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 reflections. 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 Info 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 the image of triangle ?"
• 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:
  • The image of is and the image of is .
  • The image of is .
  • The image of is .
  • The image of  is  and the image of  is . 
  • The image of  is  and the image of  is . 
• 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. (The image of triangle when reflected across line is triangle .)

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

Math Community

After the Warm-up, display the revised Math Community Chart created from student responses in Exercise 3. Tell students that today they are going to monitor for two things:

• “Doing Math” actions from the chart that they see or hear happening.
• “Doing Math” actions that they see or hear that they think should be added to the chart.

Provide sticky notes for students to record what they see and hear during the lesson.

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

This activity gives students an opportunity to determine and request the information needed to define a reflection.

The Information Gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information, they need to solve it. 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).

In this optional activity students observe that the order of the transformations in a sequence of transformations can have an effect on the image. This activity can serve as additional practice for students who need it. It is also an opportunity for investigation for students who have moved through the previous activities quickly.

Monitor for students who define a sequence that works even when the order is reversed to compare during the discussion to students whose sequences don’t work when the order is reversed.

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