**How Many Radius-Squares Can Fit inside a Circle?**

Okay, so this is the model that is used by the singapore math folks. I used it last year and it was pretty successful.

- Make a circle of radius
*r*centimeters. - Make a square of side-length
*r*centimeters. - How many of these radius-squares can you fit inside the circle? Let's experiment to find out.
- Use scissors to cut up area-squares to fit them inside the circle. Three radius-squares will completely fill-up the first three quadrants of the circle. But all those left-over bits of the radius-squares can be cut-up and will fit into the last quadrant
*and*there will be leftover space. So*approximately*three radius-squares*plus a little more*will fill the circle. That*little*bit more is about 0.14 radius-squares. - The area is
*about*3.14 radius-squares or... - A= π×r×r
*or*A= π×r².

**A Sliced-Up Circle Approximates a Rectangle**

And this model is one used by Waldorf and most other math curricula.

- Create a circle of radius
*r*. Cut the circle into three segments and glue them together, so that they kind of form a parallelogram. - Repeat, but cut the circle into 4 pieces.
- Repeat, but cut the circle into 8 pieces.
- Repeat, but cut the circle into 16 pieces.
- Now, at this point, students can see that the shape is REALLY close to a parallelogram. If we were to continue repeating this proces, the parallelogram would get steeper and would become a rectangle.
- The
*height*of that rectangle will eventually be the radius,*r*. The*base*of that rectangle will be the circumference divided by two (or π*r*). - So the area of the rectangle will be
*base**height*or...

A= πr•r*or*A= πr².

I think that for 6th graders, the more direct way of doing it is the Singapore math method and I'll probably use it. But the other one might be a great extension for my higher-skills kids.

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