Triangles and quadrilaterals: what children learn
Year 4 pupils compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes.
In this game children match descriptions of sides, angles and parallel lines to shape names, from isosceles triangles to trapeziums and kites. Each description fits only one name, so children have to read every property.
This topic covers the Year 4 statutory requirement in the National Curriculum in England (Geometry – properties of shapes): pupils should be taught to “compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes”. Year 4 pupils are usually aged 8–9.
For families following US standards, the closest Common Core standard is 4.G.A.2, which is taught in Grade 4.
How to play
Pick a card on the left, then the card on the right that matches it. Each game has 6 pairs. Wrong matches are counted as mistakes, and you get three stars for a game with no mistakes.
Step by step
- Count the equal sides. For triangles: 3 equal sides is equilateral, exactly 2 is isosceles, none is scalene.
- Look for right angles. A triangle with one right angle is a right-angled triangle. A quadrilateral with four is a square or rectangle.
- Look for parallel sides. One pair of parallel sides makes a trapezium. Two pairs make a parallelogram, rhombus, rectangle or square.
- Pick the most specific name. A square is also a rectangle, but 'square' is the best description of a shape with 4 equal sides and 4 right angles.
Worked examples
Example 1: 4 equal sides, but no right angles
Working: Equal sides like a square, but slanted.
Answer: rhombus
Example 2: exactly 1 pair of parallel sides
Working: Only one pair of opposite sides is parallel.
Answer: trapezium
Example 3: a triangle with exactly 2 equal sides
Working: Two sides match, one is different.
Answer: isosceles triangle
Common mistakes and how to fix them
- Thinking a square cannot be a rectangle. A rectangle has 4 right angles. A square has them too, so it is a special rectangle.
- Naming shapes by how they look rather than by their properties. Check the sides and angles every time, even if the shape is turned.
- Confusing a rhombus with a kite. A rhombus has 4 equal sides. A kite has 2 pairs of equal sides next to each other.
Activities to try at home
- Look for triangles and quadrilaterals in buildings, bridges and road signs.
- Fold paper to make different triangles and name them.
- Play 'guess my shape' by giving one property at a time.
Ideas for the classroom
- Pupils sort quadrilaterals into a Venn diagram: 'has right angles' and 'has parallel sides'.
- Use geoboards to make each triangle type.
- Ask: can a triangle have two right angles? Why not?
Free printable game and worksheet
The free printable starts with a game sheet, such as a colour-by-answer picture, an answer maze or a secret-code joke, followed by a worksheet. Both use the same checked questions as the online game, and the answers are on the last page. Print it, or save it as a PDF from your browser’s print menu.
Open the free printable game and worksheet
Frequently asked questions
Why do children learn so many shape names?
Classifying shapes by their properties builds reasoning: children explain why a shape belongs in a group.
Is a trapezium the same as a trapezoid?
In the UK, a trapezium has one pair of parallel sides. In the US, this shape is called a trapezoid.
Can it be played with a keyboard?
Yes. Tab to a card, press Enter to pick it, then pick its partner.