NCERT Solutions for Class 3 Maths Chapter 09 House of Hundreds - II

Exercise 9: House of Hundreds - II

Question. Circle the shapes where half of the whole is shaded.
What are you carrying? How many are there?
Number of rice sacks: [     ]
Answer:
Number of rice sacks: 632
In simple words: By counting the tile blocks, we can see there are 6 hundreds, 3 tens, and 2 ones, which makes 632 sacks of rice.

Exam Tip: Each large yellow square stands for 100, each thin rectangle stands for 10, and each tiny square stands for 1. Count them to find the total.

Question. Draw tiles like the driver to show the following numbers. You can do it in your notebook.
a. 832
b. 947
c. 726
d. 504
e. 620
f. 700
Answer:
a. 832: 8 hundreds tiles, 3 tens tiles, 2 ones tiles
b. 947: 9 hundreds tiles, 4 tens tiles, 7 ones tiles
c. 726: 7 hundreds tiles, 2 tens tiles, 6 ones tiles
d. 504: 5 hundreds tiles, 0 tens tiles, 4 ones tiles
e. 620: 6 hundreds tiles, 2 tens tiles, 0 ones tiles
f. 700: 7 hundreds tiles, 0 tens tiles, 0 ones tiles
In simple words: To show these numbers with tiles, use large square blocks for hundreds, thin strips for tens, and tiny squares for ones. For example, 832 needs 8 large squares, 3 thin strips, and 2 tiny squares.

Exam Tip: Always look at the place value - the first digit from the left shows hundreds, the middle digit shows tens, and the last digit on the right shows ones.

Question. Let us locate the following numbers on the number line: 530, 540, 628, 696, 590
Answer:
The missing numbers in the boxes on the number line are:
- First box = 540
- Second box = 580
- Third box = 640

The numbers are located as follows:
- 530 lies exactly midway between 520 and 540.
- 540 is the value of the first blank box on the line.
- 590 lies midway between 580 and 600, just before 600.
- 628 lies just before 630, between 620 and 640.
- 696 lies very close to 700.
In simple words: The big marks on the line go up by 20. The smaller marks in between go up by 10. We can find each number by counting the marks from 500.

Exam Tip: On a number line, find the scale first. Here, each small division represents 10 units.

Question. Also locate the following numbers on the number line: 703, 721, 759, 810, 855, 887
Answer:
The missing numbers in the boxes on the number line are:
- First box = 755
- Second box = 815
- Third box = 895

The numbers are located as follows:
- 703 lies just after 695.
- 721 lies just after 715.
- 759 lies just after 755.
- 810 lies midway between 795 and 825 (just before 815).
- 855 is directly on the marked tick for 855.
- 887 lies just before 895.
In simple words: The number line ticks jump by 20. The boxes are halfway between the ticks, so they go up by 10 from the previous tick. We can place our numbers by finding where they fit between these ticks.

Exam Tip: Remember that numbers like 703 and 721 will be placed very close to the marks 695 and 715 because they are only a few units away.

Question 1. Write the appropriate numbers between which each of the given numbers lie.
Answer:

In simple words: This table shows us where each number sits. We look at the closest hundreds (like 100 and 200), the closest fifties (like 150 and 200), and the closest tens (like 180 and 190) on both sides.

Exam Tip: To find neighboring fifties, find the multiples of 50 that are just smaller and just larger than your number.

Question 2. Help cranes reach their food using the number line.
First Crane (at 667):
To reach the worm:
667 - .......... steps = 650
Length of steps: ..........

To reach the fish:
667 + .......... steps = 700
Length of steps: ..........

Second Crane (at 773):
To reach the worm:
.......... - .......... steps = 750
Length of steps: ..........

To reach the fish:
.......... + .......... steps = 800
Length of steps: ..........

Answer:
First Crane (at 667):
To reach the worm:
667 - 17 steps = 650
Length of steps: 17

To reach the fish:
667 + 33 steps = 700
Length of steps: 33

Second Crane (at 773):
To reach the worm:
773 - 23 steps = 750
Length of steps: 23

To reach the fish:
773 + 27 steps = 800
Length of steps: 27
In simple words: Subtract to find how far the crane must go backward to the worm. Add to find how far it must go forward to the fish.

Exam Tip: Check your calculations: \( 667 - 17 = 650 \) and \( 667 + 33 = 700 \). The steps must match the differences between the numbers.

Question 3. Fill the grid with numbers between 570 and 630. Strike out all the numbers which match the clues below. You can strike out more than one number. The child who has most numbers cancelled is the winner. One example is given below.
Clues:
1. 597
2. A number with 4
3. Numbers between 595 and 605
4. A number with 1 as the tens digit
5. Two more than 610
6. 5 less than 625

Write different ways of making the following numbers: 368, 555, 905, 736.
Answer:
1. Number Grid with Cancelled Numbers (shown as struck out):

2. Different ways of making the numbers:

Ways to make 368:
- 3 hundreds, 6 tens, 8 ones
- 68 more than 300
- 32 less than 400 (400 - 32)
- 300 + 60 + 8

Ways to make 555:
- 5 hundreds, 5 tens, 5 ones
- 55 more than 500
- 45 less than 600 (600 - 45)
- 500 + 50 + 5

Ways to make 905:
- 9 hundreds, 0 tens, 5 ones
- 5 more than 900
- 95 less than 1000 (1000 - 95)
- 900 + 0 + 5

Ways to make 736:
- 7 hundreds, 3 tens, 6 ones
- 36 more than 700
- 64 less than 800 (800 - 64)
- 700 + 30 + 6
In simple words: Struck-out numbers are the ones that match our clues. We can also show any three-digit number in different ways, like using place values, adding, or subtracting.

Exam Tip: Read clues carefully as some numbers like 614 can match more than one clue (it has a 4 and has a 1 in the tens place).

Question. Teji and Jojo are resting. Ajji asks them to complete the number patterns. Let us help them fill in the empty boxes.
Answer:
The number patterns can be completed as follows:
- Pattern 1 (Counting by 10s): 720, 730, 740
- Pattern 2 (Counting by 100s, going upwards): 450, 550, 650, 750, 850, 950
- Pattern 3 (Counting by 10s, going right from 750): 750, 760, 770, 780
- Pattern 4 (Counting by 25s): 880, 905, 930
- Pattern 5 (Counting by 30s, bottom row): 830, 860, 890, 920, 950, 980
- Pattern 6 (Counting by 15s, diagonal arrows): 845, 860, 875, 890, 905
In simple words: Look at how the numbers jump in each path. Some jump by 10, some by 15, some by 25, some by 30, and some by 100! Fill the boxes by adding that jump number each time.

Exam Tip: To find the pattern's rule, subtract any two side-by-side numbers to see how big the jump is.

Question 1. Write number sentences for the numbers in the centre.
Answer:
Number sentences that sum to 400:
- 290 + 110 = 400
- 280 + 120 = 400
- 220 + 180 = 400
- 230 + 170 = 400
- 260 + 140 = 400

Number sentences that sum to 775:
- 750 + 25 = 775
- 725 + 50 = 775
- 710 + 65 = 775
- 765 + 10 = 775
- 715 + 60 = 775
In simple words: We are finding different pairs of numbers that add up to 400 and 775. There are many ways to split a big number into two parts!

Exam Tip: To find a new pair, you can subtract any number smaller than the target from the target number itself.

Question 2. Write numbers in the blank spaces such that they meet the conditions.
Answer:
First Group (around 400):
The alligator mouths show that all the surrounding numbers must be greater than 400:
- Top-left: 405 > 400
- Bottom-left: 407 > 400
- Top-right: 400 < 425
- Bottom-right: 400 < 430

Second Group (finding the center number):
We need a center number that is smaller than 419, 385, 425, and 436:
- Center number = 380
- This satisfies: 419 > 380, 385 > 380, 380 < 425, and 380 < 436
In simple words: The open mouth of the alligator always points to the bigger number. We choose numbers so that the alligator is eating the larger value.

Exam Tip: Remember the rule: the wide open side of the inequality sign points to the larger number, and the pointed side points to the smaller number.

Question 3. Fill the numbers 384, 23, 176, 905 in the empty circles such that they meet the conditions.
Answer:
The numbers are placed in the circles as follows:
- Top Circle = 176
- Left Circle = 23
- Right Circle = 384
- Bottom Circle = 905

This satisfies all the alligator mouth conditions:
- 176 > 23 (Top is greater than Left)
- 176 < 384 (Top is smaller than Right)
- 23 < 905 (Left is smaller than Bottom)
- 384 < 905 (Right is smaller than Bottom)
In simple words: We place the smallest number (23) on the left, the biggest number (905) at the bottom, and the other two in the top and right circles so the signs are all correct.

Exam Tip: Start by identifying the largest and smallest numbers in the given list to easily place them at the extreme ends of the inequality chains.

Question 5. Match the quantities on the left with the appropriate numbers on the right.
- Number of children in your school
- Number of books in your classroom
- Number of people in a bus
- Number of pages in your mathematics book
- Number of steps you walk in a day
- Number of stars in the sky
- Number of flowers in a garland
Answer:
- Number of children in your school: More than 1000
- Number of books in your classroom: 101-200
- Number of people in a bus: 51-100
- Number of pages in your mathematics book: 101-200
- Number of steps you walk in a day: More than 1000
- Number of stars in the sky: More than 1000
- Number of flowers in a garland: 51-100
In simple words: This activity helps us guess the sizes of different groups. Some things like stars and school children are very large groups (more than 1000), while books or people in a bus are smaller groups.

Exam Tip: Use real-world logic to estimate sizes, keeping in mind that some items can have more than one reasonable match.

Question 6. Match the following such that all the conditions are met.
- I have 2 zeroes as digits and am very close to 99
- I have 3 hundreds, 6 tens and 7 ones
- I have zero tens and zero ones
- I am century + half century
- I come between 400 and 450 and I have 5 as a digit
Answer:
- I have 2 zeroes as digits and am very close to 99: 100
- I have 3 hundreds, 6 tens and 7 ones: 367
- I have zero tens and zero ones: 400
- I am century + half century: 150
- I come between 400 and 450 and I have 5 as a digit: 425
In simple words: Read each clue like a riddle! A century is 100, and half is 50, so they make 150. A number close to 99 with two zeroes is 100.

Exam Tip: Break down terms like "century" (100) and look at the place values (hundreds, tens, ones) to find the correct number.

Question. Can you find more such numbers that follow the pattern? (111, 222, 333...)
Answer:
The next numbers that follow this pattern are:
444, 555, 666, 777, 888
In simple words: Triplet numbers are three-digit numbers where all three digits are exactly the same, like writing the same number three times in a row.

Exam Tip: These numbers are called triplet numbers because they repeat the same digit three times.

Question. Here are more numbers that look the same, from left to right, and right to left: 353, 868. Finding them is a fun game. Write other such numbers.
Answer:
Other numbers that look the same from left to right and right to left are:
292, 121, 303, 454, 616
In simple words: These numbers are like a mirror. If you read them from left to right or backward from right to left, they look exactly the same!

Exam Tip: To create these mirror numbers (palindromes), make sure the first digit and the last digit are identical, with any digit in the middle.

Question. Teji likes numbers with zeroes. She knows numbers like 210, 404 and 800. Write more such numbers:
Answer:
Other numbers containing zeroes are:
590, 302, 803, 440, 550
In simple words: We can write any three-digit numbers that have at least one zero in the tens or ones place, like 590 or 302.

Exam Tip: Zero can be placed in the tens place or ones place of a three-digit number, but never in the hundreds place if it must remain a three-digit number.

Question 1. I have 6 blank paper slips. I can write 100, 10 or 1 on each of them. What numbers can I make with these 6 slips? Discuss.
a. What will you write on these slips for making 231?
b. What will you write on these slips for making 123?
Answer:
To make these numbers using exactly 6 slips, we write:
a. For making 231: Two slips of 100, three slips of 10, and one slip of 1.
(100 + 100 + 10 + 10 + 10 + 1 = 231)

b. For making 123: One slip of 100, two slips of 10, and three slips of 1.
(100 + 10 + 10 + 1 + 1 + 1 = 123)
In simple words: We split the number into hundreds, tens, and ones, and then write those values on our 6 paper slips.

Exam Tip: Ensure that the total number of slips you use is exactly 6 and that their values add up to the target number.

Question 2. Make other numbers.
- What is the largest number that can be made?
- Are there numbers which can not be made using these slips? Find out.
- What is the smallest number that can be made?
Answer:
- Other numbers you can make:
  a. Number is 321: uses three 100s, two 10s, and one 1 (300 + 20 + 1 = 321).
  b. Number is 132: uses one 100, three 10s, and two 1s (100 + 30 + 2 = 132).

- Largest number that can be made: 600 (using six slips of 100).
- Numbers that cannot be made: 120, 230, 117, 662, and many other numbers. Since we must use exactly 6 slips, any number that cannot be split into exactly 6 slips of 100, 10, or 1 cannot be made.
- Smallest number that can be made: 6 (using six slips of 1).
In simple words: Since we have exactly 6 slips, the biggest number is when we write 100 on all of them, which makes 600. The smallest is when we write 1 on all of them, making 6. We cannot make numbers that need more or fewer slips than 6.

Exam Tip: Since you must use exactly 6 slips, the sum of the digits in the hundreds, tens, and ones places of the numbers you can make must equal 6 (e.g., for 321, 3 + 2 + 1 = 6; for 132, 1 + 3 + 2 = 6).

Question. Take the digits 3 and 8 and make as many 2 or 3 digit numbers as you can. You can repeat the digits.
- Arrange the numbers: Smaller to greater
- Smallest number: ..........
- Largest number: ..........
Answer:
The 2-digit and 3-digit numbers we can make using 3 and 8 are:

2-Digit Numbers: 33, 38, 83, 88
3-Digit Numbers: 333, 338, 383, 388, 833, 838, 883, 888

- Arranged from smaller to greater:
33, 38, 83, 88, 333, 338, 383, 388, 833, 838, 883, 888
- Smallest number: 33
- Largest number: 888
In simple words: By combining 3 and 8 in different ways, we can make four 2-digit numbers and eight 3-digit numbers. When we put them in order, the 2-digit numbers are always smaller than the 3-digit numbers.

Exam Tip: To write numbers in order from smallest to largest, always list the 2-digit numbers first, then the 3-digit numbers, starting with the smallest digits.

Question 1. Teji is making numbers using words! She shows the blue cards and says it is 12. She shows the yellow cards and says 14. Why?
Answer:
- Blue Cards (Moon and Twins): "Moon" stands for 1 (since there is only one moon) and "Twins" stands for 2. Putting 1 and 2 together makes 12.
- Yellow Cards (Qutub Minar and Char Minar): "Qutub Minar" stands for 1 (as there is only one Qutub Minar) and "Char Minar" stands for 4 ("Char" means four). Putting 1 and 4 together makes 14.
In simple words: Teji is using words that stand for numbers. "Moon" means 1 and "Twins" means 2, which makes 12. "Qutub Minar" means 1 and "Char Minar" means 4, which makes 14.

Exam Tip: Pay attention to the meaning of the words: unique things like the Moon stand for 1, while words like "Twins" (2) and "Char" (4) give the other digits.

Question 2. Ajji showed some more numbers. Write the numbers for:
a. Directions, Eyes
b. Sense organs, Hexagon
Answer:
- a. Directions, Eyes: There are 4 directions (North, South, East, West) and we have 2 eyes. Putting 4 and 2 together makes 42.
- b. Sense organs, Hexagon: We have 5 sense organs, and a hexagon has 6 sides. Putting 5 and 6 together makes 56.
In simple words: This is a fun word game! We find the number each word represents (like 4 for directions and 2 for eyes) and put them side-by-side to make a new number (42).

Exam Tip: Connect your general knowledge: there are 4 main directions, 5 sense organs, 2 eyes, and 6 sides in a hexagon.

Question 3. Think of other words for 0-9. Make new cards for the numbers 15, 27, and 94.
Answer:
1. Other words for 0 to 9:
- 0: Nil, None
- 1: Single, Ace, Sun
- 2: Pair, Couple, Hands
- 3: Trio, Triangle
- 4: Quartet, Square
- 5: Fingers, Starfish
- 6: Insect legs
- 7: Rainbow colors
- 8: Spider legs
- 9: Planets (traditional)

2. New cards for the numbers:
- For 15: Use a card with 1 on the left and 5 on the right.
- For 27: Use a card with 7 on the left and 2 on the right.
- For 94: Use a card with 9 on the left and 4 on the right.
In simple words: We can find many fun things in nature that stand for numbers, like "Rainbow" for 7 or "Hands" for 2. We can write these on cards to show numbers like 15, 27, and 94.

Exam Tip: Try to use common words that everyone knows, like "Rainbow" for 7 or "Fingers" for 5, when making your own word numeral cards.