Primary 4 Maths | Compass Directions and Angles Lesson-Prep Guide (for tutors) | 45-minute flow, teaching script, common errors

2026-11-15

Tutor lesson-prep guides · Primary Maths

South-east is not a vague mixture of south and east: it is 135 degrees on the compass circle. Once pupils hold two facts, that the eight points are 45 degrees apart and that a turn must be named clockwise or anticlockwise, direction questions stop being guesswork.

Objectives — By the end of the lesson the pupil can: (1) name the eight compass points and the 45-degree gap between them; (2) turn through a given angle from a given facing and name the new direction; (3) use grid steps and a scale to work out real distances on a route map; (4) write route instructions from school to home.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
The four cardinal points	points to north, east, south and west	names all four without swapping north and south
Right angles	says how many degrees a quarter turn is	answers 90
Multiplying by 100	works out 4.5 times 100	answers 450

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0–6 min	Entry check	sets three quick items and watches each one	answers aloud and points at the four points
6–14 min	The eight points	marks eight directions on a compass circle	says each gap is 45 degrees
14–22 min	Turning through angles	models turning 135 degrees clockwise from north	answers south-east
22–32 min	Route maps and scale	uses a map where 1 cm stands for 100 m	works out 4.5 cm as 450 m
32–41 min	Independent practice	reads the questions only	works the three items alone
41–45 min	Exit check	collects and marks at once	says which step went wrong

03 Teaching script (read it out)

Scene 1: Act 1: Eight points, 45 degrees apart

“A full clockwise turn from north back to north is 360 degrees. Split it into eight equal parts: 360 divided by 8 is 45, so each step is 45 degrees. North is 0, north-east 45, east 90, south-east 135, south 180, south-west 225, west 270, north-west 315. Memorise the four cardinal points and the 45-degree step, and the rest can be calculated. So south-east is a precise direction, not roughly both south and east.”

How many degrees is south-east, and how many 45-degree steps from north?

Scene 2: Act 2: A turn must say clockwise or anticlockwise

“A turn of 90 degrees clockwise and a turn of 90 degrees anticlockwise end up in opposite places. Facing north, 90 degrees clockwise is east; 90 degrees anticlockwise is west. So when a question asks which way you face after turning, check which direction the turn goes. Turning 270 degrees clockwise is the same as 90 degrees anticlockwise, because 360 minus 270 is 90.”

Facing east, turn 90 degrees anticlockwise. Which way do you face?

Scene 3: Act 3: A route map gives you direction and distance

“The arrows on a route map give direction and the scale gives distance. If 1 cm stands for 100 m, then 4.5 cm on the map is 450 m. If a route goes 3 cm east and then 4 cm north, the distance walked is 7 cm, or 700 m: that is the route length, not the straight line between the ends. A written instruction needs three things: where you start, which way each leg goes, and how far each leg is.”

You walked 3 cm and then 4 cm. Why can the answer not be 5 cm?

04 Question types and worked steps

Type	Example	Steps	Answer
Angle to compass point	turn 135 degrees clockwise from north	135 divided by 45 is 3 steps	south-east
Compass point to angle	how many degrees is north-west from north, anticlockwise	360 minus 315, or one step	45 degrees
Route distance	1 cm stands for 100 m; 4.5 cm on the map is what	4.5 times 100	450 m
Adding legs of a route	3 cm east then 4 cm north; real distance	(3 plus 4) times 100	700 m

Sanity check (teach this): Three checks: an angle on the compass must lie between 0 and 360, so subtract 360 if it goes past; the eight points only ever land on multiples of 45, so an answer of 60 or 100 degrees is wrong; and the route length must be at least the straight-line distance between the ends.

05 Independent practice (3 questions)

Question	Answer	What to watch
Facing north, turn 270 degrees clockwise. Which way do you face?	west	whether the pupil uses 360 minus 270 as a 90-degree anticlockwise turn
1 cm stands for 100 m. What is 6.5 cm on the map in real distance?	650 m	whether the decimal point moved correctly
A route goes south-east and then south-west. How many degrees apart are the two directions?	90 degrees	whether the pupil sees that 135 and 225 differ by 90

06 Common mistakes and what to say

Mistake	Student writes	Say this
Treating south-east as “east or south”	writes “south-east, that is eastwards”	South-east is 135 degrees. It is one direction, not two.
Swapping clockwise and anticlockwise	turns 90 degrees anticlockwise from north and answers east	Anticlockwise is to the left; facing north, left is west.
Leaving an angle above 360	answers 405 degrees	The compass only runs from 0 to 360, so subtract 360.
Multiplying the scale wrongly	answers 45 m for 4.5 cm	One centimetre stands for 100 m, so 4.5 cm is 4.5 lots of 100.

07 Homework (paper, section and question numbers)

Primary 4 maths paper 1: shape and space section — Section C, questions 1 to 4

08 Exit check (last 5 minutes)

Question	Answer	Decision
Facing east, turn 180 degrees clockwise. Which way do you face?	west	if wrong, reteach Act 2
How many degrees apart are north-east and south-west?	180 degrees	if wrong, reteach the eight-point angles
1 cm stands for 100 m. What is 2.5 cm in real distance?	250 m	if wrong, reteach the scale

09 Tutor FAQ

Where do directions and position sit in the Primary 4 syllabus?

They belong to shape and space, taught alongside symmetry and rotation. This guide focuses on the eight compass points, turning angles and route-map distances.

Is 45 minutes enough?

Yes. The flow gives 26 minutes to the compass circle and turning, 9 to independent practice and 4 to the exit check. If the four cardinal points are shaky, repair those before angles.

Is there a matching practice paper?

Yes. The homework links straight to the TutorZone Primary 4 maths paper, which carries answers for immediate checking.

Find a tutor — free Tutor Registration →

A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.

Practice papers　Paper 1 (basics)　·　Paper 2 (intermediate)　·　Paper 3 (challenge)　·　Paper 4 (error clinic)