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).

The purpose of discussion is to emphasize that the line of reflection is the perpendicular bisector of segments that connect points on the original figure to points on the image. 

Display the conjecture that the set of points that are the same distance from two given points is the perpendicular bisector of the segment connecting those two points. Ask, “What should we expect to see if we made segments connecting points to their images?” (We should expect to see that the line of reflection is the perpendicular bisector of all segments that connect points to images.) Ask students to verify this experimentally by drawing segments that connect points to images from their data card and the line of reflection.

Here are some additional questions for discussion to choose based on time and students’ understanding from the previous lesson:

• “What kinds of questions were the most useful to ask?” (What is the image of this point? What points do not move?)
• “Were there any questions you weren't sure how to answer?” (What is the line of reflection? I didn't have that exact information, but I could figure it out from the points that didn't move.) 
• “How do you know if a point is on the line of reflection?” (Reflections leave points on the line of reflection fixed where they are.)
• “What do you notice about points and their images?” (The original point and image are on opposite sides of the line the same distance apart. If one point is taken to a second point, then the second point is also taken to the first point.)
• “How can you test whether a point and its image are the same distance away from the line of reflection?” (If we construct a circle centered at any point on the line of reflection that goes through the original point, it should also go through the image.)

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).

Select previously identified students to share their responses.

Highlight that reversing the steps in a sequence of transformations sometimes results in the same transformation, and sometimes it results in a different transformation.

Reversing the order of a sequence means using the same steps, but step 2 becomes step 1. For example, 1) reflect across line , then 2) translate left 2 units would become 1) translate left 2 units, then 2) reflect across line .