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Guided Solution to Problem of the Week #8 – A Third Look at Pi

Posted by Jeff Simpson under

All Problems of the Week - And Solutions,

Geometry,

Pi | Tags:

learning math,

math instruction,

teaching math |

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1. Look at Pi Chart #1. What is the measurement of the radius? Is each radius the same length? What shape is created when the radius is squared? What is the area of that shape in square centimeters?

2. Look at Pi Chart #2. What fraction of the circle is shaded? If you multiply 35 cm x 35 cm, will that tell you the number of square centimeters in the shaded part of the circle? Why is it so hard to count how many square centimeters are in the shaded part of the circle? (Shapes?) According to our count, there are approximately 962.5 square centimeters in the shaded part of the circle?

3. Look at Pi Chart #3. If you know how many square centimeters are in the shaded part of the circle, how can you figure out how many square centimeters are inside the entire circle? What is the approximate area of the entire circle? What is the area of the radius squared?

A ratio is a comparison of two amounts, which can be written in the form of a fraction. What is the ratio of the area of the entire circle (write it on top) to the area of the radius squared (write it on the bottom)? Can this ratio be reduced? A ratio can look like an improper fraction. An improper fraction can look like a division problem (top number divided by the bottom number). Divide the area of the circle by the area of the radius squared and see what you get.

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