Through this activity students discover the formula for the area of a circle. Students are provided a circle and three squares whose side equals the measure of the radius of the circle. Students are challenged to cut the three squares apart and fit their entire area into the circle without any pieces overlapping.
Students find that the three squares do all fit and there is some space left. From this simple activity students know that the area of the circle is more than 3 r squared.
A sketchpad file, which is contained in the zip file, is also attached that allows the students to change the size of the circle (and also the squares and then compare the area of the circle and the area of one square and notice it always comes out pi. It requires you to have the sketchpad program.