The purpose of this Warm-up is to prepare students for the Information Gap activity that follows. First, students are given a problem with incomplete information. They are prompted to brainstorm what they need to know to solve a problem that involves a quilt pattern made up of triangles. Next, they practice asking for information, explaining the rationale for their request, and persevering if their initial questions are unproductive (MP1). Once students have enough information, they solve the problem.

Tell students that the problem is a part of an Information Gap routine. In the routine, one person has a problem with incomplete information, and another person has data that can help with solving it. Explain that it is the job of the person with the problem to think about what is needed to answer the question, and then request it from the person with information.

Tell students they will try to solve the problem this way as a class to learn the routine. In this round, the students have the problem, and the teacher has the information needed to solve the problem.

• Ask students, “What specific information do you need to find out which side is longer?”
• Select students to ask their questions. Encourage students to use the format of “Can you tell me ?” Respond to each question with, “Why do you need to know ?”
• Once students justify their question, only answer questions if they can be answered using these data:
  • Quadrilateral is a square.
  • Angle is 60 degrees.
  • Angle is 30 degrees.
  • Angle is 80 degrees.
  • Angle is 40 degrees.
  • Angle is 10 degrees.
• If students ask for information that is not on the data card, respond with, “I don’t have that information.”

When students think they have enough information, give them 2 minutes to solve the problem. (Side is longer than side because angle is 80 degrees, which is greater than 60-degree angle .)

Tell students they will work in small groups and use the routine to solve problems in the next activity.

This is the first Information Gap activity in the course. In this activity, students represent sequences in different ways but do not initially have enough information to do so. To bridge the gap, they need to exchange questions and ideas.

The Information Gap routine facilitates meaningful interactions by positioning some students as holders of information that is needed by other students, thereby creating a need for communication. This routine supports language development by providing students with opportunities to ask for and share information, and to justify their reasoning within conversation. 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 ask increasingly more precise questions until they get the information they need (MP6).

Students may wonder why they cannot just measure the lengths of the sides to determine which is longest. Remind students that the purpose of this activity is to practice using information about complementary and supplementary angles, as well as the Triangle Angle Sum Theorem, to find unknown angles in a figure. Another goal is to practice communicating and persevering to solve a problem with a limited amount of information.