Teacher Guidelines
Materials Needed:
This applet is fairly easy to use and is rather simple. The only aspect of the applet you can physically drag is a single slider located towards the middle of the screen. This slider controls the angle of the circle which controls almost everything on the screen. For instance, by moving the slider it changes the arc length, sine values, cosine values, and other values. With this, it allows students to play around with angle size and also with the size of the arc length, sine values, and cosine values which can lead into investigations about angle measures and its corresponding sine and cosine values across all circles rather than a single one.
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 of the activity such as the question about how cosine and sine are represented on the coordinate plane (question 6). That way, as the teacher, you can get a feel for what the class learned from the activity.
- Activity #3 worksheet
- Geogebra applet
- Computer/Laptop
This applet is fairly easy to use and is rather simple. The only aspect of the applet you can physically drag is a single slider located towards the middle of the screen. This slider controls the angle of the circle which controls almost everything on the screen. For instance, by moving the slider it changes the arc length, sine values, cosine values, and other values. With this, it allows students to play around with angle size and also with the size of the arc length, sine values, and cosine values which can lead into investigations about angle measures and its corresponding sine and cosine values across all circles rather than a single one.
Possible Misconceptions/Problems:
- One problem a student may have is that they may be overwhelmed by all the colors and formulas on the screen.
- One problem could be that, students may not remember basic right triangle trigonometry.
- One problem could be that the Internet is down so students could not access the applet or if the computers are not working.
- (2) Look at the cosine value. As you are changing the angle what is happening? [Do the same for sine]
- (2) What if you rotate around the entire circle? How does the value change?
- (4), (5), and (6) Connect the point on the circle to the origin, how can we find the coordinates of the point?
- (4), (5), and (6) Think about the slope of a line. How can that help us find the value of these points?
- (4), (5), and (6) Think about what defines a slope such as rise over run, what part of this equation would cosine represent?
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 of the activity such as the question about how cosine and sine are represented on the coordinate plane (question 6). That way, as the teacher, you can get a feel for what the class learned from the activity.