Wednesday, February 20, 2013

Gr 06 Parts of a circle Foldable

This was heavily adapted from some Waldorf materials I found online. I don't have the time to let the kids explore "circle" like Waldorf does. I'm sure they'd benefit from it. Nonetheless, my students appeared to like the process of creating and learning parts of circles this way.

Here's how I used it:
  1. First we folded the paper (fold a large + sign first, then fold the corners in). This is a picture of the finished product, but at this point, there shouldn't be any writing on it.
  2. Draw a center point on the fold underneath each flap. Each point should be a different color and should get a different label (A, B, C, D are fine, but kids could use whatever letters or colors they wanted).
  3. Point A: Ask kids to use a ruler to mark all the points they can find that are exactly 2 cm from point A. When they think they know what shape it's making, they can use a colored pencil to sketch it in. Ask them what it is that defines this shape (all the points that are the same distance from the center point). Then record the definition with them. I spiraled it in to show it was revolving around the center, but that's optional and it was kind of hard for the kids. Close the flap, place the title on it (Definition of a circle), and move on to the flap for point B.
  4. Point B: Write the title "Radius and Diameter" and ask students to construct another r= 2 cm circle around point B just like they did for point A before. Draw a line segment from the center to a point on the circle and ask them to describe what you have drawn. Ask them it if stays the same no matter what point on the circle you draw a line segment to. Formalize this distance with them as the definition of the radius. Then do a similar process with the diameter.
  5. Point C: Write the title "Circumference (C) and Arc" and ask students to construct another r= 2 cm circle around point C. Draw a point on the circle and a series of arrows that goes all around the circle and ends at the same point again. Ask students to describe what you have drawn using their geometry vocabulary, then formalize the definition of circumference with them. Now draw two new points on the circle and shade in the distance on the circle between them. Ask students to describe what you've drawn using their geometry vocabulary, then formalize the definition of Arc with them.
  6. Point D: Write the title "Chord and Tangent" and ask students to construct another r= 2 cm circle around point D. Draw two points on the circle and connect them with a straight line segment. Ask students to describe what you've drawn with their geometry vocabulary, then formalize the definition of chord with them. Do the same for tangent. Now what's cool is that students may recognize that the diameter of a circle is a special case of a chord. And if a tangent dips into the circle, it will no longer be a tangent because it will connect two points on the circle.

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