Primary 4 Maths | Perimeter and Area Problems: Teacher Prep Guide | From the two formulas to composite shapes in 45 minutes

2026-11-08

Tutor lesson-prep guides · Primary Maths

Pupils can recite length times breadth, then freeze at an L-shape, a fence that needs a gate, or a floor that needs tiles. This lesson is not about the formulas; it is about split first, decide perimeter or area, then fix the unit.

Objectives — Pupils can: (1) split an L-shape into two rectangles, find both areas and add them; (2) work backwards from a perimeter to a missing side; (3) tell a fencing question (perimeter, minus the gate) from a tiling question (area, divided by one tile); (4) explain why two plots with the same area can have very different perimeters.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Area of a rectangle	A rectangle 12 m by 8 m, area?	96 square metres
Perimeter of a rectangle	Same rectangle, all four sides together?	40 metres
Long multiplication	24 x 4	96
Dividing by a decimal	27 divided by 0.25	108
Unit conversion	How many centimetres in one metre?	100 centimetres

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-7 min	Starter: the two formulas side by side	Area equals length times breadth on the left, perimeter equals length plus breadth times two on the right, one example each	Say what each formula measures
7-16 min	Split the L-shape	Draw a 10 by 8 frame, cut a 4 by 3 corner, ask where to cut before writing anything	Cut the figure into two rectangles and label them
16-25 min	One edge, two jobs	Point at the inner edge of the L and ask whether it counts as perimeter	Count the perimeter and still get 36 m
25-34 min	Fencing and tiling	A 15 by 9 garden with a 2 m gate; a 6 by 4.5 room with 0.5 m tiles	Fence uses perimeter minus gate; tiles use area divided by tile area
34-42 min	Same area, different perimeter	Four plots of 24 square metres: perimeters 50, 28, 22 and 20	Explain why long and thin needs more fence
42-45 min	Exit check	Three quick questions, each starting with perimeter or area	Answer independently

03 Teaching script (read it out)

Scene 1: Perimeter and area measure different things

Pupils mix the formulas and multiply whatever numbers they see. Kill the confusion with a physical action: run a finger around the edge, that is perimeter; sweep the palm across the surface, that is area.
Then add the unit: perimeter is metres, area is square metres. Write the unit first, and a wrong unit tells you the wrong formula was chosen.

Ask: is your hand going round the edge or across the surface?

Scene 2: Split an L-shape, do not force a formula

A composite shape has no ready formula. Teach one fixed move: pick the easiest cut, make two rectangles, label length and breadth on each, then multiply.
A 10 by 8 frame with a 4 by 3 corner removed is 80 minus 12, so 68 square metres. Pupils must draw the cut line themselves; if they cannot draw it, they do not own the idea.

Ask the pupil to draw the cut line and say both sets of sides.

Scene 3: Removing a corner keeps the perimeter

This is the least intuitive point in the chapter. The area drops, so pupils assume the perimeter drops too. Make them walk the boundary: the frame is 36 m, and the two new inner edges are exactly as long as the two edges that disappeared.
Sum it up in one line: same distance walked, different shape walked.

Ask: is the perimeter 36, 34 or 30, and why?

Scene 4: Fencing uses perimeter, tiles use area

Two questions with almost the same numbers, completely different units. The only test is to ask whether the thing goes around the edge or covers the surface.
Fencing 15 by 9 is 48 m, minus a 2 m gate gives 46 m. Tiling 6 by 4.5 is 27 square metres, divided by 0.25 per tile gives 108 tiles. Pupils should say the test out loud every time.

Ask: is this going round the edge or covering the surface?

04 Question types and worked steps

Type	Example	Steps	Answer
Composite area	10 by 8 frame with a 4 by 3 corner removed	Split into two rectangles, work out each, add (or frame minus cut)	68 square metres
Missing side from perimeter	Perimeter 30 m, breadth 7 m, find the length	Perimeter divided by 2, minus breadth	8 metres
Fencing	15 m by 9 m garden with a 2 m gate	Length plus breadth times 2, minus the gate	46 metres
Tiles	6 m by 4.5 m room, tiles 0.5 m by 0.5 m	Room area divided by one tile area	108 tiles

Sanity check (teach this): Reality checks: an area answer is in square metres and a perimeter in metres; after splitting, the two pieces must add up to the frame; the perimeter is always longer than the longest side; a tile count must be a whole number, a decimal means the division or the units are wrong; fencing after the gate must be less than the full perimeter; for the same area, the closer to a square, the shorter the perimeter.

05 Independent practice (3 questions)

Question	Answer	What to watch
Three composite items	Two L-shapes and one pair of joined rectangles	Check a cut line is drawn before any arithmetic
Three fencing and tiling items	Two fencing, one with a gate, and one tile count	Check the pupil states edge or surface first
Two same-area comparisons	Area 24 square metres as 4 by 6 and as 2 by 12	Check the pupil can explain long and thin costs more fence

06 Common mistakes and what to say

Mistake	Student writes	Say this
Multiplying the perimeter	(12 + 8) x 2 and then times another number, answering 80	Your finger walks the edge, it does not go inside. Perimeter only adds, never multiply again.
Length times breadth on an L-shape	10 x 8 = 80 square metres	The top right corner is gone. You measured the frame, not the plot.
Forgetting the gate	Answering 48 metres	The gate needs no fence. Fence across it and you cannot get in.
Dividing the wrong way round	0.25 divided by 27	You are asking how many 0.25 pieces fit in 27. Big divided by small, not small by big.

07 Homework (paper, section and question numbers)

Primary 4 maths paper drills — Section on what each paper tests: ten perimeter and area items in one set, mark straight away and redraw any missing cut line
Primary maths test papers with answers — Pick a paper with Primary 4 area and perimeter items, do the composite part first, twelve minutes

08 Exit check (last 5 minutes)

Question	Answer	Decision
A 10 m by 8 m frame with a 4 m by 3 m corner removed, area?	80 minus 12 = 68 square metres	Wrong: reteach the cut line
Rectangle perimeter 30 m, breadth 7 m, length?	30 divided by 2 minus 7 = 8 metres	Wrong: reteach halving the perimeter
Fence a 15 m by 9 m garden with a 2 m gate, how much fence?	48 minus 2 = 46 metres	Wrong: reteach edge versus surface

09 Tutor FAQ

How is this different from Primary 3 perimeter?

Primary 3 only counts sides. Primary 4 works backwards from a formula and must decide whether the question wants perimeter or area. Decide wrongly and no marks are given, however neat the arithmetic.

Is 45 minutes enough?

Yes. There are two core moves: draw the cut line, and say edge or surface. Better to do two fewer items than to skip that sentence once.

Must pupils memorise the formulas?

Yes, but only after they can say that perimeter is the path walked and area is the ground covered. Without that sentence they force a formula onto every composite shape.

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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.