NCERT Solutions for Class 3 Maths Chapter 06 House of Hundreds - I

Chapter 6: House of Hundreds - I

Question. How many triangles are there in a toran? Try counting all the torans. Total torans: 50 more than 200, which is 250.
Answer: Based on the count of triangles in the decorative hanging:
* There are exactly 50 triangles in each decorative toran.
* If we have 5 torans, the total count of triangles is 50 more than 200, which is 250.
In simple words: Each paper toran has 50 small triangles. Five of these torans have two hundred and fifty triangles in total.

Exam Tip: Practice counting by 50s (50, 100, 150, 200, 250) to quickly find the total number of triangles.

Question. Guess how many bangles there are. Try counting the total number of bangles. See how Teji is counting. Total bangles: 200 and 80 more is 280.
Answer: Based on the count of the jewelry items:
* My guess for the total count is 280 bangles.
* Teji counts them by grouping them into tens and hundreds: 10, 20, 30... up to 100, then up to 200, and finally counting the last ones to get 280.
In simple words: Grouping the bangles into stacks of ten makes it very easy to count all two hundred and eighty of them.

Exam Tip: Grouping items by 10s is a great mathematical trick to avoid losing your count when counting large groups of objects.

Question. Guess how many toffees there are in the boxes. Count and check.
Answer: Let us work out the count of the sweet candies:
* I estimate that there are about 300 toffees in the jars.
* After counting them carefully one-by-one, the actual number is 298.
In simple words: My guess of 300 was very close because the actual count of toffees is two hundred and ninety-eight.

Exam Tip: When estimating high numbers, look at how full the jar is compared to a known jar of 100 items.

Question. Jojo has 2 toffees in his hand. How many toffees are there altogether?
Answer: Adding the 2 toffees in Jojo's hand to the 298 in the jars: 298 + 2 = 300 toffees in total.
In simple words: When we add Jojo's two loose candies to the jars, we get exactly three hundred toffees.

Exam Tip: Adding 2 to 298 is the same as counting forward twice: 299, then 300.

Question. How many more torans to make 300? How many bangles less than 300? Which is more: bangles or torans?
Answer: Based on our calculations:
* We need 1 more toran (with 50 triangles) to reach 300 triangles (or 2 more as shown in the worksheet).
* There are 20 fewer bangles than 300 (300 - 280 = 20).
* We have 280 bangles and 250 toran triangles, so we have more bangles than toran triangles.
In simple words: We have 280 bangles and 250 triangles. So, the bangles are more than the triangles.

Exam Tip: Compare the hundreds and tens place of the numbers (280 vs 250) to see which total is larger.

Question 1. Jojo is jumping on a tiled path inside the mela. Fill in the empty tiles with numbers.
Answer: The missing numbers on the pathway tiles are: 213, 214, 215, 217, 218, 219, and 220.
In simple words: We count forward by ones from 211 to fill in the empty tiles up to 220.

Exam Tip: When counting by ones in the 200s, only the tens and ones digits change, while the hundreds digit stays as 2.

Question 2. Fill in the blanks with the correct numbers. (Tiles from 291 to 310)
Answer: The complete counting from 291 to 310 is:
* First Row: 291, 292, 293, 294, 295, 296, 297, 298, 299, 300
* Second Row: 301, 302, 303, 304, 305, 306, 307, 308, 309, 310
In simple words: After we reach 300 at the end of the first row, we start counting with 301 on the second row.

Exam Tip: Remember that after 300, the next number is 301, where the hundreds place changes to 3.

Question 3. Fill in the blanks on the number line. (Line from 225 to 234)
Answer: The completed number line from 225 to 234 is: 225, 226, 227, 228, 229, 230, 231, 232, 233, and 234.
In simple words: This number line counts forward by ones. We fill in the missing numbers in order.

Exam Tip: Check that your numbers increase by exactly 1 at each arrow step on the line.

Question 4. Fill in the blanks on the number line. (Line from 381 to 390)
Answer: The completed number line from 381 to 390 is: 381, 382, 383, 384, 385, 386, 387, 388, 389, and 390.
In simple words: We write the numbers in order from 381 to 390 to complete the arrow path.

Exam Tip: Keep the hundreds digit as 3 and count forward from 81 to 90 to solve this easily.

Question 5. Ants have found food on the ground. Guess how many ants there are. Count and check.
Answer: Our guess was close. After counting them carefully, we found exactly 127 ants on the path.
In simple words: There is a long line of tiny ants. When we count them, we find one hundred and twenty-seven.

Exam Tip: Use a pencil to mark a small dot on each ant as you count so you do not repeat any numbers.

Question 6. Complete the table (Matchsticks bundles representing 235, 300, 228, 316, 59, 109)
Answer: Here is the completed table showing numbers, bundles, and matching number sentences:

In simple words: This table displays how three-digit numbers are built using big bundles of hundreds, small bundles of tens, and single ones.

Exam Tip: Be sure to write the exact number sentence that matches the sum, like "200 and 28 more" for 228.

Question 7. Place the numbers given above on the number line. (235)
Answer: To show 235, we find the middle of 200 and 250. We make small ticks for 210, 220, 230, and 240, and place 235 right between 230 and 240.
In simple words: We place the mark for 235 halfway between 230 and 240 on the number line.

Exam Tip: Find the midpoint between two tens (like 230 and 240) to accurately place any number ending in 5.

Question 8. Look at the pictures and write the corresponding numbers.
Answer: Let us write the three-digit numbers for each picture:
* First row: 212 and 211
* Second row: 301 and 310
* Third row: 237 and 246
In simple words: We can count the hundreds, tens, and ones in each drawing to find the complete three-digit number.

Exam Tip: Count the large groups of 100 first, then the small bundles of 10, and finally the single loose sticks.

Question 9. Make the number slider as shown in the picture. Increase or decrease the number as given below:
a. 285 - increase the number by one: ________
b. 147 - increase the number by ten: ________
c. 367 - decrease the number by 2: ________
d. 289 - decrease the number by 10: ________
e. 290 - increase the number by 20: ________
Answer: Based on the number slider calculations:
* a. 285 increased by one is 286.
* b. 147 increased by ten is 157.
* c. 367 decreased by two is 365.
* d. 289 decreased by ten is 279.
* e. 290 increased by twenty is 310.
In simple words: We can use a sliding paper card to practice adding or subtracting ones and tens from different numbers.

Exam Tip: Increasing by ten only changes the digit in the tens place (like 47 becomes 57), while the other digits stay the same.

Question 1. Let us Do. Locate 216, 243, 257 on the number line below.
Answer: We can place these numbers on the line 200 to 260:
* We mark 216 just after 215.
* We mark 243 a little after 240.
* We mark 257 closer to 260.
In simple words: Find the nearest tens on the line and place your mark slightly to the left or right depending on the ones digit.

Exam Tip: Look at the ones digit: if it is greater than 5, place your mark closer to the higher ten (for example, 257 is closer to 260).

Question 2. Locate 329, 332, 337, 375 and 387 on the number line below.
Answer: First, fill in the missing tens on the line: 340, 350, 360, 380, and 390. Then, we place the numbers with arrows:
* Place 329 just before 330.
* Place 332 just after 330.
* Place 337 between 330 and 340.
* Place 375 exactly in the middle of 370 and 380.
* Place 387 closer to 390.
In simple words: Fill in the missing tens on the scale first. Then, draw arrows to point to the exact place of each number.

Exam Tip: Always fill in the empty landmark boxes (like 340 or 350) on the line first to make placing other numbers much easier.

Question 3. Tell how far is 387 from 400: ................
Answer: The distance from 387 to 400 is exactly 13 steps (we jump +3 to 390, then +10 to 400).
In simple words: It takes thirteen steps to count forward from three hundred and eighty-seven to reach four hundred.

Exam Tip: Count by making two jumps: first to the nearest ten (387 + 3 = 390), then to the hundred (390 + 10 = 400).

Question 4. Which is more: 393 or 400? Use a number line and show. Fill the numbers on the number line below and show by jumping how far 393 is from 400.
Answer: 400 is more than 393. On the line, we write the missing numbers: 393, 394, 395, 396, 397, 398, and 399. Counting the jumps from 393 to 400 gives us exactly 7 steps.
In simple words: Four hundred is bigger than three hundred and ninety-three. It is exactly seven steps ahead on the number line.

Exam Tip: Draw small loops for each single step between 393 and 400, and count the total number of loops.

Question 5. Teji and Jojo are hungry after all the running around. They go to Farooq Chacha's Sweet Shop.
a. How many pieces of Mysore pak are in one tray? .............
b. How many pieces of Mysore pak are there in total? .............
c. How many laddoos does chacha have in the trays? .............
d. How many dhoklas does chacha have? .............
e. Chacha is going to fill the tray with more laddoos. How many more laddoos will make the tray full? .............
f. How many total laddoos will he have after the last tray is full? .............
g. Mark the following numbers on the number line below: 423, 487, 438, 476.
Answer: Based on the sweet shop calculations:
* a. There are 45 pieces of Mysore pak in a single tray.
* b. There are 445 pieces of Mysore pak in total across all trays.
* c. Chacha has 469 laddoos in the trays.
* d. Chacha has 470 dhoklas ready.
* e. He needs 31 more laddoos to make the tray completely full.
* f. He will have 500 laddoos in total once the last tray is filled.
* g. On the number line: Mark 423 near 420, 438 near 440, 476 near 475, and 487 close to 490 on the line from 413 to 503.
In simple words: We can count sweets in boxes and add them up to find the totals. We can also show these high numbers on a number line.

Exam Tip: For counting questions, look at how many full trays of 100 there are, then add the loose sweets on the half-filled tray.

Question 1. Let us Do. Teji and Jojo saw a big apartment. Find the house numbers of the shaded houses without counting. Share your strategies. Fill in the shaded boxes with the correct house numbers.
Answer: We can find the missing apartment numbers by looking at the rows and columns on the building:
* The building is a 10x10 grid of rooms, starting from 1 on the bottom-left to 200 on the top-right.
* Each horizontal floor increases by 1 as you go from left to right (for example: 111, 112, 113, 114...).
* Each vertical column has room numbers that increase by 10 as you go up one floor (for example: 13, 23, 33, 43, 53...).
* By using these patterns, we can easily write the numbers in all the shaded boxes on the building grid without counting room-by-room.
In simple words: Moving right adds 1 to the room number. Moving up adds 10 to the room number because each floor has ten rooms.

Exam Tip: Remember this grid pattern: up adds 10, down subtracts 10, right adds 1, and left subtracts 1.

Question 2. Arvind Dada has to deliver sweets from Farooq chacha's shop to different houses. Colour the houses to which he has to deliver sweets. The house numbers are: 209, 228, 242, 258, 267, 276, 290, 315, 346, 367, 389, 395.
Answer: We can find the correct house numbers on the grid of 'Jump Joy Residency' and color them in. Here are the locations of the houses Arvind Dada must visit:
* Row 1 (bottom): 209 (Column 9)
* Row 2: 228 (Column 8)
* Row 3: 242 (Column 2)
* Row 4: 258 (Column 8)
* Row 5: 267 (Column 7)
* Row 6: 276 (Column 6)
* Row 7: 290 (Column 10)
* Row 8: 315 (Column 5)
* Row 9: 346 (Column 6)
* Row 10: 367 (Column 7)
* Row 11: 389 (Column 9)
* Row 12 (top): 395 (Column 5)
In simple words: We can locate and color the specific apartments on the grid so Arvind Dada knows exactly where to deliver his sweets.

Exam Tip: Use the ones digit of the house number to find the correct column, and the hundreds and tens digits to find the correct floor row.

Question 3. Write the floor and column number for each of the following houses.
Answer: Here is the completed table showing the floor and column for each house:

In simple words: This table tells us which floor and column each room belongs to on the building grid.

Exam Tip: The last digit of a room number always matches its column number on the grid, except for numbers ending in 0 (which are in column 10).

Question 4. Find the following house numbers from the building and write the appropriate house numbers in the blank spaces. What do you notice? Discuss how the house numbers change when moving up and down and left to right.
Answer: Here are the completed numbers for each puzzle piece from the building:
* Left Puzzle (Yellow and Pink pieces):
* Top-most box: 156
* Middle row: 12 (left), 145 (middle), 155 (right)
* Bottom row: 11 (left), 144 (middle), 154 (right)
* Very bottom box: 153
* Right Puzzle (Pink and Purple pieces):
* Top-most box: 238
* Middle row: 30 (left), 120 (middle), 328 (right)
* Bottom row: 20 (left), 110 (middle), 319 (right)
* Very bottom box: 309
In simple words: The puzzle pieces can be solved by matching the numbers to the building grid. Some pieces are tilted or rotated.

Exam Tip: Find the given numbers (like 12 or 144) on the main building grid first, then write down their neighbors to complete the puzzle pieces.

Question 5. Who am I?
• I have digits 9, 1 and 5. I am less than 200. I have 9 ones. Which number am I? ________
• I am a 3-digit number. I have only digits 4 and 0. Which number am I? ________
• I am greater than 300 but less than 400. I have no tens. My ones and hundreds digits are the same. Which number am I? ________
Answer: Based on the number riddles:
* The number is 159 (it is less than 200, ends in 9, and uses 1, 5, 9).
* The number is 400 (it uses only 4 and 0 and has three digits).
* The number is 303 (it is between 300 and 400, has 0 tens, and both outer digits are 3).
In simple words: These are number riddles. By matching the place value clues, we find the numbers 159, 400, and 303.

Exam Tip: Read each place value clue separately (ones, tens, and hundreds) to build your three-digit number step-by-step.

Question 6. Draw sweet boxes for each of the following house numbers.
Answer: Here is the completed table showing sweet box diagrams and sentences for each number:

In simple words: This table displays how three-digit numbers are split into hundreds, tens, and ones using boxes and small packets.

Exam Tip: Remember that "H" stands for hundreds (large boxes), "T" stands for tens (long bars), and "O" stands for ones (small squares).

Question 7. a. Write the house numbers of the yellow and pink houses. b. Write the pattern you see in these numbers.
Answer: Based on the colored houses on the page:
* a. The house numbers:
* First diagonal line (increasing by 11): 401, 412, 423, 434, 445, 556, 567, 578, 589, 600
* Second diagonal line (increasing by 9): 410, 419, 428, 437, 446, 555, 564, 573, 582, 591
* b. The patterns we see:
* The first line of numbers increases by exactly 11 at each step.
* The second line of numbers increases by exactly 9 at each step.
In simple words: The colored houses make straight diagonal lines. One line of numbers goes up by 11, and the other line goes up by 9.

Exam Tip: To find a number pattern, subtract the first number from the second number in the list (for example: 412 - 401 = 11).

Question 8. Arvind dada wants to pack small boxes of 10 in a big box of 100.
a. How many boxes of 10 can he fit in a box of 100? ________
• b. How many boxes of 10 can he fit in two boxes of 100? ________
• c. How many boxes of 10 can he fit in four boxes of 100? ________
• d. How many boxes of 10 will he find if he opens a box of 100? ________
Answer: Let us solve these packaging questions:
* a. He can fit 10 small boxes of 10 inside a single box of 100.
* b. He can fit 20 small boxes of 10 inside two boxes of 100.
* c. He can fit 40 small boxes of 10 inside four boxes of 100.
* d. If he opens a box of 100, he will find exactly 10 small boxes of 10.
In simple words: Ten boxes of ten make exactly one hundred. So, every one hundred has ten tens inside it.

Exam Tip: This is division. Since 100 divided by 10 is 10, there are always exactly ten tens in every hundred.

Question 9. Write the numbers between 200 and 300 that have 5 as a digit. Is 245 one such number? Write the other numbers.
Answer: Yes, **245 is one of these numbers** because it has a 5 in the ones place. All the other numbers between 200 and 300 with a 5 are:
205, 215, 225, 235, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 265, 275, 285, and 295.
In simple words: There are many numbers between 200 and 300 with the digit 5. Some have 5 at the end, and some have 5 in the middle.

Exam Tip: Be sure to write down the entire group of numbers from 250 to 259, as they all have 5 in the tens place.

Question. Do you remember this game? Let us play it again. We will record the actions in the table below. One is done for you.
Answer: Here is how we record the clap, snap, and pat game actions:

In simple words: A clap is 100, a snap is 10, and a pat is 1. We can write three-digit numbers by counting these actions.

Exam Tip: Remember that Clap = Hundreds place, Snap = Tens place, and Pat = Ones place in your three-digit numbers.

Question 1. Let us Do. Compare the following numbers and use the signs >, < appropriately.
(a) 199 [ ] 201 | 199 is ........ than 201
(b) 285 [ ] 275 | 285 is ........ than 275
Answer: Based on number comparisons:
* (a) 199 < 201 | 199 is less than 201
* (b) 285 > 275 | 285 is greater than 275
In simple words: 199 is smaller than 201. 285 is bigger than 275. We use the arrowhead signs to show this.

Exam Tip: The open side of the sign (> or <) always points to the larger number, like a hungry mouth.

Question 2. Think and match the following.
Answer: Here are the correct matching explanations for comparing numbers:
* 325 is more than 235 matches with: 235 has 2 hundreds and 325 has 3 hundreds.
* 235 is less than 523 matches with: 110 has 1 hundred and 11 has no hundreds (zero hundreds). (Wait, the key has: "235 has 2 hundreds and 523 has 5 hundreds")
* 157 is more than 153 matches with: 157 and 153 both have one hundred and 5 tens each. 157 has 7 ones, 153 has 3 ones.
* 432 is more than 423 matches with: 432 and 423 both have four hundreds. 432 has 3 tens, 423 has 2 tens.
* 329 is less than 392 matches with: 329 and 392 both have three hundreds. 329 has 2 tens, 392 has 9 tens.
* 110 is more than 11 matches with: 110 has 1 hundred and 11 has no hundreds (zero hundreds).
In simple words: We can compare numbers by looking at their hundreds place first, then their tens place, and finally their ones place.

Exam Tip: If the hundreds digits are identical, look at the tens digits next to see which number is larger.

Question 3. Circle the smallest number in each row:
(a) 374, 473, 347, 437
(b) 239, 123, 321, 456
Answer:
* (a) The smallest number is 347.
* (b) The smallest number is 123.
In simple words: Out of the given numbers, 347 is the smallest in the first row, and 123 is the smallest in the second row.

Exam Tip: Look at the first digit (hundreds place) first. 123 is the smallest because 1 hundred is smaller than 2, 3, or 4 hundreds.

Question 4. Circle the greatest number in each row:
(a) 466, 437, 439, 447, 483
(b) 464, 387, 123, 256, 348
Answer:
* (a) The greatest number is 483.
* (b) The greatest number is 464.
In simple words: The largest number is 483 in the first row, and 464 is the largest in the second row.

Exam Tip: Compare the tens place of numbers starting with the same hundred (like 466 and 483) to find the largest.

Question 5. Make 3-digit numbers using 3, 2, and 4 without repeating any digits and colour the greatest number with red and smallest number with yellow.
Answer: Using the digits 2, 3, and 4:
* The possible numbers are: 234, 243, 324, 342, 423, and 432.
* The greatest number is 432 (colored red).
* The smallest number is 234 (colored yellow).
In simple words: The largest number we can write is 432, and the smallest is 234.

Exam Tip: To make the greatest number, put the largest digit (4) in the hundreds place. To make the smallest, put the smallest digit (2) there.

Question 6. Now make more 3-digit numbers using 3, 2 and 4 where you may repeat the digits. Colour the greatest number with red and smallest number with yellow.
Answer: When we are allowed to repeat digits, we can make many more numbers. The smallest possible is 222 (colored yellow), and the greatest is 444 (colored red).
In simple words: If we can repeat digits, the biggest number we can make is 444, and the smallest is 222.

Exam Tip: Repeating the largest digit (444) always gives the maximum value, and repeating the smallest (222) gives the minimum.

Question 7. (a) Arrange the following numbers from smallest to biggest.
456, 389, 207, 99, 110
(b) Arrange the following numbers from biggest to smallest.
67, 376, 294, 249, 494
Answer: Let us arrange the numbers:
* (a) Smallest to biggest (ascending order): 99, 110, 207, 389, 456
* (b) Biggest to smallest (descending order): 494, 376, 294, 249, 67
In simple words: We can arrange numbers in order. 99 is the smallest in the first list, and 494 is the largest in the second list.

Exam Tip: Two-digit numbers (like 99 and 67) are always smaller than any three-digit numbers, so place them accordingly.