1. Will the app download in time for the game?
2. Write down a guess.
3. What information would be useful to figure this out?
4. Write down some questions you have in your head right now.
I decided to give a couple screenshots in order for the students to measure the central angle and use proportional reasoning to determine the download time.
I thought it would be neat for the kids to use Desmos to measure the angles, so I created the following graphs:
Here’s a screencast of what it will look like for the students (thanks to Robert Kaplinsky for the suggestion).
5. What would happen if at 4 seconds the download meter formed a 45° central angle?
Understand ratio concepts and use ratio reasoning to solve problems.
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
Apply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems