Teacher Guidelines
Materials Needed:
This applet is easy to use but there are a lot of things you can do with this applet. Lets start with the original screen. At this screen you have many options at your disposal. At the top of the applet you have options that will allow you to hide the picture of the ferris wheel and a button that will turn off the pivot feature. Below that there are options labelled hide extra seats, unit circle, and green seat. With the hide extra seats, you can click this to hide the light blue points that are revolving around the circle with the main dark blue point. With the unit circle option, it will basically pull up a diagram of the circle with a single measure. Once you click the unit circle option five more options pop up. These are labeled: Show eight points which basically plots 8 new points on the circle, show degrees which will place degree measures on the 8 points, show radians which will replace the degree measures with radian measures, show coordinates which show the sine and cosine coordinates on the 8 points, and lastly the show blue seat coordinate shows the coordinates of the blue point and the cosine and sine values. Next we will look at the options under the coordinate plane, make a graph and show a graph. For make a graph, if you click the option, points will show up on the graph where you can drag the points and make a graph. For the show graph button, three options will come up, vertical line, graph the function, and coordinate point. With vertical line it basically takes a vertical line and connects it to the moving green dot under the graph to simulate time. With the graph the function button it basically shows what it says. It displays the path of the blue seat. With the coordinate point option two more options pop up, connect circle and curve and coordinate point value. For the connect circle and curve option, it takes a horizontal line and connects the points of the circle and the curve. For the coordinate point value, it shows the x and y coordinate values for the blue point on the graph. The applet can graph both the sine and cosine functions through the sin(x) and cos(x) options and also showcase the values of sine, cosine, and tangent located under the value option. Lastly located at the very bottom of the screen in the left hand corner of the screen, there are options to pause and control the speed of the animation.
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 key features of both the sine and cosine functions. That way, as the teacher, you can get a feel for what the class learned from the activity.
- Activity #4 worksheet
- Geogebra
- Computer/Laptop
This applet is easy to use but there are a lot of things you can do with this applet. Lets start with the original screen. At this screen you have many options at your disposal. At the top of the applet you have options that will allow you to hide the picture of the ferris wheel and a button that will turn off the pivot feature. Below that there are options labelled hide extra seats, unit circle, and green seat. With the hide extra seats, you can click this to hide the light blue points that are revolving around the circle with the main dark blue point. With the unit circle option, it will basically pull up a diagram of the circle with a single measure. Once you click the unit circle option five more options pop up. These are labeled: Show eight points which basically plots 8 new points on the circle, show degrees which will place degree measures on the 8 points, show radians which will replace the degree measures with radian measures, show coordinates which show the sine and cosine coordinates on the 8 points, and lastly the show blue seat coordinate shows the coordinates of the blue point and the cosine and sine values. Next we will look at the options under the coordinate plane, make a graph and show a graph. For make a graph, if you click the option, points will show up on the graph where you can drag the points and make a graph. For the show graph button, three options will come up, vertical line, graph the function, and coordinate point. With vertical line it basically takes a vertical line and connects it to the moving green dot under the graph to simulate time. With the graph the function button it basically shows what it says. It displays the path of the blue seat. With the coordinate point option two more options pop up, connect circle and curve and coordinate point value. For the connect circle and curve option, it takes a horizontal line and connects the points of the circle and the curve. For the coordinate point value, it shows the x and y coordinate values for the blue point on the graph. The applet can graph both the sine and cosine functions through the sin(x) and cos(x) options and also showcase the values of sine, cosine, and tangent located under the value option. Lastly located at the very bottom of the screen in the left hand corner of the screen, there are options to pause and control the speed of the animation.
Possible Misconceptions/Problems:
- One problem a student may have is that they may be overwhelmed by how much activity is going on by the screen, especially when the applet starts to animate.
- Since the applet runs on Geogebra and it is an Internet program, if the Internet is down in the school this applet can not be accessed. This can cause a huge problem since the worksheet was built around the applet.
- (4) Look at the coordinates. As time is changing how are the coordinates in both the graph and the circle change?
- (5) Think about what we learned in the previous lesson with the unit circle. What did the x and y coordinates represent in that instance? Do you believe that it will be the same for a graph as well?
- (6) Look at both of the blue seat's coordinates on the circle and the graph. What do you notice about the values of the x and y coordinates?
- (6) Why do you think that the y-coordinate remains constant? What does the value of the y-coordinate represent in terms of the unit circle?
- (8) What were some similarities and differences amongst the sine and cosine functions?
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 key features of both the sine and cosine functions. That way, as the teacher, you can get a feel for what the class learned from the activity.