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).

Ensure students have access to their geometry toolkits, especially centimeter rulers.

Learning Targets

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.

CCSS Standards

Building On

Addressing

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.

    a floor plan with a scale of 1 inch equals 8 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.

    a to-scale map of part of Oklahoma

Print Formatted Materials

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Additional Resources

Google Slides

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PowerPoint Slides

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