Teacher Guide: Scale Drawings

@ Learning Objective 5-10 min lesson

Students will: Understand and apply scale factors to find missing dimensions, solve real-world problems involving scale drawings using proportions, and create scale drawings with given scale factors.

Why this matters for FAST: Scale drawings connect proportional reasoning to geometry. Students must interpret scales on maps, blueprints, and models, then use proportional thinking to find actual or scaled measurements.

% Materials Needed

Whiteboard/projector
Student Concept Worksheet
Rulers (inch and cm)
Sample maps
Graph paper
Blueprint examples

! Common Misconceptions to Address

Misconception #1: Confusing Scale Direction

Students multiply when they should divide (or vice versa) when converting between scale and actual dimensions.

How to Address:

"Scale to actual: multiply by scale factor. Actual to scale: divide by scale factor. Ask yourself: should my answer be bigger or smaller? If the scale is 1 inch = 10 feet, actual measurements will be BIGGER numbers than the drawing."

Misconception #2: Adding Instead of Multiplying

Students think if scale is 1:5, they should add 5 to each measurement instead of multiplying by 5.

How to Address:

"Scale factor is a MULTIPLIER, not an addend! If the scale is 1:5, everything in real life is 5 TIMES bigger than the drawing. A 2-inch drawing represents 2 x 5 = 10 inches, NOT 2 + 5 = 7 inches."

Misconception #3: Ignoring Units

Students forget to convert units when the scale uses different units (e.g., 1 cm = 5 km).

How to Address:

"Always check the units! If your scale says '1 inch = 20 miles,' your answer will be in miles, not inches. Write out your units to make sure they match what the question asks for."

$ Lesson Steps

1

Activate Prior Knowledge (1 min)

Show a simple map. Ask: "If 1 inch on this map equals 10 miles in real life, how far apart are two cities that are 3 inches apart on the map?" Connect to proportional reasoning.

2

Introduce Scale Factor (2 min)

SAY THIS:

"A scale factor tells us how many times bigger or smaller something is. If a model car has a scale of 1:24, the real car is 24 times bigger than the model. We use proportions to find missing measurements."

Understanding Scale

Scale: 1 inch = 5 feet

This means: 1 inch on drawing = 5 feet in real life

Scale factor = 5 (or 1:5 or 1/5)

Drawing measurement x Scale factor = Actual measurement

3

Finding Actual Dimensions (2 min)

Example: Scale Drawing to Actual

A room on a blueprint is 4 inches long. Scale: 1 in = 3 ft

Method 1: Multiply

4 inches x 3 = 12 feet (actual length)

Method 2: Proportion

1 in / 3 ft = 4 in / x ft

1 x x = 3 x 4

x = 12 feet

4

Finding Scale Dimensions (2 min)

Example: Actual to Scale Drawing

A building is 150 feet tall. Draw it with scale: 1 cm = 25 ft

150 / 25 = 6 cm on the drawing

Check: 6 cm x 25 ft/cm = 150 ft

SAY THIS:

"To go from actual to scale, divide by the scale factor. To go from scale to actual, multiply by the scale factor. Always ask: should my answer be bigger or smaller?"

5

Guided Practice (2-3 min)

Work through these together:

A map scale is 1 inch = 50 miles. Two cities are 3.5 inches apart. Actual distance? (3.5 x 50 = 175 miles)
A model airplane has scale 1:72. The real plane is 36 feet long. Model length? (36 / 72 = 0.5 feet = 6 inches)
A blueprint shows a room 5 inches wide. Scale: 1/4 inch = 1 foot. Actual width? (5 / 0.25 = 20 feet)

? Check for Understanding

Quick Exit Ticket (Ask the whole class):

"A map has a scale of 1 cm = 20 km. If two towns are 4.5 cm apart on the map, what is the actual distance between them?"

A) 4.5 km B) 24.5 km C) 80 km D) 90 km

Correct answer: D) 90 km. Multiply: 4.5 cm x 20 km/cm = 90 km.

& IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Scale drawings: find the scale factor Scale drawings: find the actual length Scale drawings: find the scaled length Scale drawings: word problems Perimeter and area of scale drawings

^ Differentiation & Extension

For struggling students: Use concrete manipulatives and grid paper. Start with simple whole-number scales before fractions. Use visual models showing the relationship between scaled and actual objects.

For advanced students: Challenge with finding area of scaled figures (remember: area changes by scale factor SQUARED!). Have them create their own scale drawings of their classroom or home.

For home: Send Parent Activity sheet. Families can explore map reading, model kits, and room design projects.