Mathematics K–6 · Kindergarten
Which covers more: comparing areas by laying one shape on another
Measurement and space
The idea
Area is the amount of surface a shape covers, and two surfaces are compared by placing one on top of the other, not by how tall or wide they look.
Safety card
Hazards
- scissors
Controls
- an adult cuts the strip, or children use rounded-tip safety scissors
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.
What you need
- 6 pairs of card shapes: 5 pairs where one shape fits inside the other (for example a 10 cm square and a 12 cm square) and 1 pair where neither fits inside the other: a 6 cm by 20 cm strip and a 10 cm square
- a picture book, an exercise book and a tissue box
- rounded-tip safety scissors
How to do it
- Take a pair of card shapes. Put the smaller on top of the larger so that two edges line up. Say which covers more and show the part that is left uncovered.
- Take the 6 cm by 20 cm strip and the 10 cm square. Predict which covers more, then lay the strip on the square and see that neither fits inside the other.
- Cut the strip into two 6 cm by 10 cm pieces and lay both on the square, side by side. See that the pieces cover the whole square and still hang over one edge.
- Compare the two book covers and the top of the tissue box by laying one on another. Order the three surfaces from least to most.
- Record each comparison as a drawing with the words covers more and covers less.
What you should see
For nested pairs the uncovered border shows the larger area at once. For the strip and the square, laying the strip flat does not settle it, and only cutting and rearranging shows the strip covers more: the two 6 cm by 10 cm pieces side by side make a 12 cm by 10 cm shape that covers the whole 10 cm square with a 2 cm band hanging over one edge. Judging by length alone points to the strip (20 cm against 10 cm) and judging by width points to the square (10 cm against 6 cm), so neither look settles it; the cut pieces do.
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.
- The taller shape has more area.
- The longer shape has more area.
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 AuthorityMAE-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