Exploring Rotations 2: On the plane

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SWBAT perform rotations about the origin, using coordinates.

Big Idea

Using Sketchpad, students recognize the patterns of rotations in 90 degree multiples and come up with coordinate rules.

Access Prior Knowledge

10 minutes

To begin the lesson I hand each student an Entrance Slip and ask that they complete the task individually. This task gets those neurons fired up and helps students settled down and focused. I give the class a few minutes to complete it and then call on volunteers to share their answers.

Each time one of the rotations is answered, I "milk" the task a bit, by asking the students to give me the magnitude of the rotation, and then, to give me a negative magnitude that also works for that particular image. So if the rotation image as a magnitude of 90 degrees, a magnitude of -270 also is correct.  

When a translation is found, I ask if this could also be a rotation. Most students pick this up and answer that "yes, it can be a 360 degree rotation". 

I like to make sure students have mastered  the clockwise or counter-clockwise rotations given the angle magnitude, as well as with the vertical or horizontal flips, so I question the students, asking them how they know it's a rotation, or how they know it's a reflection, etc.  


30 minutes

After the Launch, I pair up my students and ask that they open Geometer's Sketchpad on their computers. One computer per pair will do; one student can handle the program while the other writes down results. I hand each pair of students the Sketchpad Rotation Guide and ask that they work together to complete the steps. 

Teaching Note: If computers or sketchpad, are not available, teachers can ask students to construct points on graph paper, and go through the steps in the resource using their rulers and protractors Students should be able to handle this after the Exploring Rotations 1 lesson. Yet, it may take longer than the alloted time. 

In this activity, the idea is to take the four points in quadrilateral BCDE, record their coordinates, rotate them 90 degrees about the origin and record the coordinates of their images. Once the information is registered, students will figure out the rotation rule. The same task is repeated for rotations of 180 and 270 degrees. In Questions 6 and 7, I ask students to state how they went about proving their answer and provide measurements they found. 


Video tutorials for Sketchpad use:

  1. Measuring lengths and angles and shading in quadrilaterals
  2. Rotating an image choosing any center of rotation point 
  3. Rotation about the origin (sketchpad)


10 minutes

To close the lesson on Rotations, I ask that students use their completed Sketchpad Rotation Guide and go through it labeling the sections in it as follows:

  • Use a Triangle ∆ to indicate the concept is totally clear to you.
  • Use a  to indicate that the concept Squares with things I already know.
  • Draw a Circle ○ to indicate where there is a concept or idea that still is going around in your head. 

This coding system helps me get a quick picture of what ideas students are confident about and which ones they probably need help with over the next couple of days. If a lot of students label circles in the same areas, I make sure I target these areas the next day, usually with a different task that addresses these particular concepts.