Measuring Length

Given: The picture shows students measuring the depth of something (e.g., a well or container).

From the picture, the students are measuring depth.

Tick marks (✓):
- a) Length ✓ (depth is a form of length measurement)
- b) Height ✓ (height is also a form of length measurement)
- c) Weight ☐ (not being measured)
- d) Depth ✓ (already ticked — this is what is directly shown)
- e) Breadth ✓ (breadth is also a form of length measurement)
- f) Temperature ☐ (not being measured)

Note: As the teacher's note explains, height, width, depth, and breadth all refer to length measurement. So length, height, breadth, and depth can all be ticked.

Given: The picture shows students measuring height.

Answer:
A measuring tape (or metre scale/metre rope) is being used to measure the height in the picture.

Other tools that can be used to measure height:
1. A metre scale (ruler)
2. A metre rod
3. A measuring tape used by tailors
4. A metre rope

All these tools help us find out how tall (high) something is.

Given: We need to check each statement against real classroom observations. (Answers may vary; typical expected answers are given below.)

Concept: 1 metre = 100 cm. Average height of Class 4 students ≈ 120–140 cm (more than 1 m). Arm length ≈ 50–60 cm (less than 1 m). Door height ≈ 200 cm (more than 1 m). Blackboard breadth ≈ 150–200 cm (more than 1 m).

a) The height of most of the students in my grade is more than a metre. → Correct (Most Class 4 students are taller than 1 m.)

b) The length of my arm is less than a metre. → Correct (An arm is usually about 50–60 cm, which is less than 100 cm = 1 m.)

c) The height of the door of the grade is less than a metre. → Incorrect (A standard door is about 2 m tall, which is more than 1 m.)

d) The breadth of the blackboard is more than a metre. → Correct (A classroom blackboard is usually more than 1 m wide.)

Given: We have a 1 m rope.

How to make the lines:
- 1 m line: Place the 1 m rope on the floor and draw a line along it. This gives a 1 m line.
- 5 m line: Place the 1 m rope end-to-end 5 times on the floor, marking each end. Join the marks to get a 5 m line.
- 10 m line: Place the 1 m rope end-to-end 10 times on the floor, marking each end. Join the marks to get a 10 m line.

Activity: Walk, jump, and crawl along each line to get a feel for how long 1 m, 5 m, and 10 m are.

*This is a hands-on activity. Results will vary for each student.*

Given: Students perform a long jump and measure the distance using 1 m, ½ m, and ¼ m ropes.

How to measure:
- After each jump, place the 1 m rope from the starting line to where the student landed.
- If the distance is more than 1 m, use the 1 m rope first, then use the ½ m or ¼ m rope for the remaining part.
- Record whether the jump is less than 1 m, equal to 1 m, or more than 1 m.

Sample filled table (answers will vary for each class):

| Name of the student | Less than 1 m | 1 m | More than 1 m | Actual measurement |
|---|---|---|---|---|
| Riya | | | ✓ | 1 m and ¼ m |
| Amit | ✓ | | | ¾ m |
| Priya | | ✓ | | 1 m |

*Students should fill in their own classmates' names and measurements.*

Given: We need to estimate and then measure the length and breadth of the classroom.

How to measure:
- Use the 1 m rope repeatedly along the length of the classroom, counting how many times it fits.
- Do the same for the breadth.

Sample answer (will vary by classroom):
- Estimated length of classroom: about 8 m
- Actual length of classroom: 8 m (measured using the 1 m rope 8 times)
- Estimated breadth of classroom: about 6 m
- Actual breadth of classroom: 6 m (measured using the 1 m rope 6 times)

*Students should record their own classroom's measurements.*

Given: Pictures of a bus and a cricket bat are shown (images not visible, but standard sizes are used).

Standard lengths:
- Length of one bus ≈ 12 metres (a standard city bus is about 12 m long)
- Length of one cricket bat ≈ 1 metre (a standard cricket bat is about 96 cm ≈ 1 m)

Answer:
- Length of one bus = approximately 12 m
- Length of one cricket bat = approximately 1 m

*(Answers may vary slightly depending on the values given in the pictures in the textbook.)*

Given: (Based on typical textbook values)
- Length of one blue whale ≈ 30 m
- Length of two blue whales = 30 × 2 = 60 m
- Length of one bus ≈ 12 m

Calculation:
$$\text{Number of buses} = \frac{60}{12} = 5$$

Answer: 5 buses would be equal to the length of two blue whales.

*(Note: If the textbook uses different values for bus/whale length, apply the same method with those values.)*

Given: (Based on typical textbook values)
- Length of one blue whale ≈ 30 m
- Length of one cricket bat ≈ 1 m

Calculation:
$$\text{Number of cricket bats} = \frac{30 \text{ m}}{1 \text{ m}} = 30$$

Answer: 30 cricket bats will be needed to measure one whale.

*(Apply the same method if the textbook gives different values.)*

Given: (Based on typical textbook values)
- Height of one ostrich ≈ 2.5 m
- Height of two ostriches stacked = 2.5 × 2 = 5 m

Looking at the picture clues, two ostriches stacked would be equal to the height of a giraffe (a giraffe is about 5 m tall).

Answer: If two ostriches stand one above another, their height will be equal to the height of a giraffe.

*(Answer depends on the picture values given in the textbook.)*

Given: (Based on typical textbook values)
- Length of one blue whale ≈ 30 m
- Length of one crocodile ≈ 5 m

Calculation:
$$\text{Number of crocodiles} = \frac{30}{5} = 6$$

Answer: 6 crocodiles will be equal to the length of a blue whale.

*(Apply the same method if the textbook gives different values for crocodile length.)*

Given: 1 metre (m) = 100 centimetre (cm)

Finding $\frac{1}{2}$ m in cm:
$$\frac{1}{2} \text{ m} = \frac{1}{2} \times 100 \text{ cm} = 50 \text{ cm}$$

Finding $\frac{1}{4}$ m in cm:
$$\frac{1}{4} \text{ m} = \frac{1}{4} \times 100 \text{ cm} = 25 \text{ cm}$$

Answer:
$$\frac{1}{2} \text{ m} = \boxed{50} \text{ cm}, \quad \frac{1}{4} \text{ m} = \boxed{25} \text{ cm}$$

Given: Various objects are shown in the pictures (images not visible, but the method is described).

How to measure:
- Place the object along the scale starting from the 0 cm mark.
- Read the measurement at the other end of the object.
- Record the length in cm.

To write in increasing order:
- Measure each object and note its length.
- Arrange from the shortest (smallest cm) to the longest (largest cm).

Example (actual measurements will depend on the pictures):
If the objects are a pencil (10 cm), an eraser (4 cm), a sharpener (2 cm), and a crayon (7 cm), then increasing order would be:
\text{Sharpener (2 cm) < Eraser (4 cm) < Crayon (7 cm) < Pencil (10 cm)}

*Students should measure the actual objects shown in their textbook and write the order accordingly.*

Given: We need to estimate and then measure each item.

Concept: 1 cm is the length of one small division on a ruler. It is roughly the width of a fingernail.

Expected answers (typical values; actual measurements may vary):

| Length of items | Equal to 1 cm | More than 1 cm | Less than 1 cm | Actual measurement |
|---|---|---|---|---|
| A fingernail | ✓ | | | ≈ 1 cm |
| An eraser | | ✓ | | ≈ 4–5 cm |
| An ant | | | ✓ | ≈ 0.5 cm |
| A grain of wheat | | | ✓ | ≈ 0.6 cm |
| A rajma seed | | ✓ | | ≈ 1.5 cm |

Examples of things less than or equal to 1 cm:
- A grain of rice
- A sesame seed (til)
- An ant
- A mustard seed

*Students should verify by actually measuring with a scale.*

Given: Three toy cars are rolled down a ramp and the distance each travels is measured.

How to measure:
- Place the measuring tape from the bottom of the ramp to where the car stops.
- Read the measurement in cm.
- Rank: Car that travels the farthest = Rank 1; shortest distance = Rank 3.

Sample answer (actual values will vary):

| Car | Distance from the ramp | Rank |
|---|---|---|
| Car 1 | 45 cm | 2 |
| Car 2 | 60 cm | 1 |
| Car 3 | 30 cm | 3 |

*Students should fill in their own measured values.*

Given: A treasure hunt map is shown on a dot grid where 1 square = 1 cm (images not fully visible).

Method:
- Trace each possible route on the yellow tiles.
- Count the number of 1 cm squares (tiles) along each route.
- The route with the most tiles is the longest route.
- The route with the fewest tiles is the shortest route.

Answer: (Will depend on the actual map in the textbook)
- Count each tile step as 1 cm.
- Add up all the steps for each route.
- Compare and identify the longest and shortest routes.

*Students should trace the routes in their textbook map and count the tiles to find the lengths in cm.*

Given: Students trace their own hand and measure its length.

How to measure:
- Trace your hand on paper with fingers together.
- Place the scale from the bottom of the palm (wrist line) to the tip of the longest finger (middle finger).
- Read the measurement.

Sample answer:
Length of my hand = 15 cm (This will vary for each student; typical range for Class 4 students is 13–17 cm.)

*Students should measure their own hand and write the actual value.*

Given: First, measure the length of your own hand (from Q5). Use it to estimate other objects.

Method:
- If your hand = 15 cm, and the textbook takes 2 hand-lengths, then estimated length = 2 × 15 = 30 cm.
- Verify by measuring with a cm scale.

Sample table (values will vary):

| Object | Number of hands | Estimate using hand | Actual measure using the cm scale |
|---|---|---|---|
| 1. Length of my textbook | 2 | 30 cm | 28 cm |
| 2. Height of my chair | 3 | 45 cm | 42 cm |
| 3. Width of my desk | 4 | 60 cm | 58 cm |
| 4. Height of a flowerpot | 2 | 30 cm | 25 cm |

*Students should use their own hand measurement and fill in actual values.*

Given: Ashwin has a broken scale (the 0 mark is missing or the scale starts from a number other than 0, e.g., it starts from 2 cm).

Concept: To measure with a broken scale, note the starting mark and the ending mark, then subtract.

$$\text{Length of object} = \text{Ending mark} - \text{Starting mark}$$

Example: If the object starts at the 2 cm mark and ends at the 9 cm mark:
$$\text{Length} = 9 - 2 = 7 \text{ cm}$$

Answer: Even with a broken scale, we can measure accurately by subtracting the starting reading from the ending reading.

*Students should apply this method to the specific measurements shown in their textbook's picture.*

Given: A number line related to centimetres is shown (image not fully visible).

Concept: A number line for cm goes: 0, 1, 2, 3, 4, 5, ... Each step = 1 cm.

Method: Identify the pattern (the gap between given numbers) and fill in the missing values.

Example: If the number line shows 0, __, 2, __, 4, __, 6:
- Missing values are: 1, 3, 5

Answer: Fill in the consecutive whole numbers (or the numbers following the pattern shown) in the blank spaces on the number line.

*Students should look at the number line in their textbook and fill in the missing numbers following the pattern.*

Given:
- Length of the board = 2 m
- Length of one sticker = 20 cm

Step 1: Convert the length of the board into centimetres.
$$2 \text{ m} = 2 \times 100 \text{ cm} = 200 \text{ cm}$$

Step 2: Find the number of stickers needed.
$$\text{Number of stickers} = \frac{\text{Length of board}}{\text{Length of one sticker}} = \frac{200 \text{ cm}}{20 \text{ cm}} = 10$$

Answer: Sonu needs 10 stickers to cover the length of the board completely.

Given: 1 m = 100 cm

Concept: To convert metres to centimetres, multiply by 100. To convert centimetres to metres, divide by 100.

i) $2 \text{ m} = 2 \times 100 = 200 \text{ cm}$ ✓ (already given)

ii) $\_ \text{ m} = 400 \text{ cm}$
$$\text{m} = \frac{400}{100} = 4 \text{ m}$$
So, $\boxed{4} \text{ m} = 400 \text{ cm}$

iii) $6 \text{ m} = \_ \text{ cm}$
$$6 \times 100 = 600 \text{ cm}$$
So, $6 \text{ m} = \boxed{600} \text{ cm}$

iv) $\_ \text{ m} = 800 \text{ cm}$
$$\text{m} = \frac{800}{100} = 8 \text{ m}$$
So, $\boxed{8} \text{ m} = 800 \text{ cm}$

Given: Wells are labelled with depths in metres and centimetres (images show wells with different depth labels).

Concept: Convert all measurements to the same unit (cm) and match equal values.

Method:
- 2 m = 200 cm → match the well labelled 2 m with the well labelled 200 cm
- 4 m = 400 cm → match the well labelled 4 m with the well labelled 400 cm
- 6 m = 600 cm → match the well labelled 6 m with the well labelled 600 cm
- 8 m = 800 cm → match the well labelled 8 m with the well labelled 800 cm

Answer: Match each well showing depth in metres with the well showing the equivalent depth in centimetres:
- 2 m ↔ 200 cm
- 4 m ↔ 400 cm
- 6 m ↔ 600 cm
- 8 m ↔ 800 cm

*Students should draw lines connecting the matching wells in their textbook.*

Given: Students measure their heights and record them in a table.

Method: Look at the 'Height in cm' column in the table. Find the largest value.

Answer: The height of the tallest child is the largest value in the table.

*Example: If heights are 125 cm, 132 cm, 118 cm, 140 cm — the tallest child's height is 140 cm.*

*Students should fill in the actual tallest height from their class table.*

Given: Students measure their heights and record them in a table.

Method: Look at the 'Height in cm' column. Find the smallest value.

Answer: The height of the shortest child is the smallest value in the table.

*Example: If heights are 125 cm, 132 cm, 118 cm, 140 cm — the shortest child's height is 118 cm.*

*Students should fill in the actual shortest height from their class table.*

Given: 1 m = 100 cm. Students have recorded their heights in cm.

Method: Count all students whose height is more than 100 cm.

Answer: Count the number of entries in the table where height > 100 cm.

*Example: If all 4 students have heights 125 cm, 132 cm, 118 cm, 140 cm — all 4 are more than 1 m tall, so the answer is 4.*

*Students should count from their own class table.*

Given: 1 m = 100 cm.

Method: Count all students whose height is less than 100 cm.

Answer: Count the number of entries in the table where height < 100 cm.

*Example: If all students are taller than 100 cm, the answer is 0.*

*Students should count from their own class table.*

Given: Three different garden shapes are shown (images not fully visible).

Concept: The length of the boundary of a shape is called its perimeter. To find the perimeter, add up the lengths of all the sides.

Method:
- Count the number of unit sides (bricks/tiles) along the boundary of each garden shape.
- The shape with the most unit sides has the longest boundary (perimeter).
- Circle that shape.

Answer: Count the boundary units for each garden shape and circle the one with the highest count.

*Students should count the bricks/tiles on the boundary of each shape in their textbook and circle the longest one.*

Given: Shapes are drawn on a dot grid where the distance between two adjacent dots = 1 cm.

Concept: Perimeter = total length of all sides of the shape. On a 1 cm dot grid, each side between two adjacent dots = 1 cm.

Method:
- Count the number of 1 cm segments along the boundary of each shape.
- That count gives the perimeter in cm.

Example:
- A rectangle 3 cm × 2 cm: Perimeter = 3 + 2 + 3 + 2 = 10 cm
- A square 2 cm × 2 cm: Perimeter = 2 + 2 + 2 + 2 = 8 cm
- An L-shape with boundary of 12 segments: Perimeter = 12 cm

a) Colour in blue the shape with the largest perimeter value.
b) Colour in green the shape with the smallest perimeter value.
c) Tick any two shapes that have equal perimeter values.

*Students should count the boundary segments of each shape in their textbook dot grid and apply the above steps.*

Given: Several shapes are shown on a dot grid (1 dot gap = 1 cm).

Concept: Perimeter = sum of all sides. Two shapes have the same perimeter if the total length of their boundaries is equal.

Method:
- Count the boundary segments (each = 1 cm) for every shape.
- Compare the totals.
- Tick the shapes that have equal perimeters.

Example: If Shape A has perimeter 12 cm and Shape C also has perimeter 12 cm, tick both Shape A and Shape C.

*Students should count the boundary of each shape in their textbook and tick the ones with matching perimeters.*

Given: Several garden shapes are shown on a dot grid.

Concept: Minimum perimeter = the shape whose boundary is the shortest.

Method:
- Count the boundary segments (each = 1 cm) for each garden shape.
- The shape with the fewest boundary segments has the minimum perimeter.
- Tick that shape.

Answer: Count the perimeter of each garden shape and tick the one with the smallest total.

*Students should count from their textbook and tick accordingly.*

Given: We need to estimate and then measure the perimeter of real objects.

Concept: Perimeter = sum of all sides of the shape.

For a rectangular object: Perimeter = 2 × (length + breadth)

Method:
- First estimate the perimeter by looking at the object.
- Then measure each side using a scale or measuring tape.
- Add all sides to get the actual perimeter.

Sample table (values will vary):

| S. No. | Object | Estimated perimeter | Actual measure |
|---|---|---|---|
| 1. | Desk | 200 cm | 210 cm |
| 2. | Blackboard | 500 cm | 480 cm |
| 3. | Classroom floor | 28 m | 26 m |
| 4. | Notebook | 80 cm | 76 cm |
| 5. | Door | 700 cm | 680 cm |
| 6. | Window | 300 cm | 290 cm |

*Students should measure actual objects in their classroom and fill in real values.*

Given: We need to draw three different shapes, each with a perimeter of 20 cm, on a dot grid (1 dot gap = 1 cm).

Concept: Perimeter = total length of boundary = 20 cm. There are many ways to make a boundary of 20 cm.

Three possible shapes:

Shape 1 — Rectangle:
- Length = 6 cm, Breadth = 4 cm
- Perimeter = 6 + 4 + 6 + 4 = 20 cm ✓

Shape 2 — Square:
- Each side = 5 cm
- Perimeter = 5 + 5 + 5 + 5 = 20 cm ✓

Shape 3 — L-shape (irregular):
- Sides: 6 cm, 2 cm, 2 cm, 2 cm, 4 cm, 4 cm
- Perimeter = 6 + 2 + 2 + 2 + 4 + 4 = 20 cm ✓

*Students should draw these (or other valid shapes) on the dot grid in their textbook, making sure the total boundary = 20 cm.*