Lesson plan

# Lesson 1: What are Scaled Copies?

teaches Alabama State Standards 7-17.
teaches Arizona State Standards 7.G.A.1
teaches Common Core State Standards MP1 http://corestandards.org/Math/Practice/MP1
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
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.
teaches Pennsylvania State Standards CC.2.3.7.A.2.

# Lesson 1: What are Scaled Copies?

This lesson introduces students to the idea of a scaled copy of a picture or a figure. Students learn to distinguish scaled copies from those that are not—first informally, and later, with increasing precision. They may start by saying that scaled copies have the same shape as the original figure, or that they do not appear to be distorted in any way, though they may have a different size. Next, they notice that the lengths of segments in a scaled copy vary from the lengths in the original figure in a uniform way. For instance, if a segment in a scaled copy is half the length of its counterpart in the original, then all other segments in the copy are also half the length of their original counterparts. Students work toward articulating the characteristics of scaled copies quantitatively (e.g., “all the segments are twice as long,” “all the lengths have shrunk by one third,” or “all the segments are one-fourth the size of the segments in the original”), articulating the relationships carefully (MP6) along the way.

The lesson is designed to be accessible to all students regardless of prior knowledge, and to encourage students to make sense of problems and persevere in solving them (MP1) from the very beginning of the course.

Lesson overview

• 1.1 Warm-up: Printing Portraits (10 minutes)
• There is a digital applet in this activity.
• 1.2 Activity: Scaling F (10 minutes)
• There is a digital applet in this activity.
• 1.3 Activity: Pairs of Scaled Polygons (15 minutes)
• Includes "Are you Ready for More?" extension problem
• There is a digital applet in this activity.
• Lesson Synthesis
• 1.4 Cool-down: Scaling L (5 minutes)

Learning goals:

• Describe (orally) characteristics of scaled and non-scaled copies.
• Identify scaled copies of a figure and justify (orally and in writing) that the copy is a scaled copy.

Learning goals (student facing):

• Let’s explore scaled copies.

Learning targets (student facing):

• I can describe some characteristics of a scaled copy.
• I can tell whether or not a figure is a scaled copy of another figure.

Required materials:

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

Required preparation:

• You will need the Pairs of Scaled Polygons blackline master for this lesson. (See Additional Materials section of this lesson)
• Print and cut slips A–J for the Pairs of Scaled Polygons activity.
• Prepare 1 copy for every 2 students.
• If possible, copy each complete set on a different color of paper, so that a stray slip can quickly be put back.

Glossary:

• scaled copy - A scaled copy is a copy of a figure where every length in the original figure is multiplied by the same number. For example, triangle $$DEF$$ is a scaled copy of triangle $$ABC$$. Each side length on triangle $$ABC$$  was multiplied by 1.5 to get the corresponding side length on triangle $$DEF$$.

• 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/.