Many students in the US think of Pi as a number they should memorize, when the most important idea for students to learn is that Pi is a very cool relationship, that exists inside all circles in the world. In this task students will find that relationship themselves, through cutting and folding, and be asked to reflect on it.
Task Instructions
- Construct a circle with a radius of 2 – 4 inches
- Fold the circle into quarters and cut along the folds
- Cut one of the quarters into eighths, two equal parts
- Glue the pieces onto a piece of paper and draw the rectangle
- The rectangle, ABCD has approximately the same area as the circle.
- Calculate the area of rectangle ABCD
- Construct another circle congruent to your first circle
- Fold the circle into eighths, or eight equal sectors
- Fit the circle pieces into a rectangle
- Calculate the approximate area by determining the area of the rectangle.
- Repeat the steps for a congruent circle cut into 16 sectors
- AB is approximately half of the circumference, 2πr, why? This means AB = πr
- Why does BC = r?
- The area of rectangle ABCD is
Area ABCD = AB x BC = πr x r = πr²
Materials
- Paper
- Compass/something to make a circle with a radius between 2 and 4 inches
- Scissors
- Glue