Mathematics 7–10 · Years 9–10
Enlargement on grid paper: lengths scale by k, areas by k squared
Measurement and space
The idea
An enlargement from a centre multiplies every length by the scale factor and every area by the square of it, and counting squares on the enlarged figure shows the square.
What you need
- 1 cm grid paper (A3), ruler, pencil
How to do it
- Draw a 3 by 4 rectangle and mark a centre of enlargement O outside it. From O draw rays through each vertex.
- Along each ray mark the point twice as far from O as the vertex; join the four points. Measure the sides and count the squares inside.
- Repeat for scale factor 3 and for scale factor 1/2.
- Tabulate scale factor, side lengths, perimeter and area; write area ratio as a power of the scale factor.
- Repeat with an L-shaped figure to show the rule does not depend on the shape being a rectangle.
What you should see
Scale factor 2 gives a 6 by 8 rectangle: perimeter 28 (twice 14) and area 48 (four times 12). Scale factor 3 gives 9 by 12: area 108, nine times 12. Scale factor 1/2 gives 1.5 by 2 with area 3, a quarter of 12. Angles are unchanged at 90 degrees and corresponding sides are parallel. The learner knows it worked when the counted squares equal 12 × k² for every k tried.
What changes
- What you change
- scale factor k
- What you measure
- area of the image
- What you keep the same
- same original figure
- same centre of enlargement
- distances measured from O along the rays
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Doubling the lengths doubles the area.
- Enlargement changes the angles.
- A scale factor less than 1 is not an enlargement.
Safety card
Hazards
No hazard is listed.
Controls
No control is listed.
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; ordinary classroom supervision.
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), Stage 5 Properties of geometrical figures A; page read 2026-09-22MA5-GEO-C-01
- Mathematics K–10 Syllabus (2022), Stage 5 Properties of geometrical figures B (Path); page read 2026-09-22MA5-GEO-P-01
- Australian Curriculum v9AC9M9SP02AC9M10M05
Sources
The pages the author read to write this activity.