In this lesson, students build on their experiences with perpendicular bisectors to answer questions about allocating resources in a realworld situation (MP4). To complete more steps in the mathematical modeling cycle, use the optional activity Now Who Is Closest? Then students study a tessellation (an arrangement of figures that cover the entire plane), create a Voronoi diagram by applying perpendicular bisectors, and conjecture that the Voronoi diagram of a tessellation is also a tessellation.
Some of the activities in this lesson work best when each student has access to GeoGebra Geometry from Math Tools, because students are using perpendicular bisectors to determine which regions of a map are closest to certain points. In Who Is Closest?, they do this with 3 and 4 points, but doing it with more in Now Who is Closest? will require help from technology.
Lesson overview
 9.1 Warmup: Notice and Wonder: Dots in a Square (5 minutes)

9.2 Activity: Who Is Closest? (15 minutes)
 Digital applet in this activity
 Includes "Are you Ready for More?" extension problem

9.3 Optional Activity: Now Who is Closest? (20 minutes)
 Digital applet in this activity

9.4 Activity: Another Layer (15 minutes)
 Digital applet in this activity
 Lesson Synthesis
 9.4 Cooldown: Write a Letter (5 minutes)
Learning goals:
 Choose geometric methods to solve design problems.
 Construct perpendicular bisectors and explain (in writing) how they are used to solve problems.
Learning goals (student facing):
 Let’s use perpendicular bisectors.
Learning targets (student facing):
 I can construct perpendicular bisectors to help solve problems.
 I can use my geometry knowledge to solve problems.
Required materials:
 Copies of blackline master
 Dynamic geometry software
 Geometry toolkits
Required preparation:
 Acquire computers or tablets that can run GeoGebra Geometry from Math Tools, with one for every 2–3 students.
 The digital version is recommended for all classes over the paper and pencil version.
 Ensure that students have at least 4 colors in their toolkits if they will be doing the paper and pencil version of Who is Closest?.
Glossary:

tessellation  An arrangement of figures that covers the entire plane without gaps or overlaps.
 Access the complete Geometry Course glossary.
Standards:
 This lesson builds on the standard: CCSS.HSGCO.D.12MS.GCO.12MO.G.CO.D.11
 This lesson builds towards the standard: CCSS.HSGMG.A.3MS.GMG.3MO.G.MG.A.3
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