Scale and Proportions Introduction

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📏 Part 1: Understanding Scale

1. What does a scale of 1:10 mean?

1 cm on the drawing represents 10 cm in real life

10 cm on the drawing represents 1 cm in real life

The drawing is exactly the same size as the real object

The drawing is 10 times bigger than the real object

2. A scale drawing of a room uses a scale of 1:50. If a wall measures 3 cm on the drawing, what is the actual length of the wall?

6 cm

150 cm

1.5 metres

15 metres

3. Which of these are examples of scale being used in real life? (Select all that apply)

Maps of New Zealand

Architectural plans for houses

Model cars and trains

Life-size photographs

4. A toy car is built to a scale of 1:64. If the real car is 4.8 metres long, how long should the toy car be?

Answer: _______ cm

📐 Part 2: Creating Scale Drawings

5. You need to draw a scale drawing of your desk. The desk measures 120 cm long and 60 cm wide. Using a scale of 1:20, what will the dimensions be on your drawing?

Length on drawing: _______ cm

Width on drawing: _______ cm

6. Look at the rectangle below. If this represents a rugby field drawn to a scale of 1:1000, calculate the actual dimensions of the field.

Rectangle on drawing: 10 cm long, 7 cm wide

Actual length: _______ metres

Actual width: _______ metres

7. Explain in your own words why scale drawings are useful. Give two specific examples.

🎯 Part 3: Problem Solving

8. A map of Auckland uses a scale of 1:25,000. If the distance between two points on the map is 8 cm, what is the actual distance in kilometres?

Actual distance: _______ kilometres

9. You want to make a scale model of the Sky Tower (328 metres tall) that will fit on your desk. If your model can be no taller than 20 cm, what scale should you use?

Appropriate scale: 1:_______

10. Challenge: If you double the scale factor of a drawing (e.g., from 1:10 to 1:5), how does this affect the size of the drawing? Explain your reasoning.