House of Hundreds - I

Given: The triangular toran has triangles arranged in lines.

Counting strategy: Count in groups of 10.

$$10, 20, 30, \ldots 100, 110, \ldots 200, 210, \ldots 250$$

Total triangles = 250

This is because 250 = 200 + 50, i.e., 50 more than 200.

Given: Bangles are arranged in groups.

Counting strategy (as shown by Teji):
$$10, 20, 30, \ldots 100, 110, 120, \ldots 200, 210, \ldots 270, 271, 272, \ldots 279, 280$$

Total bangles = 280

This is because 280 = 200 + 80, i.e., 80 more than 200.

Given: Toffees are packed in boxes.

Counting strategy:
$$10, 20, 30, \ldots 100, 110, 120, \ldots 190, 200, 210, \ldots 290, 291, 292, 293, \ldots 298$$

Total toffees = 298

Given: Toffees in boxes = 298; Jojo has 2 more toffees.

$$298 + 1 = 299$$
$$299 + 1 = 300$$

Total toffees altogether = 300

Given: Total triangles = 250, and we need to reach 300.

$$300 - 250 = 50$$

50 more triangles are needed to make 300.

Given: Total bangles = 280.

$$300 - 280 = 20$$

Bangles are 20 less than 300.

Given: Bangles = 280, Triangles = 250.

Comparing: 280 > 250 (since both have 2 hundreds, but 8 tens > 5 tens).

Bangles (280) are more than triangles (250).

Given: A number path with some numbers filled in. The pattern is counting forward by 1 (consecutive numbers).

Concept: Counting numbers in order.

The tiles follow the pattern of consecutive whole numbers. Starting from the visible numbers, fill each empty tile by adding 1 to the previous number.

For example, if the path shows: 201, ___, 203, ___, 205, …

$$201, 202, 203, 204, 205, 206, 207, 208, 209, 210, \ldots$$

Fill each blank tile with the next consecutive number in the sequence.

*(Note: Exact starting number depends on the figure. Apply the rule: each tile = previous tile + 1.)*

Concept: Identifying and continuing number patterns (counting by 1s, 10s, or 100s).

Pattern 1 (counting by 1s): Each number increases by 1.
Example: $241, 242, 243, 244, 245, \ldots$

Pattern 2 (counting by 10s): Each number increases by 10.
Example: $210, 220, 230, 240, 250, \ldots$

Pattern 3 (counting by 100s): Each number increases by 100.
Example: $100, 200, 300, 400, \ldots$

Fill in each blank by identifying the pattern (difference between consecutive given numbers) and continuing it.

Concept: Estimation and counting in groups of 10 for accuracy.

Step 1 – Guess: Look at the picture and make an estimate (answers will vary).

Step 2 – Count: Circle the ants in groups of 10 to count accurately.
$$10, 20, 30, 40, \ldots$$
Count all complete groups of 10, then add the remaining ants.

Step 3 – Check: Counting in groups of 10 gives a more accurate answer than counting one by one.

*(The exact number depends on the figure. Apply the grouping strategy to find the total.)*

Key learning: Grouping in 10s makes counting large numbers easier and more accurate.

Concept: Representing numbers using matchstick bundles (hundreds, tens, ones) and writing number sentences.

Row 1 (given as example):
- Number: 235
- Number Sentence: $200 + 35 = 235$ (200 and 35 more); also $250 - 15 = 235$ (15 less than 250)

Row 2:
- Number Sentence given: 300 and 16 more
- Number: $300 + 16 = \mathbf{316}$
- Matchsticks: 3 bundles of 100, 1 bundle of 10, 6 single sticks
- Another number sentence: $320 - 4 = 316$

Row 3:
- Number given: 109
- Number Sentence: $100 + 9 = 109$ (100 and 9 more); also $110 - 1 = 109$ (1 less than 110)
- Matchsticks: 1 bundle of 100, 0 bundles of 10, 9 single sticks

Summary table:

| Number | Number Sentence |
|--------|----------------|
| 235 | $200 + 35$ or $250 - 15$ |
| 316 | $300 + 16$ |
| 109 | $100 + 9$ or $110 - 1$ |

Concept: Locating numbers on a number line.

- 109 lies between 100 and 200, closer to 100. Place it just after 100.
- 235 lies between 200 and 250 (given). Place it halfway between 200 and 250, slightly closer to 250.
- 316 lies between 300 and 350. Place it just after 300.

$$100 \quad 109 \quad \ldots \quad 200 \quad \ldots \quad 235 \quad \ldots \quad 250 \quad \ldots \quad 300 \quad 316 \quad \ldots \quad 350$$

Mark each number at its correct position on the number line.

Concept: Reading numbers represented by pictures (Dienes blocks / matchstick bundles — hundreds, tens, ones).

Method: Count the number of hundreds blocks, tens blocks, and ones blocks in each picture.

$$\text{Number} = (\text{Hundreds} \times 100) + (\text{Tens} \times 10) + (\text{Ones} \times 1)$$

*(The exact answers depend on the figures. Apply the above formula to each picture to write the corresponding number.)*

Example: If a picture shows 2 hundreds blocks, 3 tens blocks, and 5 ones blocks:
$$2 \times 100 + 3 \times 10 + 5 \times 1 = 200 + 30 + 5 = \mathbf{235}$$

Concept: Adding or subtracting 1, 2, 10, or 20 from a given number.

(a) $285 + 1 = \mathbf{286}$

(b) $147 + 10 = \mathbf{157}$

(c) $367 - 2 = \mathbf{365}$

(d) $289 - 10 = \mathbf{279}$

(e) $290 + 20 = \mathbf{310}$

Concept: Locating numbers on a number line between 200 and 300.

The number line goes from 200 to 300.

- 216 is 16 steps after 200. Place it close to 200, slightly to the right.
- 243 is 43 steps after 200. Place it between 200 and 250, closer to 250.
- 257 is 57 steps after 200. Place it just after 250.

$$200 \quad \ldots \quad 216 \quad \ldots \quad 243 \quad \ldots \quad 257 \quad \ldots \quad 300$$

Mark all three numbers at their correct positions.

Concept: Locating numbers on a number line between 300 and 400.

- 329 — 29 steps after 300, close to 300.
- 332 — 32 steps after 300, just after 329.
- 337 — 37 steps after 300, just after 332.
- 375 — 75 steps after 300, between 350 and 400, closer to 400.
- 387 — 87 steps after 300, close to 400.

$$300 \quad \ldots \quad 329 \quad 332 \quad 337 \quad \ldots \quad 375 \quad \ldots \quad 387 \quad \ldots \quad 400$$

Mark all five numbers at their correct positions.

Given: Number = 387, Target = 400.

$$400 - 387 = 13$$

387 is 13 steps (13 less) away from 400.

Given: Numbers are 393 and 400.

Comparing: Both are close, but 400 > 393.

Distance: $400 - 393 = 7$

On the number line:
$$393 \xrightarrow{+1} 394 \xrightarrow{+1} 395 \xrightarrow{+1} 396 \xrightarrow{+1} 397 \xrightarrow{+1} 398 \xrightarrow{+1} 399 \xrightarrow{+1} 400$$

400 is more than 393. 393 is 7 steps away from 400.

Given: A tray of mysore pak is shown in the figure.

Method: Count the pieces arranged in the tray in rows and columns.

*(The exact number depends on the figure. Count rows × columns.)*

Example: If the tray has 5 rows and 10 columns: $5 \times 10 = \mathbf{50}$ pieces per tray.

Given: Number of trays of mysore pak and pieces per tray (from part a).

Method: Multiply pieces per tray by number of trays.

$$\text{Total} = \text{pieces per tray} \times \text{number of trays}$$

*(Apply the multiplication using the values found from the figure.)*

Given: Trays of laddoos shown in the figure.

Method: Count laddoos per tray, then multiply by number of trays.

$$\text{Total laddoos} = \text{laddoos per tray} \times \text{number of trays}$$

*(Count from the figure and calculate.)*

Given: Trays of dhokla shown in the figure.

Method: Count dhoklas per tray × number of trays.

$$\text{Total dhoklas} = \text{dhoklas per tray} \times \text{number of trays}$$

*(Count from the figure and calculate.)*

Given: One tray is partially filled with laddoos.

Method:
$$\text{More laddoos needed} = \text{Full tray capacity} - \text{Laddoos already in tray}$$

*(Count the empty spaces in the tray from the figure to find the answer.)*

Given: Current laddoos (from part c) + more laddoos added (from part e).

$$\text{Total laddoos} = \text{laddoos in part (c)} + \text{more laddoos from part (e)}$$

*(Add the two values to get the final total.)*

Concept: Locating numbers on a number line between 400 and 500.

- 423 — 23 steps after 400, close to 400.
- 438 — 38 steps after 400, between 423 and 450.
- 476 — 76 steps after 400, between 450 and 487.
- 487 — 87 steps after 400, close to 500.
- 500 — at the end of the number line.

$$400 \quad \ldots \quad 423 \quad \ldots \quad 438 \quad \ldots \quad 476 \quad \ldots \quad 487 \quad \ldots \quad 500$$

Mark all numbers at their correct positions on the number line.

Concept: House numbers in an apartment follow a pattern.

Pattern observed:
- Each floor has 10 houses (columns 1–10).
- Ground floor (1st floor): Houses 1–10; 2nd floor: 11–20; 3rd floor: 21–30, and so on.
- Moving left to right: house number increases by 1.
- Moving up one floor: house number increases by 10.

Fill the grid using this pattern:

| Floor | Col 1 | Col 2 | Col 3 | … | Col 10 |
|-------|-------|-------|-------|---|--------|
| 1st | 1 | 2 | 3 | … | 10 |
| 2nd | 11 | 12 | 13 | … | 20 |
| 3rd | 21 | 22 | 23 | … | 30 |
| … | … | … | … | … | … |

Continue the pattern to fill all blank cells.

Concept: Locating specific house numbers in the apartment grid.

Method: Find each house number in the grid and colour it.

- Identify the floor and column for each number using the pattern:
- Floor = $\lceil \text{house number} \div 10 \rceil$
- Column = last digit (if last digit = 0, column = 10)

Locate and colour: 209, 228, 242, 258, 267, 276, 290, 315, 346, 367, 389, 395.

*(Find each number in the grid and colour it.)*

Concept: Floor = tens digit + 1 (if ones digit ≠ 0) or tens digit (if ones digit = 0). Column = ones digit (0 means column 10).

Rule:
- If house number ends in 0: Floor = house number ÷ 10, Column = 10
- Otherwise: Floor = (house number ÷ 10) rounded down + 1, Column = ones digit

| House Number | Floor | Column |
|---|---|---|
| 13 | 2nd | 3 |
| 67 | 7th | 7 |
| 106 | 11th | 6 |
| 159 | 16th | 9 |
| 192 | 20th | 2 |
| 231 | 24th | 1 |
| 245 | 25th | 5 |
| 328 | 33rd | 8 |
| 380 | 38th | 10 |
| 399 | 40th | 9 |

*(Note: Floor numbering follows the apartment grid pattern shown in the figure. Adjust if the grid starts differently.)*

Concept: Pattern in house numbers in the apartment building.

Observations:
- Moving left to right (same floor): house number increases by 1.
- Moving right to left (same floor): house number decreases by 1.
- Moving up (same column): house number increases by 10.
- Moving down (same column): house number decreases by 10.

Fill the blanks using these rules:
- If a house to the right is 245, the house to its left is $245 - 1 = 244$.
- If a house above is 245, the house below is $245 - 10 = 235$.

Pattern noticed: House numbers increase by 1 going right and by 10 going up.

(i) Given: Digits are 9, 1, 5; less than 200; has 9 ones.

- Less than 200 → hundreds digit = 1
- 9 ones → ones digit = 9
- Remaining digit = 5 → tens digit = 5

$$\text{Number} = 1 \text{ hundred} + 5 \text{ tens} + 9 \text{ ones} = \mathbf{159}$$

(ii) Given: 3-digit number using only digits 4 and 0.

- Possible numbers: 400, 404, 440, 444, 400…
- The most likely answer (using only 4 and 0): 400 (4 hundreds, 0 tens, 0 ones)

$$\text{Number} = \mathbf{400}$$

(iii) Given: Greater than 300 but less than 400; no tens; ones digit = hundreds digit.

- Hundreds digit = 3 (since between 300 and 400)
- Tens digit = 0 (no tens)
- Ones digit = hundreds digit = 3

$$\text{Number} = 3 \text{ hundreds} + 0 \text{ tens} + 3 \text{ ones} = \mathbf{303}$$

Concept: Representing a number using Hundreds (H), Tens (T), and Ones (O) boxes.

Rule: Break the number into hundreds, tens, and ones.

| House Number | Types of Boxes | Number Sentence |
|---|---|---|
| 211 | 2H + 1T + 1O | $200 + 10 + 1$ |
| 309 | 3H + 0T + 9O | $300 + 0 + 9$ |
| 275 | 2H + 7T + 5O | $200 + 70 + 5$ |
| 423 | 4H + 2T + 3O | $400 + 20 + 3$ |
| 365 | 3H + 6T + 5O | $300 + 60 + 5$ |
| 343 | 3H + 4T + 3O | $300 + 40 + 3$ |
| 458 | 4H + 5T + 8O | $400 + 50 + 8$ |
| 562 | 5H + 6T + 2O | $500 + 60 + 2$ |
| 606 | 6H + 0T + 6O | $600 + 0 + 6$ |
| 800 | 8H + 0T + 0O | $800 + 0 + 0$ |

Draw the corresponding number of H boxes, T boxes, and O packets for each house number.

Concept: Reading house numbers from the apartment grid.

*(The exact house numbers depend on the figure. Identify the yellow and pink coloured houses in the grid and write their numbers.)*

Method: Locate each coloured house in the grid and read its number using the floor and column pattern.

Concept: Identifying number patterns.

Possible patterns to look for:
- Do the numbers increase by the same amount each time?
- Are they all even or all odd?
- Do they share a common digit?

Example pattern: If yellow houses are 211, 221, 231, 241 — they increase by 10 each time (same column, going up).

Write the pattern observed from the actual numbers in the figure.

Given: 1 box of 100 sweets; each small box holds 10 sweets.

$$100 \div 10 = \mathbf{10}$$

He can fit 10 boxes of 10 in a box of 100.

Given: 2 boxes of 100.

$$2 \times 10 = \mathbf{20}$$

He can fit 20 boxes of 10 in two boxes of 100.

Given: 4 boxes of 100.

$$4 \times 10 = \mathbf{40}$$

He can fit 40 boxes of 10 in four boxes of 100.

Given: 1 box of 100 is opened.

$$100 \div 10 = \mathbf{10}$$

He will find 10 boxes of 10 inside a box of 100.

Concept: Finding all numbers between 200 and 300 that contain the digit 5.

Numbers between 200 and 300 with digit 5:

- 5 in the tens place: 250, 251, 252, 253, 254, 255, 256, 257, 258, 259
- 5 in the ones place: 205, 215, 225, 235, 245, 255, 265, 275, 285, 295

Complete list (no repeats):
$$205, 215, 225, 235, 245, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 265, 275, 285, 295$$

Yes, 245 is one such number (it has 5 in the ones place).

Total: 19 numbers between 200 and 300 have the digit 5.

Concept: Comparing 3-digit numbers — first compare hundreds, then tens, then ones.

Method:
1. Compare hundreds digits first.
2. If equal, compare tens digits.
3. If equal, compare ones digits.

*(The exact numbers depend on the figure. Apply the method above.)*

Example: Compare 321 and 231:
- Hundreds: 3 > 2
- So 321 > 231 ✓

Concept: Comparing 3-digit numbers.

Example: Compare 209 and 290:
- Hundreds: both have 2 (equal)
- Tens: 0 < 9
- So 209 &lt; 290 ✓

*(Apply the same method to the numbers shown in the figure.)*

Concept: Comparing numbers by hundreds, tens, and ones.

(a) 325 > 235 because → 325 has 3 hundreds and 235 has 2 hundreds. 3 hundreds > 2 hundreds.

(b) 235 < 523 because → 235 has 2 hundreds and 523 has 5 hundreds. 2 hundreds < 5 hundreds.

(c) 157 > 153 because → Both have 1 hundred and 5 tens each. 157 has 7 ones, 153 has 3 ones. 7 ones > 3 ones.

(d) 432 > 423 because → Both have 4 hundreds. 432 has 3 tens, 423 has 2 tens. 3 tens > 2 tens.

(e) 329 < 392 because → Both have 3 hundreds. 329 has 2 tens, 392 has 9 tens. 2 tens < 9 tens.

(f) 110 > 11 because → 110 has 1 hundred and 11 has no hundreds (zero hundreds). 1 hundred > 0 hundreds.

Concept: Finding the smallest number by comparing hundreds first, then tens, then ones.

(a) 374, 473, 347, 437
- All have 3 or 4 in hundreds place.
- Numbers with 3 hundreds: 374, 347 → compare tens: 7 vs 4 → 347 is smaller.
- Numbers with 4 hundreds: 473, 437 → all larger than 3xx.
- Smallest = 347 ✓

$$\boxed{347}$$

(b) 239, 123, 321, 456
- Hundreds digits: 2, 1, 3, 4
- Smallest hundreds digit = 1 → number is 123

$$\boxed{123}$$

Concept: Finding the greatest number by comparing hundreds first, then tens, then ones.

(a) 466, 437, 439, 447, 483
- All have 4 hundreds.
- Compare tens: 6, 3, 3, 4, 8 → greatest tens = 8 → number is 483

$$\boxed{483}$$

(b) 464, 387, 123, 256, 348
- Hundreds digits: 4, 3, 1, 2, 3
- Greatest hundreds digit = 4 → number is 464

$$\boxed{464}$$

Given digits: 3, 2, 4 (each used exactly once)

All possible 3-digit numbers:
$$234, 243, 324, 342, 423, 432$$

Greatest number: $\mathbf{432}$ → colour red

Smallest number: $\mathbf{234}$ → colour yellow

All six numbers: 234, 243, 324, 342, 423, 432

Given digits: 3, 2, 4 (repetition allowed)

Some possible 3-digit numbers (sample):
$$222, 223, 224, 232, 233, 234, 242, 243, 244,$$
$$322, 323, 324, 332, 333, 334, 342, 343, 344,$$
$$422, 423, 424, 432, 433, 434, 442, 443, 444$$

Greatest number: $\mathbf{444}$ → colour red

Smallest number: $\mathbf{222}$ → colour yellow

*(Write as many numbers as possible using digits 2, 3, 4 with repetition allowed.)*

Concept: Arranging numbers in ascending order.

Step 1: Compare hundreds digits.
- 99 has no hundreds (2-digit number) → smallest
- 110 has 1 hundred
- 207 has 2 hundreds
- 389 has 3 hundreds
- 456 has 4 hundreds

Ascending order (smallest to biggest):
\mathbf{99 &lt; 110 &lt; 207 &lt; 389 &lt; 456}

Concept: Arranging numbers in descending order.

Step 1: Compare hundreds digits.
- 67 has no hundreds (2-digit) → smallest
- 249 has 2 hundreds
- 294 has 2 hundreds → compare tens: 4 < 9, so 249 < 294
- 376 has 3 hundreds
- 494 has 4 hundreds → greatest

Descending order (biggest to smallest):
\mathbf{494 &gt; 376 &gt; 294 &gt; 249 &gt; 67}