Classifying Triangles and Quadrilaterals by Properties

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Build a Property Table in Your Copy
5 Class Challenge
6 What Did We Notice?
7 What's Next
Pupil practice

1 - Getting Started ~4 mins

Hands up: is a square also a rectangle? And is a rectangle also a square? Take a moment to decide what you think, then be ready to defend your answer to the class.

Teacher Notes

Take three hands-up answers, not open call-outs. Don't settle the argument yet, that's the whole lesson. Listen for pupils who say 'a square is a rectangle but not the other way round' and hold that thought for the wrap.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

Illustration for Watch and Notice

Triangles by their sides

Watch as we reveal the sides and angles of three triangles. A scalene triangle has no equal sides, an isosceles triangle has two equal sides, and an equilateral triangle has three equal sides. Notice how the equal sides line up with equal angles.

Triangles by their angles

We can also name a triangle by its biggest angle. A right-angled triangle has one square corner of exactly 90°. An acute triangle has every angle smaller than 90°, so it looks sharp all over. An obtuse triangle has one angle bigger than 90°, so one corner is opened out wide. An equilateral triangle, with three angles of 60° each, is an acute triangle.

A parallelogram and a rhombus

Look at these two four-sided shapes side by side. Both have two pairs of parallel sides. The difference is in the sides: the rhombus has all four sides equal, while the parallelogram does not.

A trapezium

This shape is a little different. A trapezium has just one pair of parallel sides, not two. Watch the parallel pair light up.

Teacher Notes

Walk each example aloud, one at a time.

Triangles by sides — reveal the sides and angles, then say 'equal sides give equal angles'; ask pupils which triangle has none equal.
Triangles by angles — name the three angle types as you point: a right-angled triangle has one square 90° corner; an acute triangle has every angle under 90°; an obtuse triangle has one angle over 90°. Make the point that an equilateral triangle is acute because its angles are all 60°, since the Class Challenge sort relies on this.
Rhombus and parallelogram — both are on screen together; point at the two parallel pairs on each, then stress that all four sides being equal is the extra feature of the rhombus.
Trapezium — the misconception to head off is thinking every four-sided shape has two parallel pairs; this one has only one.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~8 mins

The shapes from today are on the board together. We will name a property, such as 'has two pairs of parallel sides' or 'has a right angle', and then check each shape on the board in turn to decide whether it fits. We tag the ones that fit and agree as a class before we move on.

Find the shapes that fit

Teacher Notes

This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.

Call one property at a time. Invite a pupil to the board to check each shape against that property and tag the ones that fit. Start with an easy property (three sides) and build to a trickier one (exactly one pair of parallel sides, which catches the trapezium). Revoice strong answers: 'so a square fits because it has two pairs of parallel sides AND four equal sides'. Watch for pupils who forget that a square satisfies rectangle properties too.

+15 XP

4 - Build a Property Table in Your Copy ~3 mins

COPYBOOK MOMENT

Illustration for Build a Property Table in Your Copy In your maths copy, draw a property table with three columns: sides, angles and parallel lines. Enter each shape from the lesson into the table, one per row. Then tick the properties each shape has.

Teacher Notes

Walk the room glancing at the column headings and the ticks — this is whole-class copybook practice, not marking. Prompt any pupil who has left the parallel-lines column blank for a square.

+10 XP

5 - Class Challenge ~10 mins

Today we sort shapes into groups by their properties. First we sort triangles by their angle type: right-angled, acute or obtuse. Then we sort quadrilaterals into an overlap: shapes with parallel sides, shapes with equal sides, and the shapes that belong in both. One of the quadrilaterals is a kite, which has two pairs of equal sides but no parallel sides at all.

Sort by property

Teacher Notes

This round is the practice bank — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.

Run the bank in order so the difficulty builds. Remind the class that an equilateral triangle is acute (all angles 60°), since the first sort relies on it. The final round asks pupils to name a shape in the overlap of both 'parallel sides' and 'equal sides' — a square or rhombus fits, and that is the link back to the opening question. Fast finishers wait and mouth the next sort.

+15 XP

6 - What Did We Notice? ~2 mins

MATHS TALK

One pupil says every square is a rectangle. Another says no square is a rectangle. Who is right, and how would you settle it using properties?

Here is the reasoning. A square has four right angles and two pairs of parallel sides, which is every box a rectangle needs, so a square counts as a rectangle. But a rectangle does not have four equal sides, so it is missing a box the square needs, which means a rectangle does not count as a square. So every square is a rectangle, but not every rectangle is a square.

Teacher Notes

Listen for pupils who reason from properties rather than from the look of the shape: a square has four right angles and two pairs of parallel sides, so it has every property a rectangle needs. Revoice: 'a square ticks every rectangle box plus one more, so it fits inside the rectangle group, but a rectangle is missing the equal-sides box so it does not fit inside the square group'. Head off the gut answer that 'they just look different'.

+10 XP

7 - What's Next ~2 mins

What we did today

We sorted triangles by their sides and by their angles, and quadrilaterals by their parallel sides and equal sides.
We learned that every square is a rectangle, because a square has every rectangle property plus four equal sides; but not every rectangle is a square, because a rectangle is missing the four-equal-sides property.

Coming up

Next we use a ruler and compass to construct triangles from given measurements, so that only one triangle can be built from the right facts.

Teacher Notes

Recap the big idea: shapes are sorted by the properties they have, not by how they look at first glance.

+5 XP

Pupil practice

Module 7 · 2D Shape, 3D Shape and Angles Data & Chance

Lesson 70 · Classifying Triangles and Quadrilaterals by Properties

Download Activity Book page (PDF)

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Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~9 mins

Triangles by their sides

Triangles by their angles

A parallelogram and a rhombus

A trapezium

3 - Try It Together ~8 mins

Find the shapes that fit

4 - Build a Property Table in Your Copy ~3 mins

5 - Class Challenge ~10 mins

Sort by property

6 - What Did We Notice? ~2 mins

7 - What's Next ~2 mins

What we did today

Coming up

Unlock the full learning experience

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