Mathematics 7–10 · Years 7–8
Scale drawing of the classroom at 1:50
Number and algebra
The idea
A ratio of 1:50 turns every measured length in the room into a drawn length one fiftieth as long, and every drawn length back into a real one by multiplying by 50.
What you need
- 8 m tape measure per group
- A4 or A3 grid paper (1 cm squares) and ruler
- Clipboard and pencil
How to do it
- Measure the length and width of the room and the position and width of the door and windows to the nearest 10 cm.
- Convert each measurement to a drawn length at 1:50 (divide by 50) and record both in a table.
- Draw the outline and features on grid paper; add the desks by measuring one desk and placing it at scale.
- Check the drawing by picking two points on it, measuring their drawn separation, multiplying by 50 and measuring the real distance.
- Redraw one feature at 1:100 and describe what changed.
What you should see
An 8.00 m wall draws as 16.0 cm at 1:50 and 8.0 cm at 1:100; a 90 cm door draws as 1.8 cm. The check in step 4 agrees with the tape within about 10 cm real (2 mm on the drawing). The learner knows it worked when a person given only the drawing can predict a real distance in the room to within 10 cm.
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.
- 1:50 means the drawing is 50 times bigger.
- Scale applies to lengths and areas in the same ratio.
- 1:50 means 1 cm on the drawing stands for 50 m in the room.
Safety card
Hazards
- tape measure retracting on fingers
- moving furniture
Controls
- retract the tape slowly
- measure around furniture rather than moving it
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 4 Ratios and rates; covers the ratio arithmetic the entry uses, the unitary method and dividing a quantity in a given ratio, but carries no content point on scale, scale drawings or scale factor: the points on applying a scale to enlarge or reduce a diagram and on solving problems involving scale drawings sit in Stage 5 Properties of geometrical figures A (MA5-GEO-C-01), and neither Stage 4 Length (MA4-LEN-C-01) nor Stage 4 Geometrical figures (MA4-GEO-C-01) carries one either, so the 1:50 drawing itself has no Stage 4 home; pages read 2026-09-23MA4-RAT-C-01
- Australian Curriculum v9AC9M7N08AC9M7M06
Sources
The pages the author read to write this activity.