This is the first Math Talk activity in the course. See the Launch for extended instructions for facilitating this activity successfully.

The purpose of this Math Talk is to review angle pairs in figures made up of one to three triangles to prepare students for figures made up of several triangles. It encourages students to think about complementary, supplementary, and vertical angle pairs, as well as the Triangle Angle Sum Theorem, and to rely on what they know about these angle relationships to mentally solve problems. The understanding elicited here will be helpful later in the lesson when students find unknown angles in more complex figures.

To find unknown angles, students need to look for and make use of structure (MP7).

The goal of this discussion is to review students’ strategies for finding unknown angles when they encounter common angle pairs and special triangles. To involve more students in the conversation, consider asking:

• “Who can restate ’s reasoning in a different way?”
• “Did anyone use the same strategy but would explain it differently?”
• “Did anyone solve the problem in a different way?”
• “Does anyone want to add on to ’s strategy?”
• “Do you agree or disagree? Why?”
• “What connections to previous problems do you see?”

If not brought up in students’ explanations, discuss with students the meaning of “complementary,” “supplementary,” “vertical angles,” and “isosceles triangles.” Remind students what the tick marks mean on the legs of the isosceles triangle and that the base angles in an isosceles triangle are congruent.

Math Community
After the Warm-up, display the class Math Community Chart for all to see and explain that the listed “Doing Math” actions come from the sticky notes students wrote in the first exercise. Give students 1 minute to review the chart. Then invite students to identify something on the chart they agree with and hope for the class or something they feel is missing from the chart and would like to add. Record any additions on the chart. Tell students that the chart will continue to grow and that they can suggest other additions that they think of throughout today’s lesson during the Cool-down.

In this activity, students practice using the idea that, in a triangle, larger angles are opposite longer sides. Students also critique a statement or response that is intentionally unclear, incorrect, or incomplete and improve it by clarifying meaning, correcting errors, and adding details (MP3).

This is the first time Math Language Routine 3: Critique, Correct, Clarify is suggested in this course. In this routine, students are given a “first draft” statement or response to a question that is intentionally unclear, incorrect, or incomplete. Students analyze and improve the written work by first identifying what parts of the writing need clarification, correction, or details, and then writing a second draft (individually or with a partner). Finally, the teacher scribes as a selected second draft is read aloud by its author(s), and the whole class is invited to help edit this “third draft” by clarifying meaning and adding details to make the writing as convincing as possible to everyone in the room. Typical prompts are: “Is anything unclear?” and “Are there any reasoning errors?” The purpose of this routine is to engage students in analyzing mathematical writing and reasoning that is not their own, and to solidify their knowledge and use of language.

Students look for and make use of structure (MP7) in a figure made up of several triangles to find unknown angles. Then, using what they know about the relationship between sides and angles in a triangle, students find the longest and shortest sides in each triangle. Students will have the opportunity to discuss their work with a partner. Monitor for students that change their answers after discussing with a partner.