In this activity, students solve for an unknown angle measure in a multi-step problem but do not initially have enough information to do so. To bridge the gap, they need to exchange questions and ideas.

The Information Gap structure requires students to make sense of a problems by determining what information is necessary, and then to ask for the information they need to solve the problem. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and to ask increasingly more precise questions until they get the information they need (MP6).

After students have completed their work, share the correct answers, and ask students to discuss the process of solving the problems. Here are some questions for discussion:

• “Did you need all of the information from the data card?” (No, it is possible to calculate the angle measure without using all of the information from the data card.)
• “How was your approach to the first card different from your approach to the second card?”

Highlight for students that writing and solving equations is an efficient strategy to show their reasoning about multi-step angle problems.

Math Community
Invite 2–3 students to share the norm they chose and how it supported the work of the group or a realization they had about a norm that would have worked better in this situation. Provide these sentence frames to help students organize their thoughts in a clear, precise way:

• “I picked the norm ‘.’ It really helped me/my group because .”
• “I picked the norm ‘.’ During the activity, I realized the norm ‘’ would be a better focus because .”

The purpose of this activity is for students to match relationships between angles in a figure with equations that can represent those relationships. This prepares students for writing and solving equations that represent relationships between angles in the next lesson. As students explain their reasoning, they construct logical arguments about the structure of the equation and the diagram (MP3).

The goal of this discussion is for students to articulate the angle relationships that they noticed in each figure and equation. Display the figures for all to see. Select previously identified students to share their explanations for each figure. If not mentioned in students’ explanations, be sure that students see the vertical, supplementary, straight, and right angle relationships in the figures.