# Lesson 11

Scales without Units

### Lesson Narrative

In previous lessons, students worked with scales that associated two distinct measurements—one for the distance on a drawing and one for actual distance. The units used in the two measurements are often different (centimeter and meter, inch and foot, etc.). In this lesson, students see that a scale can be expressed without units. For example, consider the scale 1 to 60. This means that every unit of length on the scale drawing represents an actual length that is 60 times its size, whatever the unit may be (inches, centimeters, etc.).

Expressing the scale as 1 to 60 highlights the scale factor relating the scale drawing to the actual object. Each measurement on the scale drawing is multiplied by 60 to find the corresponding measurement on the actual object. This relates closely to the scaled copies that were examined earlier in the unit in which each copy was related to the original by a scale factor. Students gain a better understanding of both scaled copies and scale drawings as they understanding the common underlying structure (MP7).

### Learning Goals

Teacher Facing

• Explain (orally and in writing) how to use scales without units to determine scaled or actual distances.
• Interpret scales expressed without units, e.g., “1 to 50,” (in spoken and written language).

### Student Facing

Let’s explore a different way to express scales.

### Required Preparation

You will need the Apollo Lunar Module blackline master for this lesson. Prepare one copy per student.

Ensure students have access to geometry toolkits, especially rulers and graph paper.

### Student Facing

• I can explain the meaning of scales expressed without units.
• I can use scales without units to find scaled distances or actual distances.

### 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.