Double Century

These are estimation questions based on a picture that students observe. Since the picture cannot be seen here, students should look at the picture carefully and write their best estimate.

General approach:
- Look at the picture carefully.
- Group the objects in your mind (e.g., groups of 5 or 10).
- Count the groups and multiply to get an estimate.

Sample estimated answers (actual answers depend on the picture):
(a) Oranges : approximately 20
(b) Bangles : approximately 30
(c) Laddoos : approximately 15
(d) Barfi : approximately 25
(e) Bindis : approximately 50
(f) Bananas : approximately 12

Note: Students should write their own estimates after looking at the picture in their textbook.

The board is a snakes and ladders grid. Numbers go from 1 to 100. Fill in the missing numbers by continuing the sequence:

Row 1 (bottom): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Row 2: 20, 19, 18, 17, 16, 15, 14, 13, 12, 11
Row 3: 21, 22, 23, 24, 25, 26, 27, 28, 29, 30
Row 4: 40, 39, 38, 37, 36, 35, 34, 33, 32, 31
Row 5: 41, 42, 43, 44, 45, 46, 47, 48, 49, 50
Row 6: 60, 59, 58, 57, 56, 55, 54, 53, 52, 51
Row 7: 61, 62, 63, 64, 65, 66, 67, 68, 69, 70
Row 8: 80, 79, 78, 77, 75, 76, 74, 73, 72, 71
Row 9: 81, 82, 83, 84, 85, 86, 87, 88, 89, 90
Row 10 (top): 100, 99, 98, 97, 96, 95, 94, 93, 92, 91

All missing numbers are filled by continuing the counting sequence from 1 to 100.

Given: The ladder starts at 13 on the snakes and ladders board.

In a standard snakes and ladders game, a ladder takes you to a higher number. Looking at the board, the ladder from 13 takes you up to 84.

Answer: You will reach 84 by taking the ladder from 13.

Given: You are at 25, which is the snake's mouth.

The snake at 25 slides you down to a lower number. Looking at the board, the snake from 25 takes you down to 5.

Answer: You will reach 5.

Given: You are standing on 96.

Looking at the board, the snake's mouth is at 99.

Difference = $99 - 96 = 3$

So, if you roll a 3 on the die, you move from 96 to 99, which is the snake's mouth.

Answer: Rolling a 3 on the die will take you to the snake's mouth at 99.

Given: We need to find the tail of the longest snake on the board.

The longest snake goes from 99 (mouth) down to 5 (tail). So the tail number is 5.

Representing 5 using bundles and loose sticks:
- 5 = 0 bundles of 10 + 5 loose sticks

Draw: | | | | | (five loose sticks)

Answer: The tail of the longest snake is at 5, shown as 5 loose sticks: $|\;|\;|\;|\;|$

The Talking Pot always says one more than the number you say.

Given number: 39
One more than 39 = $39 + 1 = 40$

Answer: Pot said 40.

The Talking Pot says one more than the number you say.

Pot said 90, so the number said must be one less than 90.
$90 - 1 = 89$

Answer: I said 89.

One more than 63:
$63 + 1 = 64$

Answer: Pot said 64.

This is an open-ended question where students can choose any number. For example:

I said 75, Pot said 76.
(Because one more than 75 is 76.)

Students may write any number and its successor.

We need to find pairs of numbers that add up to 100.

Given: $70 + 30 = 100$ ✓

For the second row (using the number line with Bholu jumping):
$65 + 35 = 100$
So: 65 and 35 makes 100

For the third row (another pair):
$50 + 50 = 100$
So: 50 and 50 makes 100

(Students may write different pairs as long as they add up to 100, for example: 40 and 60, 20 and 80, etc.)

We use the fact that two numbers make 100 when they add up to 100.

60 and 40 makes 100 → $60 + 40 = 100$ ✓

45 and 55 makes 100 → $45 + 55 = 100$ ✓

75 and 25 makes 100 → $75 + 25 = 100$ ✓

15 and 85 makes 100 → $15 + 85 = 100$ ✓

... and ... makes 100 (students choose their own pairs):
Example 1: 30 and 70 makes 100 → $30 + 70 = 100$ ✓
Example 2: 10 and 90 makes 100 → $10 + 90 = 100$ ✓

This question is based on a picture of flowers with petals. The concept is: each pair of numbers in opposite petals must add up to 100.

General rule: If one petal has the number $n$, the opposite petal has $100 - n$.

Examples:
- If one petal is 40, the other is $100 - 40 = 60$
- If one petal is 35, the other is $100 - 35 = 65$
- If one petal is 55, the other is $100 - 55 = 45$
- If one petal is 20, the other is $100 - 20 = 80$

Students should fill in the petals so that each pair adds to 100.

This is a hands-on activity. Students should:

Step 1: Look at the matchbox and estimate (without counting). Write the estimate.
Step 2: Take out all matchsticks and count them carefully.
Step 3: Compare estimate with actual count.
Step 4: Divide 100 by the number of matchsticks in one box.

Example: If one box has 50 matchsticks,
$$\text{Number of boxes} = 100 \div 50 = 2 \text{ boxes}$$

If one box has 40 matchsticks,
$$\text{Number of boxes} = 100 \div 40 \approx 2\text{–}3 \text{ boxes}$$

Answer: Students fill in their own observed values.

This is a hands-on activity. Students should:

Step 1: Take a handful of seeds and estimate the count.
Step 2: Count the seeds one by one.
Step 3: Divide 100 by the number of seeds in one handful.

Example: If one handful has 25 seeds,
$$\text{Number of handfuls} = 100 \div 25 = 4 \text{ handfuls}$$

If one handful has 20 seeds,
$$\text{Number of handfuls} = 100 \div 20 = 5 \text{ handfuls}$$

Answer: Students fill in their own observed values.

We continue the pattern of adding to 100:

$$100 + 3 = 103 \Rightarrow \text{One Hundred } \mathbf{Three}$$
$$100 + 4 = 104 \Rightarrow \text{One Hundred } \mathbf{Four}$$
$$100 + 5 = 105 \Rightarrow \text{One Hundred Five} \rightarrow \mathbf{105}$$
$$100 + 6 = 106 \Rightarrow \text{One Hundred } \mathbf{Six}$$
$$100 + 7 = 107 \Rightarrow \text{One Hundred Seven} \rightarrow \mathbf{107}$$
$$100 + 8 = 108 \Rightarrow \text{One Hundred } \mathbf{Eight}$$
$$100 + 9 = 109 \Rightarrow \text{One Hundred } \mathbf{Nine} \rightarrow \mathbf{109}$$
$$100 + 10 = 110 \Rightarrow \text{One Hundred Ten} \rightarrow 110$$

Given information: Each row shows matchstick bundles representing a 3-digit number.

The place value structure is:
$$\text{Number} = (\text{100s} \times 100) + (\text{10s} \times 10) + (\text{1s} \times 1)$$

Example (given): 1 hundred-bundle + 2 ten-bundles + 3 loose sticks
$$= 1 \times 100 + 2 \times 10 + 3 = 100 + 20 + 3 = \mathbf{123}$$

For the row with answer 104:
$$104 = 1 \times 100 + 0 \times 10 + 4 \times 1$$
So: 1 hundred-bundle, 0 ten-bundles, 4 loose sticks.

For the row with answer 120:
$$120 = 1 \times 100 + 2 \times 10 + 0 \times 1$$
So: 1 hundred-bundle, 2 ten-bundles, 0 loose sticks.

For the remaining rows, students count the bundles and loose sticks shown in the picture and write the corresponding number.

All numbers from 100 to 150 have 1 hundred-bundle in common — this is the pattern students should observe.

Given: A number line from 100 to 150 (or similar range).

To mark numbers on a number line:
- Identify the position of each number between the marked values.
- Each number is placed at its correct position.

(a) 125 — This is exactly halfway between 120 and 130. Place an arrow at 125.

(b) 112 — This is 2 steps after 110. Draw a tree at 112.

(c) 149 — This is 1 step before 150. Draw a smiley at 149.

(d) 137 — This is 7 steps after 130. Put a cross at 137.

Students should mark these on the number line in their textbook.

The pattern: all numbers from 150–159 have 1 hundred-bundle, 5 ten-bundles, and varying loose sticks.

$$152: \text{100s}=1,\; \text{10s}=5,\; \text{1s}=2,\; \text{Sentence: } 100 \text{ and } 52$$
$$153: \text{100s}=1,\; \text{10s}=5,\; \text{1s}=3,\; \text{Sentence: } 100 \text{ and } 53$$
$$154: \text{100s}=1,\; \text{10s}=5,\; \text{1s}=4,\; \text{Sentence: } 100 \text{ and } 54$$
$$155: \text{100s}=1,\; \text{10s}=5,\; \text{1s}=5,\; \text{Sentence: } 100 \text{ and } 55$$
$$156: \text{100s}=1,\; \text{10s}=5,\; \text{1s}=6,\; \text{Sentence: } 100 \text{ and } 56$$
$$157: \text{100s}=1,\; \text{10s}=5,\; \text{1s}=7,\; \text{Sentence: } 100 \text{ and } 57$$
$$158: \text{100s}=1,\; \text{10s}=5,\; \text{1s}=8,\; \text{Sentence: } 100 \text{ and } 58,\; \text{Name: One hundred and fifty eight}$$
$$159: \text{100s}=1,\; \text{10s}=5,\; \text{1s}=9,\; \text{Sentence: } 100 \text{ and } 59,\; \text{Name: One hundred and fifty nine}$$

All numbers from 150–159 share: 1 hundred-bundle and 5 ten-bundles.

This is a hands-on home activity.

Step 1: Fill the container with seeds (kidney beans, chickpeas, etc.).
Step 2: Look at the container and estimate the number of seeds. Write your estimate.
Step 3: Count the seeds one by one. Write the actual count.
Step 4: To find how many containers make 200:
$$\text{Number of times} = \frac{200}{\text{seeds in one container}}$$

Example: If one container holds 40 seeds,
$$\frac{200}{40} = 5 \text{ times}$$

Students fill in their own values based on their experiment.

Given numbers on stones: 150, 158, 163 (and others visible in the picture).

The numbers should be written in increasing order on the stones.

The sequence goes: $150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, \ldots$

Students fill in the missing numbers between 150 and 163 in order on the stones shown in the picture.

Starting from 100, we jump 5 at a time:

$$100,\; 105,\; 110,\; 115,\; 120,\; 125,\; 130,\; 135,\; 140,\; 145,\; 150$$

Each jump adds 5 to the previous number.
$$100 + 5 = 105,\quad 105 + 5 = 110,\quad 110 + 5 = 115, \ldots$$

Students draw arcs of equal size above the number line and write these numbers in the spaces provided.

Starting from 100, we jump 20 at a time:

$$100,\; 120,\; 140,\; 160,\; 180,\; 200$$

Each jump adds 20:
$$100 + 20 = 120,\quad 120 + 20 = 140,\quad 140 + 20 = 160,\quad 160 + 20 = 180,\quad 180 + 20 = 200$$

Students draw larger arcs and fill in the missing numbers.

Rule: 1 less = subtract 1; 1 more = add 1.

(a) $160 - 1 = \mathbf{159}$; $160 + 1 = \mathbf{161}$
$$\boxed{159 \quad 160 \quad 161}$$

(b) $129 - 1 = \mathbf{128}$; $129 + 1 = \mathbf{130}$
$$\boxed{128 \quad 129 \quad 130}$$

(c) $187 - 1 = \mathbf{186}$; $187 + 1 = \mathbf{188}$
$$\boxed{186 \quad 187 \quad 188}$$

(d) $134 - 1 = \mathbf{133}$; $134 + 1 = \mathbf{135}$
$$\boxed{133 \quad 134 \quad 135}$$

(e) $158 - 1 = \mathbf{157}$; $158 + 1 = \mathbf{159}$
$$\boxed{157 \quad 158 \quad 159}$$

(a) Making 125 with matchstick bundles:

$125 = 1 \times 100 + 2 \times 10 + 5 \times 1$

Way 1: 1 hundred-bundle + 2 ten-bundles + 5 loose sticks

Way 2: 1 hundred-bundle + 1 ten-bundle + 15 loose sticks
(since $100 + 10 + 15 = 125$)

(b) Making 145 using a ginladi (number strip/bead string):

$145 = 100 + 45$

Way 1: Mark 145 on the ginladi by counting 145 beads.

Way 2: Count 1 hundred, then 4 tens, then 5 more.

(c) Making 170 on a number line:

Way 1: Start at 0, jump to 100, then jump 70 more to reach 170.
$$0 \xrightarrow{+100} 100 \xrightarrow{+70} 170$$

Way 2: Start at 150, jump 20 more.
$$150 \xrightarrow{+20} 170$$

We use: $\text{Number} = 100 \times \text{(hundreds)} + 10 \times \text{(tens)} + 1 \times \text{(ones)}$

Row 1: 114
$114 = 1 \times 100 + 1 \times 10 + 4 \times 1$
Matchstick bundles: 100s = 1, 10s = 1, 1s = 4
Number sentence: 100 and 14 more ✓

Row 2: 100 and 32 more
$100 + 32 = \mathbf{132}$
$132 = 1 \times 100 + 3 \times 10 + 2 \times 1$
Matchstick bundles: 100s = 1, 10s = 3, 1s = 2

Row 3: (pictorial form shown — students count bundles)
Students count from the picture and write the number and sentence.

Row 4: 172
$172 = 1 \times 100 + 7 \times 10 + 2 \times 1$
Matchstick bundles: 100s = 1, 10s = 7, 1s = 2
Number sentence: 100 and 72 more

Row 5: 108
$108 = 1 \times 100 + 0 \times 10 + 8 \times 1$
Matchstick bundles: 100s = 1, 10s = 0, 1s = 8
Number sentence: 100 and 8 more

Row 6: 30 more than 150
$150 + 30 = \mathbf{180}$
$180 = 1 \times 100 + 8 \times 10 + 0 \times 1$
Matchstick bundles: 100s = 1, 10s = 8, 1s = 0

Row 7: Matchstick bundles = 1, 6, 0
$\text{Number} = 1 \times 100 + 6 \times 10 + 0 \times 1 = \mathbf{160}$
Number sentence: 100 and 60 more

To mark numbers on a number line, identify the position of each number relative to the nearest tens.

(a) Numbers: 109, 112, 124, 134, 146 (Number line from 100 to 150)

- 109: 9 steps after 100 → mark between 100 and 110, close to 110
- 112: 2 steps after 110 → mark just after 110
- 124: 4 steps after 120 → mark between 120 and 130, close to 120
- 134: 4 steps after 130 → mark between 130 and 140, close to 130
- 146: 6 steps after 140 → mark between 140 and 150, closer to 150

(b) Numbers: 155, 163, 178, 189, 198 (Number line from 150 to 200)

- 155: 5 steps after 150 → halfway between 150 and 160
- 163: 3 steps after 160 → just after 160
- 178: 8 steps after 170 → between 170 and 180, close to 180
- 189: 9 steps after 180 → between 180 and 190, close to 190
- 198: 8 steps after 190 → between 190 and 200, close to 200

(c) Numbers: 125, 142, 153, 174, 199 (Number line from 100 to 200)

- 125: halfway between 120 and 130
- 142: 2 steps after 140
- 153: 3 steps after 150
- 174: 4 steps after 170
- 199: 1 step before 200

Students should mark each number at its correct position on the number lines in their textbook.