In this activity, students are invited to make a choice without explicit instructions on how to divide the map. Monitor for students who use a perpendicular bisector and students who take the context into consideration.

Students will examine a simplified version of this diagram in the next activity and then have the opportunity to interact with an even more complex version in the optional activity “Now Who Is Closest?”

Invite students to share their regions and their reasoning. Acknowledge that there isn’t enough information to make a final decision, so there is no one right answer. Explain that the shaded areas on the map represent large buildings. 

Math Community

After the Warm-up, display the Math Community Chart with the “Doing Math” actions added to the teacher section for all to see. Give students 1 minute to review. Then share 2–3 key points from the teacher section and your reasoning for adding them. For example, 

• If “questioning vs. telling,” a shared reason could focus on your belief that students are capable mathematical thinkers and your desire to understand how students are making meaning of the mathematics.

• If “listening,” a shared reason could be that sometimes you want to sit quietly with a group just to listen and hear student thinking and not because you think the group needs help or is off-track.

After sharing, tell students that they will have the opportunity to suggest additions to the teacher section during the Cool-down.

In this activity, students are building skills that will help them in mathematical modeling (MP4). The method of modeling stores in a city with points in a square is provided, but students need to realize they can use perpendicular bisectors to determine which stores should take responsibility for which parts of the city. Students also need to decide how to allocate the 100 employees. It is expected that students who do not use digital tools to measure areas will approximate areas using decomposition techniques and estimation. Students working on paper will likely not have time for the fourth store analysis. These students do not need to see this question to participate in the discussion.

This activity works best when each student has access to the GeoGebra Geometry Tool from Math Tools (https://im612.org/geometry-tool) or similar dynamic geometry software because it would take too long to do otherwise. If students don't have individual access, projecting the GeoGebra Geometry Tool would be helpful during the Activity Synthesis.

This is the first time Math Language Routine 6: Three Reads is suggested in this course. In this routine, students are supported in reading a mathematical text, situation, or word problem three times, each with a particular focus. During the first read, students focus on comprehending the situation. During the second read, students identify quantities. During the third read, the final prompt is revealed and students brainstorm possible starting points for answering the question. The intended question is withheld until the third read so students can make sense of the whole context before rushing down a solution path. The purpose of this routine is to support students’ reading comprehension as they make sense of mathematical situations and information through conversation with a partner.

In this optional activity, students continue to build skills that will help them in mathematical modeling (MP4). Students can either continue studying the same map provided or use a map of their choosing. Instead of creating regions for store deliveries, students could study a map of school districts, grocery stores, or polling places.

Suggest students use different colors or markings to indicate the regions for the first and last parts of the activity. 

Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).

This optional activity builds on the “Who Is Closest?” activity by employing the same technique of finding regions that are closest to certain points and decorating those regions to make new and interesting patterns.

Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).