What did you do yesterday?

Can I turn a circle into a rectangle?

Too bumpy on the top

and bottom!

Hmm, odd

number of

pieces . . .

trapezoid.12 pieces and

I have a parallelogram, not so bumpy across the top and bottom.

The more sectors, the more the shape looks like a rectangle/parallelogram.

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

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

The base is about one-half the circumference of the circle

1

1

2

2

3

3

4

4

5

5

6

6

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.

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

height

1

1

2

2

3

3

4

4

5

5

6

6

In my picture, you can see that the sides of the parallelogram are about the same length as a side of a sector.

The height of the parallelogram is about the radius of the circle. 7

7

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.

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?

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.