Understand that different shapes can have the same perimeter | Maths

Starter quiz

Match the number of sides to the shape name.

3 sides

⇔

triangle ✓

4 sides

⇔

quadrilateral ✓

5 sides

⇔

pentagon ✓

6 sides

⇔

hexagon ✓
Select all of the names of shapes that are polygons.

Cube

Square ✓

Triangle ✓

Circle
Which of these shapes are regular polygons?

A

B

C ✓

D ✓
Rearrange these phrases to make a sentence.

1

⇔

Perimeter is

2

⇔

the distance around

3

⇔

the outside of

4

⇔

a 2D shape.
Which of these shows the perimeter of the triangle?

A ✓

B

C
In terms of perimeter, which of the statements are true of this image?

a has the same perimeter as b

a has a longer perimeter than b ✓

a has a shorter perimeter than b

b has a shorter perimeter than a ✓

b has a longer perimeter than a

Exit quiz

Which of these is true?

Two different shapes can have the same perimeter. ✓

Two different shapes cannot have the same perimeter.

Two different shapes may or may not have the same perimeter. ✓
Always, sometimes or never true? A regular polygon can have the same perimeter as a shape with curved sides.

Always true.

Sometimes true. ✓

Never true.
Select the two shapes with the same perimeter.
Which of these statements is true?

The shapes have the same perimeter.

The square has the longer perimeter.

The triangle has the longer perimeter. ✓
Which statement is true of the polygons created inside these number rods?

The shapes are different but the perimeter is the same. ✓

The shapes are different and the perimeter is different.

It is impossible to tell whether the perimeter is the same or different.
Which of these statements is true about these three rectangles?

The rectangles could have the same perimeter. ✓

The rectangles cannot have equal perimeter because sides lengths are different.

B has the longest perimeter because it has the longest side length.

Worksheet

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Presentation

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Video

Lesson Details

Key learning points

Shapes that look different can have the same perimeter.
You can draw or create more than one 2D shape with the same perimeter.
Shapes with different numbers of sides can have the same perimeter.

Common misconception

Pupils will most likely understand that different shapes can and most often do have different perimeters. They may not realise that the perimeters can potentially be the same.

Allowing pupils to recreate perimeters using string or number rods and rearranging themselves to make a new shape is a powerful way of showing that different shapes can have equal perimeters.

Keywords

Polygon - A polygon is a 2D shape made up of 3 or more straight lines.
Perimeter - The distance around a two-dimensional shape.