Stage 11 · Shape & space
Directions
N up, E right; each step round is 45°.
How to do it
Method
N up, E right; each step round is 45°
NE → S: 3 × 45 = 135
Another way
Count right angles
90 + 45 = 135
In full
First know the eight directions by heart: north, north-east, east, south-east, south, south-west, west, north-west, going round clockwise. A map usually has north up, south down, west left and east right: north-east is between north and east, so up and to the right; south-west is down and to the left. Check the north arrow first, since north isn't always up: when it points right, count round clockwise and east is down. Turning: next-door directions are 45° apart, so count the steps turned and multiply by 45: facing north-east, turn clockwise to face south, north-east → east → south-east → south, 3 steps, 3 × 45 = 135, so 135°. Another way: count right angles, 90° each: north-east to south-east is one right angle, and on to south is half of one more, 90 + 45 = 135 — the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
North of the school: ?
Show the answer and working
Answer: North of the school: 4
North points up on this map, so north is above the school: number 4
Example 2
South-east of the school: ?
Show the answer and working
Answer: South-east of the school: 1
North points up on this map, so south-east (between east and south) is down and to the right of the school: number 1
Example 3
NW → E, clockwise: ?°
Show the answer and working
Answer: NW → E, clockwise: 135°
Clockwise from north-west to east: north-west → north → north-east → east, 3 eighths of a turn, each 45°: 3 × 45 = 135, so 135°
Example 4
NE → SW, clockwise: ?°
Show the answer and working
Answer: NE → SW, clockwise: 180°
Clockwise from north-east to south-west: north-east → east → south-east → south → south-west, 4 eighths of a turn, each 45°: 4 × 45 = 180, so 180°
Practise directions in the game →Stage 11 · Shape & space · Free to start, unlimited questions, no download