 Lesson plan

# Lesson 10: Changing Scales in Scale Drawings

teaches Alabama State Standards 7-17.
teaches Arizona State Standards 7.G.A.1
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
teaches Georgia State Standards MGSE7.G.1.
teaches Kansas State Standards 7.G.1.
teaches Minnesota State Standards 7.3.2.3.
teaches Minnesota State Standards 7.3.2.2.
teaches Minnesota State Standards 7.3.2.1.
teaches New York State Standards NY-7.G.1.
teaches Ohio State Standards 7.G.1.b.
teaches Ohio State Standards 7.G.1.a.
teaches Ohio State Standards 7.G.1.
teaches Pennsylvania State Standards CC.2.3.7.A.2.
teaches Pennsylvania State Standards CC.2.3.7.A.1.

# Lesson 10: Changing Scales in Scale Drawings

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 $$(\mathrm{scale}\;\mathrm{factor})^2$$. 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 cm$$^2$$ represents $$50\cdot50$$, or 2,500 m$$^2$$.

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.

Lesson overview

• 10.1 Warm-up: Appropriate Measurements (5 minutes)
• 10.2 Activity: Same Plot, Different Drawings (15 minutes)
• Includes "Are you Ready for More?" extension problem
• 10.3 Activity: A New Drawing of the Playground (15 minutes)
• Lesson Synthesis
• 10.4 Cool-down: Window Frame (5 minutes)

Learning goals:

• 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.

Learning goals (student facing):

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

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.

Required materials:

• pre-printed slips, cut from copies of the blackline master
• geometry toolkits

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.

Glossary:

• Access the complete Grade 7 glossary.

Standards

• This lesson builds on the standards: CCSS.2.MD.ACCSS.6.G.A.1MS.6.G.1MO.6.GM.A.1MO.2.GM.B.4
• This lesson builds towards the standard: CCSS.7.G.B.6MS.7.G.6MO.7.GM.B.6aCCSS.7.RP.AMO.7.RP.A.3CCSS.7.RP.A.3MS.7.RP.3MS.7.RP

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/.