Class 5 Mathematics Chapter 14: Maps and Locations

Early at the window

Manu wakes up early. The sky is orange behind the trees. He stands at the window and watches the Sun come up over the neem tree. His grandmother comes and stands beside him. She asks him a question. Which way are you facing?

The Sun shows the way

The Sun rises in the east. So Manu is facing east as he watches it. That is true every single morning. In the evening the Sun goes down on the other side of the sky. That side is west.

Two more to find

Manu stretches out both arms as wide as he can. His left hand points to one side. That side is north. His right hand points to the other side. That side is south. He says the two names out loud.

Behind his back

West is now easy. It lies straight behind him. The Sun will set there in the evening. Manu turns right round and points at it. Then he turns back to the window again.

Four in all

North, south, east and west are the four main directions. They are drawn on maps as a small star with four arms. North is nearly always at the top of that star, and of the map.

Opposite pairs

The four go together in pairs. North faces south across the star. East faces west. If you walk north and turn right round, you are walking south.

From where you stand

Manu's cot is on one side of the room and the door is on the other. He stands in the middle of the floor and names them both. The cot is north of him. The door is south of him.

Not the same for everyone

His sister stands near the door and says the cot is west. Both of them are right. A direction depends on the spot you are standing on. So always say where you are before you name a direction.

When the Sun is hidden

On a cloudy day the Sun cannot help at all. Then a compass does the job instead. Its needle swings round for a moment and settles pointing north. Sailors have used one for hundreds of years.

Remember

• The Sun rises in the east and sets in the west.
• Face east and north is on your left.
• North faces south, and east faces west.
• Always say where you are standing.

Scenario:

A class goes into the yard in the morning to find north. Meena points at random. Their teacher asks where the Sun is. It is rising, so that side is east. The children face east and stretch their arms. The left hand points north and the right hand points south. Behind them is west. Meena checks against a compass and the directions agree. She sees that she did not need the compass at all. The Sun gave one direction, and the other three follow from it because they sit in a fixed order round a circle.

Analysis:

One known direction fixes all four. East comes from the rising Sun, and north, south and west follow from the order round the circle.

Activity:

Find north in the morning using the Sun. Mark all four directions in your yard and check with a compass.

Title:

Chalk a compass in your courtyard

Safety:

Do not look straight at the Sun. Look at the ground in front of it instead.

What You Notice:

Your chalk cross points the same way all day, even at noon. The Sun moves across the sky, but north, south, east and west stay exactly where you drew them.

Siberian cranes fly thousands of kilometres south to India and find their way without a map.

A compass needle always swings to point north.

Naming the four directions — Face the sunrise: left is north. — Stand facing the rising Sun and the other three directions fall into place.

A new map on the wall

Rekha's class has drawn a big map of the area around their school. The place is called Neem Chowk. The map is pinned to the wall beside the blackboard. Everybody crowds round it to look.

Two roads and a crossing

Lake Road runs from the top of the map right down to the bottom. Neem Road runs across from one side to the other. The two of them cross in the middle. A bus stop is drawn at that crossing.

North at the top

A small arrow in a corner points up and is marked N. So the top of the map is north. That makes the bottom south, the right side east and the left side west.

Four corners, four buildings

The two roads cut the map into four corners. The school sits in the north-west corner. The clinic is in the north-east. The post office is south-west and the market is south-east.

Reading the key

Beside the map is a small box called the key. It lists every symbol used on the map. A book stands for the school and a red cross for the clinic. An envelope means the post office and a basket means the market.

Who is next to whom

Rekha asks where the clinic is from the school. Both are at the top of the map, so she looks across. The clinic lies east of the school.

Up and down the map

The post office sits below the school. So the post office is south of the school. Looking the other way, the school is north of the post office.

Making a turn

Rekha walks north up Lake Road from the post office. At the bus stop she turns right. A right turn while facing north sends her east along Neem Road. Had she been facing south, the same turn would have sent her west.

Which one is nearer

Her friend lives beside the market. From the bus stop the market is one corner away. The school is one corner away as well. Rekha counts the corners on the map to decide which walk is shorter.

Remember

• A map is a view from above, with north at the top.
• The key tells you what each symbol means.
• Facing north, right is east and left is west.
• Give a route as roads, turns and directions in order.

Scenario:

A class is given a street map and asked which way the market lies from the school. Ravi says left. His teacher asks whether left means the same for everybody. It does not; it depends which way you are facing. The class uses the map's directions instead. North is at the top, so the right side is east. The market is to the east of the school. Ravi sees why directions beat left and right on a map. A direction stays the same whoever reads the map, and left changes with the reader.

Analysis:

Left is a true answer only for one reader facing one way. East is true for everybody, which is why maps use it.

Activity:

Draw a map of your route to school with north at the top. Mark two places using directions, not left and right.

Title:

Draw a map of your street

What You Notice:

Once the north arrow is on, anybody can read your map. The same map without it leaves a reader guessing which side is which.

A metro map shows each line in a different colour so that riders can follow one easily.

Many maps show distance with a small scale bar in one corner.

Reading sides of a map — North up, east right. — Once north is at the top, east is on the right and west is on the left.

A plan of Green Park

Ayaan's class visits Green Park on a Saturday morning. The warden gives them a plan drawn on a grid. Thin lines run up the sheet and across it. Each crossing point is a place that can be named.

Counting the lines

The upright lines are called the columns. They are numbered one, two, three and so on, going east. The level lines are called the rows. They are numbered one, two, three and so on, going north from the bottom.

Starting at zero

The bottom left corner of the plan is marked zero. Every count begins from that one corner. Ayaan puts his finger on the zero before he starts. Everybody in the class does the same.

Finding the gate

He moves one step east along the bottom of the plan. That brings him to the first column. Then he moves one step north. That brings him to the first row. The gate of the park stands where the two lines meet.

Writing it down

The class writes that place as (1, 1). The first number is always the column. The second number is always the row. The brackets keep the two numbers together as one answer.

Along, then up

The order matters a great deal here. Always go along first and only then go up. Ayaan says a little rhyme to himself as he counts. Along the hall, then up the stairs. It keeps him from swapping the numbers.

Two different places

The pond is at (4, 5). The flag pole is at (5, 7). Swapping the numbers of the pond would give (5, 4). That is quite a different spot on the plan, and there is no pond there.

Walking a route

Each square of the grid is one metre across. From the gate at (1, 1), Ayaan walks two metres east. Then he walks one metre north. He is now standing at the swing, which is at (3, 2).

More than one path

His friend goes north first and then east. She arrives at the swing as well. The two paths trace different shapes on the grid. Yet both of them are three metres long in the end.

Remember

• Start at zero in the bottom left corner.
• Count along first, then count up.
• Write the column, then the row, in brackets.
• A route gives a distance and a direction for each leg.

Scenario:

A wildlife park near Bharatpur in Rajasthan draws its bird hides on a grid. Each square of the grid stands for one hundred metres. The entrance gate is at (1, 1). The lake hide is at (4, 5) and the crane hide is at (5, 7). Siberian cranes fly here every winter from a very cold land far to the north. A school group wants to reach the lake hide first. A guide tells them to count along the path before they count up it. One boy writes the lake hide as (5, 4) in his notebook. The guide checks his page and sends him back to the numbers along the bottom. The group then sets off, walking east and then north.

Analysis:

A grid fixes each hide with two numbers, and links map work to the winter journey of birds.

Activity:

Draw a grid of your school ground and mark four places on it with their number pairs.

Chess boards use the same idea, with letters along the bottom and numbers up the side.

Ships at sea are found on a grid of lines drawn right around the Earth.

The order of the two numbers — Along the hall, then up the stairs. — Walk along the corridor first, and only then climb. Column first, row second.