Skip to main content
\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
International Baccalaureate · PYP 5

Location: Grids, Compass and Scale

⌚ ~58 min ▢ 5 blocks ✓ 20 exercises ➣ Prerequisites : Lines and Angles, Position, Grids and Scale, Grids, Maps and Compass Directions
I The Eight Compass Points
The four cardinal points — North, East, South and West — name only four directions. On a map, a place that is halfway between North and East, along the diagonal, has no name yet. Four more directions fill the gaps between the cardinal points.
Figure
Report an error
Definition — Intercardinal Points
Halfway between two neighbouring cardinal points lies an intercardinal point (also called an ordinal point). There are four of them:
  • north-east (NE), halfway between North and East;
  • south-east (SE), halfway between South and East;
  • south-west (SW), halfway between South and West;
  • north-west (NW), halfway between North and West.
The name of an intercardinal point always starts with North or South: we say north-east, never “east-north”. With the four cardinal points, they make the eight points of the compass rose.
Figure
Method — Finding the Direction of One Point from Another
On a map where North is up, to find the direction of a place \(B\) seen from a place \(A\):
  • Start from \(A\). “\(B\) from \(A\)” means: stand at \(A\) and look towards \(B\).
  • Count the squares from \(A\) to \(B\): how many to the East or to the West, and how many to the North or to the South.
  • Moves of one kind only: \(B\) is in a cardinal direction (North, East, South or West).
  • As many squares East or West as North or South: \(B\) lies along the diagonals of the squares, in an intercardinal direction. Join the two words, North or South first: \(2\) squares East and \(2\) squares North give north-east.
The way back is the opposite direction: if \(B\) is north-east of \(A\), then \(A\) is south-west of \(B\). In everyday language, “north-east” is also said when \(B\) is only roughly in that direction; in this section, the places are always exactly in one of the eight directions.
Example
On this map, North is up.
  1. From the Well, in which direction is each of the seven other places?
  2. In which direction is the Castle from the Lake?
  3. In which direction is the Well from the Castle?
Figure

  1. The Well is in square C3. For each place, count the squares from the Well, then name the direction:
    Place East or West North or South Direction from the Well
    Tower (C5) none \(2\) North North
    Castle (E5) \(2\) East \(2\) North north-east
    Bridge (F3) \(3\) East none East
    Farm (E1) \(2\) East \(2\) South south-east
    Cave (C1) none \(2\) South South
    Lake (A1) \(2\) West \(2\) South south-west
    Mill (A5) \(2\) West \(2\) North north-west
    The seven arrows start from the Well:
    Figure
  2. From the Lake (A1) to the Castle (E5): \(4\) squares East and \(4\) squares North, as many East as North. The Castle is north-east of the Lake. The Lake, the Well and the Castle are on the same diagonal.
  3. From the Castle (E5) to the Well (C3): \(2\) squares West and \(2\) squares South. The Well is south-west of the Castle — the opposite of question 1, where the Castle is north-east of the Well.

Method — Turning from One Direction to Another
Going round the compass rose the way the hands of a clock turn (clockwise), the eight points come in this order: N, NE, E, SE, S, SW, W, NW, then N again. Turning the other way is turning anticlockwise.
  • An eighth of a turn (half a right angle, \(45^\circ\)) moves to the next point.
  • A quarter turn (a right angle, \(90^\circ\)) moves two points.
  • A half turn (\(180^\circ\)) moves four points: it gives the opposite direction, whichever way you turn.
  • Count the steps on the compass rose, one eighth of a turn per step, in the direction of the turn.
Turning clockwise is turning to the right, like the robot's quarter turn to the right \(\curvearrowright\).
Figure
Example
  1. Léa faces north-east and makes a quarter turn clockwise. Which way does she face now?
  2. Then she makes a half turn. Which way does she face?
  3. Tom faces west and makes three eighths of a turn anticlockwise. Which way does he face now?
  4. What is the smallest turn that takes someone facing North to facing south-west?

  1. A quarter turn is two steps. Clockwise from NE: E (\(1\)), SE (\(2\)). Léa faces south-east.
  2. A half turn is four steps and gives the opposite direction. From SE: S (\(1\)), SW (\(2\)), W (\(3\)), NW (\(4\)). She faces north-west, the opposite of south-east.
  3. Three eighths of a turn is three steps. Anticlockwise from W: SW (\(1\)), S (\(2\)), SE (\(3\)). Tom faces south-east.
  4. Clockwise, from N to SW takes \(5\) steps (NE, E, SE, S, SW). Anticlockwise, it takes \(3\) steps (NW, W, SW). The smallest turn is three eighths of a turn anticlockwise.
Figure \(\qquad\) Figure

Example
On a grid with North up, moving one square north-east means moving to the square that is one column to the right and one row up, across the corner of the square. A robot starts in square A2 and follows these moves: \(2\) squares north-east, then \(3\) squares East, then \(2\) squares south-west. In which square does it arrive?
Figure

One move at a time, one square at a time:
  • \(2\) squares north-east: from A2 to B3, then to C4 (each step: one column right, one row up);
  • \(3\) squares East: D4, E4, F4;
  • \(2\) squares south-west: E3, then D2 (each step: one column left, one row down).
The robot arrives in square D2.
Figure

Skills to practice
  • Recognising Compass Points
  • Finding the Direction of One Place from Another
  • Turning Between Compass Points
  • Finding Directions and Distances on a Map
  • Explaining with Compass Points
II Review & Quizz
Skills to practice
  • Quiz