# Lesson 10

Changing Scales in Scale Drawings

### Lesson Narrative

In the previous lesson, students created multiple scale drawings using different scales. In this lesson, students are given a scale drawing and asked to recreate it at a different scale. Two possible strategies to produce these drawings are:

• Calculating the actual lengths and then using the new scale to find lengths on the new scale drawing.
• Relating the two scales and calculating the lengths for the new scale drawing using corresponding lengths on the given drawing.

In addition, students previously saw that the area of a scaled copy can be found by multiplying the area of the original figure by $$(\text{scale factor})^2$$. In this lesson, they extend this work in two ways:

• They compare areas of scale drawings of the same object with different scales.
• They examine how much area, on the actual object, is represented by 1 square centimeter on the scale drawing. For example, if the scale is 1 cm to 50 m, then 1 cm2 represents $$50 \boldcdot 50$$, or 2,500 m2.

Throughout this lesson, students observe and explain structure (MP7), both when they reproduce a scale drawing at a different scale and when they study how the area of a scale drawing depends on the scale.

### Learning Goals

Teacher Facing

• Determine how much actual area is represented by one square unit in a scale drawing.
• Generalize (orally) that as the actual distance represented by one unit on the drawing increases, the size of the scale drawing decreases.
• Reproduce a scale drawing at a different scale and explain (orally) the solution method.

### Student Facing

Let’s explore different scale drawings of the same actual thing.

### Required Preparation

Print and cut the scales for the Same Plot, Different Drawings activity from the blackline master (1 set of scales per group of 5–6 students).

### Student Facing

• Given a scale drawing, I can create another scale drawing that shows the same thing at a different scale.
• I can use a scale drawing to find actual areas.

Building On

Building Towards

### Glossary Entries

• scale

A scale tells how the measurements in a scale drawing represent the actual measurements of the object.

For example, the scale on this floor plan tells us that 1 inch on the drawing represents 8 feet in the actual room. This means that 2 inches would represent 16 feet, and $$\frac12$$ inch would represent 4 feet.

• scale drawing

A scale drawing represents an actual place or object. All the measurements in the drawing correspond to the measurements of the actual object by the same scale.