Answer Sheet for Activity #2
Question #1:
The purpose of this question is to have students using the applet to figure out how many radians make up a complete circle. For the first part of the question is simply has students counting segments created by the applet, but the second and third parts have students drawing concepts from the previous lesson about the definition of a radian. By asking this question it allows for student to physically see how many radii make up a circle and allow them to reflect on why not all of the arc lengths are equal. Thus the solution for this question is pretty straight forward. For the first part the answer is roughly 6 or 6.28 to be more exact. With the explanations (second and third parts) the solution needs to be along the lines of the sizes are different because one of the lengths of the "segments" does not measure a full radius length. This is a concept drawn from the last activity.
Question #2:
This question is simply instructions on how to measure angle with Geogebra. Thus there is no solution to this question.
Question #3:
The purpose of this question is to realize that a radian measure has a different sum of the angles than the sum of the angle
Question #4:
The purpose of this question is to see if they understood or retained the definition of a radian. This is basically a question that simply asks for the student to recite what was learned previously. Thus the answer is simply the definition of a radian that was learned in the previous activity. That is the solution is a radian is an angle measure determined by the ratio of the arc length and the radius.
Question #5:
The purpose of this question is to have students start building foundations to derive the conversion formula. In this question, students must use the applet to determine how many degrees are in a radian and vice versa. Thus for the first part of finding out how many degrees are in a radian they simply have to look at the angle measures they did in question 2. Thus the solution is 57.3 degrees are in 1 radian. For the second part of how many radians are in 1 degree students may need to do some cross multiplying. After doing so they can get the solution of 0.017 radians are in 1 degree.
Question #6:
The purpose of this question is for students to realize that the amount of radians in a full circle is 2pi and to help come further to deriving the conversion formula. Thus for this students can use the previous answer to figure this out again by cross multiplying which will look as such: (360/x) = (57.3/1). After some algebra, the solution becomes that there are roughly 6.28 or 2pi radians are in an entire circle.
Question #7:
The purpose of this question is to have students to find the radian measure of semicircle, which in turn gives lead into deriving the conversion formula. Thus for this question, students can simply use the number they calculated from the previous question and simply divide that by 2. That in turn will give us the answer for the radian of a semicircle which is 3.14 or pi.
Question #8:
The purpose of this question is to have students using the applet to figure out how many radians make up a complete circle. For the first part of the question is simply has students counting segments created by the applet, but the second and third parts have students drawing concepts from the previous lesson about the definition of a radian. By asking this question it allows for student to physically see how many radii make up a circle and allow them to reflect on why not all of the arc lengths are equal. Thus the solution for this question is pretty straight forward. For the first part the answer is roughly 6 or 6.28 to be more exact. With the explanations (second and third parts) the solution needs to be along the lines of the sizes are different because one of the lengths of the "segments" does not measure a full radius length. This is a concept drawn from the last activity.
Question #2:
This question is simply instructions on how to measure angle with Geogebra. Thus there is no solution to this question.
Question #3:
The purpose of this question is to realize that a radian measure has a different sum of the angles than the sum of the angle
Question #4:
The purpose of this question is to see if they understood or retained the definition of a radian. This is basically a question that simply asks for the student to recite what was learned previously. Thus the answer is simply the definition of a radian that was learned in the previous activity. That is the solution is a radian is an angle measure determined by the ratio of the arc length and the radius.
Question #5:
The purpose of this question is to have students start building foundations to derive the conversion formula. In this question, students must use the applet to determine how many degrees are in a radian and vice versa. Thus for the first part of finding out how many degrees are in a radian they simply have to look at the angle measures they did in question 2. Thus the solution is 57.3 degrees are in 1 radian. For the second part of how many radians are in 1 degree students may need to do some cross multiplying. After doing so they can get the solution of 0.017 radians are in 1 degree.
Question #6:
The purpose of this question is for students to realize that the amount of radians in a full circle is 2pi and to help come further to deriving the conversion formula. Thus for this students can use the previous answer to figure this out again by cross multiplying which will look as such: (360/x) = (57.3/1). After some algebra, the solution becomes that there are roughly 6.28 or 2pi radians are in an entire circle.
Question #7:
The purpose of this question is to have students to find the radian measure of semicircle, which in turn gives lead into deriving the conversion formula. Thus for this question, students can simply use the number they calculated from the previous question and simply divide that by 2. That in turn will give us the answer for the radian of a semicircle which is 3.14 or pi.
Question #8: