Primary 3 Maths | Introduction to Area: Counting Squares, cm2 and Perimeter

2026-11-08

Tutor lesson-prep guides · Primary maths

Most P3 pupils meet area for the first time by measuring four sides with a ruler and then writing cm. The difficulty is not arithmetic but unit sense: they have not separated “around the outside” from “covering the inside”. This lesson makes area something they count with their hands.

Objectives — Pupils can: (1) find the area of a shape by counting 1 cm squares and answer in cm2; (2) explain the rule that two half squares count as one square; (3) calculate the perimeter in cm and the area in cm2 for the same rectangle and say how they differ.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Meaning of multiplication	4 rows of 3 squares each: how many squares	12 squares, from 4 x 3
Length units	How many mm in 1 cm on a ruler	10 mm
Perimeter idea	The distance right round a rectangle is called	The perimeter, measured in cm

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	Opening question	Hold up a large sheet and a small sheet; ask which has the greater area and why	Say “the inside is bigger”, not “the side is longer”
5-15 min	One square is 1 cm2	Draw a 1 cm square on squared paper and name it one square centimetre	Cover one square and say “one square”
15-25 min	Counting squares	Model the three steps: ring whole squares, pair half squares, then add	Count 8 whole and 6 half, write 8 + 3
25-34 min	Multiply for rectangles	Match counting 4 x 3 with the multiplication 4 x 3 and name length x width	Count once, then check with multiplication
34-41 min	Perimeter vs area	Same 4 by 3 card: walk the edge, then fill it with squares	Write 14 cm and 12 cm2 separately
41-45 min	Exit check	Collect three answers and mark at once, naming the error type	Work independently

03 Teaching script (read it out)

Scene 1: Act 1: Turn area into something countable

Do not start with the formula. Give each pupil a sheet of 1 cm squared paper and ask them to shade one square. Say: “This one square is called one square centimetre. We write 1 cm2.” Shade two squares, then five, asking “how many cm2 now” each time. Pupils count with a finger and arrive at the idea that area is how many squares fit.
Place a 4 cm by 3 cm card on the paper and ask them to count the squares it covers: 12, so 12 cm2. Only then ask: “Is there a faster way?” Most will say four times three, because they can see 4 rows of 3. Pupil task: tick every square, then write 4 x 3 = 12 beside the shape.

Say this: “cm measures an edge. cm2 measures a surface. If you write cm, I cannot tell whether you measured an edge or a surface.”

Scene 2: Act 2: Counting squares in three fixed steps

Irregular shapes are the real test. Fix the order: (1) ring every whole square in red and count them; (2) pair the leftover half squares in blue, two halves to one square; (3) add the two numbers. Worked example: 8 whole squares and 6 half squares, so 6 / 2 = 3 and 8 + 3 = 11, answer 11 cm2.
Explain why two halves make one square: two halves fit together exactly, so this is not an estimate. If a pupil is left with a single half square, ask them to recheck the count first. If the question really leaves one half, say the answer is “about 11 cm2” rather than pretending a half is a whole.

Pupil task: count independently and write the number sentence under the picture, never just the final answer.

Scene 3: Act 3: Same rectangle, perimeter and area side by side

With the 4 by 3 card, start with perimeter: “An ant walks right round the edge. How far does it walk?” Pupils answer 4 + 3 + 4 + 3 = 14 cm. Then area: “How many 1 cm2 tiles cover the card?” 12 tiles, so 12 cm2.
Write both on the board: perimeter 14 cm, area 12 cm2. Then ask the key question: “14 and 12 are close. Is the difference always 2?” There is no such rule: a 5 by 2 rectangle gives 14 cm and 10 cm2. That question stops pupils from blending the two formulas.

Say this: “The perimeter is the length of a line. The area is the size of a surface. A line and a surface can never share a unit.”

Scene 4: Act 4: Same area, very different perimeter

Ask for every rectangle with an area of 18 cm2 and whole centimetre sides. Use factor pairs: (1,18), (2,9), (3,6). Their perimeters are 38 cm, 22 cm and 18 cm. Pupils are surprised: the same area can need 20 cm more fencing.
Close with the everyday version: the same 18 tiles laid as one long corridor need the most fencing; laid as 3 by 6 they need the least. So when a question talks about fencing, calculate perimeter; when it talks about tiles, calculate area. Always ask which one is being asked.

Pupil task: fill a table of the three size pairs and three perimeters, circle the shortest perimeter, and say in one sentence why it is shortest.

04 Question types and worked steps

Type	Example	Steps	Answer
Area by counting squares	8 whole squares + 6 half squares	Count whole, 6 / 2 = 3 half pairs, then add	11 cm2
Rectangle area	4 cm by 3 cm	Length x width, write the unit as cm2	12 cm2
Perimeter and area together	4 cm by 3 cm	Perimeter (4 + 3) x 2; area 4 x 3	14 cm and 12 cm2
Reverse: find the sides	Area 18 cm2, whole cm sides	List factor pairs, then compute perimeters	(1,18) 38; (2,9) 22; (3,6) 18

Sanity check (teach this): Run two checks every time: (1) the squares counted in a rectangle must equal length x width, so 4 x 3 counted as 12 squares means 12 cm2; (2) the unit check: an edge answer is in cm, a surface answer is in cm2. If a pupil answers just “14”, ask “did you measure an edge or a surface?”.

05 Independent practice (3 questions)

Question	Answer	What to watch
A 5 cm by 2 cm rectangle: area and perimeter?	Area 10 cm2; perimeter 14 cm	Watch for 10 written as cm
A shape with 10 whole squares and 4 half squares: area?	12 cm2 (4 / 2 = 2, then 10 + 2)	Did they pair the halves
List whole-cm rectangles with area 18 cm2 and give the shortest perimeter.	(1,18), (2,9), (3,6); shortest 18 cm	Did they stop after one pair

06 Common mistakes and what to say

Mistake	Student writes	Say this
Wrong unit	Area answered as 12 cm	An edge is cm, a surface is cm2. If you write 12 cm, I read it as the length of one side
Half square counted as whole	6 half squares counted as 6, answer 14 cm2	Two halves make one square, so 6 halves are worth 3 squares
Perimeter used as area	4 + 3 + 4 + 3 = 14, answer 14 cm2	You walked round the edge but did not cover the surface. Count the squares
Counting only edge squares	Counting round the border, answer 10 cm2	The border is only the frame. Tick every square inside it

07 Homework (paper, section and question numbers)

Independent practice in this chapter (questions 1-3 above) — Q1 separate perimeter and area; Q2 pair the half squares; Q3 find all three size pairs
Primary maths test papers (area and perimeter items) — Do three area questions from the paper, writing the number sentence and the unit each time
Primary maths chapter index (same level) — Revise the P3 perimeter and length chapter and copy its unit table once

08 Exit check (last 5 minutes)

Question	Answer	Decision
How big is 1 cm2?	A square with 1 cm sides	Cannot say: back to Act 1
8 whole squares plus 6 half squares: area?	11 cm2	Answering 14 means halves were not paired
Perimeter and area of a 4 cm by 3 cm rectangle?	14 cm and 12 cm2	Swapped units: reteach Act 3
Area 18 cm2: which shape needs the least fencing?	3 cm by 6 cm, perimeter 18 cm	Cannot answer: back to Act 4

09 Tutor FAQ

Why separate area and perimeter as early as P3?

Because both formulas arrive in the same year and the numbers are often close: a 4 by 3 rectangle gives 12 for area and 14 for perimeter. Pupils who never separate them keep confusing the two through the P5 area and volume work. Starting with counting squares gives them a physical basis instead of two memorised rules.

Counting is slow. May I just give the formula?

Yes, but only after at least three counted examples. Counting builds the idea; the formula only adds speed. Pupils who never counted freeze completely when an irregular shape appears.

What if one half square is left over?

Recheck the count first. Primary questions normally pair the halves. If a single half truly remains, say the answer is approximate rather than silently treating a half as a whole.

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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.