Mathematics

Intermediate

50 mins

Teacher/Student led

+80 XP

What you need:
Chromebook/Laptop/PC or iPad/Tablet
IWB/Projector/Large Screen

Properties of 2D Shapes Including Quadrilaterals

Learn the names and properties of six quadrilaterals (square, rectangle, rhombus, parallelogram, trapezium and kite) and discover how a square belongs to two different families.

Warning: Your screen size is quite small for viewing this. Rotate your device into landscape mode if you can.

1 Getting Started: a Family of Four-sided Shapes
2 Meet the Six Named Quadrilaterals
3 Try Together: Sort the Quadrilaterals
4 Sketch Four Quadrilaterals in Your Jotter
5 Independent Challenge: Name the Shape
6 Maths-talk Wrap: Regular or Irregular?
7 What's Next
Pupil practice

1 - Getting Started: a Family of Four-sided Shapes

Look at the photos on the board. A school window with four right angles. A flying kite over Tollymore Forest Park. A diamond pattern on a GAA county jersey. A road sign warning of a steep hill ahead. Every one of these is a four-sided flat shape, but no two are quite the same.

Today you will meet the family of quadrilaterals and learn the names mathematicians give to each of them. Some you already know: square, rectangle. Others you may not have met before: rhombus, parallelogram, trapezium, kite.

Quick maths-talk: which of these shapes can you already name? What makes a square different from a kite, even though both have four sides?

Teacher Notes

Open with the three Processes — Making and Monitoring Decisions, Communicating Mathematically, Mathematical Reasoning — all in play. Take 30 seconds of whole-class maths-talk: call on three pupils, revoice each answer back to the class. Listen for 'diamond' said about a rhombus (keep that) and ask 'what is the maths name for a diamond?'

👇 Mark your steps as done as you complete them.

+5 XP

2 - Meet the Six Named Quadrilaterals

We'll meet the six shapes in three short waves. Watch the IWB carefully: as we read each row, your teacher will sketch the shape next to it so you can see the maths name and the picture together.

Wave 1: the parallelogram family

These four shapes all belong to ONE big family called parallelograms. In every parallelogram, opposite sides are parallel.

Shape	Sides	Angles
Square	All 4 sides equal; opposite sides parallel	All 4 angles are right angles (90°)
Rectangle	Opposite sides equal and parallel	All 4 angles are right angles (90°)
Rhombus	All 4 sides equal; opposite sides parallel	Opposite angles equal, but NOT right angles (unless it's a square)
Parallelogram	Opposite sides equal and parallel	Opposite angles equal, but NOT right angles

Wave 2: the two outsiders

Now meet two shapes that are NOT in the parallelogram family. Each one breaks the parallel-sides rule in a different way.

Shape	Sides	Angles
Trapezium	ONLY one pair of parallel sides	No special angle rule
Kite	Two pairs of adjacent sides equal; NO parallel sides	One pair of opposite angles equal

Wave 3: the surprise — a square belongs to TWO families

Look back at Wave 1. A square has all 4 sides equal (that's the rhombus rule) AND 4 right angles (that's the rectangle rule). So a square is BOTH a rhombus AND a rectangle at the same time.

Your teacher will sketch a quick Venn-style picture on the IWB: two overlapping ovals labelled Rhombus family and Rectangle family, with the Square sitting in the overlap. That tiny overlap is the only place a quadrilateral can belong to both families at once.

Teacher Notes

Pace this in three clear waves with a short pause between each — don't try to land all six shapes in one read. WAVE 1: walk down the parallelogram-family table row by row on the IWB, sketching each shape next to its row as you read. WAVE 2: sketch the trapezium and kite to one side of the parallelogram set so pupils see them as visually separate. WAVE 3: draw the Venn diagram — two big overlapping ovals, one labelled 'Rhombus family' (containing rhombus + square), one labelled 'Rectangle family' (containing rectangle + square), with the square in the overlap. Anti-pitfall: pupils often think 'rhombus = diamond on its corner'. Show a rhombus sitting on its flat side too — the name does not depend on orientation.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try Together: Sort the Quadrilaterals

Now the class works through the sorting tool together on the IWB. Each shape card lifts up and drops into the bucket that names its key property. Take turns coming to the board: predict the answer in your head first, then come up to drag.

Watch carefully when the square comes up. It could go in more than one bucket. Which bucket does it belong in MOST cleanly, and why?

Sort six quadrilaterals by their key property

Teacher Notes

Run the widget on the IWB in explore mode. Call a pupil to drag each card; the rest of the class predicts first by holding up fingers (1 = bucket 1, 2 = bucket 2, etc.). If a card lands wrongly, do NOT correct it immediately — ask 'who thinks this is right?' and let a second pupil revoice the property. The square is the deliberate hard case: it fits 'all sides equal' AND '4 right angles' — narrate that this is exactly why a square is special, and point back to the Venn sketch from step 2.

+15 XP

4 - Sketch Four Quadrilaterals in Your Jotter

COPYBOOK MOMENT

In your jotter, sketch four quadrilaterals of your choice from today's table and label one property of each. Pick four different ones, don't draw the square four times.

Underneath each shape, write one sentence about the sides OR the angles. For example, under a rhombus you might write 'all 4 sides are equal'; under a trapezium you might write 'only one pair of parallel sides'.

Teacher Notes

Walk the row, glance for: (1) clearly four-sided shapes drawn with a ruler, (2) at least one named property under each. Do NOT mark — this is parallel-work accountability while pupils watch the IWB sort wrap up. If a pupil draws a triangle by mistake, point silently and let them notice.

+10 XP

5 - Independent Challenge: Name the Shape

Time to work on your own. Read each problem carefully and write your answer in your jotter. The teacher will reveal the answers one at a time after everyone has had a go.

Some problems ask you to NAME a shape from its properties. Others ask you to EXPLAIN whether one shape is also another. Take your time on those: the answer is usually 'yes' or 'no' AND a reason.

Teacher Notes

Pupils work individually in their jotters. Circulate and prompt; if a pupil writes only 'yes' or 'no' for problems 5 and 6, prompt 'and why?' rather than supplying the answer. Reveal the answers one at a time at the end and revoice the reasoning for problems 5 and 6 — these test the 'a square is also a rhombus AND a rectangle' insight from the model step.

+15 XP

Pupil practice

Module 7 · Shape and Space: 2D and 3D Shape, Symmetry, Angles, Coordinates and Compass Shape & Space

Activity Book — Page 79

Lesson 79 · Properties of 2D Shapes Including Quadrilaterals

Unlock the Full Learning Experience

Get ready to embark on an incredible learning journey! Get access to this lesson and hundreds more on our learning platform.

Get started

Copyright Notice
This lesson is copyright of Coding Ireland 2017 - 2025. Unauthorised use, copying or distribution is not allowed.

Properties of 2D Shapes Including Quadrilaterals

Teacher Class Feed

1 - Getting Started: a Family of Four-sided Shapes

2 - Meet the Six Named Quadrilaterals

Wave 1: the parallelogram family

Wave 2: the two outsiders

Wave 3: the surprise — a square belongs to TWO families

3 - Try Together: Sort the Quadrilaterals

Sort six quadrilaterals by their key property

4 - Sketch Four Quadrilaterals in Your Jotter

5 - Independent Challenge: Name the Shape

Unlock the Full Learning Experience

XP