Mathematics K–6 · Years 1–2
Covering a surface: area in rows and columns
Measurement and space
The idea
Area is measured by covering a surface with identical units that leave no gaps, and the units line up in rows and columns so the count can be found by rows times columns.
What you need
- 50 square tiles 5 cm by 5 cm cut from card
- 50 square tiles 2.5 cm by 2.5 cm cut from card
- 20 round counters about 2.5 cm across
- a rectangle of card 20 cm by 15 cm and an exercise book
How to do it
- Estimate how many 5 cm tiles will cover the 20 cm by 15 cm card. Write the estimate down.
- Cover the card with 5 cm tiles, edges touching, starting from one corner. Count the tiles in one row and the number of rows, then count all the tiles.
- Cover the same card with 2.5 cm tiles. Record rows, columns and the total.
- Lay the 20 round counters touching in rows on one corner of the card. Look at the gaps between them and say why counters are a poor unit for area.
- Cover the exercise book cover with 5 cm tiles and compare its area with the card by comparing the counts.
What you should see
The 20 cm by 15 cm card takes 4 tiles in a row and 3 rows, 12 tiles in all, and the count matches 4 times 3. With 2.5 cm tiles it takes 8 by 6, which is 48 tiles, four times as many because each big tile is replaced by four small ones. Round counters leave uncovered gaps between them however they are packed, so their count under-reports the surface. Children who count tiles one by one and children who use rows times columns get the same total.
What changes
- What you change
- the size of the square unit
- What you measure
- the number of units needed to cover the card
- What you keep the same
- the same card
- units touching with no gaps or overlaps
- starting from a corner
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Any small object can be used to measure area, gaps do not matter.
- A longer shape always has a bigger area than a shorter one.
Safety card
Hazards
- none beyond ordinary classroom materials
Controls
- none needed
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 AuthorityMA1-2DS-02MAO-WM-01
- Australian Curriculum v9No Australian Curriculum v9 code is listed.
Sources
The pages the author read to write this activity.
- curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/outcomes
- education.nsw.gov.au/content/dam/main-education/teaching-and-learning/curriculum/key-learning-areas/mathematics/media/documents/mathematics-es1-s1-teaching-measurement.pdf
- education.nsw.gov.au/teaching-and-learning/curriculum/literacy-and-numeracy/teaching-and-learning-resources/numeracy/understanding-units-of-measurement