For my hands-on activity, I chose to do a lesson where the students will need to determine the value of pi and the radii in a unit circle. To do this, the students (or teacher) will construct two different size circles using GeoGebra and then measure each circles circumference, diameter, and radius using string. To determine pi, the students will see how many times the radius string goes into the circumference string of that corresponding circle. To determine radii in the unit circle, the students will start the radius at 0 degrees or 360 degrees on each circle and mark where the radius ends. They will then measure the angle using a protractor and record it. The students will start the radius where it ended on the circle last and do this process again. They will repeat this process until they get all the way around the circle. Once students have done so, they will then convert the degrees measured to radians. The activity will be concluded by the students explaining why pi is 3.14 (from the circumference and diameter and from the third angle being pi when determining radii) and determining what other radii in the unit circle are missing from this activity and why. The students will also determine any possible errors that could have occurred throughout this activity to change their results. Below, you can find the worksheet and a powerpoint with a list of steps, pictures, and questions when doing this activity.
This activity is a great way for students to develop an understanding as to where the value of pi came from and to determine the radii in the unit circle. This will serve as a good first activity in a trigonometry course when introducing the unit circle. Before even teaching the students the unit circle, the teacher can have the students determine the radii of the unit circle themselves. When doing this activity in the classroom, I would suggest to pre-make the two different size circles using GeoGebra and to cut each circles circumference, diameter, and radius strings. I would also suggest that rather than having the students mark up the circumference string when determining the value for pi, have the students use a ruler to measure both the circumference and diameter string to get a more accurate value for pi. Overall, I believe this is a great activity that will get the students thinking critically and developing an understanding for the curriculum.