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Year 4 Maths Position

Follow & describe pathways

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Theory

Following and describing pathways is a Year 4 maths position skill: tracing a route on a grid map and writing it as a list of compass directions (north, south, east and west) and counts of squares. This page explains grid references, how to follow a drawn path, how to describe a route between two places, and how to work out a return journey. Curriculum: VC2M4SP03 / AC9M4SP02.

A grid map has columns named with letters and rows named with numbers. A grid reference names one square. You write the column letter first, then the row number, like \(E2\).

The compass shows four directions. North is up the page, south is down, east is to the right and west is to the left. A small compass rose usually sits in the corner of the map.

A pathway is a route across the grid. To follow a path you start on the marked square and move the way each direction tells you, counting the squares. To describe a route you write the directions and counts in order, such as east \(4\) squares, then north \(2\) squares.

Zoo grid map with a drawn path from the entry to the monkeys A zoo grid map with columns A to F and rows 1 to 6, north pointing up. A red arrowed path starts at a green dot on the entry (B5), goes east 3 squares to the kiosk, then north 3 squares to the monkeys. A B C D E F 1 2 3 4 5 6 Entry Lions Ducks Monkeys Kiosk Reptiles N S E W
Follow the arrows: east 3 squares to the kiosk, then north 3 squares to the monkeys.
Zoo grid map with a drawn path from the kiosk to the lions to describe The same zoo grid map. A red arrowed path starts at a green dot on the kiosk (E5), goes west 3 squares to the entry, then north 3 squares to the lions. The reader describes this route. A B C D E F 1 2 3 4 5 6 Entry Lions Ducks Monkeys Kiosk Reptiles N S E W
Describe this route from the kiosk to the lions: west 3 squares, then north 3 squares.

Pathways do not need formulas, but these facts help you follow and describe any route on a grid map.

DirectionOn the mapOpposite
NorthUpSouth
SouthDownNorth
EastRightWest
WestLeftEast
\[ \text{length of a path} = \text{squares in part 1} + \text{squares in part 2} + \ldots \]
length of a path = sum of the squares in each part
Shortest route. When you may only move north, south, east or west, the fewest squares between two places is the number of columns apart plus the number of rows apart.

How to describe a route on a grid map

  1. Find the start and finish. Point to the square you begin on and the square you want to reach. Say each grid reference out loud.
  2. Move in straight parts. Go along one direction until you must turn. Name that direction (north, south, east or west) and count the squares.
  3. List each turn. Write one direction and count for every straight part, in order, until you reach the finish.
Return journey. To go back the way you came, reverse the order of the steps and swap each direction for its opposite: north for south, east for west.

How long is a path?

  1. Count each straight part. Write down the number of squares for every part of the path.
  2. Add the parts. East \(3\), then south \(2\) is \(3 + 2 = 5\) squares long. Add the numbers; do not join the digits to make \(32\).

How to find the shortest route

  1. Count across. How many columns apart are the two places?
  2. Count up or down. How many rows apart are they?
  3. Add them. Moving only north, south, east or west, the shortest route is the columns apart plus the rows apart. A route that turns back on itself is longer.
Loops. If a path ends back where it started, the squares walked north equal the squares walked south, and the squares walked east equal the squares walked west.
Example 1 — Follow a path
A path is drawn from the ducks. Follow the arrows and name where it ends.
Zoo grid map with a path from the ducks to the entry The zoo grid map. A red arrowed path starts at a green dot on the ducks (D3), goes south 2 squares, then west 2 squares, ending at the entry (B5). ABC DEF 123 456 Entry Lions Ducks Monkeys Kiosk Reptiles NSEW
Solution
\(\text{south }2\)\(:\)\(D3 \to D5\)
\(\text{west }2\)\(:\)\(D5 \to B5\)
D3→D5→B5

The path ends at \(B5\) — the entry.

Example 2 — Describe a route
Write directions from the ducks (D3) to the kiosk (E5), using compass directions and counts of squares.
Zoo grid map with a path from the ducks to the kiosk The zoo grid map. A red arrowed path starts at a green dot on the ducks (D3), goes east 1 square, then south 2 squares, ending at the kiosk (E5). ABC DEF 123 456 Entry Lions Ducks Monkeys Kiosk Reptiles NSEW
Solution
\(D3 \to E3\)\(:\)\(\text{east }1\)
\(E3 \to E5\)\(:\)\(\text{south }2\)
east 1, then south 2

East \(1\) square, then south \(2\) squares.

Example 3 — Return journey
The route from the kiosk to the lions is west \(3\), then north \(3\) (the second diagram). Write the return journey from the lions back to the kiosk.
Solution

Reverse the order and swap each direction for its opposite.

\(\text{last out: north }3\)\(\to\)\(\text{first back: south }3\)
\(\text{first out: west }3\)\(\to\)\(\text{last back: east }3\)
south 3, then east 3

South \(3\) squares, then east \(3\) squares.

Example 4 — Fix a wrong route
Sam goes from the entry (B5) to the ducks (D3) and writes: east \(2\), then north \(1\). Where does Sam really finish, and what is the correct route?
Solution
\(\text{east }2\)\(:\)\(B5 \to D5\)
\(\text{north }1\)\(:\)\(D5 \to D4\)
correct: east 2, then north 2

Sam finishes at \(D4\), not the ducks. The north step is too short. The correct route is east \(2\), then north \(2\).

Example 5 — How long is the path?
A path goes east \(4\) squares, north \(2\) squares, east \(1\) square, then south \(3\) squares. How many squares long is the whole path?
Solution
\(4 + 2\)\(=\)\(6\)
\(6 + 1\)\(=\)\(7\)
\(7 + 3\)\(=\)\(10\)

The path is \(10\) squares long.

Example 6 — The shortest route
Use the zoo map. What is the smallest number of squares you must travel from the ducks (D3) to the reptiles (F6), moving only north, south, east or west? Give a route.
Solution
\(\text{D} \to \text{F}\)\(=\)\(2\text{ columns}\)
\(3 \to 6\)\(=\)\(3\text{ rows}\)
\(2 + 3\)\(=\)\(5\)

The shortest route is \(5\) squares, for example east \(2\) squares, then south \(3\) squares.

Common pitfalls

Count squares, not lines. Watch out when counting. East \(3\) squares means the square three to the right, not the third grid line.
Add the parts of a path. A path of east \(3\), then south \(2\) is \(3 + 2 = 5\) squares long, not \(32\). Add the counts for every straight part.
North is up the page. Follow the direction shown on the compass rose, not the way you are facing or holding the map.
A return journey is not the same list. To go back, reverse the order of the steps and swap each direction for its opposite, or you will end up somewhere else.

Frequently asked questions

How do you follow a path on a grid map?

Start on the marked square. Read each direction in turn and move that many squares, following the compass: north is up, south is down, east is right and west is left. Each new turn starts a new step.

What do north, south, east and west mean on a map?

On a map north points up the page, south points down, east points right and west points left. The compass rose in the corner shows these four directions.

How do you describe a route between two places?

Write a list of directions and counts of squares. For example, east \(4\) squares then north \(2\) squares. Give one direction and count for each straight part of the path.

What is a grid reference?

A grid reference names one square on the map. You write the column letter first, then the row number, such as \(E2\). It tells you exactly where a place sits on the grid.

How do you work out the return journey?

Do the steps in reverse order and swap each direction for its opposite. North becomes south, east becomes west, and the last step out becomes the first step back.

Which way is north on a map?

North is up the page, shown by the N on the compass rose. Follow the compass direction, not the way you happen to be facing.

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