Hands-on Exploring the Movement of Reflections in the Plane
Lesson 4 of 23
Objective: Students will be able to understand the movement of a reflection and the properties of a reflected image on a conceptual level.
I opened class today with a hands on formative assessment. Using a package of thin craft foam I purchased from the Dollar Tree for $1 and a non-symmetric die cut from school (a camera), I cut 30 cameras from the foam. I used a roll of large one inch square grid paper and cut about 20sections of paper. Using a marker, I drew in a large x and y axis. Each partner group received two foam cameras and one section of graph paper. I told the class I wanted to see a reflection of the camera across the y-axis, anywhere across the y-axis. One foam camera was to be the pre-image and other was the image after the reflection. I did not give any further instructions. I then traveled about the room with my ipad formatively assessing their pre-knowledge of reflections and taking pictures of reflections I wanted to share under the document camera with the class (students love it when you pick their work to share with everyone. I even had one group get very creative and put their camera on a diagonal to reflect just so I would pick their work to show).
I asked each group to show me the movement of the pre-image that would map it onto the image they were showing me (most students flipped one camera over and placed it on top of the other). It was a very useful lesson pre-assessment. I discussed with each group this motion of flipping, was it a congruent pre-image and image which meant a rigid motion? Yes.
Then I put my ipad screen under the document camera and we looked at different reflections that groups created and added important properties of a reflection to our organizer "Triangles, Turned, Twisted, and Tweaked." We also added the key movement word for reflections "flip" and that it was a rigid motion so pre-image and image were congruent.
Beginning the Activity
Pass out the handout Exploring Reflections in the Plane. in this activity I begin by discussing how the movement word "flip" might affect how we use the tracing paper to perform a reflection. Students usually answer we will flip the tracing paper over. I ask students to work with their partner to reflect the given trapezoid in question one using tracing paper and then answer the following questions. As students work to complete the reflection, I walk about the room assessing, answering questions, and passing out rulers and protractors. After discussing the warm-up activity, this first reflection was not difficult for students to complete on their own within partner groups. After about eight minutes of work most groups were finished and ready to discuss what they observed when measuring with a ruler and protractor. I pulled several student groups up to the document camera to show and discuss their work on question one. I scripted all the key points mentioned so students could add important information to their organizer.
I usually offer several incorrect reflections as options after students present and ask groups to discuss if my reflections are extra correct options that we could consider. My incorrect examples usually include reflections that are not crossing the line of reflection at a 90 degree angle but are instead off to one side. I also offer a translation as an option. While discussing my choices I usually have a large mirror handy for demonstrations. As students look into the mirror and wave, which hand is waving back? The opposite hand is waving back as reflections reverse the orientation. I also ask two students to stand and then everyone looks at the two students in the mirror, who looks closer in the reflections? (the same student who is closer in real life, so name corresponding vertices as they relate to the line of reflection in the pre-image. ) There is an endless list of ways to demonstrate a reflection including simply pulling a student up front to face you and then move different arms and legs to show opposite limbs. I also like to use the funny situation where students run into each other and tell each other, "You go left and I'll go right." Just to run into each other again.
After whole group discussion, allow students to again work with partners on reflection two, the rhombus. After students complete reflections two and I have checked the work of each member of the group, then I allow them to move on to the next page. The back side is really giving students the space and time to reflect on all the important properties of a reflection so when you discuss these key properties as whole group for the organizer every student has had time to think and write about the key ideas. Then, the last exercises on page two are further practice with reflections across horizontal and vertical lines.
Wrapping Up the Lesson
After about 15 minutes of time to work students should be ready to discuss their answers to the thinking questions on page two. Again, work with student groups as they complete these questions and pick or create your experts who will present during whole group discussion. If you do not find enough student experts to share answers then create some by questioning and helping student groups - helping struggling students to become experts, then asking them share out during group discussion is a great way to build confidence and enthusiasm for math.
Homework: The additional practice at the bottom of page two if not completed during class.