This is the first Which Three Go Together? routine in the course. In this routine, students are presented with four items or representations and asked: “Which three go together? Why do they go together?” 

Students are given time to identify a set of three items, explain their rationale, and refine their explanation to be more precise or find additional sets. The reasoning here prompts students to notice common mathematical attributes, look for structure (MP7), and attend to precision (MP6), which deepens their awareness of connections across representations.

Before students begin, consider establishing a small, discreet hand signal that students can display when they have an answer they can support with reasoning. This signal could be a thumbs-up, a certain number of fingers that tells the number of responses they have, or another subtle signal. This is a quick way to see if students have had enough time to think about the problem. It also keeps students from being distracted or rushed by hands being raised around the class.

This Warm-up prompts students to compare four polygons. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.

Invite each group to share one reason why a particular set of three goes together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations, and ensure the reasons given are correct.

During the discussion, ask students to explain the meaning of any terminology they use, such as “regular,” “equilateral,” or “equiangular.” Also, press students on unsubstantiated claims.

In this activity, students construct a square given a side. This is similar to how students constructed a parallel line with two successive perpendicular lines, except they also have to pay attention to marking equal distances along the perpendicular lines.

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

The purpose of this activity is for students to construct a square inscribed in a circle. Just like the construction of the equilateral triangle inscribed in a circle, this construction provides an opportunity to preview rotation symmetry.

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