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Lesson plan

Lesson 12: Units in Scale Drawings

teaches Common Core State Standards MP8 http://corestandards.org/Math/Practice/MP8
teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards 7.G.A.1 http://corestandards.org/Math/Content/7/G/A/1

Lesson 12: Units in Scale Drawings

In previous lessons, students learned to express scales with or without units that can be the same or different. In this lesson, they analyze various scales and find that sometimes it is helpful to rewrite scales with units as scales without units in order to compare them. They see that equivalent scales relate scaled and actual measurements by the same scale factor, even though the scales may be expressed differently. For example, the scale 1 inch to 2.5 feet is equivalent to the scale 5 m to 150 m, because they are both at a scale of 1 to 30.

This lesson is also the culmination of students' work on scaling and area. Students have seen many examples of the relationship between scaled area and actual area, and now they must use this realization to find the area of an irregularly-shaped pool (MP7, MP8).

Here is some information about equal lengths that students may want to refer to during these activities.

Customary Units

  • 1 foot (ft) = 12 inches (in)
  • 1 yard (yd) = 36 inches
  • 1 yard = 3 feet
  • 1 mile = 5,280 feet

Metric Units

  • 1 meter (m) = 1,000 millimeters (mm)
  • 1 meter = 100 centimeters
  • 1 kilometer (km) = 1,000 meters

Equal Lengths in Different Systems

  • 1 inch = 2.54 centimeters
  • 1 foot \(\approx\) 0.30 meter
  • 1 mile \(\approx\) 1.61 kilometers
  • 1 centimeter \(\approx\) 0.39 inch
  • 1 meter \(\approx\) 39.37 inches
  • 1 kilometer \(\approx\) 0.62 mile

Lesson overview

  • 12.1 Warm-up: Centimeters in a Mile (5 minutes)
  • 12.2 Optional Activity: Card Sort: Scales (15 minutes)
  • 12.3 Activity: The World’s Largest Flag (15 minutes)
  • 12.4 Optional Activity: Pondering Pools (10 minutes)
    • Includes "Are you Ready for More?" extension problem
  • Lesson Synthesis
  • 12.5 Cool-down: Drawing the Backyard (5 minutes)

Learning goals:

  • Comprehend that the phrase “equivalent scales” refers to different scales that relate scaled and actual measurements by the same scale factor.
  • Generate a scale without units that is equivalent to a given scale with units, or vice versa.
  • Justify (orally and in writing) that scales are equivalent, including scales with and without units.

Learning goals (student facing):

  • Let's use different scales to describe the same drawing.

Learning targets (student facing):

  • I can write scales with units as scales without units.
  • I can tell whether two scales are equivalent.

Required materials:

  • copies of blackline master
  • metric and customary unit conversion charts
  • pre-printed slips, cut from copies of the blackline master
  • geometry toolkits

Required preparation:

  • Note: This lesson contains optional activities. Decide which activities you will do before preparing the materials!
    • For the Card Sort: Scales activity, print and cut the slips from the blackline master, so that each group of 3–4 students gets one complete set. If possible, copy each complete set on a different color of paper, so that a stray slip can quickly be put back.
    • For the Pondering Pools activity, prepare one copy of the blackline master for every two students.
  • Ensure students have access to geometry toolkits.
  • It is also recommended that a conversion chart for metric and customary units of length be provided while students are working on the activities in this lesson.


  • Access the complete Grade 7 glossary. 


  • This lesson builds on the standard: CCSS.6.RP.A.3.dMS.6.RP.3dMO.6.RP.A.3d






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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