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Part I - Topic Discussion

Teaching Circles and Pi

The topic of circles and pi is a geometric subject area that enhances measurement and spatial reasoning. This requires prior knowledge using measurement tools, perimeter, and understanding basic definitions of properties of a circle such as perimeter, area, center, radius, and diameter. Prior GPS standards that are related to circles are:

M3G1. Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties.
 * d. Identify the center, diameter, and radius of a circle.

The entirety of our wiki space covers the expansion of student knowledge and giving them fluency in the areas of circles and pi. The standards that should be addressed and covered by this wiki are:

M5G2. Students will understand the relationship of the circumference of a circle to its diameter is pi (3.14).

M5M1. Students will extend their understanding of area of geometric plane figures.
 * e. Estimate the area of a circle through partitioning and tiling.
 * g. Derive the formula for the area of a circle.
 * h. Find the area of a circle using the formula and pi § 3.14.

M5M2. Students will extend their understanding of perimeter to include circumference. A description of the topic (including the mathematics and connection to the GPS). Important ideas:
 * a) Derive the formula for the circumference of a circle.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12pt;">b) Find the circumference of a circle using the formula and pi (3.14).
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12pt;">Students build their knowledge of circles throughout multiple standards. According to the standards, students build on their prior knowledge of parallelograms and their properties to learn about circles.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12pt;">Properties of the circlecircumference divided by diameter of the circle will always be piarea of a circle
 * center, diameter, radius, circumference

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 12pt;">The teacher should be able to help the students walk away with confidence and a conceptual understanding of circles and the magical, mysterious number pi. After accomplishing the derivation of pi and noting the properties of circles and circle measurement through hands-on exploration, students will have gained a new appreciation for the beautiful shape, the circle.