Lesson 2

Scale of the Solar System

Lesson Narrative

In this optional lesson, students practice finding an unknown value in a proportional relationship while completing part of the modeling cycle to figure out how to create a scale drawing of the solar system (MP4). This lesson serves both as practice with proportional relationships and extension into an interesting context. Students also have the opportunity to work with large numbers and consider what they mean - how vast is space, really?

As students learn why it would be nearly impossible to make a scale drawing of the solar system that fits in a classroom, they review scale drawings and methods for finding unknown values in proportional relationships. Students may come from middle school with many different strategies for representing and finding unknown values in proportional relationships. For example, students may be proficient at finding a scale factor, $$k$$, by comparing the lengths of two known sides. Students may also represent the situation as $$\frac{\text{length 1 in scaled figure}}{\text{length 1 in original figure}} = \frac{\text{length 2 in scaled figure}}{\text{length 2 in original figure}}$$. Students can then multiply or divide strategically to find the value of the unknown length. This lesson gives students a chance to see other students’ strategies and work towards proficiency at finding unknown values in proportional relationships. If students are not confident after the Shrinking the Solar System activity, there is an additional optional activity (Shrinking the Solar System, Take 2) which provides more practice with the same skill and an additional opportunity to grapple with the vastness of space.

When students verify their calculations of how far the Moon would have to be from Earth to fully eclipse the Sun by comparing their calculations to what actually happens during a total solar eclipse they have a chance to reason both abstractly and quantitatively (MP2).

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.

Learning Goals

Teacher Facing

• Calculate measurements of scaled drawings.
• Create and interpret scaled drawings of figures (using words and other representations).

Student Facing

• Let’s dilate figures.

Required Preparation

Prepare 6 inch lengths of string for groups with large planets in Shrinking the Solar System to use as a large-scale compass.

Prepare a circle with a diameter of 2 cm to represent a scale drawing of Earth.

Select a video for the lesson synthesis and be prepared to play it for all to see.

Student Facing

• I can calculate the lengths of parts of a scaled drawing.

Building On

Building Towards

Glossary Entries

• dilation

A dilation with center $$P$$ and positive scale factor $$k$$ takes a point $$A$$ along the ray $$PA$$ to another point whose distance is $$k$$ times farther away from $$P$$ than $$A$$ is.

Triangle $$A'B'C'$$ is the result of applying a dilation with center $$P$$ and scale factor 3 to triangle $$ABC$$.

• scale factor

The factor by which every length in an original figure is increased or decreased when you make a scaled copy. For example, if you draw a copy of a figure in which every length is magnified by 2, then you have a scaled copy with a scale factor of 2.