Exploring Reflections 1

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Objective

SWBAT understand reflections, their properties, and the symmetry that results.

Big Idea

Students explore reflections through a series of drawing activities and measuring tasks.

Access Prior Knowledge

15 minutes

To begin this lesson I pair up my students, give each pair a Reflections APK slip, and ask that they answer each question in parts I and II.  Most 8th graders should have have worked with symmetry before. Yet I allow them to use any resource they wish to answer the questions. I encourage the use of their cell phones or ipads, that when turned off, can be used as mirrors, placed along the "reflecting" line, of the figures in part II. This concrete demonstration can help learners see if the given line is a reflecting line (or not) for a figure.

As students work I walk around assessing their work. Some may want to use their phones for the letters in Part I, but find them too small, so I encourage the drawing of vertical or horizontal lines (using pencils) for these cases. I also encourage folding the paper, showing that if folded along the symmetry line, both the pre-image and image of the letter should should coincide.  I hold up and demonstrate this with a letter on a sheet of paper for all to see. 

Some students may want to rewrite a letter on another sheet of paper big enough to easily work with. When students are done, I project the Reflections APK document on the whiteboard so we can go over the questions together. I will ask students to share how they were able to determine if the symmetry line, if any, was horizontal or vertical for a letter. I also ask for explanations on how they determined the answers to Part II. 

Common mistake: Students may think that a letter like N, for example has a vertical line of symmetry, because when drawn, both sides of the letter are identical (same with letter S).  I ask these students to fold the paper along the vertical line and see for themselves that the image and pre-image do not coincide, and therefore, N has no vertical symmetry line. I ask that they test a horizontal line through N, as well. 

New Info

15 minutes

To open this section of the lesson, I hand out the About Face graphic organizer. The first two transformations are a translation and a dilation, which students have seen in our previous lessons. I ask the class to complete the entire page with their partners. Although I have not formally discussed reflections with the class, I ask that they analyze the reflection in Figure 3 and make at least three conclusions based on what they see.  Before calling on students, I project this reflection on the board. When they step up to write their responses, here are some of the answers that students have given:

(1) "The images have the same size and shape" 

(2) "The tip of the nose on the pre-image and image is the same distance to the vertical line"

(3) "The images face opposite direction" 

(4) "The distance between two points on one face is the same as between the same two points on the image."

Students may not make any conclusions with respect to angles, so I will be prepared to ask the class if they can conclude anything about the images with respect to angles. I've had students state that the angle that the girl's chin or lower jar, makes with her neck looks the same in both images. I ask if these corresponding angles should be equal and why should they? I don't expect students to see that the line connecting a point and its reflection image are perpendicular to the reflecting line. They will discover this in the following section.  

 

Application

20 minutes

For this activity I pass out the resource Exploring Reflections. Then, I ask students to work with their partners and take the measurements required in Question 1. I remind students to use their ruler and protractor. I walk around the room assessing the students proficiency and answering students' questions.

I am most interested in the conclusions students make at the end of Question 1. I ask the class to stop at the end of Question 1.  I then choose a pair of students with correct answers and ask that they share their responses. This question is usually not difficult for students to answer and discuss.  

After discussing this question, I tell students to reflect on these properties when answering the rest of the questions. In Question IV, students encounter a good "flip" reflection. I ask if anyone recalls the informal word for translations (slide) and I state that "flip" is the informal word for reflections.

In Questions V, I added some triangles that are not reflections of any preimage on the plane. I encourage students to use their phones or iPads as mirrors to find the reflections. Students often find that using rulers to measure distances is easier. I allow each student to choose the method that works best for him/her. Some students may forget how to state the equation of a horizontal or vertical line when stating the reflecting line in reflections A>>B and F>>H, so I may decide to provide students with a quick refresher.

 

Closure

10 minutes

To close this lesson, I like to have a group discussion and have students share answers with the whole class. I've found that students that have been struggling can benefit a lot when listening to how other students got their answers. After going around the room assessing students' work on Exploring Reflections, and getting  a good idea of who these students are, I make sure I call on these students to share an answer to one of the questions. I may even create a question based on a concept already discussed. This informal assessment helps me, and helps those struggling students. If time runs out, I tell my students to finish this activity for homework and I make sure I discuss Question V during the next class.