Double Century — NCERT Solutions

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.