Gr 06 Introducing Parts of the Area of a Circle

Today was a very busy day. We are transitioning from talking about the circumference of a circle to talking about the inside of a circle, so I wanted to introduce some vocabulary that we might use to help us navigate what we're doing.

I used a foldable to introduce the vocabulary for Sector, Segment, Semicircle, and Quadrant.

1. Fold an 8.5" x 11" piece of paper once length-wise and twice width-wise. Cut the length wise fold from the outside of the paper to the first fold perpendicular to it. You will have four flaps that you can title like this:
   
   
2. Under the segment flap, have the kids construct a circle around point A with a radius of 3 cm. Have them construct and label two points on the circle and make a chord. Then they dark-color the perimeter of that piece of the circle, shade it in lightly in the same color and use their geometry vocabulary to describe what they see. Derive with them the definition of a segment:
   
   
3. Under the semicircle flap, have them construct a similar circle around another point, but this time add points on the fold that passes through the center point and construct a chord at the diameter of the circle. Then they dark-color the perimeter of half of the circle, shade it in lightly in the same color and use their geometry vocabulary to describe what they see. Derive with them the definition of a semicircle:
   
   
4. Under the sector flap, have the kids construct a similar circle around another point. Have them construct and label two points near each other on the circle and draw line segments between each point and the center. Then they dark-color the perimeter of that piece of the circle, shade it in lightly in the same color and use their geometry vocabulary to describe what they see. Derive with them the definition of a sector:
   
   
5. Under the quadrant flap, have the kids construct a similar circle around another point. Have them construct and label one point on the fold going through the center point and another point that is at the top of the circle 90-deg. Ask them to draw line segments between each point and the center point. They dark-color the perimeter of that piece of the circle, shade it in lightly in the same color and use their geometry vocabulary to describe what they see. Derive with them the definition of a quadrant:
   
   

For homework, I merely asked them to take it home and to share with their families what they made today. In class, our goal is to try and use the vocabulary to talk about things we are seeing... so this is kind of like a take-home word wall.