Today is rung 9 of 11 on this topic
Scale drawings and similar figures
Can do: Uses a scale factor to convert between drawing and reality, and knows what happens to area.
Why it matters
It's proportionality made visual, and the area trap — doubling the sides quadruples the area — surprises almost everyone.
What it looks like when it's wobbly
Doubles the sides and expects the area to double.
⏱️ Two-minute check
"A 1:50 plan shows a 6 cm wall. How long is it really? If you double every side of a rectangle, what happens to the area?"
Solid looks like: 3 m, and area ×4.
The full activity for this topic · 30 minutes
Scale Plan of a Room
- 1Measure a real room and choose a sensible scale.
- 2Draw the plan accurately including doors and furniture.
- 3Check by measuring the drawing and converting back.
- 4Then draw it at double the scale and compare the areas of the two drawings.
- 5Work out how much paint or carpet the real room needs from the plan.
If it's too hard
Scale one rectangle up and down by a whole factor.
If it's too easy
Find a missing side in similar triangles, and reason about volume scaling by the cube.
Say this
"You doubled the sides — draw it and count the squares. How many times bigger is the area really?"