This Warm-up prompts students to compare four images. 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. 

Some students might be concerned that rotating the parallelogram will reverse the direction of the arrows. Emphasize that the arrows are markings to indicate the segments are parallel, but not actually part of the parallelogram itself.

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 “line of symmetry” or “diagonal.” Also, press students on unsubstantiated claims.

In this activity, students work together to investigate rotation symmetry and communicate their thinking in a visual display. As you monitor, ask groups if they have found all possible angles of rotation that produce symmetry and to explain how they know these angles apply to all shapes of that type.

This is the first time Math Language Routine 7: Compare and Connect is suggested in this course. In this routine, students are given a problem that can be approached using multiple strategies or representations, and they record their method for all to see. They then compare and identify correspondences across strategies by means of a teacher-led gallery walk with commentary or teacher think-aloud (such as “I notice . . . . I wonder . . . .”). A typical discussion prompt is “What is the same, and what is different?” comparing their own strategy to the others. The purpose of this routine is to allow students to make sense of mathematical strategies and, through constructive conversations, develop awareness of the language used as they compare, contrast, and connect other ways of thinking to their own.

In this activity, students write out a description of a parallelogram’s rotation symmetry. This invites students to apply the definition of rotation.