The four directions
Birds like the Siberian Crane fly thousands of kilometres and still find their way. People find directions by facing the rising Sun or by using a compass.
The four main (cardinal) directions are North, East, South and West. The Sun rises in the east and sets in the west. If you face east, north is on your left, south on your right and west behind you. North and south are opposite; east and west are opposite.
Formula: Facing a direction: right = next clockwise (N→E→S→W→N), left = next anticlockwise, behind = opposite.
In the figure: The Sun rises in the east. A person facing north has east on the right, west on the left and south behind.
Rule 1: Finding directions — Stand facing the rising Sun: that is east. Stretch your arms: left is north, right is south, back is west.
The four directions
In the app you can move this figure with your finger.
Open in the app- Easy: Morning shadow falls towards the west.
- Medium: A compass needle always points north.
- Exam-type: Face the setting Sun: it is west, so north is on your right.
Rule 2: Left, right and behind — Go clockwise N, E, S, W for right turns and anticlockwise for left turns.
- Easy: Facing south: right is west, left is east, behind is north.
- Medium: Facing west: right is north, left is south, behind is east.
- Exam-type: Facing east: right is south, left is north, behind is west.
Directions never change, but left and right depend on which way you face.
Thinking east is always on the right; that is true only when you face north.
Never Eat Soggy Waffles: N, E, S, W clockwise. Memory clue: "Sun rises east; face it, left is north."
Spot the difference
| Facing | Right | Left | Behind |
|---|---|---|---|
| North | East | West | South |
| East | South | North | West |
| South | West | East | North |
| West | North | South | East |
Practice questions
- 1Where does the Sun rise?
- 2You face north. What is on your left?
- 3You face south. What is behind you?
- 4You face west. What is on your right?
- 5Which direction is opposite to east?
- 6In the evening your shadow points to the east. Which way are you facing the Sun?
- 7A girl faces east and turns around completely (half turn). Which way does she face now?
- 8The compass needle is on your right when you face a direction. Which direction do you face?
Show answers (try them yourself first)
- 1East
- 2West
- 3North
- 4North
- 5West
- 6West (the Sun sets in the west)
- 7West
- 8West (north is on the right)
Reading a map: north, south, east, west of
Birdwatchers get a camp map: "the blue tent is west of the road, the purple tent is north of the green tent". A map tells where each place is compared with others.
A map is a flat drawing of a place seen from above. A north arrow shows direction: usually north is at the top, so east is on the right, south at the bottom and west on the left. A key explains the symbols. If A is north of B then B is south of A.
Formula: A north of B ⇔ B south of A. A east of B ⇔ B west of A.
In the figure: On this map the post office is north of the library, the library is north of the school, the park is west and the bank is east of the library.
Rule 1: Reverse the direction — To say where B is from A, give the opposite direction of where A is from B.
- Easy: School is south of the library, so the library is north of the school.
- Medium: Park is west of the library, so the library is east of the park.
- Exam-type: Post office north of library and library north of school: post office is north of school.
Rule 2: Using the key and the north arrow — First find the north arrow, then read the key for each symbol, then answer.
- Easy: North arrow pointing up: the right side of the map is east.
- Medium: Key: a blue line is a river, a green patch is a garden.
- Exam-type: Classroom: board north of door, window east of board: window is north-east of door.
If a map has no north arrow, ask or assume north is up, and say so.
Saying the wrong side when reversing: if A is east of B, B is not east of A.
Draw a tiny sketch with a north arrow first. Memory clue: "A north of B? B south of A."
Spot the difference
| If A is … | B is … |
|---|---|
| north of B | south of A |
| east of B | west of A |
| south of B | north of A |
| west of B | east of A |
Practice questions
- 1The bank is east of the park. Where is the park from the bank?
- 2The temple is north of the market and the market is north of the school. Where is the school from the temple?
- 3On a map north is at the top. Which side is west?
- 4What does a key on a map do?
- 5The well is south of the hospital and west of the bakery. Where is the bakery from the well?
- 6In your room, the window is east of you and the door is west of you. Which is on your right when you face north?
- 7Draw a simple map with a school, a park and a shop using the words north, east and west. Describe it.
- 8A is north of B, B is east of C. Where is C from A: exactly west, south-west or south?
Show answers (try them yourself first)
- 1West
- 2South
- 3Left
- 4Explains the symbols
- 5East of the well
- 6The window (east)
- 7Any correct map, e.g. park north of school, shop east of school
- 8South-west
Left and right turns on a route
A school bus starts at the parking area, goes north and then turns right onto Park Road. Which way is it driving now? To follow a route we need direction and turns together.
A right turn is a quarter turn clockwise; a left turn is a quarter turn anticlockwise. After a turn your direction changes to the next or previous cardinal direction. Two turns the same way make a half turn (U-turn).
Formula: Right: N→E→S→W→N. Left: N→W→S→E→N. Right then left = same direction as before.
In the figure: Walking north, a right turn makes you walk east.
Rule 1: One turn — Use the clockwise order N, E, S, W for right and the reverse for left.
Left and right turns on a route
In the app you can move this figure with your finger.
Open in the app- Easy: North + right = east.
- Medium: East + left = north.
- Exam-type: South + right = west.
Rule 2: Many turns — Turn one at a time and write the new direction each time.
- Easy: North, right, left: east, then north.
- Medium: East, left, left: north, then west.
- Exam-type: South, right, right, right: west, north, east.
Three right turns equal one left turn; four right turns bring you back.
Turning left when the answer needs a right turn because you imagine the map instead of yourself.
Hold your right hand out and turn your body that way. Memory clue: "Right goes round like a clock."
Spot the difference
| Now facing | Turn | Then facing |
|---|---|---|
| North | right | East |
| East | left | North |
| South | right | West |
| West | left | South |
Practice questions
- 1Walking north, turn left. Direction?
- 2Walking east, turn right. Direction?
- 3Walking south, turn left. Direction?
- 4Start facing north: right, right. Direction?
- 5Start facing west: left, right, right. Direction?
- 6A bus goes north, turns right, then turns left. Which two directions does it drive in?
- 7How many left turns make a half turn?
- 8You face east and want to face south. Which single turn is needed?
Show answers (try them yourself first)
- 1West
- 2South
- 3East
- 4South
- 5North
- 6East, then north
- 72
- 8A right turn
Locating a point on a grid (x, y)
The zoo map is drawn on a grid. To find the panda, start from 0, move 1 step east, then 1 step north: the position is (1, 1). Always move along first, then up.
A point on a grid is written as (x, y): x is the number of steps east (along the columns) and y is the number of steps north (up the rows), both counted from the origin (0, 0). The order matters: (4, 1) and (1, 4) are different places.
Formula: Position = (steps east, steps north). Origin = (0, 0). Same y → same row; same x → same column.
In the figure: To reach (4, 1): 4 steps east (red along the bottom), then 1 step north. (1, 4) is a different point: 1 east and 4 north.
Rule 1: Write the position — Count steps east first, then steps north, and write them in this order.
Locating a point on a grid (x, y)
In the app you can move this figure with your finger.
Open in the app- Easy: 5 east and 2 north: (5, 2).
- Medium: The starting point is (0, 0).
- Exam-type: A point on the bottom line has y = 0, for example (6, 0).
Rule 2: Find the point — From (x, y) move x steps east along the bottom, then y steps up.
- Easy: (3, 6): 3 east, 6 north.
- Medium: (8, 5) and (3, 5) are in the same row (same y).
- Exam-type: (6, 2) and (6, 9) are in the same column (same x).
First number: along (east). Second number: up (north).
Writing (y, x) instead of (x, y).
"Along the corridor, then up the stairs." Memory clue: "First along, then up."
Spot the difference
| Point | Meaning |
|---|---|
| (4, 1) | 4 east, 1 north |
| (1, 4) | 1 east, 4 north |
| (0, 0) | origin |
| (6, 0) | 6 east, on the bottom line |
Practice questions
- 1Write the position of the point 3 east and 5 north.
- 2How many steps east is (7, 2)?
- 3How many steps north is (7, 2)?
- 4Is (2, 5) the same as (5, 2)?
- 5Which of (4, 6), (6, 4), (4, 1) lie in the same column as (4, 3)?
- 6Plot (2, 3), (5, 3) and (5, 6) on grid paper. What shape do you get if you add (2, 6)?
- 7A panda is at (1, 1) and a tortoise at (4, 1). In which direction and how many steps from the panda to the tortoise?
- 8Name two points that are 3 steps east of (2, 4) and 2 steps north of (2, 4).
Show answers (try them yourself first)
- 1(3, 5)
- 27
- 32
- 4No, different places
- 5(4, 6) and (4, 1)
- 6A square (3 by 3)
- 73 steps east
- 83 east: (5, 4); 2 north: (2, 6)
Distance and routes on a grid
An ant can crawl only along the dotted grid lines to reach the apple: first east, then north, then east again. We can count the length of its route.
Along grid lines, the length of a route is the total of its straight parts. Moving east increases x; north increases y. The shortest route between two points uses only the two needed directions: |x2 − x1| steps one way and |y2 − y1| steps the other.
Formula: Shortest route length = (change in x) + (change in y). Route length = sum of all legs.
In the figure: The ant goes 3 cm east, 2 cm north and 2 cm east: 3 + 2 + 2 = 7 cm, ending at (5, 2).
Rule 1: Follow a route — Add steps for east, subtract for west; add for north, subtract for south.
Distance and routes on a grid
In the app you can move this figure with your finger.
Open in the app- Easy: From (1, 1): 4 east, 3 north: (5, 4).
- Medium: From (6, 5): 2 west, 4 south: (4, 1).
- Exam-type: (3, 2) to (3, 7): 5 steps north.
Rule 2: Compare routes — Add each route's legs. Routes that go only east and north are shortest and have equal length.
- Easy: (0, 0) to (4, 3): east 4 + north 3 = 7; also north 1, east 4, north 2 = 7.
- Medium: A route that goes west and comes back is longer than 7.
- Exam-type: Shortest route to (5, 5) from the origin: 10 units.
Back-and-forth moves make a route longer but do not change where you end.
Multiplying the two differences instead of adding them for the route length.
Count east/west first, then north/south, and add. Memory clue: "Shortest: only two directions."
Spot the difference
| From | To | Shortest route |
|---|---|---|
| (0, 0) | (4, 3) | 7 |
| (1, 1) | (5, 4) | 7 |
| (2, 2) | (6, 2) | 4 |
| (0, 0) | (5, 5) | 10 |
Practice questions
- 1An ant crawls 3 cm east then 4 cm north. How far in all?
- 2From (2, 1), 3 east and 2 north: where does it reach?
- 3From (6, 4), 2 west and 3 south: where?
- 4Shortest route from (0, 0) to (6, 2)?
- 5Route A: east 5 then north 2. Route B: north 2 then east 5. Which is shorter?
- 6An ant goes 2 east, 3 north, 1 west. Where does it end if it starts at (0, 0), and how far did it crawl?
- 7Name two different shortest routes from (0, 0) to (3, 2).
- 8Starting at (1, 1) an ant must visit (4, 1) and then (4, 5). Total shortest distance?
Show answers (try them yourself first)
- 17 cm
- 2(5, 3)
- 3(4, 1)
- 48 units
- 5Both 7 units
- 6(1, 3); 6 units
- 7East 3, north 2; or north 2, east 3 (length 5)
- 83 + 4 = 7 units
Map word problems
A bus trip, a metro route, a treasure hunt in school: all use directions, turns, grid positions and distances together. Read slowly, sketch, and solve step by step.
Steps: (1) sketch with a north arrow; (2) mark start; (3) follow each leg, changing direction at turns; (4) add distances for the total distance travelled; (5) compare start and end for how far you are from the start.
Formula: Total distance = sum of legs. Position change = (east − west, north − south). Map scale: real = map × scale.
In the figure: 4 km north + 3 km east + 2 km south = 9 km travelled, but the bus ends only 2 km north (and 3 km east) of the start.
Rule 1: Distance travelled and distance from start — Travelled distance adds every leg. Position cancels opposite moves.
- Easy: 3 km east then 3 km west: travelled 6 km, back at the start.
- Medium: 4 N, 3 E, 2 S: 9 km travelled; 2 km north and 3 km east of start.
- Exam-type: Rohan: 3 E, 3 W, 2 N: school is 2 km north of home.
Rule 2: Scale and routes — Multiply the map length by the scale for real distance. For metro or bus routes compare the number of stops or kilometres.
- Easy: 1 cm = 2 km: 3 cm is 6 km.
- Medium: 1 cm = 5 km: 4 cm is 20 km.
- Exam-type: Metro: 9 stops direct or 5 + 3 = 8 stops with a change; the change route has fewer stops.
A route with fewer stops is not always faster: changing lines takes time.
Mixing up total distance travelled with the distance from the start.
Draw first: a quick sketch with arrows solves most questions. Memory clue: "Travelled adds, position cancels."
Spot the difference
| Question | How |
|---|---|
| Total distance | add all legs |
| Distance from start | cancel opposites |
| Real distance | map × scale |
Practice questions
- 1A bus goes 5 km north, 2 km east, 3 km south. Total distance travelled?
- 2For that bus, how far north of the start does it end?
- 3Scale 1 cm = 3 km. The map distance is 5 cm. Real distance?
- 4Two towns are 40 km apart. At 1 cm = 10 km, how many cm on the map?
- 5A girl walks 2 km west to a shop, then 2 km east. How far is she from home and how far did she walk?
- 6Metro: Route 1 has 12 stops. Route 2 has 7 stops then 4 stops after a change. Which has fewer stops?
- 7From the school gate facing east, the shop is 100 m ahead and the temple is 50 m behind. In which direction is the temple?
- 8A treasure is hidden at (6, 4). You start at (2, 1). Give the shortest route and its length.
Show answers (try them yourself first)
- 110 km
- 22 km
- 315 km
- 44 cm
- 50 km from home; walked 4 km
- 6Route 2 (11 stops)
- 7West
- 84 east and 3 north: 7 units