Mathematics K–6 · Years 3–4

Perimeter with string: the distance around a shape

Measurement and space

PracticalLow risk

The idea

Perimeter is the length of the boundary of a shape, so a string laid around the edge and then measured straight gives the same length as adding the sides.

What you need

4 m of thin string per pair and a marker
a 1 m rule and a 30 cm ruler marked in millimetres
an A4 sheet, a hardback book, a desk top and a circular plate
a sheet of 1 cm grid paper

How to do it

Lay the string around the edge of the A4 sheet, mark where it meets itself, then straighten it against the metre rule and read the length.
Measure each side of the sheet with the ruler and add the four lengths. Compare with the string reading.
Repeat for the book and the desk top, recording both methods each time.
Measure the plate with the string only, since its edge has no straight sides.
Draw three different shapes on the grid paper that each have a perimeter of 20 cm and check by counting edges.

What you should see

An A4 sheet measures 297 mm by 210 mm, so adding the sides gives 297 + 210 + 297 + 210 = 1014 mm, and the straightened string reads close to that; string stretch and slack at the corners explain any difference. The book and the desk top show the same close agreement between the two methods. The plate's perimeter comes only from the string method. Shapes drawn with perimeter 20 cm include a 5 by 5 square, a 2 by 8 rectangle and a 1 by 9 rectangle, and their areas differ (25, 16 and 9 square centimetres).

What changes

What you change: the method (string around the edge, or adding measured sides)
What you measure: the perimeter in millimetres
What you keep the same: the same object
string pulled taut at each corner
reading from the zero mark

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

Shapes with the same perimeter have the same area.
Perimeter is the number of squares inside a shape.

Safety card

Low riskLearners carry it out

Hazards

string can tangle around fingers

Controls

keep the string on the table; no loops around necks or wrists

Note

No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA2-GM-02 MAO-WM-01
Australian Curriculum v9AC9M4M02

Sources

The pages the author read to write this activity.

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