In this unit, students study scaled copies of plane figures and scale drawings of real-world objects. Students learn that all lengths in a scaled copy are the result of multiplying the original lengths by a scale factor. Also, the angle measures in a scaled copy are the same as in the original figure.

This work builds on what students learned in previous grades about measuring lengths, areas, and angles. This unit provides a geometric context to preview the type of reasoning that students will use with proportional relationships later in grade 7. It also lays the foundation for grade 8 work on dilations and similarity.

Students begin the unit by looking at copies of a picture and describing what differentiates scaled and non-scaled copies. They calculate scale factors and draw scaled copies of figures. Note that the study of scaled copies is limited to pairs of figures that have the same orientation — in other words, they are not rotations or reflections of each other. In grade 8, students will extend their knowledge of scaled copies when they study translations, rotations, reflections, and dilations.

Next, students study scale drawings. They see that the principles and strategies that they used to reason about scaled copies of figures can also be used with scale drawings. They use scale drawings to calculate actual lengths and areas, and they create scale drawings.

A note about the geometry toolkit:

In the unit, several lesson plans suggest that each student have access to a geometry toolkit. Each toolkit contains tracing paper, graph paper, colored pencils, scissors, a centimeter ruler, a protractor (clear protractors with no holes that show radial lines are recommended), and an index card to use as a straightedge or to mark right angles. Providing students with these toolkits gives opportunities for students to develop abilities to select appropriate tools and use them strategically to solve problems (MP5). Note that even students in a digitally enhanced classroom should have access to such tools. Applets and simulations should be considered additions to their toolkits, not replacements for physical tools.

Progression of Disciplinary Language

In this unit, teachers can anticipate students using language for mathematical purposes, such as representing, generalizing, and explaining. Throughout the unit, students will benefit from routines designed to grow robust disciplinary language, both for their own sense-making and for building shared understanding with peers. Teachers can formatively assess how students are using language in these ways, particularly when students are using language to:

Represent

• A scaled copy for a given scale factor (Lessons 3 and 5).
• Distances using different scales (Lesson 11).
• Relevant features of a classroom with a scale drawing (Lesson 13).

Generalize

• About corresponding distances and angles in scaled copies (Lesson 4).
• About scale factors greater than, less than, and equal to 1 (Lesson 5).
• About scale factors and area (Lessons 6 and 10).
• About scale factors with and without units (Lesson 12).

Explain

• How to use scale drawings to find actual distances (Lessons 7 and 11).
• How to use scale drawings to find actual distances, speed, and elapsed time (Lesson 8).
• How to use scale drawings to find actual areas (Lesson 12).

In addition, students are expected to describe features of scaled copies, justify and critique reasoning about scaled copies, and compare how different scales affect drawings. Over the course of the unit, teachers can support students’ mathematical understandings by amplifying (not simplifying) language used for all of these purposes as students demonstrate and develop ideas.

The table shows lessons where new terminology is first introduced in this course, including when students are expected to understand the word or phrase receptively and when students are expected to produce the word or phrase in their own speaking or writing. Terms that appear bolded are in the Glossary. Teachers should continue to support students’ use of a new term in the lessons that follow where it was first introduced.

lesson	new terminology
	receptive	productive
7.1.1	scaled copy original polygon
7.1.2	corresponding scale factor figure segment
7.1.4	quadrilateral measurement distance	corresponding scale factor original
7.1.5	reciprocal
7.1.6	area one-dimensional two-dimensional	squared
7.1.7	scale drawing scale represent actual three-dimensional	scaled copy
7.1.8	estimate travel constant speed	scale
7.1.9	floor plan
7.1.10	appropriate dimension	actual  represent
7.1.11	scale without units ___ to ___	scale drawing
7.1.12	equivalent scales	___ to ___