Mathematics K–6 · Years 3–4

Square centimetres and a square metre: covering with a grid

Measurement and space

Practical, model not builtLow risk

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The idea

Area is measured in square units of a fixed size, a square centimetre for small surfaces and a square metre for large ones, and 10 000 square centimetres fit in a square metre.

What you need

a transparent 1 cm grid overlay (printed on overhead film) per pair
100 card tiles 1 cm by 1 cm and 20 tiles 10 cm by 10 cm
sheets of newspaper, sticky tape and a metre rule
an A4 sheet, a hand outline traced on paper, a card rectangle 8 cm by 5 cm

How to do it

Cover the 8 cm by 5 cm card rectangle with 1 cm tiles, then lay the grid overlay on it and count the squares along one edge and the rows. Record the area in square centimetres.
Lay the overlay on the hand outline. Count whole squares, then pair up part squares as halves, and record the area as an estimate.
Tape newspaper into a square 1 m by 1 m using the metre rule. Lay 10 cm by 10 cm tiles along one edge and count them, then work out how many cover the whole square.
Stand on the square metre as a group and count how many children fit standing. Estimate the classroom floor in square metres by pacing, then measure the length and width with the metre rule.
Record every area with its unit and write the relationship between square centimetres and a square metre.

What you should see

The 8 cm by 5 cm card rectangle holds 8 tiles in a row and 5 rows, 40 square centimetres, and the overlay count agrees. A hand outline gives an estimate in square centimetres that differs from child to child; counting whole squares only gives a smaller number than pairing the part squares, which shows why part squares count. The square metre takes 10 tiles along an edge and 10 rows, 100 tiles of 100 square centimetres, which is 10 000 square centimetres. A classroom 8 m by 7 m would have 56 square metres of floor, and the pacing estimate is checked against the length times the width measured with the metre rule.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

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

A square metre is 100 square centimetres because there are 100 centimetres in a metre.
Part squares can be ignored when counting area.

Safety card

Low riskLearners carry it out

Hazards

newspaper on the floor is slippery

Controls

tape the square down and walk, do not run, on it

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 AuthorityMA2-2DS-03 MAO-WM-01
Australian Curriculum v9AC9M4M02

Sources

The pages the author read to write this activity.

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