Teacher Guidelines
Materials Needed:
This applet is fairly easy to use. The only aspect of the applet you can physically drag are the two sliders located at the top of the screen. The upper most slider controls the angle which drags colored segments around the circle the size of the radius, while the other slider controls the length of the radius and also the colored segments. With this allows students to play around with angle size and also with the size of the circle, which can lead into investigations about angle measures across all circles rather than a single one. Another feature this applet allows is to measure angle. With this select the angle button at the top left hand corner of the applet, and select three points to measure the angle. The thing is that this tool is direction sensitive. So in order to correctly measure the angle you must click on a point and in order select the vertex of the angle and then on a point in the direction you want to go either clockwise or counter-clockwise.
Possible Misconceptions/Problems:
A possible way to finish the lesson is to simply go over or review the activity. With this it will allow for all students to come together and discuss the results that they found from this activity. Based on the class, start with or focus on the questions that students were struggling with the most. That way as a class they can discuss and build a better understanding of those hard questions. Next, review the most influential questions such as the very last question about the deriving the conversion formula. That way, as the teacher, you can get a feel for how the class understands conceptually what this formula means and how to actually use it.
- Activity #2 worksheet
- Geogebra Applet
- Computer/Laptop
This applet is fairly easy to use. The only aspect of the applet you can physically drag are the two sliders located at the top of the screen. The upper most slider controls the angle which drags colored segments around the circle the size of the radius, while the other slider controls the length of the radius and also the colored segments. With this allows students to play around with angle size and also with the size of the circle, which can lead into investigations about angle measures across all circles rather than a single one. Another feature this applet allows is to measure angle. With this select the angle button at the top left hand corner of the applet, and select three points to measure the angle. The thing is that this tool is direction sensitive. So in order to correctly measure the angle you must click on a point and in order select the vertex of the angle and then on a point in the direction you want to go either clockwise or counter-clockwise.
Possible Misconceptions/Problems:
- Students may have a problem measuring angles, since there is a specific way you must measure the angles
- Students may be confused on the representation of the angles in this applet. For instance, a student may use the slider which does change the angle of the circle, but they may be confused since they may be used to seeing the angle markers when determining an angle. In other words, students may not know that the colored segments do represent angle measure with out the angle markers.
- One misconception could be that some students might not
- (5), (6), and (7) What could you do algebraically that could help you find the solution?
- (8) and (9) How could we use the previous answers to help us find this solution? What could you do algebraically that could help with finding the solution?
A possible way to finish the lesson is to simply go over or review the activity. With this it will allow for all students to come together and discuss the results that they found from this activity. Based on the class, start with or focus on the questions that students were struggling with the most. That way as a class they can discuss and build a better understanding of those hard questions. Next, review the most influential questions such as the very last question about the deriving the conversion formula. That way, as the teacher, you can get a feel for how the class understands conceptually what this formula means and how to actually use it.