Mathematics notes, unit 8

Location

Textbook Mathematics Year 3 (DLP), Part 1 and Part 2, pages Part 2, 97–106

What this chapter covers

You can say where something is from a starting point, using left, right, up, down, north, south, east and west (8.1.1)
You can name the horizontal axis and the vertical axis on a grid, and read columns and rows (8.1.2)
You can write the location of an object as a letter and a number, such as D4, and find the object at a location (8.1.3)
You can solve everyday problems about location using a grid (8.2.1)

8.1Where is it? Recognising location

The location of something is the place where it is. We say a location from a starting point, called the reference point.

Look at the paddy field below. It is cut into squares. A column is a line of squares going up and down. A row is a line of squares going across. This field has 4 columns and 3 rows.

The hut is our starting point. We count the squares from the hut.

Paddy field with 4 columns and 3 rows. Acik is at column 1, row 2. Along is at column 2, row 3. Angah is at column 3, row 1. Uda is at column 4, row 2. A hut is at the bottom-left corner. — Four family members planting paddy. We count the squares from the hut.

Word	Meaning
to the right	the same as east
to the left	the same as west
to the top (up)	the same as north
to the bottom (down)	the same as south

Saying where each person is

Angah: from the hut, count 3 squares to the right and 1 square to the top. Angah is at column 3, row 1.
Acik is at column 1, row 2.
Along: from the hut, count 2 squares to the east and 3 squares to the north. Along is at column 2, row 3.
Uda is 4 squares to the east and 2 squares to the north of the hut. Uda is at column 4, row 2.

Did you know? On a map, north is usually at the top. So "go north" means "go up", and "go east" means "go to the right".

We can also say where something is from another person. Uda and Acik are in the same row. Uda is 3 squares to the east of Acik, so Acik is 3 squares to the west of Uda.

Look at the paddy field. Who is in the same row as Acik? Who is in the top row?

Show answerHide answer

Uda is in the same row as Acik (row 2). Along is in the top row (row 3).

8.2Columns, rows and axes

A grid is a picture made of squares. Each square has a name made from a letter and a number.

The horizontal axis goes across the bottom of the grid. It has the letters A, B, C, … for the columns.
The vertical axis goes up the side of the grid. It has the numbers 1, 2, 3, … for the rows.

Horizontal means lying flat, like the floor. Vertical means standing straight up, like a flagpole.

5 by 5 grid of pupils' seats. Columns A to E, rows 1 to 5. — Where the pupils sit during a test. A to E is on the horizontal axis. 1 to 5 is on the vertical axis.

Who sits at D4?

Find the letter D on the horizontal axis (at the bottom).
Go up column D until you reach row 4.
The pupil in that square is Mei Ling. So Mei Ling sits at D4.

Where does Kumar sit?

Find Kumar in the grid.
Look down to the horizontal axis: Kumar is in column D.
Look across to the vertical axis: Kumar is in row 2.
Write the letter first, then the number: Kumar sits at D2.

We write a location with the horizontal axis first (the letter), followed by the vertical axis (the number). Example: C5 means column C, row 5.

Writing the number first. 4D is wrong. Always write the letter first: D4. A good way to remember: you must walk along the corridor (across) before you go up the stairs.

Look at the seating grid. (a) Who sits at C5? (b) Who sits at A2, B1 and E3? (c) Where does Haziq sit?

Show answerHide answer

(a) Kavitha. (b) A2: Ravi, B1: Hui Min, E3: Zara. (c) C3.

8.3Writing and finding locations

Every square on a grid has its own location. Let us visit a pasar malam (night market). Each stall is in one square.

Pasar malam grid, columns A to E and rows 1 to 5. Toys A5, apam balik E5, satay B4, you are here C3, cendol D3, nasi lemak A2, air tebu E2, roti john C1. — Stalls at a pasar malam. The star shows where you are standing.

State the location of the satay stall

The satay stall is in column B.
It is in row 4.
Its location is B4.

Stall	toys	apam balik	cendol	nasi lemak	air tebu	roti john
Location	A5	E5	D3	A2	E2	C1

Same column, same row

Things in the same column have the same letter. Nasi lemak (A2) and toys (A5) are both in column A.
Things in the same row have the same number. Apam balik (E5) and toys (A5) are both in row 5.

Which is nearest?

You are standing at C3. To find the nearest stall, count how many squares you must walk (across and up or down). The fewest squares means the nearest.

Which stall is nearest to you: cendol, satay or nasi lemak?

Cendol (D3): 1 square to the right. That is 1 square.
Satay (B4): 1 square to the left and 1 square up. That is 2 squares.
Nasi lemak (A2): 2 squares to the left and 1 square down. That is 3 squares.
The cendol stall is the nearest.

Moving on a grid

Sometimes we follow directions to find a place. Start at the star, then count the squares you move.

Start at A1. Move 3 squares to the right, then 2 squares up. You reach D3.

Start at A1. Move 3 squares to the right and 2 squares up.

Moving right changes the letter: A → B → C → D (3 squares). You are at D1.
Moving up changes the number: 1 → 2 → 3 (2 squares). You are at D3.

Counting the square you start on. When you move, do not count your starting square. From A1, "3 squares to the right" ends at D1, not C1.

Look at the pasar malam grid. (a) What stall is at E2? (b) Which stall is in the same row as the air tebu stall? (c) Start at roti john (C1). Move 1 square to the right and 2 squares up. Which stall do you reach?

Show answerHide answer

(a) Air tebu. (b) Nasi lemak (A2). Both are in row 2. (c) C1 → D1 → D2 → D3: the cendol stall.

8.4Solving problems about location

To solve a problem, use these steps: Understand (what is given, what to find), Plan (look at the grid, or make a table), Solve, then Check.

Map of Taman Ceria with columns A to D and rows 1 to 4. Aiman's house A1, park C1, school B2, clinic D2, library C3, market A4, fire station B4, mosque D4. — Map of Taman Ceria.

Problem 1: Encik Karim took his family to C3 during the school holidays. Where did they go?

Given: the place is at C3. Find: the name of the place.
Plan: look at column C, row 3.
Solve: the place at C3 is the library.
Answer: They went to the library.

Problem 2: Aiman walks from his house to the library. How many squares to the east and to the north does he walk?

Aiman's house is at A1. The library is at C3.
A → C: A to B to C is 2 squares to the east.
1 → 3: 1 to 2 to 3 is 2 squares to the north.
Answer: 2 squares to the east and 2 squares to the north.

Problem 3: Puan Zainab's son has a fever. Which place should they go to? State its location.

Make a table and tick the place that helps.

Place	park	clinic	library	market
Suitable?	✗	✓	✗	✗
Location	C1	D2	C3	A4

Answer: They should go to the clinic. It is at D2.

Did you know? Car parks, cinemas and chessboards use the same idea. A cinema ticket that says "Seat F7" tells you the row and the seat number, so you can find your place quickly.

Look at the map of Taman Ceria. (a) Which two places are in row 4 and in columns A and B? (b) It is Friday. Aiman's father goes to pray. Where does he go? State the location.

Show answerHide answer

(a) Market (A4) and fire station (B4). (b) The mosque, at D4.

Summary

Remember	Key fact
Reference point	The starting point we count squares from (like the hut)
Directions	Right = east, left = west, up = north, down = south
Columns and rows	Columns go up and down (letters). Rows go across (numbers).
Axes	Horizontal axis: A, B, C, … at the bottom. Vertical axis: 1, 2, 3, … at the side.
Writing a location	Letter first, then number: D4 (not 4D)
Moving	Right or left changes the letter. Up or down changes the number. Do not count the starting square.
Nearest	Count the squares to walk. The fewest squares is the nearest.