Lesson: Reflections Over a Line
Start [slide 1] by having students in pairs, standing facing each other. Now explain that the students are going to act like the mirror image of their partner. Whatever movements their partner makes, they have to do opposite in order to be the mirror image. (This is really fun to watch!) Give students examples of things to do: raising your hand, picking something up, buttoning a shirt, waving, doing a dance, making funny faces, etc. Have a couple pairs who do a really good job demonstrate their reflections to the class. (Bonus if you have twins in your class!)
[Slide 2] names the objective. [Slide 3] asks students to graph the line y = 3x - 2. My students used individual whiteboards with graphs on the back side. Graph paper will serve the same purpose. Students will probably needed to be reminded of slope-intercept form y = mx + b. Ask students what the slope of the line is and what the y-intercept is. Circulate the room to help answer questions and remind students of how to graph a line.
Click through to the next equations and have students graph y = -5x + 1 and y = ½x + 8. Remind students that ½ means up 1, to the right 2, and not up ½ of a square.
Bring the class back together for [slide 4]. Ask students to graph y= 3. They will probably make a point at (0, 3) and call it done. Ask students how we could use that to make a line. Guide them into realizing that this will be a horizontal line through the point (0,3). Explain that it cannot be vertical because that would just be the y-axis.
Have students graph x = -4 on the same graph and ask for their intersection.
[Slide 5] My students needed a lot of help remembering how to graph y = x. Remind them that there is an imaginary 1 in front of the x that represents their slope. Ask what we are adding to x. When they tell you ‘nothing’, ask what number we write to represent ‘nothing’. When they 0, emphasize that 0 is our y-intercept. Help them graph y= x and y= -x on the same graphs to show that the lines are the same with opposite slope.
Students can now put away their whiteboards/graph paper. I printed out the next 4 slides for them to use as notes. In PowerPoint, go to Print. Click the dot next to ‘Slides’ and then type in 6-9 into the white box. Go down to where it says ‘Print what:’ and click ‘Handouts’. Change ‘Color’ to ‘Pure Black and White’. Go to the right where it says ‘Slides per page:’ and click 2. Then click ‘OK’ to print.
[Slide 6] Ask students how to graph y = -2. Once students have verbally given you the answer, instruct them to draw the line with a ruler and then reflect the shape over that line. Circulate the room to check and correct. Most students won’t know what to do with point I because it stays on the line of reflection. Have a student call out the new ordered pairs. Draw the points and connect the dots. Ask the rest of the class for confirmation that this answer is correct.
[Slide 7] is the most difficult part of this lesson. Ask students how to graph y = -x. They should know how now but still may not remember. Graph the line. Ask students to start with point A and reflect it over the line. My students told me to go left 2 squares to get to y = -xx and then 2 more squares past that to create the new line. While this is the method we learned for reflecting points over a line, we always had a horizontal or vertical line, not a diagonal line. Continue with the students instructions until they realize that this shifts the shape too far to the left, off of the graph. If they still don’t notice, ask what would happen if they took their papers and folded it on the line y = -x. By now they should realize their shape is in the wrong place. Go back to the original figure, start with point A, and count to the line y = -x but counting diagonally. Students should catch on pretty quickly and be able to finish the rest of this reflection on their own.
Have students complete [slide 8] and [slide 9] on their own. [Slide 8] should be easy. On [slide 9] students will tell you they don’t know what to do but encourage them to keep trying and keep doing the same process we’ve been doing. When they are done, the figure reflects on itself and creates a 3d looking letter X.
In closing, this is just a method to help them summarize. I bought an old Scrabble game at a yard sale and used the tiles. If you don’t have a Scrabble game, you could easily write letters on pieces of paper and have them draw it out of a hat; or have them use the letter their name starts with. Giving them a random letter helps jog their memory for a way they can relate it to something they’ve learned while doing reflections.
This lesson was more a review of graphing lines than of doing reflections. But graphing lines was a necessary piece that comes next in the process of doing reflections. I’m glad I thought to include y = -x as one of the examples. Also, I think the scrabble tiles are a really fun way to summarize.
What Didn’t Work
When I originally taught this, I didn’t realize what would happen when we reflected over a diagonal line. It was literally during the moment we were doing this slide in class that I realized we would have to count diagonally. It was a good place to let the students take control so they could see where they went wrong, but it was not part of my plan!
|Reflections Over a Line Classwork||