Students will solve proportions to find lengths of sides and find angle measures in similar polygons.

Students move about the room, seeking their partner in similarity and calculating missing values.

5 minutes

Students were given three_Similar_Figures problems for homework, intended to reinforce the learning of the day before and to set up this lesson. I quickly survey the class to see if there were any issues with any of these problems and I answer any questions. I then explain how the today’s lesson will work:

Each student will reach into a small paper bag or basket in which I have placed a set of Similar Figures Cards. Once each student has a card, they will move about the room, taking an Answer Sheet with them, seeking the person who has the card that matches their own card. As soon as a match is found students will park at a pair of empty desks, where they are to copy **both** their diagrams onto their answer sheets, give the correct name for their polygons, and solve for the values of the unknown measurements (x, y, and z).

**Resource Note**: My pack of Similar Figures Cards contains 14 pairs of similar triangles or 28 cards. Teachers with more than 28 students will need to create a few more pairs.

35 minutes

The students begin the exercise, each student drawing a card. The question I am most frequently asked is “Do I have to write down the equations?” and I always reply, “Yes!” This helps immensely when I grade these exercises, so that I can see where students are making their mistakes. I think it is also an important aspect of **MP6**.

While the students are setting up and solving their equations, I circulate throughout the room, picking up the Similar Figures Cards and answering questions as they arise. By picking up the cards while students work, I am ready for the next round as soon as a round is completed. As the rounds progress, the students typically become quicker and more adept at solving the problems, so that the time between rounds decreases. I recommend completing at least four rounds. With some students, four rounds is typically sufficient. After four turns, I sense that everyone is comfortable with the concepts and ready to move on. With some students, more than four rounds is beneficial (**MP8**)

In the case of an uneven number of students, one student will be without a partner. I give that student the matching card and he or she works alone for that round. I check in periodically to make sure it’s going okay for that student, and this has never presented a problem.

I collect the students' Answer Sheets at the end of the activity. During the evening I correct the studemts work, and enter a grade for the activity. This helps to inform my teaching for the next day, cluing me into any problems they might be having as a group or as individuals. My experience has been, however, that it’s easy grading; very few mistakes are made and the students are ready to move on after this activity.

10 minutes

With about ten minutes to go in the lesson, I give the students a worksheet containing algebraic problems, intended to reinforce the algebra skills learned in their previous course. I want my students to gain some practice on skills they will use throughout this unit. I also want to change the pace a little bit during the day’s lesson.

The algebraic concepts on which the worksheet focuses include simplifying radicals, multiplying binomials, and factoring. These skills are then applied to solving proportions. At this point in time, I include only trinomials for which the coefficient of x^{2} is 1.

Some students have difficulty with these concepts and require considerable help. At the same time, however, I have found that others fly through the work, enjoy working at their own pace, and seem to derive pleasure in their ability to recall and apply these concepts. It is helpful for me to observe who is performing at each level.

Any work that is not completed during the class period is homework.