and finally how many ones.
  For example: The number 123 is written as "one hundred twenty-three."
• We say
  (i) "one hundred" for the digit in the hundreds place (1),
  (ii) "twenty" for the digit in the tens place (2), and
  (iii) "three" for the digit in the ones place (3).

Let's look at some examples:
(i) 256: This is read as "two hundred fifty-six."
(ii) 378: This is read as "three hundred seventy-eight."
(iii) 429: This is read as "four hundred twenty-nine."

Let's Practice - 2

• In the colorful land of Numerica, there were three best friends: Two-hundred and Thirteen, Three Hundred and Sixty Seven, and One Hundred and Ten. They wanted to know whose name was the longest, so they decided to count the letters in their names
• They gathered around a magical counting tree, where each leaf had a letter written on it.
  (i)  Two-hundred and Thirteen suggested they count the letters in their names.
  (iiThree Hundred and Sixty Seven suggested they take turns counting each other's letters to make sure they didn't miss any.
• They started with Number Two-hundred and Thirteen and counted 21 letters.
• Then, they counted 23 letters in Number Three hundred and Sixty Seven.
  
• Finally, they counted 16 letters in Number One Hundred and Ten.
  
• They discovered that Number Three hundred and Sixty Seven had the longest name with 25 letters.

They agreed that each of their names was unique and special. They were happy to learn how to count the letters in their names.

Counting Numbers on Number Line

Number Line 

A number line is like a road where numbers go for a walk! It's a line where we put numbers in order from smallest to biggest, just like when we line up for lunch.

Imagine you're standing at one end of the number line. As you walk along it, you'll see numbers getting bigger and bigger. If you go the other way, numbers get smaller and smaller.

Counting on a number line is like taking steps. Let's say we want to count from 100 to 110. We start at 101, then take a step to 102, then 103, then 104, and finally we'll reach 110 by continuing in the same manner. Each step we take brings us closer to the next number.

So, number lines help us see how numbers are arranged and how we can move between them by taking steps. It's like walking along a path of numbers, one step at a time

Understanding Place Value

• In math, every number has different parts called digits. 
• Each digit has a special value based on where it is in the number. This special value is called its "place value."
• For example, let's look at the number 786. In this number:
  (i) The digit 7 is in the hundreds place. So, its place value is 7 hundreds, which is 700.
  (ii) The digit 8 is in the tens place. So, its place value is 8 tens, which is 80.
  (iii) The digit 6 is in the ones place. So, its place value is just 6.

So, when we put all these values together, we get 700 (from 7 hundreds), plus 40 (from 4 tens), plus 3 (from 3 ones), which equals 743.

• Let's take the number 24 as an example.
  (i) It has two digits.
  (ii) The digit 4 represents four single items, and it's placed in the ones position. (iii) The digit 2 in the tens place represents two bundles of ten items each, which makes twenty.
  (iv) So, when we combine the value of 20 with the value of 4, we get the number 24.

Comparing Numbers 

• '=' is the symbol used for 'equal to'.
• 3 = 3 is read as '3 is equal to 3'.
• Look at the numbers from 11 to 20 in order.
  The number 13 is to the left of 14. So, 13 < 14.The number 14 is to the right of 13. So, 14 > 13.Every number is equal to itself. 14 = 14, 15 = 15, 16 = 16, etc.

Comparing 3-digit Numbers

• We can compare numbers by looking at their hundreds, tens, and ones places.
• If two numbers have the same hundreds place, we look at the tens place to see which one is bigger.
  If the tens places are the same, we look at the ones place.
• Let's look at some examples:
  (i) 329 and 392: 
  Both numbers have three hundreds, but 329 has 2 tens while 392 has 9 tens. So, 392 is greater than 329.
  (ii) 235 and 523: 
  Here, 235 has 2 hundreds and 3 tens, while 523 has 5 hundreds and 2 tens. Since 523 has more hundreds, it's greater than 235.

Ascending and Descending Orders

There are 5 members in the Dubey family— Mr. Dubey, Ms. Dubey, Tina, Rahul, and their pet Rocky.They are standing height-wise from the tallest to the shortest (in descending order) in picture 1 and from the shortest to the tallest (in ascending order) in picture 2.
In case of numbers:

• Arranging or moving from the greatest number to the smallest number is called the descending order or decreasing order.
• Arranging or moving from the smallest number to the greatest number is called the ascending order or increasing order. 

For example: The numbers 2, 4, 5, 8, and 9 are in ascending order whereas 9, 8, 5, 4, and 2 are in descending order.

Use of > or < in Forward and Backward Counting

• Jiya starts climbing the stairs from stair number 11. She has to reach stair number 20 to pick her pencil pouch that she dropped over there.
• As she goes up, she counts up (forward) as 11, 12, 13, 14, 15, 16, 17, 18, 19 and 20. While coming back with her pencil pouch, she counts backward as 20, 19, 18, 17, 16, 15, 14, 13, 12, and 11.
• 11 < 12 < 13 < 14 < 15 < 16 < 17 < 18 < 19 < 20 is the ascending order of the numbers from 11 to 20. 20 > 19 > 18 > 17 > 16 > 15 > 14 > 13 > 12 > 11 is the descending order of the numbers from 20 to 11.

Edurev Tips: Numbers get “bigger/greater” when counting forward and “smaller/ lesser” when counting backwards.

Forming 3-Digit Numbers

Forming the Greatest Number

• To form the greatest number, we arrange the digits in descending order, starting from the hundreds place.
• We choose the largest digit for the hundreds place, the next largest for the tens place, and the smallest for the ones place.

Forming the Smallest Number

• To form the smallest number, we arrange the digits in ascending order, starting from the hundreds place.
• We choose the smallest digit for the hundreds place, the next smallest for the tens place, and the largest for the ones place.

Examples: 
(i) Digits: 3, 7, 2
Greatest 3-digit Number: 732 (Descending order: 7 > 3 > 2)
Smallest 3-digit Number: 237 (Ascending order: 2 < 3 < 7)

(ii) Digits: 5, 6, 2
Greatest Number: 652 (Descending order: 6 > 5 > 2)
Smallest Number: 256 (Ascending order: 2 < 5 < 6)