What did you do yesterday?

1. What did you do yesterday? Can I turn a circle into a rectangle?

2. Too bumpy on the top and bottom! Hmm, odd number of pieces . . . trapezoid. 12 piecesand I have a parallelogram, not so bumpy across the top and bottom.

3. What did you find out? rect·an·gle: a four-sided shape that is made up of two pairs of parallel lines and that has four right angles; especially : a shape in which one pair of lines is longer than the other pair par·al·lel·o·gram: a four-sided shape made up of two pairs of straight parallel lines that are equal in length :  a quadrilateral with opposite sides parallel and equal The more sectors, the more the shape looks like a rectangle/parallelogram.

4. What does the base of the parallelogram have in common with the circle?

5. The base is about one-half the circumference of the circle 6 1 5 2 3 4 In my picture, you can see that the bottom or base of the parallelogram is the same as half of the circumference of the red circle. I drew the sectors onto the shapes to show that the edges of the sectors make the base and the circumference. 2 4 1 3 5 6

6. What does the height of the parallelogram have in common with the circle? height

7. The height of the parallelogram is about the radius of the circle. 7 1 6 5 2 3 4 In my picture, you can see that the sides of the parallelogram are about the same length as a side of a sector. 7 2 4 1 3 5 6 I say “about” because the sides of the sectors are a bit shorter than the distance from the vertex of the sector to its outside edge.

8. On your own/with a partner, decide which parallelogram best represents the area of the circle. Justify your answer using evidence! What could you do to get a better estimate for the area?

9. What happens to the height and radius when the number of congruent/equal sectors increases? (What happens when you use more equal sectors?) As you use more pieces, the height and radius become closer in value.