Conversions and Comparisons

  1. Convert the angles 30, 45, 90, and 135 degrees into radians. Can you develop a formula that will simply allow you to plug in the degrees and get radians?
  2. Similar to number one, convert π/6, 3π/2, 5π/4, and 2π radians into degrees and develop a formula for this conversion.
  3. A person begins to walk around a circular garden with radius 10 meters. If they travel 120 degrees around the garden’s circumference. How far have they walked? What if they traveled 225 degrees? 450 degrees? Have you developed a technique for doing this quickly?
  4. Check out this Three-Act Math task from Dan Meyer: Attempt this problem and explain your proof/results to the sequel.
  5. When deciding who will reach a destination first, distance may only be one factor. What else may apply? Give another Three-Act Math task a try: Include a proof of your work to the sequels.

**To be expanded