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

Illustration for Getting Started 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

Look at the sides and angles marked on some triangles, then two four-sided shapes and a trapezium. Notice the marks and see what makes each shape different from the others.

Teacher Notes

Triangles by sides: reveal sides and angles. Scalene none equal, isosceles two equal, equilateral three equal. Point out equal sides give equal angles. Ask which triangle has none equal.

Triangles by angles: name by biggest angle. Right-angled one square 90° corner, acute all angles under 90°, obtuse one angle over 90°. Stress equilateral is acute, three 60° angles, this feeds the Class Challenge sort.

Rhombus and parallelogram together: point to two parallel pairs on each, then stress the rhombus has all four sides equal, the parallelogram does not.

Trapezium: only one parallel pair. Head off the idea that every four-sided shape has two.

👇 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 inspect each shape in turn to see whether its marks show that property. We agree as a class which ones fit 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 First we build one row of a property table together on the board for a square, so you can see exactly how the ticks work. The table has three columns: sides, angles and parallel lines. For the square we tick: four equal sides, four right angles, and two pairs of parallel sides. Then we do the same for a rectangle: opposite sides equal (not all four), four right angles, and two pairs of parallel sides. After that, draw the same three-column table in your maths copy. Enter each shape from the lesson, one per row, and tick the properties each shape has.

Teacher Notes

Board demo before any copywork. Draw the three-column table (sides | angles | parallel lines). Work the square row end to end: sides → four equal; angles → four 90°; parallel lines → two pairs. Tick each as you name it. Then the rectangle row: sides → opposite equal only (not all four); angles → four 90°; parallel lines → two pairs. Point out the square ticks every rectangle box plus the all-sides-equal box. Pupils then copy the blank table and fill rows for the lesson shapes (include square and rectangle). Walk the room for column headings and ticks, not full marking. Slip to watch: blank parallel-lines cell on the square, or ticking all-four-equal on the rectangle.

+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 all sides equal, and the shapes that belong in both.

Sort by property

Teacher Notes

These are the practice questions — 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 practice set 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?

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 four equal sides is not required of a rectangle.

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

Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~9 mins

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

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