Primary 2 Maths | Quadrilaterals Guide | Sorting by Right Angles and Opposite Sides

2026-11-09

Tutor lesson-prep guides · Primary Maths

A child calls a parallelogram a rectangle because both look oblong when tilted. The difference is not the outline but the corners: one has four right angles, the other has none.

Objectives — Students can: (1) count that every quadrilateral has four sides and four angles; (2) separate rectangle, square, parallelogram and trapezium using two questions, right angles and opposite sides; (3) find perimeter by adding the four sides, or twice length plus twice width for a rectangle.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Lines and angles	Point to one corner of a shape	Names the vertex and both arms
Right angles	Test a table corner with a paper corner	Decides correctly
Addition	What is 5 plus 3 plus 5 plus 3	Reaches 16

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-6 min	Sorting warm-up	Four shape cards, split into two piles	State the reason
6-16 min	Sides and angles	Count on each card and write 4 and 4	Count each card
16-30 min	Right angles and sides	Paper corner on all four corners, then compare sides	Two cards done
30-42 min	Four names	Define rectangle, square, parallelogram, trapezium	State four definitions
42-52 min	Perimeter	Rectangle 5 by 3 has perimeter 16	Two sums alone
52-60 min	Exit check	Three questions collected and marked	Work independently

03 Teaching script (read it out)

Scene 1: Count sides and angles: a quadrilateral is four and four

Every quadrilateral shares exactly two features: 4 straight sides and 4 angles. Those two numbers are the entry ticket. Anything else is not a quadrilateral, since a triangle has three sides and a circle has no straight sides.
Primary 2 children recognise shapes by outline memory, so a tilted card makes them hesitate. Turn counting into an action: run a finger right round the edge and a tilted shape proves it has four sides like any other.

Students do: count sides and angles on four tilted and upright cards, writing 4 and 4 on each.

Scene 2: Two questions separate all four shapes

Question one: are all four angles right angles? If yes, four equal sides makes it a square and only opposite sides equal makes it a rectangle. Question two: if not right angles, two pairs of parallel equal sides makes a parallelogram, and one pair of parallel sides makes a trapezium.
A rhombus and a square both have four equal sides, but the square adds right angles. Say plainly that a square is a special rectangle, not a cousin of one. A rectangle 5 by 3 has perimeter 16; a square of side 4 also has perimeter 16. Equal perimeter does not mean equal shape.

Students say: holding a parallelogram, give two differences from a rectangle, no right angles and it can lean.

Scene 3: Perimeter adds the four sides, it is not length times width

Perimeter is the distance all the way round, so add the four sides. A rectangle 5 by 3 gives 5 plus 3 plus 5 plus 3, which is 16; later this becomes 2 times (5 plus 3) equals 16. A parallelogram with base 6 and slant side 4 gives 2 times (6 plus 4) equals 20.
Length times width gives area, measured in square units, not in centimetres. Skip this distinction and the two ideas stay fused for years. Sanity check: the perimeter always exceeds the longest side, and usually exceeds the sum of any two sides.

Students do: find the perimeter of a square of side 4 and explain why the answer is 16 rather than 4 times 4.

04 Question types and worked steps

Type	Example	Steps	Answer
Counting	How many sides and angles	Walk a finger round the edge	Count vertices, not edges
Sorting	Which quadrilateral is this	Right angles first, then opposite sides	Name plus reason
Drawing	Draw a parallelogram	Two parallel lines, then join them	It must not be a right angle
Perimeter	Perimeter of 5 by 3	Add four sides or double length plus width	Units are units of length

Sanity check (teach this): Sanity check: a quadrilateral always has 4 sides and 4 angles; a square has 4 right angles and four equal sides; a parallelogram has no right angles but two pairs of equal sides; 5 by 3 gives 16 and a square of side 4 gives 16, the same perimeter with a different shape; perimeter is measured in centimetres, never square centimetres.

05 Independent practice (3 questions)

Question	Answer	What to watch
Counting	Three cards, sides and angles	Each is 4 and 4
Sorting	Six cards into four groups	Reasons given
Drawing	One square and one parallelogram	Right angles distinguished
Perimeter	Two perimeter sums	Units correct

06 Common mistakes and what to say

Mistake	Student writes	Say this
Naming by outline	Calling a tilted rectangle a parallelogram	Test the four corners with a paper corner. Are they right angles? Then it is a rectangle.
Denying that a square is a rectangle	A square and a rectangle are two different things	A rectangle needs four right angles and equal opposite sides. Does a square meet that?
Perimeter done as length times width	Answering 16 square centimetres	Is perimeter the distance round, or the surface covered? Which unit belongs to each?
Missing a side when counting	Three sides on a tilted shape	Start at one corner, walk a finger round until you are back, and count how many sides you passed.

07 Homework (paper, section and question numbers)

Primary maths chapter index — All chapters by level
Teaching guide index — Same structure, other subjects
Redo this chapter — Questions 1 to 4 again, writing the sorting reason before each perimeter

08 Exit check (last 5 minutes)

Question	Answer	Decision
Sides and angles of a quadrilateral	4 sides, 4 angles	Wrong means act one again
Rectangle against parallelogram	Check for right angles	Looks tilted means act two again
Perimeter of 5 by 3	16 centimetres	16 square centimetres means act three

09 Tutor FAQ

Why insist a square is a rectangle?

Because sorting must run on conditions, not names. Children who sort by condition handle rhombus and kite later without memorising a new list.

How far should parallelograms go?

At Primary 2 only parallel equal opposite sides and no right angles. Area and height would bury the sorting point.

May they use the formula?

Yes, after adding four sides by hand. A formula memorised without its origin collapses on irregular shapes.

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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.