Maps, Directions, and Scales

Mathematics

Class 5 | CBSE, NCERT & ICSE

Learning Objectives

Understand the 4 main and 4 intermediate compass directions
Read and use a compass rose on a map
Understand what a map scale means and how to use it
Calculate actual distances from map distances using scale
Draw simple maps to scale using given measurements
Read and interpret simple floor plans and route maps
Use grid references (rows and columns) to locate places on a map
Understand latitude and longitude as grid systems on Earth
Locate Indian states, major cities, rivers, and mountains on a map

Introduction — What is a Map?

A map is a flat drawing that represents a real area — like a room, a town, a country, or the whole Earth. Maps are much smaller than the real area they show, so they use a scale to maintain proportions. A map of India cannot be as large as India itself, so we shrink it — but everything stays in the correct proportion.

Maps are used by geographers, soldiers, travellers, pilots, sailors, and city planners. ISRO (Indian Space Research Organisation) makes highly detailed maps of India using satellites. Even your phone's GPS uses digital maps!

Image needed: A political map of India with major states, capital cities, and rivers labelled. Include compass rose in the corner. Colourful, child-friendly, with state borders clearly marked.
Style: Clean political map with colour-coded states, compass rose, ocean labels
Size: 600×700px

Part 1: Compass Directions

A compass helps you find directions. The four cardinal directions are North (N), South (S), East (E), and West (W). Between them are four intermediate (ordinal) directions: Northeast (NE), Northwest (NW), Southeast (SE), and Southwest (SW).

Remembering Cardinal Directions

Never Eat Soggy Waffles → N, E, S, W (clockwise from top)
Or in Hindi: U, P, D, P (Uttar, Purv, Dakshin, Paschim)
The Sun rises in the East and sets in the West
In India, the Himalayas are to the North and the Indian Ocean is to the South

Direction	Hindi Name	Symbol	Between
North	Uttar (उत्तर)	N	—
South	Dakshin (दक्षिण)	S	—
East	Purv (पूर्व)	E	—
West	Paschim (पश्चिम)	W	—
Northeast	Uttar-Purv	NE	Between N and E
Northwest	Uttar-Paschim	NW	Between N and W
Southeast	Dakshin-Purv	SE	Between S and E
Southwest	Dakshin-Paschim	SW	Between S and W

Image needed: A large, clear compass rose showing all 8 directions (N, NE, E, SE, S, SW, W, NW) with both English and Hindi names. Each direction marked with a distinct colour. Decorative compass-style design.
Style: Classic compass rose design, colourful, with bilingual labels
Size: 500×500px

Directions on a Map of India

Using the compass, we can describe where one place is relative to another:

Example	Direction
Kashmir is _____ of Kanyakumari	North
Kolkata is _____ of Mumbai	East
Chennai is _____ of Mumbai	Southeast
Rajasthan is _____ of Kerala	Northwest
Assam is _____ of Delhi	Northeast

Example 1: A school is in the centre of a town. The market is to the North, the hospital is to the Southeast, and the park is to the West. If Ravi faces the market and turns clockwise by 90°, which direction is he now facing?

Solution:

Ravi faces North (towards market). Turns 90° clockwise from North → faces East

Part 2: Map Scale

A scale tells you the relationship between a distance on the map and the actual distance on the ground. It's written as a ratio, like 1 cm : 10 km, which means every 1 cm on the map represents 10 km in real life.

The Scale Formula

Actual Distance = Map Distance × Scale

Map Distance = Actual Distance ÷ Scale

Types of Scale Representation

Type	Example	Meaning
Statement Scale	1 cm = 50 km	1 cm on map = 50 km on ground
Representative Fraction (RF)	1 : 5,000,000	1 unit on map = 5,000,000 same units on ground
Bar Scale	A line divided into segments	Read distances directly off the bar

Example 2: On a map, the scale is 1 cm : 50 km. The distance between Delhi and Agra on the map is 4 cm. What is the actual distance?

Solution:

Actual distance = Map distance × Scale

= 4 cm × 50 km/cm

= 200 km

Example 3: The actual distance between Mumbai and Pune is 150 km. On a map with scale 1 cm : 30 km, what is the map distance?

Solution:

Map distance = Actual distance ÷ Scale

= 150 km ÷ 30 km/cm

= 5 cm

Example 4: On a school map, the scale is 1 cm : 8 m. The classroom measures 4.5 cm × 3 cm on the map. Find the actual length and width of the classroom.

Solution:

Actual length = 4.5 × 8 = 36 m

Actual width = 3 × 8 = 24 m

Image needed: A simple map of a school campus showing buildings (classrooms, library, playground, canteen) with a scale bar (1 cm = 20 m) and compass rose. Grid lines overlaid. Distances marked.
Style: Top-down floor plan style, clean with coloured buildings, labelled
Size: 650×500px

Part 3: Reading Maps with Grid References

Maps often have a grid — a network of horizontal and vertical lines. Each square in the grid has a reference. We read grids by going along the corridor (horizontal/column) first, then up the stairs (vertical/row). This is called the alphanumeric grid or coordinate system.

Example 5: On a grid map, columns are labelled A–F (left to right) and rows are labelled 1–6 (bottom to top). The post office is at B3. The school is at D5. What direction is the school from the post office?

Solution:

Post office at B3: column B, row 3

School at D5: column D (further right = East) and row 5 (further up = North)

School is to the Northeast of the post office

Image needed: A 6×6 grid map of an Indian town showing: a market (A2), school (C4), temple (E1), hospital (B5), park (D3), and railway station (F4). Columns A–F, rows 1–6. Clear grid lines, icons for each place.
Style: Clean grid map, cartoon icons, colourful
Size: 600×600px

Latitude and Longitude — The World's Grid

The entire Earth is covered by an imaginary grid called latitude (horizontal lines) and longitude (vertical lines). This helps locate any place on Earth precisely.

Feature	Latitude	Longitude
Direction of lines	Horizontal (east-west)	Vertical (north-south)
Measure	0° to 90° N or S	0° to 180° E or W
Starting line	Equator (0°)	Prime Meridian (0°)
Important Indian lines	Tropic of Cancer (23.5°N) passes through India	82.5°E Standard Time Meridian

India lies between approximately 8°N to 37°N latitude and 68°E to 97°E longitude.

Part 4: Drawing a Map to Scale

To draw a map to scale:

Choose a suitable scale (e.g., 1 cm = 10 m)
Divide each actual measurement by the scale to get map measurements
Draw the map using the calculated measurements
Mark a compass rose in the corner
Write the scale clearly on the map

Example 6: Draw a map of a rectangular park that is 60 m × 40 m. Use a scale of 1 cm = 10 m.

Solution:

Map length = 60 ÷ 10 = 6 cm

Map width = 40 ÷ 10 = 4 cm

Draw a rectangle 6 cm × 4 cm, add compass rose, write "Scale: 1 cm = 10 m"

Example 7: A room is 5 m × 3.5 m. A wardrobe occupies the north wall (2 m wide), a bed is on the east side (2 m wide), and a window is on the south wall (1 m wide). Draw a floor plan at scale 1 cm = 0.5 m and mark all features.

Solution:

Room: 5 m → 10 cm (length), 3.5 m → 7 cm (width)

Wardrobe: 2 m → 4 cm (on north wall)

Bed: 2 m → 4 cm (on east wall)

Window: 1 m → 2 cm (on south wall)

Key Words

Word	Meaning
Map	A flat drawing representing a real area at a reduced size
Scale	The ratio between map distance and actual distance
Compass	An instrument that shows direction using Earth's magnetic field
Cardinal Directions	The four main directions: North, South, East, West
Intermediate Directions	NE, NW, SE, SW — between the cardinal directions
Grid Reference	A code (like B3) that locates a square on a map grid
Latitude	Imaginary horizontal lines on Earth, measured in degrees N or S
Longitude	Imaginary vertical lines on Earth, measured in degrees E or W
Compass Rose	A diagram on a map showing the directions
Legend / Key	A guide on the map explaining what symbols mean

Key Points to Remember

The 4 cardinal directions are N, S, E, W. The 4 intermediate directions are NE, NW, SE, SW
On a map, North is usually at the top unless stated otherwise
Scale formula: Actual Distance = Map Distance × Scale Value
To find map distance: Map Distance = Actual Distance ÷ Scale Value
Read grid references: column (across) first, then row (up)
Latitude lines run east-west; longitude lines run north-south
India lies between 8°N–37°N and 68°E–97°E
The Tropic of Cancer (23.5°N) passes through India
India's standard time is based on 82.5°E longitude (IST = UTC + 5:30)
Always include compass rose, scale, and legend when drawing a map

Finished learning? Now test what you know!

🎯 Quick Quiz — Test Yourself!

Answer these questions right here. You get instant feedback — no paper needed!

Score: 0 / 8

1. How many main (cardinal) directions are there?

The four cardinal directions are North, South, East and West.

2. The Sun rises in the:

The Sun rises in the East and sets in the West.

3. The direction exactly between North and East is:

Between N and E is North-East (NE).

4. On a map with scale 1 cm = 20 km, a distance of 3 cm represents:

3 cm × 20 km = 60 km.

5. If you face North, which direction is directly behind you?

The opposite of North is South.

6. Scale: 1 cm = 25 km. A map distance of 4 cm equals how many km? (digits only)

4 × 25 = 100 km.

7. Which instrument is used to find directions?

A compass — its needle points North.

8. Scale: 1 cm = 30 km. To show 150 km, how many cm long should the line be?

150 ÷ 30 = 5 cm.

Practice Questions

A. Compass Directions

1. Name the direction that is exactly between North and East:

2. Name the direction that is exactly between South and West:

3. If you face North and turn 90° clockwise, you face:

4. If you face East and turn 180°, you face:

5. If you face Southwest and turn 90° anticlockwise, you face:

6. The Hindi name for North is and for East is .

B. Map Scale — Find Actual Distance

Scale: 1 cm = 40 km

1. Map distance = 5 cm → Actual distance =

2. Map distance = 3.5 cm → Actual distance =

3. Map distance = 7.25 cm → Actual distance =

4. Map distance = 0.5 cm → Actual distance =

5. Map distance = 12 cm → Actual distance =

C. Map Scale — Find Map Distance

Scale: 1 cm = 25 km

1. Actual distance = 100 km → Map distance =

2. Actual distance = 75 km → Map distance =

3. Actual distance = 350 km → Map distance =

4. Actual distance = 12.5 km → Map distance =

5. Actual distance = 600 km → Map distance =

D. Scale Problems

1. On a map with scale 1 cm = 50 km, Delhi and Mumbai are 24 cm apart on the map. What is the actual distance between them?

2. The actual distance between Chennai and Bengaluru is 350 km. On a map with scale 1 cm = 70 km, how many cm apart will they be?

3. A rectangular garden is 80 m × 60 m. On a plan with scale 1 cm = 10 m, what are the dimensions on the plan?

4. On a floor plan, a room measures 6 cm × 4 cm. The scale is 1 cm = 2 m. Find the actual area of the room.

5. Meena's house is 3 cm from school and 5 cm from the park on a map with scale 1 cm = 0.5 km. Find both actual distances. Which is farther?

E. Grid References

Use the 6×6 grid map. Columns A–F (left to right), Rows 1–6 (bottom to top). Market at A2, School at C4, Temple at E1, Hospital at B5, Park at D3, Railway Station at F4.

1. Which place is at D3?

2. What is the grid reference for the hospital?

3. What direction is the school from the market?

4. What direction is the hospital from the park?

5. Which place is in the northeast corner of the map?

F. India — Directions on a Map

1. Which state is to the north of Tamil Nadu?

2. In which direction is Assam from Maharashtra?

3. Which ocean is to the south of India?

4. Which country is to the east of India?

5. The Tropic of Cancer (23.5°N) passes through which states of India? Name any 3.

6. What is India's approximate latitude range? °N to °N

G. Multiple Choice

1. On a map with scale 1 cm = 20 km, a distance of 3 cm represents:

a) 23 kmb) 60 kmc) 6.67 kmd) 20 km

2. The direction between South and East is:

a) SWb) SEc) NEd) NW

3. If you face North and turn 270° clockwise, you now face:

a) Southb) Eastc) Westd) North

4. India's Standard Time Meridian is:

a) 75.5°Eb) 82.5°Ec) 90°Ed) 68°E

5. The Equator passes at:

a) 23.5°Nb) 66.5°Nc) 0°d) 90°S

Activity: Draw Your Classroom Map

Materials: Graph paper, ruler, pencil, coloured pens

Instructions:

Measure the length and width of your classroom (or estimate: typical classroom = 10 m × 8 m).
Choose a suitable scale (e.g., 1 cm = 1 m).
Draw the classroom outline on graph paper.
Mark the positions of: teacher's desk (front/north), students' benches, windows, doors, blackboard.
Add a compass rose showing North at the blackboard wall.
Write the scale clearly. Add a legend/key for symbols used.

Bonus: Draw a map of your home or school campus. Mark 5 locations and write their grid references. Ask a friend to find each location using only the grid references!

Image needed: An Indian student drawing a floor plan of their classroom on graph paper, with a ruler and compass. The classroom map is shown with benches, teacher's desk, blackboard, and compass rose labelled.
Style: Flat illustration, Indian school setting, graph paper visible
Size: 650×400px

Want to review the lesson again?

Mathematics

Maps, Directions, and Scales

Class 5 | CBSE / NCERT / ICSE

Name: Class: Date:

A map is a flat drawing representing a real area at a reduced size. A scale tells us the ratio between map distance and actual distance. Directions tell us where one place is relative to another.

Compass Directions

Cardinal (4)	Intermediate (4)	Hindi Names
North (N)	Northeast (NE)	Uttar, Purv, Dakshin, Paschim
South (S)	Northwest (NW)	Uttar-Purv, Uttar-Paschim
East (E)	Southeast (SE)	Dakshin-Purv, Dakshin-Paschim
West (W)	Southwest (SW)	—

Memory trick: Never Eat Soggy Waffles → N, E, S, W (clockwise)

Turning clockwise: N → E → S → W → N. Turning anticlockwise: N → W → S → E → N

Compass rose with 8 directions in English and Hindi

Map Scale

Actual Distance = Map Distance × Scale Value

Map Distance = Actual Distance ÷ Scale Value

Ex 1: Scale: 1 cm = 40 km. Map distance = 5 cm. Actual distance = 5 × 40 = 200 km

Ex 2: Scale: 1 cm = 30 km. Actual distance = 150 km. Map distance = 150 ÷ 30 = 5 cm

Ex 3: Scale: 1 cm = 8 m. Room = 4.5 cm × 3 cm on plan. Actual: 4.5×8=36 m long, 3×8=24 m wide

Grid References

Read grids: column (across) first, then row (up). Example: B3 = column B, row 3.

India on the Map

Feature	Direction from India's centre
Himalayas	North
Indian Ocean	South
Arabian Sea	Southwest
Bay of Bengal	Southeast
Assam / Northeast states	Northeast

India's latitude: 8°N to 37°N. Longitude: 68°E to 97°E. Tropic of Cancer (23.5°N) passes through India. Standard Time Meridian: 82.5°E (IST = UTC +5:30)

Political map of India with compass rose showing states and capital cities

Mathematics

Maps, Directions — Practice

Class 5 | CBSE / NCERT / ICSE

A. Compass Directions

1. Direction between North and East:

2. Face North, turn 90° clockwise:

3. Face East, turn 180°:

4. Face SW, turn 90° anticlockwise:

5. Hindi name for West:

6. How many degrees from North to South (clockwise)?

B. Scale Problems (Scale: 1 cm = 40 km)

1. Map distance 5 cm → Actual:

2. Map distance 3.5 cm → Actual:

3. Actual 200 km → Map:

4. Actual 100 km → Map:

5. Actual 60 km → Map:

C. Word Problems

1. On a map (scale 1 cm = 50 km), Delhi and Mumbai are 24 cm apart. Actual distance?

2. Chennai to Bengaluru = 350 km. Scale 1 cm = 70 km. Map distance?

3. Garden 80 m × 60 m. Scale 1 cm = 10 m. Plan dimensions?

4. Floor plan: room = 6 cm × 4 cm. Scale 1 cm = 2 m. Actual area?

D. India on the Map

1. Which state is north of Tamil Nadu?

2. Which direction is Assam from Maharashtra?

3. Ocean to south of India?

4. India's Standard Time Meridian: °E

5. Name 3 states through which Tropic of Cancer passes.

E. Multiple Choice

1. Scale 1 cm = 20 km. 3 cm = ? a) 23 kmb) 60 kmc) 6.67 kmd) 20 km

2. Direction between S and E: a) SWb) SEc) NEd) NW

3. North → 270° clockwise → face: a) Sb) Ec) Wd) N

4. Equator is at: a) 23.5°Nb) 66.5°Nc) 0°d) 90°S

Mathematics

Maps — Drawing Activity

Class 5 | CBSE / NCERT / ICSE

F. Draw a Floor Plan

1. A room is 10 m long and 8 m wide. Using scale 1 cm = 2 m, draw the floor plan in the space below. Mark the doors (2 m wide, on the south wall) and windows (1 m wide, on the east wall). Add a compass rose.

2. On the map below, mark 5 places in your town or neighbourhood. Label each with a grid reference (use columns A–E and rows 1–5).

Activity: Draw Your Classroom Map

Measure (or estimate) your classroom: length, width. Choose scale (e.g., 1 cm = 1 m). Draw the outline on graph paper. Mark teacher's desk, student benches, blackboard, doors, windows. Add compass rose and legend. Write the scale. Ask a friend to use your map to navigate!

Sample classroom floor plan drawn to scale with compass rose and legend

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