Understand the idea.
Trace the boundary
Trace the boundary of a flat shape to count its sides and corners. A side is one straight part; a corner is where two sides meet. Mark your starting corner so you stop when you return, counting each side only once.
Turning does not change a shape
A triangle has three straight sides and three corners. Squares and rectangles each have four of each. Turning or enlarging a shape keeps those counts. A circle has a curved boundary, so it has no straight sides and no corners.
See the method in action.
Count a triangle
How many straight sides and corners does shape A have?
Worked solution
- 1
Start at one corner of shape A.
Remembering the start prevents counting the same side twice.
- 2
Trace the straight boundary back to the start.
The triangle has three separate straight edges around its boundary.
- 3
Count where the sides meet.
Each meeting of two sides gives one corner, making three corners.
3 straight sides and 3 corners.
Look past the position
The square in the picture is turned. Does it now have more than four sides?
Worked solution
- 1
Trace from the top corner around the square.
There are four straight edges before returning to the starting corner.
- 2
Check what turning changed.
The square points a different way, but no edge has been added or removed.
- 3
Answer the question about extra sides.
No: the turned square still has four sides.
No. It still has 4 sides.
Try it yourself.
Check your understanding
A rectangle is made bigger. How many corners does it have now?
Show answer & reasoning
4 corners.
An enlarged rectangle still has four corners. Its sides become longer, but no new places where sides meet are added.
Keep practising
6 worksheet questions
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 ↗