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Lesson plan

Lesson 11: Scales without Units

teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards MP6 http://corestandards.org/Math/Practice/MP6
teaches Common Core State Standards 7.G.A.1 http://corestandards.org/Math/Content/7/G/A/1

Lesson 11: Scales without Units

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).

Lesson overview

  • 11.1 Warm-up: One to One Hundred (5 minutes)
  • 11.2 Activity: Apollo Lunar Module (15 minutes)
    • Includes "Are you Ready for More?" extension problem
  • 11.3 Activity: Same Drawing, Different Scales (15 minutes)
  • Lesson Synthesis
  • 11.4 Cool-down: Scaled Courtyard Drawings (5 minutes)

Learning goals:

  • 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).

Learning goals (student facing):

  • Let’s explore a different way to express scales.

Learning targets (student facing):

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

Required materials:

  • copies of blackline master
  • rulers

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.


  • Access the complete Grade 7 glossary.






IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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