Start [slide 1] by literally having the students tell you what they notice about the black and white photo. You will receive a myriad of answers. Hilarity ensues. Then click through to the photo in color. The blue shape is a smaller version of the red shape. Hence, two identical figures create one original figure. Proceed to [slide 2]. The top half is the same as the bottom half but rotated. [Slide 3] The blue figure is a reflection of the red figure that happens to intersect and create a new figure. This leads up to [slide 4] where we want the students to provide rotations or turns as the third topic. [Slide 5] names the objective.
Have the students demonstrate which way is counterclockwise. Explain that rotations are performed counterclockwise unless otherwise note. Starting at the top of the y-axis and move your hand to the left, down the second quadrant until you get to the x-axis. Ask students how many degrees you moved. (90º) Ask them how they know. (The red boxes mean right angles.) Write 90º ccw (counterclockwise) in the first quadrant. Move to quadrant III, IV, and then quadrant I, having students supply the degrees, 180º, 270º, and 360º respectively. Now ask them how many degrees are in a circle. (360º) Starting at quadrant 1 and the 360º we’ve already written, how many degrees clockwise would be needed to make 360º? (0) Moving clockwise, we are now supplying the degrees need to make a full rotation from the degrees we’ve already written. Quadrant I is 0 cw (clockwise), quadrant IV is 90º cw, quadrant III is 180º cw, and quadrant II is 270º cw. Write these alongside the degrees previously written for counterclockwise rotations. Advance to [slide 7]. Ask students how many degrees the figure on the left would have to be rotated counterclockwise to match the figure on the right. (180º) What about for clockwise? (180º)
Pass out the half sheet provided in the attached word document ‘Rotations Notes’. Students will need a ruler and protractor. Ask students what the center of rotation is. (Plus sign +). Ask students what the angle of rotations is for number one. (90º) Students should connect the dot to the plus sign with a ruler. Now, ask them if a 90º degree counterclockwise rotation will move the dot to the left or to the right. (Down to the left) So we turn our paper upside down. Place the center of the protractor on the plus sign. Line up the previously drawn line segment with the bottom of the protractor. Mark a 90º angle. Now use the ruler to connect the plus sign to the new mark. This new line segment should be shortened or lengthened to be the same length as the original line segment. (Tip: Use the centimeter side of the ruler.)
Have students complete the other 3 problems on their own. Once students realize that their protractors will not measure a 270º angle, refer back to the degree chart from [slide 6]. Students should realize that the same rotation can be performed by rotating 90 degrees clockwise. Ask students what they think a -90º rotation would be. (90º clockwise.)
Now we go back to the Powerpoint. I printed out slides 8-11 as a notes handout. In PowerPoint, go to Print. Click the dot next to ‘Slides’ and then type in 8-11 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. Have students follow the steps 1-4 given on the slide, which are similar to what we’ve already done. This should be a bit easier since they can now count squares for length instead of using the ruler to measure. Once they have rotated the point J, the figure can easily be drawn by connecting the other vertices instead of rotating every vertex individually.
Have students complete [slide 9] and [slide 10] on their own while you circulate the room to check and correct.
In closing, have the students complete the exit slip [slide 11] from their notes packet. Either collect these
at the end of class or read them before allowing students to leave. We are looking for answers that have to do with measuring angles, measuring line segments, and translating figures.
I liked the comic drawings that led into this and the exercise of rotating a dot before rotating an entire figure. Depending on your class size, I found it helpful to have my students arrange their chairs in a circle with me in a chair in the very middle so that they could all watch me one step at a time. In a larger class, I used my document camera to do one step at a time. But they key was to circulate the room and check to make sure every student was with me after every step.
What Didn’t Work
I suck at rotations and it was definitely reflected in my teaching. This was a hard concept for the students to grasp and I rushed them instead of giving them enough practice to become familiar with it. Also, [slide 7] was really the only mention of rotational symmetry when it was heavily mentioned in the upcoming transformation station activity and assessed on the unit quiz. It was unfair to the students to barely skim the topic and then assess it later.
|Rotations Notes Notes||