Scale Drawings and Proportion

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📐 Part 1: Understanding Scale

1. What is a scale drawing?

A drawing that is exactly the same size as the real object

A drawing that shows an object larger or smaller than its actual size, but keeps the same proportions

A drawing that only shows the outline of an object

A drawing made using only a ruler

2. If a scale is written as 1:50, this means:

1 cm on the drawing represents 50 cm in real life

50 cm on the drawing represents 1 cm in real life

The drawing is 50 times larger than real life

There are 50 objects in the drawing

3. A bedroom measures 4 metres by 3 metres. Using a scale of 1:100, what would be the dimensions on the scale drawing?

4 cm by 3 cm

40 cm by 30 cm

400 cm by 300 cm

0.4 cm by 0.3 cm

4. Which of these are examples of scale drawings? (Tick all that apply)

A map of New Zealand

House plans for a new whānau home

A photograph of your pet

Plans for a new marae layout

📏 Part 2: Scale Calculations

5. A rectangular garden is 12 metres long and 8 metres wide. Draw this garden using a scale of 1:200 in the box below. Show your working.

6. On a scale drawing using 1:25, a table appears to be 6 cm long. What is the actual length of the table in real life?

Working: _________________________________________________

Answer: The actual length is ________ metres.

7. A community hall measures 20 metres by 15 metres. If you want to draw it on A4 paper (21 cm wide), what would be a suitable scale to use? Explain your reasoning.

🏠 Part 3: Real-World Applications

8. You are helping to plan a new playground for your community. The actual playground will be 30 metres by 20 metres. Using a scale of 1:500, draw the outline of the playground and add at least 3 features (swings, slide, sandpit, etc.) with appropriate sizes.

9. Explain how scale drawings help whānau and communities when planning new spaces or buildings. Give at least two specific examples.

10. Extension Challenge: If the scale factor from a drawing to real life is 1:150, and a room on the drawing has an area of 8 cm², what is the actual area of the room in square metres? Show all working.