The idea, step by step
Trace the boundary
A side is a straight part of the edge of a flat shape. A corner is where two straight sides meet. Start at one corner and trace all the way around. Count each side once.
Triangles have three straight sides and three corners. Rectangles and squares each have four sides and four corners. A circle has a curved boundary and no straight sides or corners.
Turning does not change a shape
A shape keeps its sides and corners when you turn it. A square can stand on a side or on a corner. Both are squares.
Use a finger or a small mark to remember where you started counting. A longer side is still one side; do not split it into several sides.
A common trap
A turned square is a different shape with more sides.
Instead: Turning changes the position, not the number of sides or corners.
See the thinking
Count a triangle
How many straight sides and corners does shape A have?
- Start at the top corner.
- Trace three straight edges back to the start.
- The three places where edges meet are its corners.
Look past the position
The square in the picture is turned. Does it now have more than four sides?
- Trace its boundary, starting at the top corner.
- You still meet four straight sides and four corners.
- Turning the square has not added any sides.
Check your understanding
A rectangle is made bigger. How many corners does it have now?
Show answer
4 corners.
Making it bigger does not add corners.
Your turn
6 questions · Work at your own pace.
Read the questions online
- Count the straight sides of shape A.
- Count the corners of shape B.
- Which pictured shape has no straight sides?
- A flat shape has five straight sides. How many corners does an ordinary pentagon have?
- Draw a triangle with one side along the bottom. Then draw a triangle pointing in another direction. How many sides does each have?
- Mia says turning a rectangle upright makes it a different shape. Explain what is wrong.
Read the worked solutions
- Count the straight sides of shape A.
Shape A is a triangle. Trace three sides.
3 - Count the corners of shape B.
Shape B is a rectangle. It has four corners.
4 - Which pictured shape has no straight sides?
A and B have straight sides. C has a curved boundary.
C, the circle. - A flat shape has five straight sides. How many corners does an ordinary pentagon have?
Going around a pentagon, each side meets the next at a corner.
5 corners. - Draw a triangle with one side along the bottom. Then draw a triangle pointing in another direction. How many sides does each have?
Changing the direction does not change the three straight sides.
Each triangle has 3 sides. Drawings may vary. - Mia says turning a rectangle upright makes it a different shape. Explain what is wrong.
Its sides and corners remain the same when it is turned.
A rectangle can be turned upright and still be a rectangle.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Sides and spatial features; straight/curved/opposite/parallel; quarter/half/three-quarter/full turns.
Official curriculum source ↗