Scale Drawing Basic 6 Mathematics Lesson Note

What is Scale Drawing?

Scale drawing is a way to draw objects smaller or larger than their real size while keeping the same shape and proportions.

Understanding Scale

Scale tells us the relationship between the drawing size and the real size.

Common Scales:

• 1:10 means 1 cm on paper = 10 cm in real life
• 1:100 means 1 cm on paper = 100 cm (1 meter) in real life
• 1:1000 means 1 cm on paper = 1000 cm (10 meters) in real life

How to Read Scale

Example: Scale 1:50

• Drawing measurement: 3 cm
• Real measurement: 3 × 50 = 150 cm

Formula: Real size = Drawing size × Scale factor

Scale Drawing of Objects

Example 1: Drawing a Classroom

Real classroom: 8 meters long, 6 meters wide Scale: 1:100 (1 cm = 1 meter) Drawing size: 8 cm long, 6 cm wide

Example 2: Drawing a Table

Real table: 120 cm long, 80 cm wide Scale: 1:20 (1 cm = 20 cm) Drawing size: 120 ÷ 20 = 6 cm long, 80 ÷ 20 = 4 cm wide

Exercise A – Object Scaling

Calculate the drawing sizes:

1. A car 4 meters long using scale 1:100 Drawing size: ______ cm
2. A door 200 cm tall using scale 1:50 Drawing size: ______ cm
3. A pencil 18 cm long using scale 2:1 (enlarging) Drawing size: ______ cm
4. A book 24 cm long, 18 cm wide using scale 1:6 Drawing size: ______ cm × ______ cm
5. A bicycle 180 cm long using scale 1:30 Drawing size: ______ cm

Exercise B – Real Size from Drawings

Calculate the real sizes:

1. Drawing: 5 cm, Scale: 1:20 Real size: ______ cm
2. Drawing: 8 cm, Scale: 1:100 Real size: ______ cm (______ meters)
3. Drawing: 12 cm, Scale: 1:50 Real size: ______ cm (______ meters)
4. Drawing: 3.5 cm, Scale: 1:40 Real size: ______ cm
5. Drawing: 7 cm, Scale: 1:200 Real size: ______ cm (______ meters)

Scale Drawing of Maps

Understanding Map Scales

Maps use scales to show large areas on small paper.

Common Map Scales:

• 1:10,000 (1 cm = 100 meters)
• 1:50,000 (1 cm = 500 meters)
• 1:100,000 (1 cm = 1 kilometer)

Example: School Map

Scale: 1:500 (1 cm = 5 meters) Distance from gate to library on map: 6 cm Real distance: 6 × 5 = 30 meters

Exercise C – Map Calculations

Using the given scales, find real distances:

1. Map scale: 1:1000, Map distance: 8 cm Real distance: ______ meters
2. Map scale: 1:50,000, Map distance: 4 cm Real distance: ______ meters (______ km)
3. Map scale: 1:25,000, Map distance: 12 cm Real distance: ______ meters (______ km)
4. Map scale: 1:2000, Map distance: 15 cm Real distance: ______ meters
5. Map scale: 1:100,000, Map distance: 5 cm Real distance: ______ kilometers

Exercise D – Creating Map Distances

Calculate map distances from real distances:

1. Real distance: 500 meters, Scale: 1:10,000 Map distance: ______ cm
2. Real distance: 2 kilometers, Scale: 1:50,000 Map distance: ______ cm
3. Real distance: 750 meters, Scale: 1:25,000 Map distance: ______ cm
4. Real distance: 300 meters, Scale: 1:5000 Map distance: ______ cm
5. Real distance: 1.5 kilometers, Scale: 1:75,000 Map distance: ______ cm

Distance Calculations

Finding Scale from Measurements

Formula: Scale = Real distance ÷ Map distance

Example: Real distance: 400 meters Map distance: 8 cm Scale: 400 ÷ 8 = 50 Scale is 1:50

Exercise E – Finding Scales

Calculate the scale ratios:

1. Real: 600 cm, Drawing: 12 cm Scale: 1:______
2. Real: 15 meters, Map: 3 cm Scale: 1:______
3. Real: 2.4 km, Map: 6 cm Scale: 1:______
4. Real: 800 cm, Drawing: 16 cm Scale: 1:______
5. Real: 450 meters, Map: 9 cm Scale: 1:______

Exercise F – Journey Problems

Solve these distance problems:

1. Lagos to Ibadan Route: On a map with scale 1:2,000,000, the distance between Lagos and Ibadan is 6.5 cm. What is the real distance? Answer: ______ km
2. School Compound: The distance from the main gate to the assembly ground is 120 meters. On a scale drawing of 1:600, what would this distance be? Answer: ______ cm
3. Football Field: A football field is 100 meters long. If drawn to scale 1:250, how long would it be on paper? Answer: ______ cm

Real Life Applications

Exercise G – Practical Problems

Solve these real-world problems:

1. House Plan: An architect draws a house plan using scale 1:200. If a room measures 3 cm by 4 cm on the plan, what are the real dimensions? Answer: ______ m × ______ m
2. Garden Design: A garden is 24 meters long and 18 meters wide. If you want to draw it using scale 1:300, what size paper would you need? Answer: ______ cm × ______ cm
3. City Planning: On a city map with scale 1:25,000, a park appears as 2 cm by 1.5 cm. What is the actual area of the park? Answer: ______ m × ______ m = ______ square meters

Exercise H – Map Reading

Use this information to answer questions:

School Map Scale: 1:800

• Library to canteen: 5 cm on map
• Classroom to playground: 8 cm on map
• Main gate to principal’s office: 6 cm on map

Questions:

1. Real distance from library to canteen: ______ meters
2. Real distance from classroom to playground: ______ meters
3. Real distance from main gate to principal’s office: ______ meters
4. If the assembly ground is 120 meters from the library, how far would it be on the map? ______ cm

Exercise I – Problem Solving

Think and solve:

1. Model Making: A toy car manufacturer makes models at 1:64 scale. If a real car is 4.8 meters long, how long should the toy car be? Answer: ______ cm
2. Travel Planning: On a road map, two cities are 15 cm apart. If the map scale is 1:500,000, how far apart are the cities in real life? Answer: ______ km
3. Building Design: A building architect needs to fit a 40-meter tall building on a 20 cm tall drawing paper. What scale should she use? Answer: 1:______

Exercise J – Mixed Problems

Solve these challenging problems:

1. Sports Field: A basketball court is 28 meters long and 15 meters wide. Draw it to scale 1:200 and calculate the paper dimensions needed. Answer: ______ cm × ______ cm
2. Route Planning: The distance between two villages is 12 km. On three different maps, this distance appears as:
   1. Map A: 24 cm
   2. Map B: 12 cm
   3. Map C: 6 cm
3. Find the scale of each map. Map A Scale: 1:______ Map B Scale: 1:______
   Map C Scale: 1:______
4. Comparison: Which is larger on paper: a 500-meter road drawn at 1:10,000 or a 2-kilometer road drawn at 1:50,000? Answer: ______________________

Answer Key

Exercise A:

1. 4 cm
2. 4 cm
3. 36 cm
4. 4 cm × 3 cm
5. 6 cm

Exercise B:

1. 100 cm
2. 800 cm (8 meters)
3. 600 cm (6 meters)
4. 140 cm
5. 1400 cm (14 meters)

Exercise C:

1. 80 meters
2. 2000 meters (2 km)
3. 3000 meters (3 km)
4. 300 meters
5. 5 kilometers

Exercise D:

1. 5 cm
2. 4 cm
3. 3 cm
4. 6 cm
5. 2 cm

Exercise E:

1. 1:50
2. 1:500
3. 1:40,000
4. 1:50
5. 1:5000

Exercise F:

1. 130 km
2. 20 cm
3. 40 cm

Exercise G:

1. 6 m × 8 m
2. 8 cm × 6 cm
3. 500 m × 375 m = 187,500 square meters

Exercise H:

1. 40 meters
2. 64 meters
3. 48 meters
4. 15 cm

Exercise I:

1. 7.5 cm
2. 75 km
3. 1:200

Exercise J:

1. 14 cm × 7.5 cm
2. Map A: 1:50,000, Map B: 1:100,000, Map C: 1:200,000
3. The 500-meter road at 1:10,000 (5 cm vs 4 cm)